Related papers: An application of Kapteyn series to a problem from…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
An elementary and rigorous justification of Dynkin's identity with an extended infinitesimal operator based on the idea of a complete probability formula is given for queueing systems with a single server and discontinuous intensities of…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into…
We develop a unified sampling theory based on sheaves and show that the Shannon-Nyquist theorem is a cohomological consequence of an exact sequence of sheaves. Our theory indicates that there are additional cohomological obstructions for…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Adapting the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, we compute their power series solutions, study the properties of the set of exponents of the solutions and give a bound for their…
A system of q-Painlev\'e type equations with multi-time variables t_1,...,t_M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type A^{(1)}_{M-1} \times A^{(1)}_{N-1}. Its…
We consider the airplane refueling problem, where we have a fleet of airplanes that can refuel each other. Each airplane is characterized by specific fuel tank volume and fuel consumption rate, and the goal is to find a drop out order of…
The purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks. These methods build on and generalize existing methods for series (or cascade) connections by allowing for…
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…
In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the…
This work studies the problem of constructing a representative workload from a given input analytical query workload where the former serves as an approximation with guarantees of the latter. We discuss our work in the context of workload…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
A recursive algorithm is constructed which finds all solutions to a class of Diophantine equations connected to the problem of determining ordered n-tuples of positive integers satisfying the property that their sum is equal to their…
An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…