Results 31 to 40 of about 1,707 (110)
On the grasshopper problem with signed jumps
, 2011 The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, was the following. Let $a_1,a_2,...,a_n$ be distinct positive integers and let $M$ be a set of $n-1$ positive integers not containing $s=a_1+a_2+...+a_n$.
Kós, Géza
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A Deductive Approach towards Reasoning about Algebraic Transition Systems
Mathematical Problems in Engineering, Volume 2015, Issue 1, 2015., 2015 Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems.
Jun Fu +3 more
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Groebner Bases Based Verification Solution for SystemVerilog Concurrent Assertions
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We introduce an approach exploiting the power of polynomial ring algebra to perform SystemVerilog assertion verification over digital circuit systems. This method is based on Groebner bases theory and sequential properties checking. We define a constrained subset of SVAs so that an efficient polynomial modeling mechanism for both circuit descriptions ...
Ning Zhou +5 more
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Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 This work presents an efficient solution using computer algebra system to perform linear temporal properties verification for synchronous digital systems. The method is essentially based on both Groebner bases approaches and symbolic simulation. A mechanism for constructing canonical polynomial set based symbolic representations for both circuit ...
Ning Zhou +3 more
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The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)‐dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher‐order nonlinear Schrodinger equation in nonlinear optical ...
Shoukry Ibrahim Atia El-Ganaini +1 more
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On the natural nullcones of the symplectic and general linear groups
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Consider a group acting on a polynomial ring S$S$ over a field K$\mathbb {K}$ by degree‐preserving K$\mathbb {K}$‐algebra automorphisms. Several key properties of the invariant ring can be deduced by studying the nullcone of the action, that is, the vanishing locus of all nonconstant homogeneous invariant polynomials.
Vaibhav Pandey +2 more
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Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel′d‐Sokolov‐Wilson system (DSWE), (2 + 1)‐dimensional Davey‐Stewartson system, and generalized Hirota‐Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous
Shoukry Ibrahim Atia El-Ganaini +1 more
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On some matrix counting problems
Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.Abstract We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime p$p$. In particular, in the integer case, we improve a recent bound of V. Blomer and J. Li (2022).
Ali Mohammadi +2 more
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On linear algebraic semigroups III
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 4, Page 667-690, 1981., 1981 Using some results on linear algebraic groups, we show that every connected linear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that E(T) intersects each regular J‐class of S. It is also shown that the lattice (E(T), ≤) is isomorphic to the lattice of faces of a rational polytope in some ℝn.
Mohan S. Putcha
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Gr\"obner Bases and Nullstellens\"atze for Graph-Coloring Ideals [PDF]
, 2014 We revisit a well-known family of polynomial ideals encoding the problem of graph-$k$-colorability. Our paper describes how the inherent combinatorial structure of the ideals implies several interesting algebraic properties.
De Loera, Jesús A. +7 more
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