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The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
With the development of computer-assisted techniques, research communities including biochemistry and deep learning have been devoted into the drug discovery field for over a decade. Various applications of deep learning have drawn great…
This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.
With the rapid advancement of information technology, the complexity of applications continues to increase, and the cybersecurity challenges we face are also escalating. This paper aims to investigate the methods and practices of system…
The search for prior art is crucial in patent application processing, it consists in retrieving other documents relevant to the invention of the application. Most methods feed a search engine with keywords that are extracted by…
In this work, we outline the entropy viscosity method and discuss how the choice of scaling influences the size of viscosity for a simple shock problem. We present examples to illustrate the performance of the entropy viscosity method under…
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
We explore the entanglement of the vacuum of a relativistic field by letting a pair of causally disconnected probes interact with the field. We find that, even when the probes are initially non-entangled, they can wind up to a final…
Physics of dielectric mixtures are presented to stimulate discussion and to provide information on the recent advances in this topic.
In this short note we would like to provide some useful remarks on our previous work about the piezonuclear decay of Thorium and in general about the methods and protocols that we used in the experiments on piezonuclear reactions. The…
A summary of the successes of and obstacles to the gauge technique (a non-perturbative method of solving Dyson-Schwinger equations in gauge theories) is given, as well as an outline of how progress may be achieved in this field.
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
A brief account is given of the problems involved in extended the pinch technique beyond the one-loop level, and of investigations into one possible approach to solving them.
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Since the number of dark energy models have rapidly increased over the last years, some model-independent methods have been developed in order to analyse the cosmological evolution in a phenomenological way. In this manuscript, we analyse…
The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems…