相关论文: Elimination theory and Newton polytopes

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…

An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…

We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…

In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…

We discuss some key results from convex analysis in the setting of topological groups and monoids. These include separation theorems, Krein-Milman type theorems, and minimax theorems.

The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the orignial polytope are hereditary to its…

New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…

Frequent itemsets form a polytope and can be found and analyzed with Linear Programming.

The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been…

We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…

We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…

An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to…

We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topology, and the study of…