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Entrez Gene: gene-centered information at NCBI

by Donna Maglott, Jim Ostell, Kim D. Pruitt, Tatiana Tatusova - Nucleic Acids Res , 2007
"... Entrez Gene (www.ncbi.nlm.nih.gov/entrez/query. fcgi?db=gene) is NCBI’s database for gene-specific information. Entrez Gene includes records from genomes that have been completely sequenced, that have an active research community to con-tribute gene-specific information or that are sched-uled for in ..."
Abstract - Cited by 340 (12 self) - Add to MetaCart
, stable and tracked integers as identifiers. The content (nomenclature, map loca-tion, gene products and their attributes, markers, phenotypes and links to citations, sequences, varia-tion details, maps, expression, homologs, protein domains and external databases) is provided via interactive browsing

INTEGER

by unknown authors
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BBF computes means and standard deviations of variables, sums of squares and cross-products of deviation ..."
Abstract - Add to MetaCart
Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BBF computes means and standard deviations of variables, sums of squares and cross-products

INTEGER

by unknown authors
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BUF calculates the sample means and sums of squares and cross-products, or sums of squares and cross-pro ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BUF calculates the sample means and sums of squares and cross-products, or sums of squares and cross-products

Applying interval arithmetic to real, integer and Boolean constraints

by Frederic Benhamou, William J. Older , 1997
"... We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any n-ary relation on <. The basic idea is to de ne, for every such relation, a narrowing function;! based on the approximation of by a Cartesian product ..."
Abstract - Cited by 187 (22 self) - Add to MetaCart
We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any n-ary relation on <. The basic idea is to de ne, for every such relation, a narrowing function;! based on the approximation of by a Cartesian product

On sums and products of integers

by P. Erdős, E. SZEMERÉDI - STUDIES IN PURE MATHEMATICS -- TO THE MEMORY O/&apos;PAUL TURÁN , 1983
"... Let 1 <a, <... <a, he a sequence of integers Consider the integers of the form 1 a; + aj, a;aj, 1 < = t < _.j < n. It is tempting to conjecture that for every E>0 there is an n, so that for every n> n:, there are more than n '- ' distinct integers of the form (1). ..."
Abstract - Cited by 75 (2 self) - Add to MetaCart
Let 1 <a, <... <a, he a sequence of integers Consider the integers of the form 1 a; + aj, a;aj, 1 < = t < _.j < n. It is tempting to conjecture that for every E>0 there is an n, so that for every n> n:, there are more than n '- ' distinct integers of the form (1

Division by Invariant Integers Using Multiplication

by Torbjörn Granlund, Peter L. Montgomery - In Proceedings of the SIGPLAN &apos;94 Conference on Programming Language Design and Implementation , 1994
"... Integer division remains expensive on today's processors as the cost of integer multiplication declines. We present code sequences for division by arbitrary nonzero integer constants and run--time invariants using integer multiplication. The algorithms assume a two's complement architectur ..."
Abstract - Cited by 49 (1 self) - Add to MetaCart
architecture. Most also require that the upper half of an integer product be quickly accessible. We treat unsigned division, signed division where the quotient rounds towards zero, signed division where the quotient rounds towards -#, and division where the result is known a priori to be exact. We give some

On sums and products of integers

by Yong-gao Chen - PROC. AMER. MATH. SOC , 1999
"... Erdös and Szemerédi proved that if A is a set of k positive integers, then there must be at least ck1+δ integers that can be written as the sum or product of two elements of A, wherecisaconstant and δ>0. Nathanson proved that the result holds for δ = 1 31 result holds for δ = 1 1 and c = 5 20.. ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
Erdös and Szemerédi proved that if A is a set of k positive integers, then there must be at least ck1+δ integers that can be written as the sum or product of two elements of A, wherecisaconstant and δ>0. Nathanson proved that the result holds for δ = 1 31 result holds for δ = 1 1 and c = 5 20

DENSITY OF INTEGER POINTS ON AFFINE HOMOGENEOUS VARIETIES

by W. Duke, Z. Rudnick, P. Sarnak - DUKE MATHEMATICAL JOURNAL , 1993
"... Let F be an affine variety defined over Z by integral polynomials x,]: (1.1) V {x e C": f(x) O, j 1,..., v} A basic problem of diophantine analysis is to investigate the asymptotics as T of (1.2) N(T, V) = {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of A-points of V. Henc ..."
Abstract - Cited by 105 (4 self) - Add to MetaCart
cases N(T, V) can be given in the form predicted by the Hardy-Littlewood method, that is, as a product of local densities: (,) N(T, V) l--I l,(V)lUoo ( T, v), p <oo where the "singular series " I-I,< #(V) #,(V) is given by p-adic densities: lira k # v(z/pz) and/(T, V) is a real

Products of integers in short intervals

by P. Erdös , et al. , 1984
"... ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
Abstract not found

A PRODUCT OF INTEGER PARTITIONS

by Alain Goupil , 906
"... Abstract. I present a bijection on integer partitions that leads to recursive expressions, closed formulae and generating functions for the cardinality of certain sets of partitions of a positive integer n. The bijection leads also to a product on partitions that is associative with a natural gradin ..."
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Abstract. I present a bijection on integer partitions that leads to recursive expressions, closed formulae and generating functions for the cardinality of certain sets of partitions of a positive integer n. The bijection leads also to a product on partitions that is associative with a natural
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