Results 1  10
of
498
The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
Abstract

Cited by 474 (7 self)
 Add to MetaCart
This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X
Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
Abstract

Cited by 347 (7 self)
 Add to MetaCart
It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection
THE ONEDIMENSIONAL MODEL FOR DCONES REVISITED
"... Abstract. A dcone is the shape one obtains when pushing an elastic sheet at its center into a hollow cylinder. In a simple model, one can treat the elastic sheet in the deformed configuration as a developable surface with a singularity at the “tip ” of the cone. In this approximation, the renormali ..."
Abstract
 Add to MetaCart
Abstract. A dcone is the shape one obtains when pushing an elastic sheet at its center into a hollow cylinder. In a simple model, one can treat the elastic sheet in the deformed configuration as a developable surface with a singularity at the “tip ” of the cone. In this approximation
Combinatorial Properties of OneDimensional Arrangements
 Experimental Mathematics
, 1997
"... Arrangements are an omnipresent topic in computational geometry, since many problems in computer graphics and robotics reduce to the study of such sets. Motivated by two problems from these areas more precisely from raytracing and assembly planning, we study in this paper the combinatorial stru ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
structure of arrangements of segments on a line and of cones on a circle. We show that the numbers of such arrangements are respectively 1.3.5 . . . (2n1) and (2n)!/n!, that the probabilities for the i th vertex of a random arrangement to be a beginning point are 1(i1)/(2n1) and 1
Light cone renormalization and quantum quenches in onedimensional Hubbard models
 NEW JOURNAL OF PHYSICS
, 2012
"... The Lieb–Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with shortrange interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolu ..."
Abstract
 Add to MetaCart
evolution of prepared initial states in the thermodynamic limit in onedimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies
Differential operators on toric varieties and Fourier transform
, 2007
"... We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans are related to each other by reflections of onedimensional c ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans are related to each other by reflections of onedimensional
Local quantum quenches in critical onedimensional systems: entanglement, the Loschmidt echo, and lightcone effects
"... Abstract. We study a particular type of local quench in a generic quantum critical onedimensional system, using conformal field theory (CFT) techniques, and providing numerical checks of the results in free fermion systems. The system is initially cut into two subsystems A and B which are glued tog ..."
Abstract
 Add to MetaCart
Abstract. We study a particular type of local quench in a generic quantum critical onedimensional system, using conformal field theory (CFT) techniques, and providing numerical checks of the results in free fermion systems. The system is initially cut into two subsystems A and B which are glued
A Wasserstein approach to the onedimensional sticky particle system
, 2009
"... Abstract. We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky ” particles, we obtain new explicit ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
Abstract. We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky ” particles, we obtain new explicit
Positive Solutions for Discrete Boundary Value Problems to OneDimensional Laplacian with Delay
"... We study the existence of positive solutions for discrete boundary value problems to onedimensional Laplacian with delay. The proof is based on the GuoKrasnoselskii fixedpoint theorem in cones. Two numerical examples are also provided to illustrate the theoretical results. ..."
Abstract
 Add to MetaCart
We study the existence of positive solutions for discrete boundary value problems to onedimensional Laplacian with delay. The proof is based on the GuoKrasnoselskii fixedpoint theorem in cones. Two numerical examples are also provided to illustrate the theoretical results.
OneDimensional Dirichlet φLaplacian BVPs with FirstOrder Derivative Dependence
, 2010
"... The aim of this paper is to present new existence results for φLaplacian Dirichlet boundary value problems on bounded intervals of the real line with a nonlinearity depending on the first derivative. A recent fixed point theorem is used to prove existence of continuously differentiable positive s ..."
Abstract
 Add to MetaCart
solutions in a suitable positive cone. AMS Subject Classifications: 34B15, 35B18.
Results 1  10
of
498