Related papers: An application of Kapteyn series to a problem from…

We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…

In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…

Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the…

Recently, it has been shown how sampling actions from the predictive distribution over the optimal action-sometimes called Thompson sampling-can be applied to solve sequential adaptive control problems, when the optimal policy is known for…

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…

For the exactly solvable Schwinger model one interesting question is how to infer the exact solution from perturbation theory. We give a systematic procedure of deriving the exact solution from Feynman diagrams of arbitrary order for…

Time series interpretation aims to provide an explanation of what is observed in terms of its underlying processes. The present work is based on the assumption that the common classification-based approaches to time series interpretation…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Using the natural extension for $\theta$-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system…

We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…

In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equation is obtained. By applying this result, the Cauchy problem for systems of Boussinesq equations of finite or infinite orders are…

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series…

This note considers the problem of statistical inference of the parameters of the input process to a queue from periodic workload observations. The main focus is the open problem of constructing statistically efficient estimators for a…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…

The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…