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 )

That is, Koyukon has two different systems that classify nouns: ( a ) a classificatory verb system and ( b ) a gender system.

However, the term " collective noun " is often used to mean " mass noun " ( even in some dictionaries ), because users confound two different kinds of verb number invariability: ( a ) that seen with mass nouns such as " water " or " furniture ", with which only singular verb forms are used because the constituent matter is grammatically nondiscrete ( although it may or may not be etically nondiscrete ); and ( b ) that seen with collective nouns, which is the result of the metonymical shift between the group and its ( both grammatically and etically ) discrete constituents.

Contra: a ) The most prominent example of a verb beginning with στ has in fact < * se-in the perfect reduplication (); b ) the words with / ts / > σ ( σ ) also have: Homer, Ion.

But people who explain intentional behavior have several choices to make, and the theory identifies the psychological antecedents and consequences of these choices: ( a ) giving either reason explanations or " causal history of reason ( CHR ) explanations " ( which refer to background factors such as culture, personality, or context — causal factors that brought about the agent's reasons but were not themselves reasons to act ); ( b ) giving either desire reasons or belief reasons ; and ( c ) linguistically marking a belief reason with its mental state verb ( e. g., " She thought that ..."; " He assumes that ...").

* Marbad, Arbad ( from the verb R / b / d meaning " to spread ")

The Aramaic word form šə < u > b </ u > aqtanî is based on the verb šə < u > b </ u > aq / šā < u > b </ u > aq, ' to allow, to permit, to forgive, and to forsake ', with the perfect tense ending-t ( 2nd person singular: ' you '), and the object suffix-anî ( 1st person singular: ' me ').

" with final * b assimilated and the resulting greminated consonant cluster * pp being simplified to * p, and the vrddhi-lenghthened root vowel of the verb * pęti, originally meaning " to strain, move " ( cf.

For ( a ) Modern English is a good example ( and in many way the code oral of French verbs ); for ( c ) Old English and Modern High German are good examples ( and in many ways the code écrit of French verb forms ); classical representatives of type ( b ) are Finnish and Hungarian.

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 ).

In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X

In the < tt > SubBytes </ tt > step, each byte in the state is replaced with its entry in a fixed 8-bit lookup table, S ; b < sub > ij </ sub > = S ( a < sub > ij </ sub >).

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.

; Racially or religiously aggravated assault occasioning actual bodily harm: This offence is created by section 29 ( 1 )( b ) of the Crime and Disorder Act 1998.

; Assaulting an officer of the court: This offence is created by section 14 ( 1 )( b ) of the County Courts Act 1984.

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.

If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.

He is among the main characters of the historical novel Agnes of France ( 1980 ) by Greek writer Kostas Kyriazis ( b. 1920 ).

Anomalous operation, also known as anomalous perturbation, is any paranormal phenomena in which it is said that an individual ( a ) uses Psi ( parapsychology ) to influence a physical event, or ( b ) to effect a physical change, in object.

In general, if y = f ( x ), then it can be transformed into y = af ( b ( x − k )) + h. In the new transformed function, a is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative a values, the function is reflected in the x-axis.

The b value compresses the graph of the function horizontally if greater than 1 and stretches the function horizontally if less than 1, and like a, reflects the function in the y-axis when it is negative.

( b ) illustrates the same process using spectroscopic notation,. The Auger effect () is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom.

The condition number is defined more precisely to be the maximum ratio of the relative error in x divided by the relative error in b.

The commutator of two elements a and b of a ring or an associative algebra is defined by

The anticommutator of two elements a and b of a ring or an associative algebra is defined by

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.

The parallelogram defined by the rows of the above matrix is the one with vertices at ( 0, 0 ), ( a, b ), ( a + c, b + d ), and ( c, d ), as shown in the accompanying diagram.

" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined by ∀ a, b ∈ (( a, 0 ) ~ ( a, 1 ) ∧ ( 0, b ) ~ ( 1, b )).

* Reflexive and symmetric: The relation R on Z, defined as aRb ↔ " a − b is divisible by at least one of 2 or 3.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

* gcd ( a, b ), where a and b are not both zero, may be defined alternatively and equivalently as the smallest positive integer d which can be written in the form d = a · p + b · q where p and q are integers.

# Associativity: If a * b and b * c are defined, then ( a * b ) * c and a * ( b * c ) are defined and equal.

# Identity: If a * b is defined, then a * b * b < sup >− 1 </ sup >