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

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.

Anaximenes () of Miletus ( b. 585 BCE, d. 528 BCE ) was an Archaic Greek Pre-Socratic philosopher active in the latter half of the 6th century BC .< ref name =" lindberg28 "> Lindberg, David C. “ The Greeks and the Cosmos .” < u > The Beginnings of Western Science </ u >.

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Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

* Base ( exponentiation ) or radix, the b in b < sup > n </ sup >

In an " extended model " which includes hot dark matter in the form of neutrinos, then if the " physical baryon density " Ω < sub > b </ sub > h < sup > 2 </ sup > is estimated at about 0. 023 ( this is different from the ' baryon density ' Ω < sub > b </ sub > expressed as a fraction of the total matter / energy density, which as noted above is about 0. 046 ), and the corresponding cold dark matter density Ω < sub > c </ sub > h < sup > 2 </ sup > is about 0. 11, the corresponding neutrino density Ω < sub > v </ sub > h < sup > 2 </ sup > is estimated to be less than 0. 0062.

All eight manuscripts were copied within 175 years, ranging from 125 BCE ( 4QDan < sup > c </ sup >) to about 50 CE ( 4QDan < sup > b </ sup >).

The four scrolls that preserve the relevant sections ( 1QDan < sup > a </ sup >, 4QDan < sup > a </ sup >, 4QDan < sup > b </ sup >, and 4QDan < sup > d </ sup >) all follow the same bilingual nature of Daniel where the book opens in Hebrew, switches to Aramaic at 2: 4b, then reverts back to Hebrew at 8: 1.

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*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

For example, if a < b, the initial quotient q < sub > 0 </ sub > equals zero, and the remainder r < sub > 0 </ sub > is a.

Therefore, c divides the initial remainder r < sub > 0 </ sub >, since r < sub > 0 </ sub > = a − q < sub > 0 </ sub > b = mc − q < sub > 0 </ sub > nc = ( m − q < sub > 0 </ sub > n ) c. An analogous argument shows that c also divides the subsequent remainders r < sub > 1 </ sub >, r < sub > 2 </ sub >, etc.

b = q < sub > 1 </ sub > q < sub > 2 </ sub >... q < sub > m </ sub > are products of primes.

* 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.

f ( p < sup > a </ sup >) f ( q < sup > b </ sup >) ...

It results in two polynomials, a quotient and a remainder that are characterized by the following property of the polynomials: given two polynomials a and b such that b ≠ 0, there exists a unique pair of polynomials, q, the quotient, and r, the remainder, such that a = b q + r and degree ( r ) < degree ( b ) ( here the polynomial zero is supposed to have a negative degree ).

Although noise levels in a digital system can be expressed using SNR, it is more common to use E < sub > b </ sub >/ N < sub > o </ sub >, the energy per bit per noise power spectral density.

If < tt >/ tmp / a </ tt > exists but < tt >/ tmp / a / b </ tt > does not, < tt > mkdir </ tt > will create < tt >/ tmp / a / b </ tt > before creating < tt >/ tmp / a / b / c </ tt >.

* Trilinear coordinates for the center of the Kiepert hyperbola are ( b < sup > 2 </ sup > − c < sup > 2 </ sup >)< sup > 2 </ sup >/ a: ( c < sup > 2 </ sup > − a < sup > 2 </ sup >)< sup > 2 </ sup >/ b: ( a < sup > 2 </ sup > − b < sup > 2 </ sup >)< sup > 2 </ sup >/ c

$ echo " test_b " >/ tmp / one / two / b

For example, consider a fixed-point type represented as a binary integer with b bits in two's complement format, with a scaling factor of 1 / 2 < sup > f </ sup > ( that is, the last f bits are fraction bits ): the minimum representable value is − 2 < sup > b-1 </ sup >/ 2 < sup > f </ sup > and the maximum value is ( 2 < sup > b-1 </ sup >- 1 )/ 2 < sup > f </ sup >.

It is required to find u so that u < sup > 3 </ sup >= a < sup > 2 </ sup > b, giving u and v = u < sup > 2 </ sup >/ a as the mean proportionals.

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 ).

: if R ( a, b ) with a ≠ b, then R ( b, a ) must not hold.

* Assault with intent to resist arrest: under section 7 ( 1 )( b ); this offence was formerly created by s. 38 of the OAPA 1861.

On one occasion he ordered some Samaritan wine, but subsequently learning that there were no longer any strict observers of the dietary laws among the Samaritans, with the assistance of his colleagues, Ḥiyya b. Abba, Rav Ammi, and Rav Assi, he investigated the report, and, ascertaining it to be well founded, did not hesitate to declare the Samaritans, for all ritualistic purposes, Gentiles ( Yer.

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

* Lucy Irvine ( b. 1956 ), writer, lived very briefley in the Summer Isles Hotel with her father, who owned it and the Hydroponicum.

Binary operations are often written using infix notation such as a * b, a + b, a · b or ( by juxtaposition with no symbol ) ab rather than by functional notation of the form f ( a, b ).

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

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.

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

( b ) Sacred furniture, such as models or actual examples of ritual objects ; of these we have also numerous pictorial representations.

; Inverse element: For each a in A, there exists an element b in A such that a • b

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

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 binary operation ∘, called composition of morphisms, such that for any three objects a, b, and c, we have.

* The integer b has a multiplicative inverse modulo a: there exists an integer y such that by ≡ 1 ( mod a ).

The direction and magnitude of such distortion is expressed in terms of a Burgers vector ( b ).

Some of the most influential contemporary classical double bass players are known as much for their contributions to pedagogy as for their performing skills, such as US bassist Oscar G. Zimmerman ( 1910 – 1987 ), known for his teaching at the Eastman School of Music and, for 44 summers at the Interlochen National Music Camp in Michigan and French bassist François Rabbath ( b. 1931 ) who developed a new bass method that divided the entire fingerboard into six positions.

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

Reflexivity follows from symmetry and transitivity if for every element a ∈ A, there exists another element b ∈ A such that a ~ b holds.

Transitive and symmetric imply reflexive if and only if for all a ∈ X, there exists a b ∈ X such that a ~ b.

: Theorem on projections: Let the function f: X → B be such that a ~ b → f ( a )

This yields a convenient way of generating an equivalence relation: given any binary relation R on X, the equivalence relation generated by R is the smallest equivalence relation containing R. Concretely, R generates the equivalence relation a ~ b if and only if there exist elements x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > in X such that a

Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).