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Nonnegative integer linear congruences
 POLYNOMIALS AND MINIMAL ZERO SEQUENCES 7
"... Abstract. We consider the problem of describing all nonnegative integer solutions to a linear congruence in many variables. This question may be reduced to solving the congruence x1 +2x2+3x3+...+(n−1)xn−1 ≡ 0 (mod n) where xi ∈ N = {0, 1, 2,...}. We consider the monoid of solutions of this equation ..."
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Cited by 3 (0 self)
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Abstract. We consider the problem of describing all nonnegative integer solutions to a linear congruence in many variables. This question may be reduced to solving the congruence x1 +2x2+3x3+...+(n−1)xn−1 ≡ 0 (mod n) where xi ∈ N = {0, 1, 2,...}. We consider the monoid of solutions
Proximity Inversion Functions on the NonNegative Integers
, 2004
"... We consider functions mapping nonnegative integers to nonnegative real numbers such that a and a + n are mapped to values at least 1 n apart. In this paper we use a novel method to construct such a function. We conjecture that the supremum of the generated function is optimal and pose some unsolve ..."
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We consider functions mapping nonnegative integers to nonnegative real numbers such that a and a + n are mapped to values at least 1 n apart. In this paper we use a novel method to construct such a function. We conjecture that the supremum of the generated function is optimal and pose some
EHRHART f ∗COEFFICIENTS OF POLYTOPAL COMPLEXES ARE NONNEGATIVE INTEGERS
"... ABSTRACT. The Ehrhart polynomial LP of an integral polytope P counts the number of integer points in integral dilates of P. Ehrhart polynomials of polytopes are often described in terms of their Ehrhart h∗vector (aka Ehrhart δvector), which is the vector of coefficients of LP with respect to a ce ..."
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the property that the f ∗vector of a unimodular simplicial complex coincides with its fvector. The main result of this article is a counting interpretation for the f ∗coefficients which implies that f ∗coefficients of integral polytopal complexes are always nonnegative integers. This holds even
AN ASYMPTOTIC FORMULA FOR THE NUMBER OF NONNEGATIVE INTEGER MATRICES WITH PRESCRIBED ROW AND COLUMN SUMS
, 2009
"... We count m×n nonnegative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n gr ..."
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Cited by 14 (4 self)
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We count m×n nonnegative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n
The asymptotic structure of nearly unstable nonnegative integervalued AR(1) models
 BERNOULLI
, 2009
"... This paper considers nonnegative integervalued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this ‘near unit root’ situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit exp ..."
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Cited by 5 (1 self)
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This paper considers nonnegative integervalued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this ‘near unit root’ situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit
The nonnegative real numbers and the nonnegative integers are denoted by R+ and Z+, respectively.
"... In this paper we present a new, compact derivation of statespace formulae for the socalled discretisationbased solution of the H1 sampleddata control problem. Our approach is based on the established technique of continuous timelifting, which is used to isometrically map the continuoustime, ..."
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In this paper we present a new, compact derivation of statespace formulae for the socalled discretisationbased solution of the H1 sampleddata control problem. Our approach is based on the established technique of continuous timelifting, which is used to isometrically map the continuoustime, linear, periodically timevarying, sampleddata problem to a discretetime, linear, timeinvariant problem. Statespace formulae are derived for the equivalent, discretetime problem by solving a set of twopoint, boundaryvalue problems. The formulae accommodate a direct feedthrough term from the disturbance inputs to the controlled outputs of the original plant and are simple, requiring the computation of only a single matrix exponential. It is also shown that the resultant formulae can be easily restructured to give a numerically robust algorithm for computing the statespace matrices.
Equation Assigns an Integer which is Greater than the Heights of Integer (Nonnegative Integer, Rational) Solutions, if these Solutions Form a Finite Set
"... We conjecture that if a system S ⊆ {xi + xj = xk, xi · xj = xk: i, j, k ∈ {1,..., n}} has only finitely many solutions in integers x1,..., xn, then each such solution (x1,..., xn) satisfies max (x1,..., xn) ≤ 22n−1. The conjecture implies that there is an algorithm which to each Diophantine eq ..."
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equation assigns an integer which is greater than the heights of integer (nonnegative integer, rational) solutions, if these solutions form a finite set. We describe an algorithm whose execution never terminates. If the conjecture is true, then the algorithm sequentially displays all integers n ≥ 2
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