Results 41 to 50 of about 1,715 (93)
Alon's Nullstellensatz for multisets
, 2011 Alon's combinatorial Nullstellensatz (Theorem 1.1 from \cite{Alon1}) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $\F$ be a field, $S_1,S_2,..., S_n$ be finite nonempty subsets of $\F$.
Kós, Géza, Rónyai, Lajos
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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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FTheoryTools: Advancing Computational Capabilities for F‐Theory Research
Fortschritte der Physik, Volume 74, Issue 1, January 2026.Abstract A primary goal of string phenomenology is to identify realistic four‐dimensional physics within the landscape of string theory solutions. In F‐theory, such solutions are encoded in the geometry of singular elliptic fibrations, whose study often requires particularly challenging and cumbersome computations.
Martin Bies +2 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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A Duality Based Proof of the Combinatorial Nullstellensatz [PDF]
The Electronic Journal of Combinatorics, 2009 In this note we present a proof of the combinatorial nullstellensatz using simple arguments from linear algebra.
openaire +2 more sources
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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On the existence of zero-sum subsequences of distinct lengths
, 2012 In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups.
Girard, Benjamin
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