Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

The roots of this equation are just the ordinates of the intersections of the graph of B with a straight line of unit slope through Af in the b-plane ( the plane of the graph of b ).

) of two numbers a and b in locations named A and B.

In 2001, Alfred Nobel's great-grandnephew, Peter Nobel ( b. 1931 ), asked the Bank of Sweden to differentiate its award to economists given " in Alfred Nobel's memory " from the five other awards.

It is also used to enumerate a list in the same manner that " a, b, c, d " ( etc.

The line running from the upper left to lower right reads mt l b < sup > c </ sup > lt.

* Theo Altenberg ( b. 1952 ), German artist

:( b ) The Apostles ' Creed, as the Baptismal Symbol ; and the Nicene Creed, as the sufficient statement of the Christian faith.

( It should be noted that in the account given of the same events, in rabbinic sources ( b. Talmud Shabbat 99a ; Exodus Rabbah 41 ) and in the Qur ' an, Aaron is not the idol-maker and upon Moses ' return begged his pardon as he had felt mortally threatened by the Israelites ( Quran 7: 142-152 ).

Exports: $ 1. 225 billion f. o. b. ( 2008 )

Imports: $ 3. 546 billion f. o. b. ( 2008 )

* The rational numbers, expressed as the quotient of two integers a and b, b not equal to zero, satisfy the above definition because is the root of.

* 1085 – Emperor Shenzong of Song ( b. 1048 )

* 1132 – St. Hugues, Bishop of Grenoble ( b. 1053 )

* 1204 – Eleanor of Aquitaine ( b. 1122 )

* 1205 – King Amalric II of Jerusalem ( b. 1145 )

Analysis of the properties of a < sub > k </ sub > and b < sub > k </ sub > shows that one is the annihilation operator for particles and the other for antiparticles.

An exception to this general tendency is his Latin treatise " De falconibus " ( later inserted in the larger work, De Animalibus, as book 23, chapter 40 ), in which he displays impressive actual knowledge of a ) the differences between the birds of prey and the other kinds of birds ; b ) the different kinds of falcons ; c ) the way of preparing them for the hunt ; and d ) the cures for sick and wounded falcons.

There are several other Abbahus mentioned in the Talmudim and Midrashim, prominent among whom is Abbahu ( Abuha, Aibut ) b. Ihi ( Ittai ), a Babylonian halakist, contemporary of Samuel and Anan ( Eruvin 74a ), and brother of Minyamin ( Benjamin ) b. Ihi.

The order of the elements in each pair of G is important: if a ≠ b, then aRb and bRa can be true or false, independently of each other.

The Book of Lamentations is recited annually on the Tisha b ' Av, the anniversary of the destruction of both of the Jewish Temples as well as numerous other unfavorable days in Jewish history.

Now the remainder of dividing either a or b by d is also of the form ax + by since it is obtained by subtracting a multiple of from a or b, and on the other hand it has to be strictly smaller in absolute value than d. This leaves 0 as only possibility for such a remainder, so d divides a and b exactly.

A proposal by the U. S. to the United Nations Atomic Energy Commission ( UNAEC ) to a ) extend between all nations the exchange of basic scientific information for peaceful ends ; b ) implement control of atomic energy to the extent necessary to ensure its use only for peaceful purposes ; c ) eliminate from national armaments atomic weapons and all other major weapons adaptable to mass destruction ; and d ) establish effective safeguards by way of inspection and other means to protect complying States against the hazards of violations and evasions.

This first connotation can be further differentiated into ( a ) pure common law arising from the traditional and inherent authority of courts to define what the law is, even in absence of an underlying statute, e. g., most criminal law and procedural law before the 20th century, and even today, most of contract law and the law of torts, and ( b ) court decisions that interpret and decide the fine boundaries and distinctions in law promulgated by other bodies.

" No person shall, except under and in accordance with a radio authorization, install, operate or possess radio apparatus, other than ( b ) a radio apparatus that is capable only of the reception of broadcasting and that is not a distribution undertaking.

In other words, b is a unit in the ring Z / aZ of integers modulo a.

On the other hand, if the condition number is small then the error in x will not be much bigger than the error in b.

Under Section 2 ( b ) of the Contempt of Courts Act of 1971, civil contempt has been defined as wilful disobedience to any judgment, decree, direction, order, writ or other process of a court or wilful breach of an undertaking given to a court.

Therefore strings beginning with C ( or any other capital letter ) would be sorted before strings with lower-case a, b, etc.

This may be followed by the first letter or letters of the title in lower-case, and / or sometimes the letters a, b, c indicating other printings of the same title.

One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i. e. given any a and b, with a > b, there exist c and d, all positive and rational, such that

In mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set A together with a reflexive and transitive binary relation ≤ ( that is, a preorder ), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.

The ecclesiastical historian Socrates Scholasticus ( b. 380 ) attributes the observance of Easter by the church to the perpetuation of its custom, " just as many other customs have been established ," stating that neither Jesus nor his Apostles enjoined the keeping of this or any other festival.

The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields " yes " ( or true ) ( more accurately the number b in location B is greater than or equal to the number a in location A ) THEN the algorithm specifies B ← B − A ( meaning the number b − a replaces the old b ).

The hymn to Hermes, fr308 ( b ), was quoted by Hephaestion ( grammarian ) and both he and Libanius, the rhetorician, quoted the first two lines of fr. 350, celebrating the return from Babylon of Alcaeus ' brother.

Chinese languages treat these two phones differently ; for example in Mandarin, ( written b in Pinyin ) and ( written p ) contrast phonemically.

: Illustrative alkynes: a, acetylene, b, two depictions of propyne, c, 1-butyne, d, 2-butyne, e, the naturally-occurring 1-phenylhepta-1, 3, 5-triyne, and f, the strained cycloheptyne.

An abelian group is a set, A, together with an operation "•" that combines any two elements a and b to form another element denoted.

According to Capp, who loved to relate the story, Kelly's two perfectly logical reasons for doing so were: a. to cement diplomatic relations between Argentina and the United States, and b. " Because you can't play the piano, anyway!

A homomorphism between two Boolean algebras A and B is a function f: A → B such that for all a, b in A:

A Punnett square depicting a cross between two pea plants heterozygous for purple ( B ) and white ( b ) blossoms

Usually, only the second and fourth line of a quatrain are rhymed ( in the scheme a, b, c, b ), which has been taken to suggest that, originally, ballads consisted of couplets ( two lines ) of rhymed verse, each of 14 syllables.

The coefficient a in the term of x < sup > b </ sup > y < sup > c </ sup > is known as the binomial coefficient or ( the two have the same value ).

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

b ) Edge-on view of the central two β strands in a, showing the righthanded twist and the pleat of Cαs and sidechains that alternately stick out in opposite directions from the sheet.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).