title: Primary decomposition

abstract: In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals. The theorem was first proven by Emanuel Lasker (1905) for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by Emmy Noether (1921). The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components. It has a straightforward extension to modules stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules. This contains the case for rings as a special case, considering the ring as a module over itself, so that ideals are submodules. This also generalizes the primary decomposition form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings over a field, it generalizes the decomposition of an algebraic set into a finite union of (irreducible) varieties. The first algorithm for computing primary decompositions for polynomial rings over a field of characteristic 0 was published by Noether's student Grete Hermann (1926). The decomposition does not hold in general for non-commutative Noetherian rings. Noether gave an example of a non-commutative Noetherian ring with a right ideal that is not an intersection of primary ideals.

text:
# Primary decomposition

In mathematics, the **Lasker–Noether theorem** states that every Noetherian ring is a **Lasker ring**, which means that every ideal can be decomposed as an intersection, called **primary decomposition**, of finitely many *primary ideals* (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by Emanuel Lasker (1905) for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by Emmy Noether (1921).

The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components.

It has a straightforward extension to modules stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules. This contains the case for rings as a special case, considering the ring as a module over itself, so that ideals are submodules. This also generalizes the primary decomposition form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings over a field, it generalizes the decomposition of an algebraic set into a finite union of (irreducible) varieties.

The first algorithm for computing primary decompositions for polynomial rings over a field of characteristic 0 was published by Noether's student Grete Hermann (1926). The decomposition does not hold in general for non-commutative Noetherian rings. Noether gave an example of a non-commutative Noetherian ring with a right ideal that is not an intersection of primary ideals.

## Primary decomposition of an ideal

Let $R$ be a Noetherian commutative ring. An ideal $I$ of $R$ is called **primary** if it is a proper ideal and for each pair of elements $x$ and $y$ in $R$ such that $xy$ is in $I$, either $x$ or some power of $y$ is in $I$; equivalently, every zero-divisor in the quotient $R/I$ is nilpotent. The radical of a primary ideal $Q$ is a prime ideal and $Q$ is said to be $\mathfrak {p}$-primary for $\mathfrak {p}={\sqrt {Q}}$.

Let $I$ be an ideal in $R$. Then $I$ has an **irredundant primary decomposition** into primary ideals:

$I=Q\_{1}\cap \cdots \cap Q\_{n}\ $.

Irredundancy means:

* Removing any of the $Q\_{i}$ changes the intersection, i.e. for each $i$ we have: $\cap \_{j\neq i}Q\_{j}\not \subset Q\_{i}$.
* The prime ideals $\sqrt {Q\_{i}}$ are all distinct.

Moreover, this decomposition is unique in the two ways:

* The set $\\{{\sqrt {Q\_{i}\mid i\\}}}$ is uniquely determined by $I$, and
* If $\mathfrak {p}={\sqrt {Q\_{i}}}$ is a minimal element of the above set, then $Q\_{i}$ is uniquely determined by $I$; in fact, $Q\_{i}$ is the pre-image of $IR\_{\mathfrak {p}}$ under the localization map $R\to R\_{\mathfrak {p}}$.

Primary ideals which correspond to non-minimal prime ideals over $I$ are in general not unique (see an example below). For the existence of the decomposition, see #Primary decomposition from associated primes below.

The elements of $\\{{\sqrt {Q\_{i}\mid i\\}}}$ are called the **prime divisors** of $I$ or the **primes belonging to** $I$. In the language of module theory, as discussed below, the set $\\{{\sqrt {Q\_{i}\mid i\\}}}$ is also the set of associated primes of the $R$-module $R/I$. Explicitly, that means that there exist elements $g\_{1},\dots ,g\_{n}$ in $R$ such that

$\sqrt {Q\_{i}=\\{f\in R\mid fg\_{i}\in I\\}.}$

By a way of shortcut, some authors call an associated prime of $R/I$ simply an associated prime of $I$ (note this practice will conflict with the usage in the module theory).

* The minimal elements of $\\{{\sqrt {Q\_{i}\mid i\\}}}$ are the same as the minimal prime ideals containing $I$ and are called **isolated primes**.
* The non-minimal elements, on the other hand, are called the **embedded primes**.

In the case of the ring of integers $\mathbb {Z} $, the Lasker–Noether theorem is equivalent to the fundamental theorem of arithmetic. If an integer $n$ has prime factorization $n=\pm p\_{1}^{d\_{1}\cdots p\_{r}^{d\_{r}}}$, then the primary decomposition of the ideal $\langle n\rangle $ generated by $n$ in $\mathbb {Z} $, is

$$\langle n\rangle =\langle p\_{1}^{d\_{1}\rangle \cap \cdots \cap \langle p\_{r}^{d\_{r}\rangle .}}$$

Similarly, in a unique factorization domain, if an element has a prime factorization $f=up\_{1}^{d\_{1}\cdots p\_{r}^{d\_{r},}}$ where $u$ is a unit, then the primary decomposition of the principal ideal generated by $f$ is

$$\langle f\rangle =\langle p\_{1}^{d\_{1}\rangle \cap \cdots \cap \langle p\_{r}^{d\_{r}\rangle .}}$$

### Examples

The examples of the section are designed for illustrating some properties of primary decompositions, which may appear as surprising or counter-intuitive. All examples are ideals in a polynomial ring over a field *k*.

#### Intersection vs. product

The primary decomposition in $k\[x,y,z\]$ of the ideal $I=\langle x,yz\rangle $ is

$$I=\langle x,yz\rangle =\langle x,y\rangle \cap \langle x,z\rangle .$$

Because of the generator of degree one, *I* is not the product of two larger ideals. A similar example is given, in two indeterminates by

$$I=\langle x,y(y+1)\rangle =\langle x,y\rangle \cap \langle x,y+1\rangle .$$

#### Primary vs. prime power

In $k\[x,y\]$, the ideal $\langle x,y^{2}\rangle $ is a primary ideal that has $\langle x,y\rangle $ as associated prime. It is not a power of its associated prime.

#### Non-uniqueness and embedded prime

For every positive integer *n*, a primary decomposition in $k\[x,y\]$ of the ideal $I=\langle x^{2},xy\rangle $ is

$$I=\langle x^{2},xy\rangle =\langle x\rangle \cap \langle x^{2},xy,y^{n}\rangle .$$

The associated primes are

$$\langle x\rangle \subset \langle x,y\rangle .$$

Example: Let *N* = *R* = *k*\[*x*, *y*\] for some field *k*, and let *M* be the ideal (*xy*, *y*2). Then *M* has two different minimal primary decompositions *M* = (*y*)  (*x*, *y*2) = (*y*)  (*x* + *y*, *y*2). The minimal prime is (*y*) and the embedded prime is (*x*, *y*).

#### Non-associated prime between two associated primes

In $k\[x,y,z\],$ the ideal $I=\langle x^{2},xy,xz\rangle $ has the (non-unique) primary decomposition

$$I=\langle x^{2},xy,xz\rangle =\langle x\rangle \cap \langle x^{2},y^{2},z^{2},xy,xz,yz\rangle .$$

The associated prime ideals are $\langle x\rangle \subset \langle x,y,z\rangle ,$ and $\langle x,y\rangle $ is a non associated prime ideal such that

$$\langle x\rangle \subset \langle x,y\rangle \subset \langle x,y,z\rangle .$$

#### A complicated example

Unless for very simple examples, a primary decomposition may be hard to compute and may have a very complicated output. The following example has been designed for providing such a complicated output, and, nevertheless, being accessible to hand-written computation.

Let

$$\begin{aligned}P&=a\_{0}x^{m}+a\_{1}x^{m-1}y+\cdots +a\_{m}y^{m}\\Q&=b\_{0}x^{n}+b\_{1}x^{n-1}y+\cdots +b\_{n}y^{n}\end{aligned}$$

be two homogeneous polynomials in *x*, *y*, whose coefficients $a\_{1},\ldots ,a\_{m},b\_{0},\ldots ,b\_{n}$ are polynomials in other indeterminates $z\_{1},\ldots ,z\_{h}$ over a field *k*. That is, *P* and *Q* belong to $R=k\[x,y,z\_{1},\ldots ,z\_{h}\],$ and it is in this ring that a primary decomposition of the ideal $I=\langle P,Q\rangle $ is searched. For computing the primary decomposition, we suppose first that 1 is a greatest common divisor of *P* and *Q*.

This condition implies that *I* has no primary component of height one. As *I* is generated by two elements, this implies that it is a complete intersection (more precisely, it defines an algebraic set, which is a complete intersection), and thus all primary components have height two. Therefore, the associated primes of *I* are exactly the primes ideals of height two that contain *I*.

It follows that $\langle x,y\rangle $ is an associated prime of *I*.

Let $D\in k\[z\_{1},\ldots ,z\_{h}\]$ be the homogeneous resultant in *x*, *y* of *P* and *Q*. As the greatest common divisor of *P* and *Q* is a constant, the resultant *D* is not zero, and resultant theory implies that *I* contains all products of *D* by a monomial in *x*, *y* of degree *m* \+ *n* – 1. As $D\not \in \langle x,y\rangle ,$ all these monomials belong to the primary component contained in $\langle x,y\rangle .$ This primary component contains *P* and *Q*, and the behavior of primary decompositions under localization shows that this primary component is

$$\\{t|\exists e,D^{e}t\in I\\}.$$

In short, we have a primary component, with the very simple associated prime $\langle x,y\rangle ,$ such all its generating sets involve all indeterminates.

The other primary component contains *D*. One may prove that if *P* and *Q* are sufficiently generic (for example if the coefficients of *P* and *Q* are distinct indeterminates), then there is only another primary component, which is a prime ideal, and is generated by *P*, *Q* and *D*.

### Geometric interpretation

In algebraic geometry, an affine algebraic set *V*(*I*) is defined as the set of the common zeros of an ideal *I* of a polynomial ring $R=k\[x\_{1},\ldots ,x\_{n}\].$

An irredundant primary decomposition

$$I=Q\_{1}\cap \cdots \cap Q\_{r}$$

of *I* defines a decomposition of *V*(*I*) into a union of algebraic sets *V*(*Q**i*), which are irreducible, as not being the union of two smaller algebraic sets.

If $P\_{i}$ is the associated prime of $Q\_{i}$, then $V(P\_{i})=V(Q\_{i}),$ and Lasker–Noether theorem shows that *V*(*I*) has a unique irredundant decomposition into irreducible algebraic varieties

$$V(I)=\bigcup V(P\_{i}),$$

where the union is restricted to minimal associated primes. These minimal associated primes are the primary components of the radical of *I*. For this reason, the primary decomposition of the radical of *I* is sometimes called the *prime decomposition* of *I*.

The components of a primary decomposition (as well as of the algebraic set decomposition) corresponding to minimal primes are said *isolated*, and the others are said *embedded*.

For the decomposition of algebraic varieties, only the minimal primes are interesting, but in intersection theory, and, more generally in scheme theory, the complete primary decomposition has a geometric meaning.

## Primary decomposition from associated primes

Nowadays, it is common to do primary decomposition of ideals and modules within the theory of **associated primes**. Bourbaki's influential textbook *Algèbre commutative*, in particular, takes this approach.

Let *R* be a ring and *M* a module over it. By definition, an **associated prime** is a prime ideal which is the annihilator of a nonzero element of *M*; that is, $\mathfrak {p}=\operatorname {Ann} (m)$ for some $m\in M$ (this implies $m\neq 0$). Equivalently, a prime ideal $\mathfrak {p}$ is an associated prime of *M* if there is an injection of *R*-modules $R/{\mathfrak {p}\hookrightarrow M}$.

A maximal element of the set of annihilators of nonzero elements of *M* can be shown to be a prime ideal and thus, when *R* is a Noetherian ring, there exists an associated prime of *M* if and only if *M* is nonzero.

The set of associated primes of *M* is denoted by $\operatorname {Ass} \_{R}(M)$ or $\operatorname {Ass} (M)$. Directly from the definition,

* If $M=\bigoplus \_{i}M\_{i}$, then $\operatorname {Ass} (M)=\bigcup \_{i}\operatorname {Ass} (M\_{i})$.
* For an exact sequence $0\to N\to M\to L\to 0$, $\operatorname {Ass} (N)\subset \operatorname {Ass} (M)\subset \operatorname {Ass} (N)\cup \operatorname {Ass} (L)$.
* If *R* is a Noetherian ring, then $\operatorname {Ass} (M)\subset \operatorname {Supp} (M)$ where $\operatorname {Supp} $ refers to support. Also, the set of minimal elements of $\operatorname {Ass} (M)$ is the same as the set of minimal elements of $\operatorname {Supp} (M)$.

If *M* is a finitely generated module over *R*, then there is a finite ascending sequence of submodules

$$0=M\_{0}\subsetneq M\_{1}\subsetneq \cdots \subsetneq M\_{n-1}\subsetneq M\_{n}=M\\,$$

such that each quotient *M**i* /*M**i−1* is isomorphic to $R/{\mathfrak {p}\_{i}}$ for some prime ideals $\mathfrak {p}\_{i}$, each of which is necessarily in the support of *M*. Moreover every associated prime of *M* occurs among the set of primes $\mathfrak {p}\_{i}$; i.e.,

$\operatorname {Ass} (M)\subset \\{{\mathfrak {p}\_{1},\dots ,{\mathfrak {p}\_{n}\\}\subset \operatorname {Supp} (M)}}$.

(In general, these inclusions are not the equalities.) In particular, $\operatorname {Ass} (M)$ is a finite set when *M* is finitely generated.

Let $M$ be a finitely generated module over a Noetherian ring *R* and *N* a submodule of *M*. Given $\operatorname {Ass} (M/N)=\\{{\mathfrak {p}\_{1},\dots ,{\mathfrak {p}\_{n}\\}}}$, the set of associated primes of $M/N$, there exist submodules $Q\_{i}\subset M$ such that $\operatorname {Ass} (M/Q\_{i})=\\{{\mathfrak {p}\_{i}\\}}$ and

$N=\bigcap \_{i=1}^{n}Q\_{i}.$

A submodule *N* of *M* is called *$\mathfrak {p}$-primary* if $\operatorname {Ass} (M/N)=\\{{\mathfrak {p}\\}}$. A submodule of the *R*-module *R* is $\mathfrak {p}$-primary as a submodule if and only if it is a $\mathfrak {p}$-primary ideal; thus, when $M=R$, the above decomposition is precisely a primary decomposition of an ideal.

Taking $N=0$, the above decomposition says the set of associated primes of a finitely generated module *M* is the same as $\\{\operatorname {Ass} (M/Q\_{i})|i\\}$ when $0=\cap \_{1}^{n}Q\_{i}$ (without finite generation, there can be infinitely many associated primes.)

## Properties of associated primes

Let $R$ be a Noetherian ring. Then

* The set of zero-divisors on *R* is the same as the union of the associated primes of *R* (this is because the set of zerodivisors of *R* is the union of the set of annihilators of nonzero elements, the maximal elements of which are associated primes).
* For the same reason, the union of the associated primes of an *R*-module *M* is exactly the set of zero-divisors on *M*, that is, an element *r* such that the endomorphism $m\mapsto rm,M\to M$ is not injective.
* Given a subset $\Phi \subset \operatorname {Ass} (M)$, *M* an *R*-module , there exists a submodule $N\subset M$ such that $\operatorname {Ass} (N)=\operatorname {Ass} (M)-\Phi $ and $\operatorname {Ass} (M/N)=\Phi $.
* Let $S\subset R$ be a multiplicative subset, $M$ an $R$-module and $\Phi $ the set of all prime ideals of $R$ not intersecting $S$. Then $\mathfrak {p}\mapsto S^{-1}{\mathfrak {p},\\,\operatorname {Ass} \_{R}(M)\cap \Phi \to \operatorname {Ass} \_{S^{-1}R}(S^{-1}M)}$ is a bijection. Also, $\operatorname {Ass} \_{R}(M)\cap \Phi =\operatorname {Ass} \_{R}(S^{-1}M)$.
* Any prime ideal minimal with respect to containing an ideal *J* is in $\mathrm {Ass} \_{R}(R/J).$ These primes are precisely the isolated primes.
* A module *M* over *R* has finite length if and only if *M* is finitely generated and $\mathrm {Ass} (M)$ consists of maximal ideals.
* Let $A\to B$ be a ring homomorphism between Noetherian rings and *F* a *B*-module that is flat over *A*. Then, for each *A*-module *E*,

$\operatorname {Ass} \_{B}(E\otimes \_{A}F)=\bigcup \_{{\mathfrak {p}\in \operatorname {Ass} (E)}\operatorname {Ass} \_{B}(F/{\mathfrak {p}F)}}$.

## Non-Noetherian case

The next theorem gives necessary and sufficient conditions for a ring to have primary decompositions for its ideals.

**Theorem**  Let *R* be a commutative ring. Then the following are equivalent.

1. Every ideal in *R* has a primary decomposition.
2. *R* has the following properties:
    * (L1) For every proper ideal *I* and a prime ideal *P*, there exists an *x* in *R* \- *P* such that (*I* : *x*) is the pre-image of *I* *R**P* under the localization map *R**R**P*.
    * (L2) For every ideal *I*, the set of all pre-images of *I* *S*−1*R* under the localization map *R**S*−1*R*, *S* running over all multiplicatively closed subsets of *R*, is finite.

The proof is given at Chapter 4 of Atiyah–Macdonald as a series of exercises.

There is the following uniqueness theorem for an ideal having a primary decomposition.

**Theorem**  Let *R* be a commutative ring and *I* an ideal. Suppose *I* has a minimal primary decomposition $I=\cap \_{1}^{r}Q\_{i}$ (note: "minimal" implies $\sqrt {Q\_{i}}$ are distinct.) Then

1. The set $E=\left\\{{\sqrt {Q\_{i}|1\leq i\leq r\right\\}}}$ is the set of all prime ideals in the set $\left\\{{\sqrt {(I:x)}|x\in R\right\\}}$.
2. The set of minimal elements of *E* is the same as the set of minimal prime ideals over *I*. Moreover, the primary ideal corresponding to a minimal prime *P* is the pre-image of *I* *R**P* and thus is uniquely determined by *I*.

Now, for any commutative ring *R*, an ideal *I* and a minimal prime *P* over *I*, the pre-image of *I* *R**P* under the localization map is the smallest *P*-primary ideal containing *I*. Thus, in the setting of preceding theorem, the primary ideal *Q* corresponding to a minimal prime *P* is also the smallest *P*-primary ideal containing *I* and is called the *P*-primary component of *I*.

For example, if the power *P**n* of a prime *P* has a primary decomposition, then its *P*-primary component is the *n*-th symbolic power of *P*.

## Additive theory of ideals

This result is the first in an area now known as the additive theory of ideals, which studies the ways of representing an ideal as the intersection of a special class of ideals. The decision on the "special class", e.g., primary ideals, is a problem in itself. In the case of non-commutative rings, the class of tertiary ideals is a useful substitute for the class of primary ideals.

1. Ciliberto, Ciro; Hirzebruch, Friedrich; Miranda, Rick; Teicher, Mina, eds. (2001). *Applications of Algebraic Geometry to Coding Theory, Physics and Computation*. Dordrecht: Springer Netherlands. ISBN 978-94-010-1011-5.
2. Hermann, G. (1926). "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale". *Mathematische Annalen* (in German). **95**: 736–788. doi:10.1007/BF01206635. S2CID 115897210.
3. In other words, $\sqrt {Q\_{i}=(I:g\_{i})}$ is the ideal quotient.
4. Bourbaki, Ch. IV, § 1, no 1, Proposition 3.
5. Bourbaki, Ch. IV, § 1, no 3, Corollaire 1.
6. Bourbaki, Ch. IV, § 1, no 4, Théorème 1.
7. Bourbaki, Ch. IV, § 1, no 4, Théorème 2.
8. Bourbaki, Ch. IV, § 2, no. 2. Theorem 1.
9. Here is the proof of the existence of the decomposition (following Bourbaki). Let *M* be a finitely generated module over a Noetherian ring *R* and *N* a submodule. To show *N* admits a primary decomposition, by replacing *M* by $M/N$, it is enough to show that when $N=0$. Now,

$$0=\cap Q\_{i}\iff \emptyset =\operatorname {Ass} (\cap Q\_{i})=\cap \operatorname {Ass} (Q\_{i})$$

where $Q\_{i}$ are primary submodules of *M*. In other words, 0 has a primary decomposition if, for each associated prime *P* of *M*, there is a primary submodule *Q* such that $P\not \in \operatorname {Ass} (Q)$. Now, consider the set $\\{N\subseteq M|P\not \in \operatorname {Ass} (N)\\}$ (which is nonempty since zero is in it). The set has a maximal element *Q* since *M* is a Noetherian module. If *Q* is not *P*-primary, say, $P'\neq P$ is associated with $M/Q$, then $R/P'\simeq Q'/Q$ for some submodule *Q'*, contradicting the maximality. Thus, *Q* is primary and the proof is complete. Remark: The same proof shows that if *R*, *M*, *N* are all graded, then $Q\_{i}$ in the decomposition may be taken to be graded as well.
10. Bourbaki, Ch. IV, § 1, Corollary 3.
11. Bourbaki, Ch. IV, § 1, Corollary 2.
12. Bourbaki, Ch. IV, § 1, Proposition 4.
13. Bourbaki, Ch. IV, § 1, no. 2, Proposition 5.
14. Matsumura 1970, 7.C Lemma
15. Cohn, P. M. (2003), *Basic Algebra*, Springer, Exercise 10.9.7, p. 391, ISBN 9780857294289.
16. Bourbaki, Ch. IV, § 2. Theorem 2.
17. Atiyah & Macdonald 1994
18. Atiyah & Macdonald 1994, Ch. 4. Exercise 11


title: Wandri Dam

abstract: Wandri Dam, is an earthfill dam on Wandri river near Palghar, Thane district in the state of Maharashtra in India.

text:
# Wandri Dam

**Wandri Dam**, is an earthfill dam on Wandri river near Palghar, Thane district in the state of Maharashtra in India.

## Specifications

The height of the dam above its lowest foundation is 29.6 m (97 ft) while the length is 1,336 m (4,383 ft). The volume content is 1,206 km3 (289 cu mi) and gross storage capacity is 36,510.00 km3 (8,759.21 cu mi).

## Purpose

* Irrigation

## InfoBox

| Wandri Dam | |
| --- | --- |
| Location of Wandri Dam in Maharashtra | |
| Official name | Wandri Dam D02843 |
| Location | Palghar |
| Coordinates | 19°36′53″N 72°57′14″E / 19.614858°N 72.953854°E / 19.614858; 72.953854 |
| Opening date | 1987 |
| Owner(s) | Government of Maharashtra, India |
| Dam and spillways | |
| Type of dam | Earthfill |
| Impounds | Wandri river |
| Height | 29.6 m (97 ft) |
| Length | 1,336 m (4,383 ft) |
| Dam volume | 1,206 km3 (289 cu mi) |
| Reservoir | |
| Total capacity | 34,710 km3 (8,330 cu mi) |
| Surface area | 4,438 km2 (1,714 sq mi) |


title: Loop Shuttle

abstract: The Loop Shuttle was a rapid transit line on the Chicago "L". It operated clockwise around the Loop, making stops at all stations. The line was inaugurated September 30, 1969, and discontinued September 30, 1977.

text:
# Loop Shuttle

The **Loop Shuttle** was a rapid transit line on the Chicago "L". It operated clockwise around the Loop, making stops at all stations. The line was inaugurated September 30, 1969, and discontinued September 30, 1977.

## Operations

The Loop Shuttle operated continuously clockwise around the inner track of the Loop, approximately 1.79 miles (2.88 km). The line provided service Monday through Saturday during the day, with no late night or Sunday service. Evening service was dropped later in its life. The line typically used two-car 6000-series assigned to Kimball Yard.

During weekday rush hours, the Evanston Express was the only other route to travel clockwise and use the inner track. Southbound Lake–Dan Ryan trains shared the inner track on the Lake and Wabash segment.

While the CTA did not formally adopt color-coded lines during its lifetime, the Loop Shuttle was depicted as gray or black on color maps.

## History

Opportunity for a continuous "L" line around the Loop was realized in 1969, when modifications were underway to allow through service of the Lake Street branch to the newly completed Dan Ryan branch. Prior to this all trains ran counter-clockwise, with Ravenswood and Evanston Express trains using the outer track and Lake Street trains using the inner track. The new Lake–Dan Ryan Line began on September 28, 1969, and Loop Shuttle service began two days later on September 30. The Ravenswood Line would continue operating counter-clockwise via the outer track and Evanston Express trains would shift to operating clockwise around the inner track on September 30.

The Loop Shuttle was quietly discontinued on September 30, 1977 as a cost-cutting measure. After the Loop Shuttle's discontinuation, the Evanston Express remained the only route to run clockwise around the Loop. Full time service around the inner loop was restored with the introduction of the Orange Line in 1993 and later the Pink Line in 2006.

## Station listing

| Station | Connecting "L" services and notes |
| --- | --- |
| Clark/Lake
(inner platform) | Lake–Dan Ryan   Ravenswood   Evanston Express
Milwaukee–Congress–Douglas  (at Lake Transfer) |
| State/Lake
(inner platform) | Lake–Dan Ryan   Ravenswood   Evanston Express
Howard–Englewood–Jackson Park  (at Washington) |
| Randolph/Wabash
(inner platform) | Lake–Dan Ryan   Ravenswood   Evanston Express |
| Madison/Wabash
(inner platform) | Lake–Dan Ryan   Ravenswood   Evanston Express |
| Adams/Wabash
(inner platform) | Lake–Dan Ryan   Ravenswood   Evanston Express |
| State/Van Buren
(inner platform) | Closed September 2, 1973 |
| LaSalle/Van Buren
(inner platform) | Ravenswood   Evanston Express |
| Quincy
(inner platform) | Ravenswood   Evanston Express |
| Madison/Wells
(inner platform) | Ravenswood   Evanston Express |
| Randolph/Wells
(inner platform) | Ravenswood   Evanston Express |
| Trains return to Clark/Lake | |

1. Graham, Garfield. "Chicago *L*.org: Operations - Lines -\> Loop Elevated". *www.chicago-l.org*. Retrieved October 5, 2022.
2. Rand McNally & Co. (1977). *RTA Map: Chicago & Suburbs* (Map) (1st ed.). November 1, 1976. Regional Transportation Authority of Chicago. p. 2.
3. Chicago Transit Authority Research Planning (February 1972). *"L" system car card map* (Map). Chicago Transit Authority.
4. Cudahy, Brian J. (1982). *Destination, Loop : the story of rapid transit railroading in and around Chicago* (1st ed.). Brattleboro, Vt.: S. Greene Press. ISBN 0-8289-0480-4.

## InfoBox

| Loop Shuttle | |
| --- | --- |
| A Loop Shuttle train operates around the inner track at Tower 18 (Lake and Wells Streets). | |
| Overview | |
| Status | Defunct |
| Locale | Chicago, Illinois, United States |
| Stations | 9 |
| Service | |
| Type | Rapid transit |
| System | Chicago "L" |
| Route number | `L` |
| Operator(s) | Chicago Transit Authority |
| Depot(s) | Kimball Yard |
| Rolling stock | 6000-series |
| History | |
| Opened | September 30, 1969 (1969-09-30) |
| Closed | September 30, 1977 (1977-09-30) |
| Technical | |
| Character | Elevated |
| Track gauge | 4 ft 8+12 in (1,435 mm) |
| Minimum radius | 90 feet (27 m) |
| Electrification | Third rail, 600  DC |
| Route map  The Loop highlighted in black | |


title: US Yachts US 305

abstract: The US Yachts US 305 is an American sailboat that was designed by William Garden as a cruiser and first built in 1978. The US 305 is a development of the 1977 Buccaneer 305, which was built by Buccaneer Yachts, also a division of Bayliner.

text:
# US Yachts US 305

The **US Yachts US 305** is an American sailboat that was designed by William Garden as a cruiser and first built in 1978.

The US 305 is a development of the 1977 Buccaneer 305, which was built by Buccaneer Yachts, also a division of Bayliner.

## Production

The design was built by US Yachts, a division of Bayliner, in the United States, starting in 1978, but it is now out of production.

## Design

The US 305 is a recreational keelboat, built predominantly of fiberglass, with wood trim. It has a masthead sloop rig, a raked stem, a nearly plumb transom, an internally mounted spade-type rudder controlled by a wheel and a fixed fin keel. It displaces 10,000 lb (4,536 kg) and carries 3,500 lb (1,588 kg) of ballast.

The boat has a draft of 4.00 ft (1.22 m) with the standard keel.

A Swedish Volvo MD11C diesel engine was a factory option. The fuel tank holds 42 U.S. gallons (160 L; 35 imp gal) and the fresh water tank has a capacity of 36 U.S. gallons (140 L; 30 imp gal).

The design has sleeping accommodation for six people, with a double "V"-berth in the bow cabin, an L-shaped settee and a straight settee in the main cabin and an aft cabin with a double berth on the starboard side. The galley is located on the port side just forward of the companionway ladder. The galley is L-shaped and is equipped with a three-burner stove and a sink. A navigation station is opposite the galley, on the starboard side. The head is located just aft of the bow cabin on the port side. Cabin headroom is 74 in (188 cm).

For sailing the design may be equipped with one of a number of jibs, genoas or a storm jib.

The design has a hull speed of 6.87 kn (12.72 km/h).

## InfoBox

US Yachts US 305
| Development | |
| --- | --- |
| Designer | William Garden |
| Location | United States |
| Year | 1978 |
| Builder(s) | US Yachts |
| Role | Cruiser |
| Name | US Yachts US 305 |
| Boat | |
| Displacement | 10,000 lb (4,536 kg) |
| Draft | 4.00 ft (1.22 m) |
| Hull | |
| Type | monohull |
| Construction | fiberglass |
| LOA | 30.00 ft (9.14 m) |
| LWL | 26.25 ft (8.00 m) |
| Beam | 10.17 ft (3.10 m) |
| Engine type | Optional Volvo MD11C diesel engine |
| Hull appendages | |
| Keel/board type | fin keel |
| Ballast | 3,500 lb (1,588 kg) |
| Rudder(s) | internally-mounted spade-type rudder |
| Rig | |
| Rig type | Bermuda rig |
| foretriangle height | 40.00 ft (12.19 m) |
| foretriangle base | 14.00 ft (4.27 m) |
| mainsail luff | 32.50 ft (9.91 m) |
| mainsail foot | 11.00 ft (3.35 m) |
| Sails | |
| Sailplan | masthead sloop |
| Mainsail area | 178.75 sq ft (16.606 m2) |
| Jib/genoa area | 280.00 sq ft (26.013 m2) |
| Total sail area | 458.75 sq ft (42.619 m2) |
| \[edit on Wikidata\] | |


title: Ferromagnetism

abstract: Ferromagnetism is a property of certain materials that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel. In physics, multiple types of material magnetism have been distinguished. Ferromagnetism is the strongest type and is responsible for the common phenomenon of everyday magnetism. An example of a permanent magnet formed from a ferromagnetic material is a refrigerator magnet. Substances respond weakly to three other types of magnetism—paramagnetism, diamagnetism, and antiferromagnetism—but the forces are usually so weak that they can be detected only by lab instruments. Permanent magnets are either ferromagnetic or ferrimagnetic, as are the materials that are attracted to them. Relatively few materials are ferromagnetic. They are typically pure forms, alloys, or compounds of iron, cobalt, nickel, and certain rare-earth metals. Ferromagnetism is vital in industrial applications and modern technologies, forming the basis for electrical and electromechanical devices such as electromagnets, electric motors, generators, transformers, magnetic storage, and nondestructive testing of ferrous materials. Ferromagnetic materials can be divided into magnetically soft materials, which do not tend to stay magnetized, and magnetically hard materials, which do. Permanent magnets are made from hard ferromagnetic materials and ferrimagnetic materials that are subjected to special processing in a strong magnetic field during manufacturing to align their internal microcrystalline structure, making them difficult to demagnetize. To demagnetize a saturated magnet, a magnetic field must be applied. The threshold at which demagnetization occurs depends on the coercivity of the material. Magnetically hard materials have high coercivity, whereas magnetically soft materials have low coercivity. The overall strength of a magnet is measured by its magnetic moment or, alternatively, its total magnetic flux. The local strength of magnetism in a material is measured by its magnetization.

text:
# Ferromagnetism

**Ferromagnetism** is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability.

Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone).

In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar effect ferrimagnetism) is the strongest type and is responsible for the common phenomenon of everyday magnetism. An example of a permanent magnet formed from a ferromagnetic material is a refrigerator magnet.

Substances respond weakly to three other types of magnetism—paramagnetism, diamagnetism, and antiferromagnetism—but the forces are usually so weak that they can be detected only by lab instruments.

Permanent magnets (materials that can be magnetized by an external magnetic field and remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are the materials that are attracted to them. Relatively few materials are ferromagnetic. They are typically pure forms, alloys, or compounds of iron, cobalt, nickel, and certain rare-earth metals.

Ferromagnetism is vital in industrial applications and modern technologies, forming the basis for electrical and electromechanical devices such as electromagnets, electric motors, generators, transformers, magnetic storage (including tape recorders and hard disks), and nondestructive testing of ferrous materials.

Ferromagnetic materials can be divided into magnetically soft materials (like annealed iron), which do not tend to stay magnetized, and magnetically hard materials, which do. Permanent magnets are made from hard ferromagnetic materials (such as alnico) and ferrimagnetic materials (such as ferrite) that are subjected to special processing in a strong magnetic field during manufacturing to align their internal microcrystalline structure, making them difficult to demagnetize. To demagnetize a saturated magnet, a magnetic field must be applied. The threshold at which demagnetization occurs depends on the coercivity of the material. Magnetically hard materials have high coercivity, whereas magnetically soft materials have low coercivity.

The overall strength of a magnet is measured by its magnetic moment or, alternatively, its total magnetic flux. The local strength of magnetism in a material is measured by its magnetization.

## Terms

Ferromagnetic material: all the molecular magnetic dipoles are pointed in the same directionFerrimagnetic material: some of the dipoles point in the opposite direction, but their smaller contribution is overcome by the others

Historically, the term *ferromagnetism* was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field; that is, any material that could become a magnet. This definition is still in common use.

In a landmark paper in 1948, Louis Néel showed that two levels of magnetic alignment result in this behavior. One is ferromagnetism in the strict sense, where all the magnetic moments are aligned. The other is *ferrimagnetism*, where some magnetic moments point in the opposite direction but have a smaller contribution, so spontaneous magnetization is present.

In the special case where the opposing moments balance completely, the alignment is known as *antiferromagnetism*; antiferromagnets do not have a spontaneous magnetization.

## Materials

Curie temperatures for some crystalline ferromagnetic materials
| Material | Curie
temp. (K) |
| --- | --- |
| Co | 1388 |
| Fe | 1043 |
| Fe2O3 | 948 |
| NiOFe2O3 | 858 |
| CuOFe2O3 | 728 |
| MgOFe2O3 | 713 |
| MnBi | 630 |
| Ni | 627 |
| Nd2Fe14 B | 593 |
| MnSb | 587 |
| MnOFe2O3 | 573 |
| Y3Fe5O12 | 560 |
| CrO2 | 386 |
| MnAs | 318 |
| Gd | 292 |
| Tb | 219 |
| Dy | 88 |
| EuO | 69 |
|  | |

Ferromagnetism is an unusual property that occurs in only a few substances. The common ones are the transition metals iron, nickel, and cobalt, as well as their alloys and alloys of rare-earth metals. It is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure. Ferromagnetism results from these materials having many unpaired electrons in their d-block (in the case of iron and its relatives) or f-block (in the case of the rare-earth metals), a result of Hund's rule of maximum multiplicity. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, called Heusler alloys, named after Fritz Heusler. Conversely, there are non-magnetic alloys, such as types of stainless steel, composed almost exclusively of ferromagnetic metals.

Amorphous (non-crystalline) ferromagnetic metallic alloys can be made by very rapid quenching (cooling) of an alloy. These have the advantage that their properties are nearly isotropic (not aligned along a crystal axis); this results in low coercivity, low hysteresis loss, high permeability, and high electrical resistivity. One such typical material is a transition metal-metalloid alloy, made from about 80% transition metal (usually Fe, Co, or Ni) and a metalloid component (, , Si, , or Al) that lowers the melting point.

A relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals.

The table lists a selection of ferromagnetic and ferrimagnetic compounds, along with their Curie temperature (*T*C), above which they cease to exhibit spontaneous magnetization.

### Unusual materials

Most ferromagnetic materials are metals, since the conducting electrons are often responsible for mediating the ferromagnetic interactions. It is therefore a challenge to develop ferromagnetic insulators, especially multiferroic materials, which are both ferromagnetic and ferroelectric.

A number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. Pu is a paramagnet with cubic symmetry at room temperature, but which undergoes a structural transition into a tetragonal state with ferromagnetic order when cooled below its *T*C = 125 K. In its ferromagnetic state, PuP's easy axis is in the ⟨100⟩ direction.

In NpFe2 the easy axis is ⟨111⟩. Above *T*C ≈ 500 K, NpFe2 is also paramagnetic and cubic. Cooling below the Curie temperature produces a rhombohedral distortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the length c along the unique trigonal axis (after the distortion has begun) and a as the distance in the plane perpendicular to c. In the cubic phase this reduces to c/a = 1.00. Below the Curie temperature, the lattice acquires a distortion

$$\frac {c}{a}-1=-(120\pm 5)\times 10^{-4},$$

which is the largest strain in any actinide compound. NpNi2 undergoes a similar lattice distortion below *T*C = 32 K, with a strain of (43 ± 5) × 10−4. NpCo2 is a ferrimagnet below 15 K.

In 2009, a team of MIT physicists demonstrated that a lithium gas cooled to less than one kelvin can exhibit ferromagnetism. The team cooled fermionic lithium-6 to less than 150 nK (150 billionths of one kelvin) using infrared laser cooling. This demonstration is the first time that ferromagnetism has been demonstrated in a gas.

In rare circumstances, ferromagnetism can be observed in compounds consisting of only s-block and p-block elements, such as rubidium sesquioxide.

In 2018, a team of University of Minnesota physicists demonstrated that body-centered tetragonal ruthenium exhibits ferromagnetism at room temperature.

### Electrically induced ferromagnetism

Recent research has shown evidence that ferromagnetism can be induced in some materials by an electric current or voltage. Antiferromagnetic LaMnO3 and SrCoO have been switched to be ferromagnetic by a current. In July 2020, scientists reported inducing ferromagnetism in the abundant diamagnetic material iron pyrite ("fool's gold") by an applied voltage. In these experiments, the ferromagnetism was limited to a thin surface layer.

## Explanation

The Bohr–Van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of material magnetism, including ferromagnetism; the explanation rather depends on the quantum mechanical description of atoms. Each of an atom's electrons has a magnetic moment according to its spin state, as described by quantum mechanics. The Pauli exclusion principle, also a consequence of quantum mechanics, restricts the occupancy of electrons' spin states in atomic orbitals, generally causing the magnetic moments from an atom's electrons to largely or completely cancel. An atom will have a *net* magnetic moment when that cancellation is incomplete.

### Origin of atomic magnetism

One of the fundamental properties of an electron (besides that it carries charge) is that it has a magnetic dipole moment, i.e., it behaves like a tiny magnet, producing a magnetic field. This dipole moment comes from a more fundamental property of the electron: its quantum mechanical spin. Due to its quantum nature, the spin of the electron can be in one of only two states, with the magnetic field either pointing "up" or "down" (for any choice of up and down). Electron spin in atoms is the main source of ferromagnetism, although there is also a contribution from the orbital angular momentum of the electron about the nucleus. When these magnetic dipoles in a piece of matter are aligned (point in the same direction), their individually tiny magnetic fields add together to create a much larger macroscopic field.

However, materials made of atoms with filled electron shells have a total dipole moment of zero: because the electrons all exist in pairs with opposite spin, every electron's magnetic moment is cancelled by the opposite moment of the second electron in the pair. Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment, so ferromagnetism occurs only in materials with partially filled shells. Because of Hund's rules, the first few electrons in an otherwise unoccupied shell tend to have the same spin, thereby increasing the total dipole moment.

These unpaired dipoles (often called simply "spins", even though they also generally include orbital angular momentum) tend to align in parallel to an external magnetic field   leading to a macroscopic effect called paramagnetism. In ferromagnetism, however, the magnetic interaction between neighboring atoms' magnetic dipoles is strong enough that they align with *each other* regardless of any applied field, resulting in the spontaneous magnetization of so-called domains. This results in the large observed magnetic permeability of ferromagnetics, and the ability of magnetically hard materials to form permanent magnets.

### Exchange interaction

When two nearby atoms have unpaired electrons, whether the electron spins are parallel or antiparallel affects whether the electrons can share the same orbit as a result of the quantum mechanical effect called the exchange interaction. This in turn affects the electron location and the Coulomb (electrostatic) interaction and thus the energy difference between these states.

The exchange interaction is related to the Pauli exclusion principle, which says that two electrons with the same spin cannot also be in the same spatial state (orbital). This is a consequence of the spin–statistics theorem and that electrons are fermions. Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are farther apart when the electrons have parallel spins than when they have opposite spins. This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are antiparallel, so the parallel-spin state is more stable. This difference in energy is called the exchange energy. In simple terms, the outer electrons of adjacent atoms, which repel each other, can move further apart by aligning their spins in parallel, so the spins of these electrons tend to line up.

This energy difference can be orders of magnitude larger than the energy differences associated with the magnetic dipole–dipole interaction due to dipole orientation, which tends to align the dipoles antiparallel. In certain doped semiconductor oxides, RKKY interactions have been shown to bring about periodic longer-range magnetic interactions, a phenomenon of significance in the study of spintronic materials.

The materials in which the exchange interaction is much stronger than the competing dipole–dipole interaction are frequently called *magnetic materials*. For instance, in iron (Fe) the exchange force is about 1,000 times stronger than the dipole interaction. Therefore, below the Curie temperature, virtually all of the dipoles in a ferromagnetic material will be aligned. In addition to ferromagnetism, the exchange interaction is also responsible for the other types of spontaneous ordering of atomic magnetic moments occurring in magnetic solids: antiferromagnetism and ferrimagnetism. There are different exchange interaction mechanisms which create the magnetism in different ferromagnetic, ferrimagnetic, and antiferromagnetic substances—these mechanisms include direct exchange, RKKY exchange, double exchange, and superexchange.

### Magnetic anisotropy

Although the exchange interaction keeps spins aligned, it does not align them in a particular direction. Without magnetic anisotropy, the spins in a magnet randomly change direction in response to thermal fluctuations, and the magnet is superparamagnetic. There are several kinds of magnetic anisotropy, the most common of which is magnetocrystalline anisotropy. This is a dependence of the energy on the direction of magnetization relative to the crystallographic lattice. Another common source of anisotropy, inverse magnetostriction, is induced by internal strains. Single-domain magnets also can have a *shape anisotropy* due to the magnetostatic effects of the particle shape. As the temperature of a magnet increases, the anisotropy tends to decrease, and there is often a blocking temperature at which a transition to superparamagnetism occurs.

### Magnetic domains

The spontaneous alignment of magnetic dipoles in ferromagnetic materials would seem to suggest that every piece of ferromagnetic material should have a strong magnetic field, since all the spins are aligned; yet iron and other ferromagnets are often found in an "unmagnetized" state. This is because a bulk piece of ferromagnetic material is divided into tiny regions called *magnetic domains* (also known as *Weiss domains*). Within each domain, the spins are aligned, but if the bulk material is in its lowest energy configuration (i.e. "unmagnetized"), the spins of separate domains point in different directions and their magnetic fields cancel out, so the bulk material has no net large-scale magnetic field.

Ferromagnetic materials spontaneously divide into magnetic domains because the exchange interaction is a short-range force, so over long distances of many atoms, the tendency of the magnetic dipoles to reduce their energy by orienting in opposite directions wins out. If all the dipoles in a piece of ferromagnetic material are aligned parallel, it creates a large magnetic field extending into the space around it. This contains a lot of magnetostatic energy. The material can reduce this energy by splitting into many domains pointing in different directions, so the magnetic field is confined to small local fields in the material, reducing the volume of the field. The domains are separated by thin domain walls a number of molecules thick, in which the direction of magnetization of the dipoles rotates smoothly from one domain's direction to the other.

### Magnetized materials

Thus, a piece of iron in its lowest energy state ("unmagnetized") generally has little or no net magnetic field. However, the magnetic domains in a material are not fixed in place; they are simply regions where the spins of the electrons have aligned spontaneously due to their magnetic fields, and thus can be altered by an external magnetic field. If a strong-enough external magnetic field is applied to the material, the domain walls will move via a process in which the spins of the electrons in atoms near the wall in one domain turn under the influence of the external field to face in the same direction as the electrons in the other domain, thus reorienting the domains so more of the dipoles are aligned with the external field. The domains will remain aligned when the external field is removed, and sum to create a magnetic field of their own extending into the space around the material, thus creating a "permanent" magnet. The domains do not go back to their original minimum energy configuration when the field is removed because the domain walls tend to become 'pinned' or 'snagged' on defects in the crystal lattice, preserving their parallel orientation. This is shown by the Barkhausen effect: as the magnetizing field is changed, the material's magnetization changes in thousands of tiny discontinuous jumps as domain walls suddenly "snap" past defects.

This magnetization as a function of an external field is described by a hysteresis curve. Although this state of aligned domains found in a piece of magnetized ferromagnetic material is not a minimal-energy configuration, it is metastable, and can persist for long periods, as shown by samples of magnetite from the sea floor which have maintained their magnetization for millions of years.

Heating and then cooling (annealing) a magnetized material, subjecting it to vibration by hammering it, or applying a rapidly oscillating magnetic field from a degaussing coil tends to release the domain walls from their pinned state, and the domain boundaries tend to move back to a lower energy configuration with less external magnetic field, thus demagnetizing the material.

Commercial magnets are made of "hard" ferromagnetic or ferrimagnetic materials with very large magnetic anisotropy such as alnico and ferrites, which have a very strong tendency for the magnetization to be pointed along one axis of the crystal, the "easy axis". During manufacture the materials are subjected to various metallurgical processes in a powerful magnetic field, which aligns the crystal grains so their "easy" axes of magnetization all point in the same direction. Thus, the magnetization, and the resulting magnetic field, is "built in" to the crystal structure of the material, making it very difficult to demagnetize.

### Curie temperature

As the temperature of a material increases, thermal motion, or entropy, competes with the ferromagnetic tendency for dipoles to align. When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order phase transition and the system can no longer maintain a spontaneous magnetization, so its ability to be magnetized or attracted to a magnet disappears, although it still responds paramagnetically to an external field. Below that temperature, there is a spontaneous symmetry breaking and magnetic moments become aligned with their neighbors. The Curie temperature itself is a critical point, where the magnetic susceptibility is theoretically infinite and, although there is no net magnetization, domain-like spin correlations fluctuate at all length scales.

The study of ferromagnetic phase transitions, especially via the simplified Ising spin model, had an important impact on the development of statistical physics. There, it was first clearly shown that mean field theory approaches failed to predict the correct behavior at the critical point (which was found to fall under a *universality class* that includes many other systems, such as liquid-gas transitions), and had to be replaced by renormalization group theory.

1. Chikazumi, Sōshin (2009). *Physics of ferromagnetism*. English edition prepared with the assistance of C. D. Graham, Jr. (2nd ed.). Oxford: Oxford University Press. p. 118. ISBN 978-0-19-956481-1.
2. Bozorth, Richard M. *Ferromagnetism*, first published 1951, reprinted 1993 by IEEE Press, New York as a "Classic Reissue". ISBN 0-7803-1032-2.
3. Somasundaran, P., ed. (2006). *Encyclopedia of surface and colloid science* (2nd ed.). New York: Taylor & Francis. p. 3471. ISBN 978-0-8493-9608-3.
4. Cullity, B. D.; Graham, C. D. (2011). "6. Ferrimagnetism". *Introduction to Magnetic Materials*. John Wiley & Sons. ISBN 978-1-118-21149-6.
5. Aharoni, Amikam (2000). *Introduction to the theory of ferromagnetism* (2nd ed.). Oxford: Oxford University Press. ISBN 978-0-19-850809-0.
6. Kittel, Charles (1986). *Introduction to Solid State Physics* (sixth ed.). John Wiley and Sons. ISBN 0-471-87474-4.
7. Jackson, Mike (2000). "Wherefore Gadolinium? Magnetism of the Rare Earths" (PDF). *IRM Quarterly*. **10** (3). Institute for Rock Magnetism: 6. Archived from the original (PDF) on 2017-07-12. Retrieved 2016-08-08.
8. Hill, Nicola A. (2000-07-01). "Why Are There so Few Magnetic Ferroelectrics?". *The Journal of Physical Chemistry B*. **104** (29): 6694–6709. doi:10.1021/jp000114x. ISSN 1520-6106.
9. Lander G. H.; Lam D. J. (1976). "Neutron diffraction study of PuP: The electronic ground state". *Phys. Rev. B*. **14** (9): 4064–4067. Bibcode:1976PhRvB..14.4064L. doi:10.1103/PhysRevB.14.4064.
10. Aldred A. T.; Dunlap B. D.; Lam D. J.; Lander G. H.; Mueller M. H.; Nowik I. (1975). "Magnetic properties of neptunium Laves phases: NpMn2, NpFe2, NpCo2, and NpNi2". *Phys. Rev. B*. **11** (1): 530–544. Bibcode:1975PhRvB..11..530A. doi:10.1103/PhysRevB.11.530.
11. Mueller M. H.; Lander G. H.; Hoff H. A.; Knott H. W.; Reddy J. F. (Apr 1979). "Lattice distortions measured in actinide ferromagnets PuP, NpFe2, and NpNi2" (PDF). *J. Phys. Colloque C4, Supplement*. **40** (4): C4-68–C4-69. Archived (PDF) from the original on 2011-05-09.
12. G.-B. Jo; Y.-R. Lee; J.-H. Choi; C. A. Christensen; T. H. Kim; J. H. Thywissen; D. E. Pritchard; W. Ketterle (2009). "Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms". *Science*. **325** (5947): 1521–1524. arXiv:0907.2888. Bibcode:2009Sci...325.1521J. doi:10.1126/science.1177112. PMID 19762638. S2CID 13205213.
13. Attema, Jisk J.; de Wijs, Gilles A.; Blake, Graeme R.; de Groot, Robert A. (2005). "Anionogenic Ferromagnets" (PDF). *Journal of the American Chemical Society*. **127** (46). American Chemical Society (ACS): 16325–16328. doi:10.1021/ja0550834. ISSN 0002-7863. PMID 16287327.
14. Quarterman, P.; Sun, Congli; Garcia-Barriocanal, Javier; D. C., Mahendra; Lv, Yang; Manipatruni, Sasikanth; Nikonov, Dmitri E.; Young, Ian A.; Voyles, Paul M.; Wang, Jian-Ping (2018). "Demonstration of Ru as the 4th ferromagnetic element at room temperature". *Nature Communications*. **9** (1): 2058. Bibcode:2018NatCo...9.2058Q. doi:10.1038/s41467-018-04512-1. PMC 5970227. PMID 29802304.
15. "'Fool's gold' may be valuable after all". *phys.org*. Retrieved 17 August 2020.
16. Walter, Jeff; Voigt, Bryan; Day-Roberts, Ezra; Heltemes, Kei; Fernandes, Rafael M.; Birol, Turan; Leighton, Chris (1 July 2020). "Voltage-induced ferromagnetism in a diamagnet". *Science Advances*. **6** (31): eabb7721. Bibcode:2020SciA....6.7721W. doi:10.1126/sciadv.abb7721. ISSN 2375-2548. PMC 7439324. PMID 32832693.
17. Feynman, Richard P.; Robert Leighton; Matthew Sands (1963). *The Feynman Lectures on Physics, Vol. 2*. Addison-Wesley. pp. Ch. 37.
18. Chikazumi, Sōshin (2009). *Physics of ferromagnetism*. English edition prepared with the assistance of C. D. Graham, Jr. (2nd ed.). Oxford: Oxford University Press. pp. 129–130. ISBN 978-0-19-956481-1.
19. Assadi, M. H. N.; Hanaor, D. A. H. (2013). "Theoretical study on copper's energetics and magnetism in TiO2 polymorphs". *Journal of Applied Physics*. **113** (23): 233913-1–233913-5. arXiv:1304.1854. Bibcode:2013JAP...113w3913A. doi:10.1063/1.4811539. S2CID 94599250.
20. García, R. Martínez; Bilovol, V.; Ferrari, S.; de la Presa, P.; Marín, P.; Pagnola, M. (2022-04-01). "Structural and magnetic properties of a BaFe12O19/NiFe2O4 nanostructured composite depending on different particle size ratios". *Journal of Magnetism and Magnetic Materials*. **547**: 168934. doi:10.1016/j.jmmm.2021.168934. ISSN 0304-8853. S2CID 245150523.
21. Aharoni, Amikam (1996). *Introduction to the Theory of Ferromagnetism*. Clarendon Press. ISBN 0-19-851791-2.
22. Feynman, Richard P.; Robert B. Leighton\>; Matthew Sands (1963). *The Feynman Lectures on Physics*. Vol. I. Pasadena: California Inst. of Technology. pp. 37.5–37.6. ISBN 0-465-02493-9.


title: The Summit at Danbury

abstract: The Summit at Danbury, formerly known as the Matrix Corporate Center and before that as the Union Carbide Corporate Center, is an architecturally unique building in Danbury, Connecticut, United States. It was constructed in 1982 as the headquarters of the Union Carbide chemical company, it is known for its unusual style and floorplan layout. The complex was designed by the late famous architect Kevin Roche who also designed other famous corporate headquarters.

text:
# The Summit at Danbury

**The Summit at Danbury**, formerly known as the **Matrix Corporate Center** and before that as the  **Union Carbide Corporate Center**, is an architecturally unique building in Danbury, Connecticut, United States. It was constructed in 1982 as the headquarters of the Union Carbide chemical company, it is known for its unusual style and floorplan layout. The complex was designed by the late famous architect Kevin Roche who also designed other famous corporate headquarters.

## History

In 1976, Union Carbide announced that it intended to relocate from New York City to a location in Connecticut. After beginning construction in 1980, Union Carbide moved its approximately 3,000 staff members to the facility in 1983.

Following several corporate realignments, space was rented out to several different companies after a 1986 leaseback arrangement transferred ownership to a Florida company. This resulted in the facility being renamed the Corporate Center in 1992. Following the purchase of Union Carbide by The Dow Chemical Company in 2001, the Union Carbide staff was further reduced and more space sublet to other companies. In 2007 the building was sold to Grubb & Ellis for $80 million, less than half its original construction cost of $190 million. In 2009, the building was resold to Matrix Reality Group for $72.4 million. Matrix Realty Group, Inc., the new owner of the building, carried out several renovations, such as new granite in the Main Reception area and in other parts of the building, and renamed it the Matrix Corporate Center.

In 2018, Matrix was sold to Summit Development, a real estate developer based in Southport, Connecticut for $18 million. The complex was renamed to reflect the new ownership, and is being renovated to include luxury apartments in multiple wings. The existing office space is being renovated as well, and now includes new restaurants and an expanded gym/health center.

## Architecture

The move to the country was a trend away from densely crowded downtowns, like Manhattan. The layout of the building is unique in that the entire building rests on 5,000 pillars driven into the ground at heights of 5 to 40 feet (1.5 to 12.2 m), to avoid having to clear the land of obstacles. The structure as a whole consists of 15 interconnected buildings around a central core.

Additionally, the outer walls of the building face into the forest while the interior walls face a completely enclosed 2,500-space parking garage. The building was designed with several pods for the then divisions of Union Carbide that would occupy the facility. Further, it was set up so that each office was very close, sometimes only 10 feet (3 m), from its related parking spot and that employees would not need to exit the building to perform any functions.

In the center of the complex are several conference rooms, libraries, a cafeteria, and other support services. Each room in the 2.1 million-square-foot (195,000 m2) complex, 1.3 million (117,000 m2) of which is office space, has separate temperature controls and natural light through a series of translucent windows. The building sits on a 646-acre (261 ha) campus which has been subdivided over the years and now also hosts jogging trails and condominiums.

## InfoBox

| The Summit at Danbury | |
| --- | --- |
|  | |
|  | |
| Former names | Matrix Corporate Center, Union Carbide Corporate Center |
| General information | |
| Type | Corporate Offices, Conference & Banquet Center |
| Location | Danbury, Connecticut |
| Coordinates | 41°22′55″N 73°31′49″W / 41.38196°N 73.53020°W / 41.38196; -73.53020 |
| Current tenants | Includes Cadenza Innovation, Department of Defense, General Motors, Attorney General, United Parcel Service, Chase Bank, Bank of America, US Bank, Scana Energy, Mastrack, Odyssey Logistics & Technology, Danbury Medical Group, Nuvance Health, Market Place Kitchen & Bar |
| Construction started | 1980 |
| Completed | 1982 |
| Owner | Summit Development, LLC |
| Technical details | |
| Floor area | 2,100,000 square feet (200,000 m2) |
| Design and construction | |
| Architect(s) | Kevin Roche |
| Other designers | Emanuel Pisetzner |
| Other information | |
| Public transit access | HARTransit: 3, 10 |
| Website | |
| summitdanbury.com | |


title: Lord George Gordon-Lennox

abstract: Lord George Charles Gordon-Lennox, was a British Conservative politician.

text:
# Lord George Gordon-Lennox

**Lord George Charles Gordon-Lennox** (né Lennox; 22 October 1829  22 February 1877), was a British Conservative politician.

## Background

Gordon-Lennox was the fifth son of Charles Gordon-Lennox, 5th Duke of Richmond and Lady Caroline, daughter of Field Marshal Henry Paget, 1st Marquess of Anglesey. Charles Gordon-Lennox, 6th Duke of Richmond, Lord Henry Lennox and Lord Alexander Gordon-Lennox were his elder brothers. George was born with the surname **Lennox**; when his father inherited the Gordon estates from his uncle, the father took the surname **Gordon-Lennox** for himself and his issue, by royal licence dated 9 August 1836.

## Political career

Gordon-Lennox sat as Member of Parliament for Lymington between 1860 and 1874. He was also a Lieutenant in the Royal Horse Guards.

## Family

Gordon-Lennox married Minnie Augusta, daughter of William Henry Palmer and widow of Edwin Adolphus Cook, in 1875. They had no children. He died in February 1877, aged 47. Lady George Gordon-Lennox remained a widow until her death in September 1913.

## InfoBox

| Lord George Gordon-Lennox | |
| --- | --- |
|  | |
| Member of Parliament for Lymington | |
| **In office**
1860-1874 | |
|  | |
| Personal details | |
| Born | (1829-10-22)22 October 1829 |
| Died | 22 February 1877(1877-02-22) (aged 47) |
| Political party | Conservative |
| Spouse | Minnie Palmer (m. 1875) |
| Parent |  |
| Relatives | Charles Gordon-Lennox (brother)
Henry Lennox (brother)
Alexander Gordon-Lennox (brother) |
|  | |


title: 1972 Ohio State Buckeyes football team

abstract: The 1972 Ohio State Buckeyes football team was an American football team that represented the Ohio State University in the 1972 Big Ten Conference football season. The Buckeyes compiled a 9–2 record, including the 1973 Rose Bowl in Pasadena, California, where they lost 42–17 to the USC Trojans.

text:
# 1972 Ohio State Buckeyes football team

1972 Big Ten Conference football standings
|  | Conf | | | | |  |  | Overall | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Team | W |  | L |  | T |  |  | W |  | L |  | T |
| No. 6 Michigan \+ | 7 |  | 1 |  | 0 |  |  | 10 |  | 1 |  | 0 |
| No. 9 Ohio State \+ | 7 |  | 1 |  | 0 |  |  | 9 |  | 2 |  | 0 |
| Purdue | 6 |  | 2 |  | 0 |  |  | 6 |  | 5 |  | 0 |
| Michigan State | 5 |  | 2 |  | 1 |  |  | 5 |  | 5 |  | 1 |
| Minnesota | 4 |  | 4 |  | 0 |  |  | 4 |  | 7 |  | 0 |
| Indiana | 3 |  | 5 |  | 0 |  |  | 5 |  | 6 |  | 0 |
| Illinois | 3 |  | 5 |  | 0 |  |  | 3 |  | 8 |  | 0 |
| Iowa | 2 |  | 6 |  | 1 |  |  | 3 |  | 7 |  | 1 |
| Wisconsin | 2 |  | 6 |  | 0 |  |  | 4 |  | 7 |  | 0 |
| Northwestern | 1 |  | 8 |  | 0 |  |  | 2 |  | 9 |  | 0 |
|  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| * \+  Conference co-champions Rankings from AP Poll | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

The **1972 Ohio State Buckeyes football team** was an American football team that represented the Ohio State University in the 1972 Big Ten Conference football season. The Buckeyes compiled a 92 record, including the 1973 Rose Bowl in Pasadena, California, where they lost 4217 to the USC Trojans.

## Schedule

| Date | Time | Opponent | Rank | Site | TV | Result | Attendance | Source |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| September 16 | 1:30 p.m. | Iowa | No. 3 |  |  | W 21–0 | 77,098 |  |
| September 30 | 1:30 p.m. | North Carolina* | No. 5 | * Ohio Stadium * Columbus, OH |  | W 29–14 | 86,180 |  |
| October 7 | 4:00 p.m. | at California* | No. 3 |  |  | W 35–18 | 45,000 |  |
| October 14 | 1:30 p.m. | Illinois | No. 4 |  |  | W 26–7 | 86,298 |  |
| October 21 | 1:30 p.m. | Indiana | No. 4 | * Ohio Stadium * Columbus, OH |  | W 44–7 | 86,365 |  |
| October 28 | 2:30 p.m. | at Wisconsin | No. 4 |  |  | W 28–20 | 78,713 |  |
| November 4 | 1:30 p.m. | Minnesota | No. 5 | * Ohio Stadium * Columbus, OH |  | W 27–19 | 86,439 |  |
| November 11 | 1:00 p.m. | at Michigan State | No. 5 |  | ABC | L 12–19 | 76,264 |  |
| November 18 | 2:00 p.m. | at Northwestern | No. 9 |  |  | W 27–14 | 34,475 |  |
| November 25 | 1:00 p.m. | No. 3 Michigan | No. 9 |  | ABC | W 14–11 | 87,040 |  |
| January 1, 1973 | 4:45 p.m. | vs. No. 1 USC* | No. 3 |  | NBC | L 17–42 | 106,869 |  |
| * \*Non-conference game * Rankings from AP Poll released prior to the game * All times are in Eastern time | | | | | | | | |

## Depth chart

## Coaching staff

* Woody Hayes – Head Coach (22nd year)
* George Chaump – Offense (5th year)
* George Hill – Defensive Coordinator (2nd year)
* Rudy Hubbard – Running Backs (5th year)
* Charles Clausen – Defense Line (2nd year)
* Edward Ferkany – Offensive Line / Punter (1st year)
* Rudy Hubbard – Running Backs (5th year)
* John Mummey – Quarterbacks (4th year)
* Ralph Staub – Tackles / Tight ends / Kickers (3rd year)
* Dick Walker – Defensive Backs (4th year)
*

## Rankings

Ranking movements
**Legend:** ██ Increase in ranking ██ Decrease in ranking
( ) = First-place votes
|  | Week | | | | | | | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Poll | Pre | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | Final |
| AP | 3 *(4)* | 3 *(5)* | 4 *(2)* | 5 *(1)* | 3 | 4 *(1)* | 4 *(1)* | 4 *(1)* | 5 *(1)* | 5 *(1)* | 9 | 9 | 4 | 3 | 9 |
| Coaches | 4 *(2)* | 4 *(4)* | 5 *(2)* | 6 *(1)* | 4 *(1)* | 4 | 5 | 3 | 4 | 4 | 9 | 8 | 4 | 3 | Not released |

## Game summaries

### Iowa

| 1 2 3 4 Total  Iowa 0 0 0 0 0  **Ohio St** 0 7 7 7 **21**   * **Date:** September 16 * **Location:** Ohio Stadium, Columbus, Ohio * **Game start:** 1:31p.m. EST * **Elapsed time:** 2:21 * **Game attendance:** 77,098 * **Game weather:** Clear, 74 °F (23 °C) |
| --- |
|  |
|  |

### North Carolina

**North Carolina Tar Heels at Ohio State Buckeyes**

| Quarter | 1 | 2 | 3 | 4 | Total |
| --- | --- | --- | --- | --- | --- |
| North Carolina | 7 | 0 | 0 | 7 | **14** |
| **Ohio St** | 3 | 6 | 14 | 6 | **29** |

*at Ohio Stadium, Columbus, Ohio*

* **Date**: September 30, 1972
* **Game time**: 1:30 p.m.
* **Game weather**: Cloudy, 49 °F (9 °C)
* **Game attendance**: 86,180
* Box Score

| Game information |
| --- |
|  |

Ohio State was the only team to beat the Tar Heels in 1972.

Archie Griffin set the school single game rushing record in just his second game.

### California

| 1 2 3 4 Total  **Ohio St** 3 0 19 13 35  California 0 9 3 6 **18** |
| --- |
|  |
|  |

### Illinois

| 1 2 3 4 Total  Illinois 0 7 0 0 7  **Ohio St** 13 6 0 7 **26**   * **Date:** October 14 * **Location:** Ohio Stadium, Columbus, Ohio * **Game start:** 1:33p.m. EST * **Elapsed time:** 2:29 * **Game attendance:** 86,298 * **Game weather:** Cloudy, 59 °F (15 °C) |
| --- |
|  |
|  |

### Indiana

| 1 2 3 4 Total  Indiana 0 7 0 0 7  **Ohio St** 14 3 14 13 **44**   * **Date:** October 21 * **Location:** Ohio StadiumColumbus, Ohio * **Game start:** 1:32p.m. EST * **Elapsed time:** 2:18 * **Game attendance:** 86,365 * **Game weather:** Cloudy, 51 °F (11 °C) |
| --- |
|  |
|  |

### Wisconsin

| 1 2 3 4 Total  Ohio St 14 14 0 0 28  Wisconsin 0 7 7 6 **20** |
| --- |
|  |
|  |

### Minnesota

| 1 2 3 4 Total  Minnesota 13 0 0 6 19  Ohio State 7 14 0 6 **27**   * **Date:** November 4 * **Location:** Ohio Stadium * **Game start:** 1:31p.m. EST * **Elapsed time:** 2:17 * **Game attendance:** 86,439 * **Game weather:** Cloudy, 49 °F (9 °C) |
| --- |
|  |
|  |

### Michigan State

| 1 2 3 4 Total  Ohio State 3 9 0 0 12  Michigan State 6 6 7 0 **19** |
| --- |
|  |
|  |

### Northwestern

| 1 2 3 4 Total  Ohio State 7 0 13 7 27  Northwestern 0 7 7 0 **14** |
| --- |
|  |
|  |

### Michigan

**Michigan Wolverines at Ohio State Buckeyes**

| Quarter | 1 | 2 | 3 | 4 | Total |
| --- | --- | --- | --- | --- | --- |
| Michigan | 0 | 3 | 8 | 0 | **11** |
| **Ohio St** | 0 | 7 | 7 | 0 | **14** |

*at Ohio Stadium, Columbus, Ohio*

| Game information |
| --- |
|  |

Ohio State made two goal line stands, one in each half, to hold on to the 14–11 victory. The first came just before halftime as Dennis Franklin fumbled on fourth down at the two. In the fourth quarter, Randy Gradishar stopped Franklin on a sneak from the one. The Buckeyes' fans tore down the goal posts with 13 seconds remaining.

### Vs. No. 1 USC (Rose Bowl)

| 1 2 3 4 Total  No. 3 Buckeyes 0 7 3 7 17  **No. 1 Trojans** 7 0 21 14 **42** |
| --- |
|  |
|  |

## draft picks

| Player | Round | Pick | Position | NFL club |
| --- | --- | --- | --- | --- |
| Rick Seifert | 8 | 194 | Defensive back | New York Jets |
| George Hasenohrl | 8 | 198 | Defensive tackle | New York Giants |
| John Bledsoe | 8 | 203 | Running back | Detroit Lions |
| Rich Galbos | 9 | 218 | Running back | Washington Redskins |
| Earl Belgrave | 17 | 435 | Tackle | Detroit Lions |

## InfoBox

| 1972 Ohio State Buckeyes football | |
| --- | --- |
|  | |
| Big Ten co-champion | |
| Rose Bowl, L 17–42 vs. USC | |
| Conference | Big Ten Conference |
| Ranking | |
| Coaches | No. 3 |
| AP | No. 9 |
| Record | 9–2 (7–1 Big Ten) |
| Head coach |  |
| MVP | George Hasenohrl |
| Captains | * Richard Galbos * George Hasenohrl |
| Home stadium | Ohio Stadium<br>(Capacity: 81,667) |
|


title: Poplin, Poland

abstract: Poplin is a village in the administrative district of Gmina Wiżajny, within Suwałki County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Lithuania. It lies approximately 9 kilometres (6 mi) south of Wiżajny, 27 km (17 mi) north of Suwałki, and 135 km (84 mi) north of the regional capital Białystok.

text:
# Poplin, Poland

**Poplin** \[ˈpɔplin\] is a village in the administrative district of Gmina Wiżajny, within Suwałki County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Lithuania. It lies approximately 9 kilometres (6 mi) south of Wiżajny, 27 km (17 mi) north of Suwałki, and 135 km (84 mi) north of the regional capital Białystok.

## InfoBox

| Poplin | |
| --- | --- |
| Village | |
| Poplin | |
| Coordinates: 54°19′N 22°53′E / 54.317°N 22.883°E / 54.317; 22.883 | |
| Country | Poland |
| Voivodeship | Podlaskie |
| County | Suwałki |
| Gmina | Wiżajny |


title: Wandre Guitars

abstract: Wandre Guitars is an electric guitar brand started by the Italian guitar manufacturer Antonio Vandrè Pioli. These guitars are famous for their original shapes, aluminium necks and unique switches. The guitars were originally designed and manufactured from 1957 to 1968 by Pioli in Cavriago, Italy. Very small productions were made, which makes these guitars very sought-after in the vintage guitar market. Some guitars by Pioli have appeared under other brand names such as Framez, Davoli, Dallas, Avalon, Noble, Lipsky.

text:
# Wandre Guitars

**Wandre Guitars** is an electric guitar brand started by the Italian guitar manufacturer Antonio Vandrè Pioli. These guitars are famous for their original shapes, aluminium necks and unique switches.

The guitars were originally designed and manufactured from 1957 to 1968 by Pioli in Cavriago, Italy. Very small productions were made, which makes these guitars very sought-after in the vintage guitar market. Some guitars by Pioli have appeared under other brand names such as Framez, Davoli, Dallas, Avalon, Noble, Lipsky.

## Models

Wandre made a lot of model of doublebasses, basses and guitars

* Classich doublebass
* Pocket bass
* Naika doublebass
* Marte duoblebass
* Quarieg doublebass
* Electro Blitz Bass
* Swedenbass
* Roc'n'Roll
* Brigitte Bardot
* Calypso
* Rock Oval
* Waid
* Selene
* Rock
* Spazial
* Blue Jeans / Teenager / *Trilam*
* Piper
* Bikini
* Twist
* Tigre
* Doris
* Polyphon
* Cobra
* Etrurian
* Powertone
* Soloist
* Psychedelic Sound
* Mini

### References

* Ballestri, Marco (2014). *Wandrè. L'artista della chitarra elettrica* \[*Wandrè. The artist of electric guitar*\] (in Italian and English). Modena: Anniversary Books. ISBN 978-88-96408-16-2.
(See also excerpted photographs: "Wandrè's guitars"  via AnniversaryBooks.it.)


title: Vishwas Mehta

abstract: Vishwas Mehta is a senior Indian Administrative Service (IAS) officer from Kerala who retired as the Chief Secretary, Government of Kerala. A native of Rajasthan, he is currently serving as the Chief Information Commissioner of Kerala.

text:
# Vishwas Mehta

**Vishwas Mehta** (born 19 February 1961) is a senior Indian Administrative Service (IAS) officer from Kerala who retired as the Chief Secretary, Government of Kerala. A native of Rajasthan, he is currently serving as the Chief Information Commissioner of Kerala.

## Career

Mehta belongs to 1986 batch of IAS. He began his civil service career as assistant collector of Kollam and Wayanad. Mehta took over as Deputy Secretary in the Revenue Department in 1991 and in 1992 he became Managing Director of the Kerala State Cooperative Rubber Marketing Federation. He had also served as District Collector of Idukki and Wayanad and as Managing Director of Milma. He also served as Principal Secretary in Revenue and Health Department, Additional Chief Secretary in Revenue, Economic Affairs and Housing. Before appointed as Chief Secretary of Kerala, he was Home Secretary. He served as the Chief Secretary, Government of Kerala during the period June 2020 to February 2021. After retirement, he was appointed as the Chief Information Commissioner of Kerala.

## InfoBox

| Vishwas Mehta | |
| --- | --- |
|  | |
| Chief Secretary, Government of Kerala | |
| **In office**
June 2020  February 2021 | |
| Governor | Arif Mohammed Khan |
| Chief Minister | Pinarayi Vijayan |
| Preceded by | Tom Jose IAS |
| Succeeded by | Dr. V. P. Joy IAS |
|  | |
| Personal details | |
| Born | (1961-02-19) 19 February 1961
Dungarpur, Rajasthan |
|  | |


title: Loreto Shrine Chapel

abstract: The Loreto Shrine Chapel is located in St. Nazianz, Wisconsin. It was added to the National Register of Historic Places in 1982.

text:
# Loreto Shrine Chapel

The **Loreto Shrine Chapel** is located in St. Nazianz, Wisconsin. It was added to the National Register of Historic Places in 1982.

## History

The chapel was created by Ambrose Oschwald, the Roman Catholic priest who founded St. Nazianz. After a storm in 2000 damaged the chapel, it was restored by the St. Nazianz Historical Society.

## InfoBox

|  | |
| --- | --- |
| Loreto Shrine Chapel | |
| U.S. National Register of Historic Places | |
|  | |
| Loreto Shrine Chapel in November 2011 | |
| Location | St. Nazianz, Wisconsin |
| NRHP reference No. | 82000679 |
| Added to NRHP | June 7, 1982 |


title: Mala Tribich

abstract: Mala Tribich is a Polish-born British Holocaust survivor and educational speaker.

text:
# Mala Tribich

**Mala Tribich** MBE (born 24 September 1930) is a Polish-born British Holocaust survivor and educational speaker.

## Early life

Tribich was born in 1930 to a Jewish family in Piotrków Trybunalski, Łódź Voivodeship, Poland. Her older brother was Ben Helfgott.

During the Holocaust, she was interned at Ravensbrück and later sent to Bergen-Belsen. She and her brother Ben were the only members of her family who survived.

## Later life

Tribich has lived in the UK since 1947. She trained as a secretary in London and in 1950 married Maurice Tribich, an architect from a British Jewish family.

She has given talks at many schools and universities across the UK about the Holocaust.

## Honours

Tribich was appointed a Member of the Order of the British Empire (MBE) in the 2012 Birthday Honours, for services to education.


title: Ferazel's Wand

abstract: Ferazel's Wand is a platform game by Ambrosia Software for Mac OS released in 1999.

text:
# Ferazel's Wand

***Ferazel's Wand*** is a platform game by Ambrosia Software for Mac OS released in 1999.

## Plot

Ferazel is a member of the Habnabit race, tunnel-dwelling creatures skilled in magic. Long have they dwelled in peace, but now they are under assault from a horde of goblins, and there are whispers of a far more foul foe leading the goblins.

The game concentrates more on thinking than fighting enemies — boss fights are often a matter of logically deducing a foe's weakness. Later levels emphasize trap-dodging, and all levels contain secret passages and hidden items. It is an RPG of sorts, but not in the traditional sense, in as much as the player fights arcade-style and gains power by finding magical crystals.

## Reception

## InfoBox

| Ferazel's Wand | |
| --- | --- |
|  | |
| Developer(s) | Ambrosia Software |
| Publisher(s) | Ambrosia Software |
| Designer(s) | Ben Spees |
| Platform(s) | Classic Mac OS |
| Release | 1999 |
| Genre(s) | Platform |


title: The War Plays

abstract: The War Plays is the name often given to a trilogy of plays by English dramatist Edward Bond: Red Black and Ignorant, The Tin Can People, and Great Peace.

text:
# The War Plays

***The War Plays*** (sometimes referred to as ***The War Trilogy***) is the name often given to a trilogy of plays by English dramatist Edward Bond: *Red Black and Ignorant*, *The Tin Can People*, and *Great Peace*.

## Reception

Max Stafford-Clark has written that with the Barbican production of *The War Plays*, Bond "reduced a talented cast into a stumbling and incoherent shambles of walking wounded. Edward Bond is simply the most difficult person I have worked with in 40 years." In 1996, author Janelle G. Reinelt described the English reception as "chilly". Author Michael Mangan commented that the 1995 Odéon-Théâtre de l'Europe performance was quite successful, however, and that in France the work "was described as the most important play written since the Second World War."

While Bond is best known for his plays in the 1960s and 1970s, Peter Billingham in 2007 referred to *The War Trilogy* as one of his major late works (along with *Restoration*, *Coffee*, and *Born*). They were collectively listed by Michael Billington as one of the five greatest works of dystopian drama. He dubbed them "\[d\]isquieting, dystopian and too important to be ignored." In a 2018 thesis, Chien-Cheng Chen listed the trilogy as a highlight among the contemporary British dramas he had read, and lauded "its versatile use of dramatic forms and its profound exploration of modern human conditions."

In *The Performance of Power* (1991), Reinelt compared the trilogy favorably with other works of contemporary British theatre that contain utopian elements, saying that "the combination of socialist and feminist issues raised in \[...\] *The War Plays* best approaches the imaginative task of conceiving and embodying an alternative reality. \[...\] \[the plays\] address important issues concerning the socialization of family roles. They deconstruct the notion of 'natural' mother, with its associations of an instinctual bond between mother and child based on birthing, and replace it with a notion of community nurturing".

Conversely, Keith Colquhoun called the plays "particularly unremitting in tone". In a 2010 thesis, Frank A. Torma criticized “Bond’s attempt in his epic works, like *The War Plays* and *Human Cannon*, to give the characters poetry to say in direct address to the audience. Bond’s poetic voice is not exceptional and the result of its insertion in his plays negatively postpones the dramatic flow.” After seeing a 2010 performance of *Red Black and Ignorant* directed by Maja Milatovic-Ovadia, Ian Shuttleworth of *Financial Times* wrote, "Bond shows his skill at flinty poetry, but also includes some crass agitprop, and even when his writing feels prophetic it seems like the prophecy of a Cassandra, encouraging repudiation rather than consideration."

## InfoBox

| The War Plays | |
| --- | --- |
| Front cover of a 1998 release containing the trilogy | |
| Written by | Edward Bond |
| Date premiered | 29 May 1985 (1985-05-29)  (*Red Black and Ignorant*)
29 May 1985 (1985-05-29) (*The Tin Can People*)
17 July 1985 (1985-07-17) (*Great Peace*)
25 July 1985 (1985-07-25) (Trilogy) |
| Original language | English |
| Subject | Nuclear war |


title: Long Grass Plantation

abstract: Long Grass Plantation is a historic house and national historic district located along what was the Roanoke River basin. In the 1950s most of it was flooded and became the Buggs Island Lake/John H. Kerr Reservoir in Mecklenburg County, Virginia. The house was built circa 1800 by George Tarry on land belonging to his father, Samuel Tarry, and Long Grass Plantation encompassed approximately 2000 acres (8 km⁲). Today, most of the land once belonging to the plantation is submerged and is owned by the US Army Corps of Engineers. Only 27 +/- acres of privately owned land make up the grounds of Long Grass plantation. The property was listed on the Virginia Landmarks Registry and the National Register of Historic Places on July 21, 1995.

text:
# Long Grass Plantation

**Long Grass Plantation** is a historic house and national historic district located along what was the Roanoke River basin. In the 1950s most of it was flooded and became the Buggs Island Lake/John H. Kerr Reservoir in Mecklenburg County, Virginia. The house was built circa 1800 by George Tarry on land belonging to his father, Samuel Tarry, and Long Grass Plantation encompassed approximately 2000 acres (8 km2).

Today, most of the land once belonging to the plantation is submerged and is owned by the US Army Corps of Engineers. Only 27 +/- acres of privately owned land make up the grounds of Long Grass plantation. The property was listed on the Virginia Landmarks Registry and the National Register of Historic Places on July 21, 1995.

## Evolution of the main structure

The original c. 1797 hall and parlor structure still exists. This small dwelling probably already existed when George Tarry moved to Long Grass Plantation. It was added to during renovations and expansions in four major phases, two in the nineteenth century and two in the twentieth century, from the 1830s to the mid-1990s.

The current structure is dominated by the additions made in 1832 by the builder-architect Jacob W. Holt of Warrenton, North Carolina. In 1831–1832, Holt was commissioned to add a 2-story, single-pile, 3-bay structure to the front of the original 1797 1+12-story house. The two sections were connected via a 1-story hyphen with large windows on its side walls. The 1832 Greek Revival home in the front is much larger in scale and mass than the original 1797 hall and parlor house. The new front has a neoclassical entrance and porch (probably salvaged from an earlier home in Warren County or along the Roanoke River), This porch features many "Jeffersonian" details, and the double front door surrounded by glass transom and sidelights which were mentioned in the book, *Life on the Roaring Roanoke*. This spacious new addition was an indication of the family's improving economic fortune generated from tobacco cultivation by slave labor. It was built as a wedding present in 1832, when George Tarry married Mary Euphemia Hamilton.

Around 1857, Holt was commissioned to make improvements to the original 1797 structure. By this time, Holt had adopted elements of the popular mid-Victorian Italianate style of architecture in his designs. He raised the roof of the original hall and parlor to make a full second story and designed a relatively ornate single-story Victorian Italianate porch across the rear of the house.

During the Depression years, the house was leased to a tenant farmer. The Tarry family returned to live at Long Grass in the late 1950s.

In the 1950s, the house was renovated and retrofitted with modern mechanical systems. The one-story hyphen connecting the two structures was raised to two stories. Two new bathrooms were created – one upstairs in the new hyphen space and one downstairs in the 1832 dining room just off of the hyphen hall. The Tarrys changed the dining room into a bedroom, and used the original 1797 parlor as their family dining room. They also added a kitchen adjoining and attached the original 1797 structure at that time. This kitchen was adjacent to the 1797 dining room.

The most recent renovation occurred in 1992–1994 after Bruce and Sudie Park of Raleigh, North Carolina purchased the property. Michael Denton of Clarksville, Virginia and Trent Park, son of the owners managed the renovation project, including manufacture of custom moldings at the farm workshop. The property was completely renovated. Spaces between the original hall and parlor and the Holt addition, on either side of the hyphen, were enclosed and a breakfast room and library were added on the first floor, and two new bathrooms upstairs. New closets were added in such a way as to maintain the symmetry of the existing rooms throughout the home. The 1950s bathroom was removed from the 1832 Holt dining room. New, updated mechanical systems were installed. Exterior and interior repairs were made to the entire structure. New foundations were built for the exterior porches when new floors were laid. A new terne metal roof was installed.

The 1831 entry hall walls are covered in an 18th-century Chinese hand-painted wall covering which was donated to Long Grass by the Marshall Cooper Family of Henderson, North Carolina. The Cooper Family owned Harriet Henderson Mills. The home that this wall covering came from was owned by Marshall Cooper, Sr. and upon his widow's death the home was demolished by the family. It was located on Charles Street in Henderson, North Carolina.

## Outbuildings

Several outbuildings or dependencies have been preserved: the ice house, smokehouse, kitchen/laundry, schoolhouse, tobacco pack house, two tobacco barns, and a Fox Trott-style tenant dwelling. The tenant house is probably C. 1850–1880. It is a hand-hewn log structure, now in an advanced state of decay. The pack house is also nearing disrepair. All of the other buildings are structurally sound. An 1857 wooden carriage house/livestock barn which, after the flooding of the reservoir sat on Army Corps of Engineer land was struck by lightning in the early 1980s. It eventually was sold to the Parks by the Corps. However, by then, it was beyond repair and was demolished. The purchase agreement between the Parks and the Army states that a new carriage house or similar building may be constructed within the foundation footprint of this destroyed building. The building may not be used as a residence, however. The Parks have maintained this foundation for future building on this site.

Items of note:

The frame ice house (c. 1832, probably built by Jacob Holt) is a two-story wood-frame building, unusually large for an ice house or dairy. The structure contains a deep ice pit underneath, with two exterior doors on the building's sides to allow access to the cold storage area at ground level. In winter months, ice was harvested from shallow ponds located in fields around the plantation. After a thick layer of ice was added to the pit, a thick layer of sawdust was added. These alternating layers filled the 14-foot hole to the level of the access doors. The volume of frozen ice/sawdust kept the ice from melting during hot Virginia summers. A series of vents just above the ground level of this building, and vents above the two access doors, aided in keeping a consistent cold temperature below the building. In time the first story was used to store corn, and the second story was used as a pigeon coop. The interior of the second story still has a lead lining to protect the building from pecking pigeons. The squab or "baby" pigeons provided the family with Sunday morning breakfasts. In the 1960s the family got rid of their pigeons.

The one-room schoolhouse (c. 1800) was renovated and expanded in the 1950s for use as a lake cottage with kitchen, bathroom and sleeping loft. This building is a square-hewn wood log cabin. The Tarry family sheathed this building in barn siding and added a tin roof when the cottage was built. It was a girls' school for families in Mecklenburg County, Virginia, until the early 1900s. The teacher slept in an upstairs loft. After the school closed, the structure was used as a blacksmith shop.

The smoke house (c. 1832) was noted in 19th-century letters as being one of the largest and most secure in the region. Remnants of a large, "strong arm" lock were discovered behind it. The door on this building was two layers thick, with wood on the outside running vertically, and the interior wood running horizontally with a strong reinforcement of iron "peg" nails every inch through it. Since the 1960s this building has been used mostly to house poultry.

The kitchen and laundry outbuilding (c. 1832 (Holt) and c. 1857 (Holt)) is a one-story frame building with two doors and two louver windows on its front side. The rear side of this building originally had two louvered windows. In modern times, one of these windows was replaced with a door. In 1832, the building was only half as large as it is today, and contained a kitchen with a wooden floor and a massive stone "cooking" fireplace with a brick chimney. Viewed from the front, the kitchen door is on the right side. Later (probably during Holt's 1857 renovation), the structure was doubled in size by adding a laundry to the original kitchen building. One can still see exterior boards from the kitchen building inside of the laundry side next to the fireplace. The original stone fireplace for the kitchen was accessed as a shared fireplace for both sides. During a storm in 2016 that blew down a giant nearby oak tree, the fireplaces collapsed. The wooden mantles survive as does the brick chimney top.

The tobacco pack house has suffered serious structural damage but is relatively well-protected. This is the building where Burley tobacco was sorted, hung on tobacco sticks, cured in a damp cellar, then dried in the second floor, before being packed into wooden casks. The barrels were then rolled to the Roanoke River and shipped to market. The structure is two stories high with an open cellar area which can be accessed from interior or exterior which is fully open at the foundation. In its current configuration, it is roughly rectangular with four irregularly shaped rooms on the first story and a large loft area above. There are few window openings. A large, stone-lined humidor pit underneath a portion of the structure was used for storage of cured tobacco.

A "two-seat" outhouse was still in existence when the Plantation was purchased by the Parks, but has since been demolished. This building was very much in the style of the Holt C.1857 addition to the main house. The brackets on the eaves were a close match to the brackets on the Italianate back porch, and the building had plaster walls. Also extant at that time was a small, portable corncrib built out of small diameter tree trunks with spaces between, and a tin roof.

Many additional foundations for tobacco curing barns can be found throughout the fields. There are two tobacco curing barns standing today which are of the turn of the century log construction.

When Buggs Island Reservoir is drained periodically for maintenance by the Corps of Engineers, many more foundations are visible along the old flooded road bed which once led to Palmer Springs. These buildings yield many fragments of metal parts, and other clues as to the uses that they served on the Plantation. There was a mill, a ferry, a mill works, a tannery, a brick making area, and a blacksmith shop. In the garden there are still two millstones from Tarry's mill. There was a ferry and a landing owned by the Tarry family.

It is rumored that George Tarry bought Bugg's Island, which the Virginia side of the Reservoir is named for. The North Carolina side of the lake is named The James H. Kerr Lake Reservoir for a North Carolina congressman responsible for getting the funding to build the lake.

According to a Civil War period map, Tarry's slave quarters were not close to the big house. The house servants stayed in the house; field hands lived approximately where the small homes are located, around and across from Center Hill Farm, from the junction of Eppes Fork Rd. and Mill Creek Rd. to the North Carolina border. After the Civil War, the Tarry family gave acreage to their former slaves, much of which is still owned by their descendants. There seemed to be a continued freed man work force at Long Grass for many years.

## Other history

The land on which Ivy Hill and later Wildwood were built resulted from land grants from the Commonwealth of Virginia to Edward Tarry, Sr. These land grants were signed by Governors Patrick Henry, John Page, and "Light Horse" Harry Lee. The original grant documents remain in the possession of the Tarry family today. Framed copies of them hang at Long Grass. Samuel Tarry built Ivy Hill Plantation House (the Tarry family seat) in the early 1730s. He had three sons, Edward, Jr., a lifelong bachelor—who never married but raped a Slave named Ellen who gave birth to one of his children, who inherited Ivy Hill (flooded by the construction of Buggs Island Reservoir, and now an archaeological park), George Tarry, who moved Long Grass with an extant small home on the land when he took over the property, and William, who inherited land that joined Ivy Hill Plantation to Long Grass Plantation, which would later be called Wildwood.

## Historic trees

Planted in the front yard of Long Grass is the "Constitution Oak" given as a remembrance gift to George Patrick Tarry when he served as a delegate from Mecklenburg County to the constitutional convention of 1901–1902. The tree is a Burr Oak and is an unusual, slow-growing species in Virginia. Each of the delegates to this constitutional convention was given a sapling to plant in their county to commemorate the event.

In 1951 there was a fiftieth anniversary celebration of the 1901 convention. A man came to Long Grass to ask Evelyn Tarry, the widow of William Tarry, if he could collect enough burr acorns to raise saplings to give out at the ceremony. He told her that he had visited all of the counties where delegates planted the original saplings, and very few had survived. The next spring he brought Mrs. Tarry a sapling, and she proudly planted her "Baby" in the back yard, where it grows today. So, Long Grass has "Big Daddy" tree in the front, and the "Son" in the back.

The huge Osage orange tree, 'Maclura pomifera', or hedge apple grows in the side yard of Long Grass House. Family legend says this tree came from Tarry cousin Meriweather Lewis of the Lewis and Clark Expedition of 1804–1806.

Each time a child was born to George Patrick Tarry, a walnut tree was planted; two of the three remain. One is next to a mature boxwood hedge at the front porch, and one is covered with ivy and Virginia creeper next to the kitchen door on the back porch.

## InfoBox

|  | |
| --- | --- |
| Long Grass | |
| U.S. National Register of Historic Places | |
| U.S. Historic district | |
| Virginia Landmarks Register | |
|  | |
| Front view of Long Grass Plantation | |
|  | |
| Location | VA 826, Eppes Fork, Virginia |
| Coordinates | 36°33′16″N 78°20′42″W / 36.55444°N 78.34500°W / 36.55444; -78.34500 |
| Area | 40 acres (16 ha) |
| Built | 1800 (1800) |
| Built by | Jacob W. Holt |
| Architectural style | Greek Revival |
| NRHP reference No. | 95000894 |
| VLR No. | 058-0185 |
| Significant dates | |
| Added to NRHP | July 21, 1995 |
| Designated VLR | April 28, 1995 |