scholarly journals Parabolic Equations in Simple Convex Polytopes with Time Irregular Coefficients

2014 ◽  
Vol 46 (3) ◽  
pp. 1789-1819 ◽  
Author(s):  
Hongjie Dong ◽  
Doyoon Kim
Keyword(s):  
Parabolic Equations ◽  
Convex Polytopes ◽  
Simple Convex

scholarly journals Projective bundles over small covers and the bundle triviality problem

2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Shintarô Kuroki ◽  
Zhi Lü
Keyword(s):  
Convex Polytopes ◽  
Necessary And Sufficient Condition ◽  
Real Projective Space ◽  
Real Vector ◽  
Small Cover ◽  
Projective Bundles ◽  
Tautological Line Bundle ◽  
Necessary And Sufficient ◽  
Open Question ◽  
Simple Convex

AbstractThe present paper investigates the projective bundles over small covers. We first give a necessary and sufficient condition for the projectivization of a real vector bundle over a small cover to be a small cover. Then associated with moment-angle manifolds, we further study the structure of such a projectivization as a small cover by introducing a new characteristic function on simple convex polytopes. As an application, we characterize the real projective bundles over 2-dimensional small covers by interpreting the fiber sum operation to some combinatorial operation. We next determine when the projectivization of Whitney sum of the tautological line bundle and the tangent bundle over real projective space is diffeomorphic to the product of two real projective spaces. This answers an open question regarding the topology of the fiber of the Monster-Semple tower.

scholarly journals On the Equivalence of B-Rigidity and C-Rigidity for Quasitoric Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jin Hong Kim
Keyword(s):  
Convex Polytopes ◽  
Cohomology Rings ◽  
Toric Topology ◽  
Quasitoric Manifolds ◽  
Simple Convex ◽  
Cohomological Rigidity

For quasitoric manifolds and moment-angle complexes which are central objects recently much studied in toric topology, there are several important notions of rigidity formulated in terms of cohomology rings. The aim of this paper is to show that, among other things, Buchstaber-rigidity (or B-rigidity) is equivalent to cohomological-rigidity (or C-rigidity) for simple convex polytopes supporting quasitoric manifolds.

scholarly journals Toric cohomological rigidity of simple convex polytopes

2010 ◽  
Vol 82 (2) ◽  
pp. 343-360 ◽  
Author(s):  
S. Choi ◽  
T. Panov ◽  
D. Y. Suh
Keyword(s):  
Convex Polytopes ◽  
Simple Convex ◽  
Cohomological Rigidity

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

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