相关论文: Poincare duality quivers
The classic Poincare inequality bounds the $L^q$-norm of a function $f$ in a bounded domain $\Omega \subset \R^n$ in terms of some $L^p$-norm of its gradient in $\Omega$. We generalize this in two ways: In the first generalization we remove…
We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties
We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fan $\Delta$ determines a volume polynomial $V_\Delta$ whose values are the volumes of multi-polytopes based on…
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
The formula for the Poincare series of the algebra of invariant of $n$-ary form is found.
The canonical description is presented for the string with pointlike masses at the ends in 1+1 dimensions in two different gauges: in the proper time gauge and in the light cone one. The classical canonical transformation is written out…
In this talk, some aspects of duality symmetries are presented.
The Polynomial Abel differential equations are considered a model problem for the classical Poincar\'e center--focus problem for planar polynomial systems of ordinary differential equations. Last decades several works pointed out that all…
In this study, we provide mathematical and practice-driven justification for using $[0,1]$ normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization,…
The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentum-vector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different…
The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre…
We consider an Abel polynomial differential equation. For two given points a and b, the "Poincare mapping" of the equation transforms the values of its solution at a into their values at b. In this article, we study global analytic…
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces…
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
As the classical $(p,q)$-Poincar\'e inequality is known to fail for $0 < p < 1$, we introduce the notion of weighted multilinear Poincar\'e inequality as a natural alternative when $m$-fold products and $1/m < p$ are considered. We prove…
The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for…
We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…