Hypergeometric Solutions of Linear Recurrences with Polynomial
... Let K be a field of characteristic zero . We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations . Let K N denote the ring of all sequences over K, with addition and multiplication defined term- ...
... Let K be a field of characteristic zero . We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations . Let K N denote the ring of all sequences over K, with addition and multiplication defined term- ...
algebraic expressions - CBSE
... Constant : A quantity which has a fixed value is called a constant. The numbers 2, 9, 100, , etc., are constants as they have fixed values. For example, number of vertices of a triangle is 3 which is a constant. Sometimes constant are also denoted by letters a, b, c, etc. Algebraic Expressions: Reca ...
... Constant : A quantity which has a fixed value is called a constant. The numbers 2, 9, 100, , etc., are constants as they have fixed values. For example, number of vertices of a triangle is 3 which is a constant. Sometimes constant are also denoted by letters a, b, c, etc. Algebraic Expressions: Reca ...
VARIATIONS ON THE BAER–SUZUKI THEOREM 1. Introduction
... then [C, C] = C ∪ {1}, but hCi = A5 is simple. We conjecture that an even stronger property holds: Conjecture 1.3. Let 5 6= p be a prime. Let C be a conjugacy class of p-elements in the finite group G. If [c, d] is a p-element for all c, d ∈ C, then C ⊂ Op (G). Using the methods of our proof of Theo ...
... then [C, C] = C ∪ {1}, but hCi = A5 is simple. We conjecture that an even stronger property holds: Conjecture 1.3. Let 5 6= p be a prime. Let C be a conjugacy class of p-elements in the finite group G. If [c, d] is a p-element for all c, d ∈ C, then C ⊂ Op (G). Using the methods of our proof of Theo ...
Slides of the talk Uniform dessins on Shimura curves
... Recall that smooth complex projective algebraic curves C with Belyı̆ functions β , i.e. with dessins, can be defined by algebraic equations with coefficients in some number field K . This is a field of definition for C , and we may introduce in the same way a common field of definition for C and β , ...
... Recall that smooth complex projective algebraic curves C with Belyı̆ functions β , i.e. with dessins, can be defined by algebraic equations with coefficients in some number field K . This is a field of definition for C , and we may introduce in the same way a common field of definition for C and β , ...
a set of postulates for ordinary complex algebra
... concepts—(the class of complex numbers, with the operations of addition and of multiplication, and the subclass of real numbers, with the relation of order)— and deducible from a small number of fundamental propositions, or hypotheses. The object of the present paper is to analyze these fundamental ...
... concepts—(the class of complex numbers, with the operations of addition and of multiplication, and the subclass of real numbers, with the relation of order)— and deducible from a small number of fundamental propositions, or hypotheses. The object of the present paper is to analyze these fundamental ...
Group cohomology - of Alexey Beshenov
... The normalization imposes u(1) = 0A . This section s0 gives rise to another 2-cocycle f 0 . A routine computation gives f 0 in terms of f: s0 (g) s0 (h) ...
... The normalization imposes u(1) = 0A . This section s0 gives rise to another 2-cocycle f 0 . A routine computation gives f 0 in terms of f: s0 (g) s0 (h) ...
A NOTE ON COMPACT SEMIRINGS
... By a topological semiring we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that x(y-{-z)=xy-\-xz and (x-\-y)z = xz-\-yz for all x, y, and z in 5. Note that, in ...
... By a topological semiring we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that x(y-{-z)=xy-\-xz and (x-\-y)z = xz-\-yz for all x, y, and z in 5. Note that, in ...
Some structure theorems for algebraic groups
... algebraic groups of a specific geometric nature, such as smooth, connected, affine, proper... A first result in this direction asserts that every algebraic group G has a largest connected normal subgroup scheme G0 , the quotient G/G0 is finite and étale, and the formation of G0 commutes with field ...
... algebraic groups of a specific geometric nature, such as smooth, connected, affine, proper... A first result in this direction asserts that every algebraic group G has a largest connected normal subgroup scheme G0 , the quotient G/G0 is finite and étale, and the formation of G0 commutes with field ...
Algebra II (MA249) Lecture Notes Contents
... for g1 , g2 ∈ G and h1 , h2 ∈ H. It is straightforward to check that G × H is a group under this operation. Note that the identity element is (1G , 1H ), and the inverse of (g, h) is just (g −1 , h−1 ). If the groups are additive, then it is usually called the direct sum rather than the direct produ ...
... for g1 , g2 ∈ G and h1 , h2 ∈ H. It is straightforward to check that G × H is a group under this operation. Note that the identity element is (1G , 1H ), and the inverse of (g, h) is just (g −1 , h−1 ). If the groups are additive, then it is usually called the direct sum rather than the direct produ ...
Square root computation over even extension
... In the case of field extensions Fpm with m odd, we revisit efficient formulations of several square root algorithms where the quadratic residue test of the input operand is interleaved in such a manner that only some constant number of multiplications are added to the overall algorithm computational ...
... In the case of field extensions Fpm with m odd, we revisit efficient formulations of several square root algorithms where the quadratic residue test of the input operand is interleaved in such a manner that only some constant number of multiplications are added to the overall algorithm computational ...
