Related papers: A Note on Derivation of Rutherford Formula within …
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified…
This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives of functions with steep gradients or discontinuities. The novelty of the method concerns how derivatives are…
The moment of inertia of even-even deformed nuclei which are derived on the basis of hydrodynamical model yield values that are too small compared with the experimental [Davidson 1965] ones. We expect that these contradictions come from the…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
Derivatives and integrals of non-integer order were introduced more than three centuries ago, but only recently gained more attention due to their application on nonlocal phenomena. In this context, the Caputo derivatives are the most…
Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…
Reynolds' lubrication approximation is used extensively to study flows between moving machine parts, in narrow channels, and in thin films. The solution of Reynolds' equation may be thought of as the zeroth order term in an expansion of the…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
Regularization for matrix factorization (MF) and approximation problems has been carried out in many different ways. Due to its popularity in deep learning, dropout has been applied also for this class of problems. Despite its solid…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and…
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
We present a new fast algorithm for computing the Boys function using a nonlinear approximation of the integrand via exponentials. The resulting algorithms evaluate the Boys function with real and complex valued arguments and are…
Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors).…