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Metric Expansions and Integer Solutions
, 2005
"... Metrics on CalabiYau manifolds are used to derive a formula that finds the existence of integer solutions to polynomials. These metrics are derived from an associated algebraic curve, together with its antiholomorphic counterpart. The integer points in the curve coincide with points on the manifol ..."
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Metrics on CalabiYau manifolds are used to derive a formula that finds the existence of integer solutions to polynomials. These metrics are derived from an associated algebraic curve, together with its antiholomorphic counterpart. The integer points in the curve coincide with points
Uniqueness of integer solution of linear equations
 Data Mining Institute, Computer Sciences Department, University of Wisconsin
, 2009
"... Editor: Abstract. We consider the system of m linear equations in n integer variables Ax = d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1,1} n by reformulating the problem as a linear program. Uniqueness characterizations of ordinary linear programming solutions ..."
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Cited by 3 (2 self)
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Editor: Abstract. We consider the system of m linear equations in n integer variables Ax = d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1,1} n by reformulating the problem as a linear program. Uniqueness characterizations of ordinary linear programming solutions
Integer Solutions to Cutting Stock Problems
"... We consider two integer linear programming models for the onedimensional cutting stock problem that include various difficulties appearing in practical real problems. Our primary goals are the minimization of the trim loss or the minimization of the number of master rolls needed to satisfy the orde ..."
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We consider two integer linear programming models for the onedimensional cutting stock problem that include various difficulties appearing in practical real problems. Our primary goals are the minimization of the trim loss or the minimization of the number of master rolls needed to satisfy
Density of integer solutions to diagonal quadratic forms
 Monatsh. Math
"... Abstract. Let Q be a nonsingular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form ..."
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Cited by 2 (1 self)
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Abstract. Let Q be a nonsingular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients
Enumeration of Integer Solutions to Linear Inequalities Defined by Digraphs
 CONTEMPORARY MATHEMATICS
, 2000
"... ..."
A integer solution of fractional programming problem,”
 General Mathematics Notes,
, 2011
"... Abstract The present paper describes a new method for solving the problem in which the objective function is a fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon simplex method, which is very easy to understand an ..."
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Cited by 1 (0 self)
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Abstract The present paper describes a new method for solving the problem in which the objective function is a fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon simplex method, which is very easy to understand and apply. This can be illustrated with the help of numerical examples.
On a generalized equation of Smarandache and its integer solutions
"... Abstract Let a 6 = 0 be any given real number. If the variables x1, x2, · · · , xn satisfy x1x2 · · ·xn = 1, the equation 1 x1 ax1 + 1 x2 ax2 + · · ·+ 1 xn axn = na has one and only one nonnegative real number solution x1 = x2 = · · · = xn = 1. This generalized the problem of Smarandache in ..."
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Abstract Let a 6 = 0 be any given real number. If the variables x1, x2, · · · , xn satisfy x1x2 · · ·xn = 1, the equation 1 x1 ax1 + 1 x2 ax2 + · · ·+ 1 xn axn = na has one and only one nonnegative real number solution x1 = x2 = · · · = xn = 1. This generalized the problem of Smarandache
INTEGER SOLUTIONS OF A SEQUENCE OF DECOMPOSABLE FORM INEQUALITIES
, 1998
"... Let F(X) = F(X0,...,Xm) ∈ Z[X] be a decomposable form, i.e. a homogeneous polynomial which factorizes into linear forms over ¯ Q. Assume that q = deg F> 2m, and consider the decomposable form inequality (1.1) ..."
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Let F(X) = F(X0,...,Xm) ∈ Z[X] be a decomposable form, i.e. a homogeneous polynomial which factorizes into linear forms over ¯ Q. Assume that q = deg F> 2m, and consider the decomposable form inequality (1.1)
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