Related papers: Sampling theorem associated with q-Dirac system
Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
A systematic derivation provides extended series of correlation inequalities in quantum systems. Each order in truncated Taylor expansion of the spectral representation for the Duhamel correlation function gives its lower and upper bounds.…
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets,…
Decoupling theorems have proven useful in various applications in the area of quantum information theory. This thesis builds upon preceding work by Fr\'{e}d\'{e}ric Dupuis [arXiv:1012.6044v1], where a general decoupling theorem is obtained…
The aim of this paper is to propose a theory of derivations for quandles. Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$ to $A$ are introduced as twisted analogues of quandle homomorphisms. It is shown that…
We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The…
In this paper, we establish the Bahadur--Kiefer representation for sample quantiles for a class of weakly dependent linear processes. The rate of approximation is the same as for i.i.d. sequences and is thus optimal.
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of…
We prove a distribution-theoretic conjecture of Robert Coleman, thereby also obtaining an explicit description of the complete set of Euler systems for the multiplicative group over Q.
The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are provided. Numerical simulations are presented to illustrate…
We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence…
Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…
We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main…
The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of…
The present paper is the continuation of the paper "Nonlinear field theory I". In the paper it is shown that a fully correspondence between the quantum and the nonlinear electromagnetic forms of the Dirac electron theory exists, so that…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…
In this paper we consider a $q$-analog of the Borel-Laplace summation process defined by Marotte and the second author, and consider two series solutions of linear $q$-difference equations with slopes $0$ and $1$. The latter are…
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.