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Showing 1 to 20 of 56 for “"positive integer"”.
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Representation by Quaternary Quadratic Forms whose Coefficients are 1, 2, 7 and 14
… formulae for the number of representations of a positive integer n by the quaternary quadratic forms a_1x_1^2+a_2x_2^2+a_3x_3^2+a_4x_4^2, where a_1, a_2, a_3, a_4 in {1,2,7,14}. We use a modular form approach.
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Delta-System Methods in Contemporary Graph Theory
… probabilistic methods, to show that for every positive integer k, almost every graph has no k-minimum-difference-representation. This answers a question of Boros, Gurvich, and Meshulam.
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Efficient Algorithms for Graph-Theoretic and Geometric Problems
… to efficient computation of matrix products for positive integer matrices. We provide an efficient approximation algorithm for the partitioning problem and several algorithms for integer matrix multiplication. The multiplication algorithms are explicitly or implicitly based on an interpretation …
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On the Number of Representations of One as the Sum of Unit Fractions
… (EFO), asks the following question: Given a positive integer n, how many ways can 1 be expressed as the sum of n non-increasing unit fractions? In this paper, we verify a result concerning the EFO problem for n=8, and show the computational complexity of the problem can be severely lessened …
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On the Projective Characters of the Finite Chevalley Groups
Let p be a prime number, let m be a positive integer and let G be a universal Chevalley group constructed over a field of order ${\rm p\sp{m}}.$ We consider the modular representations (in characteristic p) of the group G. More precisely, we study the Brauer characters of G, concentrating on the …
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Ramsey Theory
<p>The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and …
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Around the Fibonacci Numeration System
… to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of …
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Improved Runtimes and Lower Bounds for Dual-Edge Failure Replacement Path Algorithms
… runtime of k-failure Replacement Paths for any positive integer k.
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The Effect of Osmotic Stimulation of Copeptin on Glucose Metabolism in Healthy Adults
… the 120-min of infusion. During the OGTT the positive integer of the area under the curve (AUC) for glucose was greater during HYPER (401.5±190.5 mmol·L-1·min) vs. the ISO trial (354.0±205.8 mmol·L-1·min, P< 0.05). The positive integer of the AUC for insulin during OGTT did not differ between …
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The Z-densities of the Fibonacci Sequence
… ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m" to be Z(m) is the limit of x to infinity of …
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Moment sequences and their applications
… = {(t,.·.,t<sup>n</sup>): t ∈ [0,1] } for each positive integer n. Explicit formulas of these functions are derived and applied to the study of the subnormal completion problem in operator theory. Last, we show that certain power functions are the building blocks of completely positive …
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The asymptotic behavior of the integer solutions of the Rosenberger equations
… the sets of coefficients ( a, b, c, d) are all integers such that each of a, b, and c divides d, and the equations themselves have infinitely many integer solutions. Rosenberger has shown that there are only six such sets of coefficients, one of which is the Markoff equation, x2 + y2 + z2 = …
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Steklov Eigenvalue Problems on Nearly Spherical and Annular Domains
… domains in d dimensions where d is any given positive integer. By using the Green-Beltrami identity for spherical harmonic functions, the derivatives of Steklov eigenvalues with respect to the domain perturbation parameter can be determined by the eigenvalues of a matrix involving the integral …
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Questions and conjectures about multinomial coefficients
… let {ai} be any sequence (finite or infinite) of positive integers such that i1ai ≤1 . It is clear that n!&sqbl0;na1 &sqbr0;!&sqbl0;na2&sqbr0; !&sqbl0;na3&sqbr0;!&ldots; is an integer because it is a multiple of a certain multinomial coefficient. We let fan=n! Ln&sqbl0;n a1&sqbr0;!&sqbl0;na …
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Hypermaps: constructions and operations
It is conjectured that given positive integers <i>l, m, n</i> with <i>l</i><sup>-1</sup> + <i>m<sup>-</sup></i><sup>1</sup> + <i>n</i><sup>-1</sup> < 1<br/>and an integer <i>g</i> ≥ 0, the triangle group Δ = Δ (<i>l, m, n</i>) = ⟨<i>X,Y,Z|X</i><sup><i> l</i></sup> = <i>Y</i> <sup><i>m</i></sup> …
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Subconstituent Algebras of Latin Squares
Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the …
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The number of zeros of linear recurring sequences over finite fields
… where <italic>a<italic> is a positive integer. The connection with coding theory is a key ingredient. Also it is proved that the upper bound defined here is the best bound for the cardinality of the set of zeros, in the sense that it is reached infinitely often.
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The Factoradic Integers
… examined; this leads to the consideration of the integers as a metric space under the "factoradic metric", i.e., the integers equipped with a distance function defined by d(n,m)=1/N!, where N is the largest positive integer such that N! divides n-m. Via the process of metric completion, the …
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Compactness of the space of marked groups and examples of L2-Betti numbers of simple groups
… by Denis Osin and Andreas Thom [2]: for every integer n ≥ 2 and every ε ≥ 0 there exists an infinite simple group Q generated by n elements such that β(2)(Q) ≥ n − 1 − ε. As a corollary, we can prove that for every positive integer n 1 there exists a simple group Q with d(Q) = n. In the proof …
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Involutory matrices, modulo m
Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P<sup>α</sup>), without …
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