Before the Juniors entered the ring the Steward announced that after all Juniors had moved their dogs around the ring and set them up, they could relax with their dogs.

After the judge moved all the dogs individually, she selected several from the group and placed them in the center of the ring.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

This ring has the property that a · a = a for all a in A ; rings with this property are called Boolean rings.

There were twelve rules in all, and they specified that fights should be " a fair stand-up boxing match " in a 24-foot-square or similar ring.

When there are no enemy discs on the board, many ( but not all ) rules also state that a player must shoot for the centre of the board, and a shot disc must finish either completely inside the 15-point guarded ring line, or ( depending on the specifics of the rules ) be inside or touching this line.

* The spectrum of any commutative ring with the Zariski topology ( that is, the set of all prime ideals ) is compact, but never Hausdorff ( except in trivial cases ).

With the 9 main keys, ( operated by the index, middle, and ring fingers ), 2 prefix keys and one delete key, the EkaPad can produce all the inputs of a standard qwerty keyboard with one, two, and a few three finger chords.

In his acceptance speech, Powell reminded Americans that " It is for America, the Land of the Free and the Home of the Brave, to help freedom ring across the globe, unto all the peoples thereof.

The first inductee was Bob Lilly in 1975 and by 2005, the ring contained 17 names, all former Dallas players except for one head coach and one general manager / president.

For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.

Stated differently, a ring is a division ring if and only if the group of units is the set of all non-zero elements.

When his father's ring was sent to him, he begged that his father would show mercy to his mother, and that all his companions would plead with Henry to set her free.

Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.

The property ( EF1 ) can be restated as follows: for any principal ideal I of R with nonzero generator b, all nonzero classes of the quotient ring R / I have a representative r with.

As in the simple cases above, one may enumerate all distinct four-colorings of the ring ; any coloring that can be extended without modification to a coloring of the configuration is called initially good.

Surrounding all is a ring or horseshoe-shaped layer of raw coal, usually kept damp and tightly packed to maintain the shape of the fire's heart and to keep the coal from burning directly so that it " cooks " into coke first.

This paper introduced what is now called the ring of Gaussian integers, the set of all complex numbers a + bi where a and b are integers.

In a ring all of whose ideals are principal ( a principal ideal domain or PID ), this ideal will be identical with the set of multiples of some ring element d ; then this d is a greatest common divisor of a and b. But the ideal ( a, b ) can be useful even when there is no greatest common divisor of a and b. ( Indeed, Ernst Kummer used this ideal as a replacement for a gcd in his treatment of Fermat's Last Theorem, although he envisioned it as the set of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.

< http :// www. chm. bris. ac. uk / motm / hemoglobin / hemoglobjm. htm >.</ ref > The iron ion, which is the site of oxygen binding, coordinates with the four nitrogens in the center of the ring, which all lie in one plane.

However, this all changed in 450 when Honoria, sister of the Western Roman Emperor Valentinian III, sent Attila a ring and requested his help to escape her betrothal to a senator.

Everything was burnished with sweat and grease so that all of the objects seemed to have been carved from the same material and to be ageless.

No one material is best for all situations.

Sheeting cast from this material reportedly weighs only one-third as much as glass, is impervious to all kinds of weather, and will not yellow.

The material is all basically of folk origin, gleaned from every section of Poland.

Generally, there is no trial in an appellate court, only consideration of the record of the evidence presented to the trial court and all the pre-trial and trial court proceedings are reviewed — unless the appeal is by way of re-hearing, new evidence will usually only be considered on appeal in " very " rare instances, for example if that material evidence was unavailable to a party for some very significant reason such as prosecutorial misconduct.

Because virtually all extant written material on Arianism was written by its opponents, the nature of Arian teachings is difficult to define precisely today.

On the 2007 deluxe edition release, it is revealed that parts of this tape were used for the 1976 Griffith Park Planetarium launch of the original album, the 1987 remix, and various radio spots, all of which were included as bonus material.

Animism encompasses the beliefs that there is no separation between the spiritual and physical ( or material ) world, and souls or spirits exist, not only in humans, but also in all other animals, plants, rocks, geographic features such as mountains or rivers, or other entities of the natural environment.

He regarded material substance as an infinite multitude of imperishable primary elements, referring all generation and disappearance to mixture and separation respectively.

While his predecessors Thales and Anaximander proposed that the arche, the underlying material of the world, were water and the ambiguous substance apeiron, respectively, Anaximenes asserted that air was this primary substance of which all other things are made.

Interventive methodologies include all those actions taken by the conservator to directly intervene with the material fabric of the object.

Its function is to control the expulsion of feces, unwanted semi-solid matter produced during digestion, which, depending on the type of animal, may be one or more of: matter which the animal cannot digest, such as bones ; food material after all the nutrients have been extracted, for example cellulose or lignin ; ingested matter which would be toxic if it remained in the digestive tract ; and dead or excess gut bacteria and other endosymbionts.

Aside from the genetic material of the cell, nucleic acids often play a role as second messengers, as well as forming the base molecule for adenosine triphosphate, the primary energy-carrier molecule found in all living organisms.

The film is ultimately significant insofar as it displays the first enunciation of De Palma's style in all its major traits – voyeurism, guilt, and a hyper-consciousness of the medium are all on full display, not just as hallmarks, but built into this formal, material apparatus itself.

This implied sequence of pre-exilic, exilic and post-exilic material is somewhat misleading, as significant editing has clearly taken place in all three parts.

Like all other horns of antelopes, the core of a bongo's horn is hollow and the outer layer of the horn is made of keratin, the same material that makes up human fingernails, toenails and hair.

William Reginald Hall, British Director of Naval Intelligence criticized the agreement on the basis that " the Jews have a strong material, and a very strong political, interest in the future of the country " and that " in the Brown area the question of Zionism, and also of British control of all Palestine railways, in the interest of Egypt, have to be considered ".

A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions.

Unless one is completely freed of all material desires, which are caused by the dense darkness of ignorance, one cannot fully engage in the devotional service of the Lord.

" O my Lord, best of the givers of benediction, if You at all want to bestow a desirable benediction upon me, then I pray from Your Lordship that within the core of my heart there be no material desires.

It is heavily influenced by Beijing cuisine, with nearly all cooking methods identical, and differs only in material due to religious restrictions.

Not all species of fungi have cell walls but in those that do, the plasma membrane is followed by three layers of cell wall material.

The Gnome Press edition ( 1950 – 1957 ) was the first hardcover collection of Howard's Conan stories, including all the original Howard material known to exist at the time, some left unpublished in his lifetime.

The Lancer / Ace editions ( 1966 – 1977 ), under the direction of de Camp and Lin Carter, were the first comprehensive paperbacks, compiling the material from the Gnome Press series together in chronological order with all the remaining original Howard material, including that left unpublished in his lifetime and fragments and outlines.