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Entrez Gene: genecentered information at NCBI
 Nucleic Acids Res
, 2007
"... Entrez Gene (www.ncbi.nlm.nih.gov/entrez/query. fcgi?db=gene) is NCBI’s database for genespecific information. Entrez Gene includes records from genomes that have been completely sequenced, that have an active research community to contribute genespecific information or that are scheduled for in ..."
Abstract

Cited by 340 (12 self)
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, stable and tracked integers as identifiers. The content (nomenclature, map location, gene products and their attributes, markers, phenotypes and links to citations, sequences, variation details, maps, expression, homologs, protein domains and external databases) is provided via interactive browsing
INTEGER
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose G02BBF computes means and standard deviations of variables, sums of squares and crossproducts of deviation ..."
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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 implementationdependent details. 1 Purpose G02BBF computes means and standard deviations of variables, sums of squares and crossproducts
INTEGER
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose G02BUF calculates the sample means and sums of squares and crossproducts, or sums of squares and crosspro ..."
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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 implementationdependent details. 1 Purpose G02BUF calculates the sample means and sums of squares and crossproducts, or sums of squares and crossproducts
Applying interval arithmetic to real, integer and Boolean constraints
, 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 nary 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)
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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 nary 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
 STUDIES IN PURE MATHEMATICS  TO THE MEMORY O/'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)
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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
 In Proceedings of the SIGPLAN '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 runtime invariants using integer multiplication. The algorithms assume a two's complement architectur ..."
Abstract

Cited by 49 (1 self)
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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
 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)
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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
 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 Apoints of V. Henc ..."
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Cited by 105 (4 self)
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cases N(T, V) can be given in the form predicted by the HardyLittlewood method, that is, as a product of local densities: (,) N(T, V) lI l,(V)lUoo ( T, v), p <oo where the "singular series " II,< #(V) #,(V) is given by padic densities: lira k # v(z/pz) and/(T, V) is a real
A PRODUCT OF INTEGER PARTITIONS
, 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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