Examples of computer-assisted derivation of the amplitude equations valid in the vicinity of a bifurcation point are presented. The methodology created using Mathematica computer software language is outlined, so that its potential to tackle a wide class of problems in nonlinear sciences appears.

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergence...

Approximate p-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulas over those based on the

In this paper we analyze a given production network in view of stability, which means boundedness of the state of the network over time. By a mathematical point of view we will model the system by differential equations. This results in the derivation of conditions for which the production network is stable.

In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension of the variety. Additionally, we classify tangent spaces at regular points in the case of one derivation.

This document examines what appear to be a number of errors or otherwise questionable steps in the derivation of the model-based information rate (‘model-IR’) in Dubnov’s 2008 paper, ‘Unified view of prediction and repetition structure in audio signals with application to interest point detection’ [3]. A critique of Dubnov’s ‘Information Rate’ Samer Abdallah, Centre for Digital Music, QMUL

This study evaluated the use of high-resolution computed tomography (HRCT) to predict the presence of culture-positive pulmonary tuberculosis (PTB) in adult patients with pulmonary lesions in the emergency department (ED). The study included a derivation phase and validation phase with a total of 8,245 patients with pulmonary disease. There were 132 patients with culture-positive PTB in the der...

Among the scientists who in various ways paved the way for Laue’s discovery and for Bragg’s determination of crystal structures, there is one who occupies the most important place: E. S. Fedorov (18531919), the eminent Russian crystallographer. His most outstanding achievement is the derivation of the 230 symmetry space groups which now serve as the mathematical basis of structural analysis. Al...