1,721,062 research outputs found
Mathematics and Computers in Simulation
No full textAim of the Mathematics and Computers in Simulation journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Special Issue devoted to the NSCF (Nordisk Science Center Forbund , Nordic Science Center Association , nordicscience.net ) Annual Conference 2018 , hosted by the Energy Discovery Centre, Tallin, Estonia, 9–11 October 2018
Mathematics and Computers in Simulation
No full textMathematics and Computers in Simulation Special Issue for the 7th edition of SDS: Structural Dynamical Systems 2012 . Special issue devoted to collect developments in computational and theoretical methods for Dynamical Systems, their numerical approximation and their applications
Introductory Mathematical Analysis for Quantitative Finance.
No full textThe purpose of this book is to be a tool for students, with little mathematical background, who aim to study Mathematical Finance. The only prerequisites assumed are one–dimensional differential calculus, infinite series, Riemann integral and elementary linear algebra.
In a sense, it is a sort of intensive course, or crash–course, which allows students, with minimal knowledge in Mathematical Analysis, to reach the level of mathematical expertise necessary in modern Quantitative Finance. These lecture notes concern pure mathematics, but the arguments presented are oriented to Financial applications. The n–dimensional Euclidean space is briefly introduced, in order to deal with multivariable differential calculus. Sequences and series of functions are introduced, in view of theorems concerning the passage to the limit in Measure theory, and their role in the general theory of ordinary differential equations, which is also presented. Due to its importance in Quantitative Finance, the Radon–Nykodim theorem is stated, without proof, since the Von Neumann argument requires notions of Functional Analysis, which would require a dedicated course. Finally, in order to solve the Black–Scholes partial differential equation, basics in ordinary differential equations and in the Fourier transform are provided.
We kept our exposition as short as possible, as the lectures are intended to be a preliminary contact with the mathematical concepts used in Quantitative Finance and provided, often, in a one–semester course. This book, therefore, is not intended for a specialized audience, although the material presented here can be used by both experts and non-experts, to have a clear idea of the mathematical tools used in Finance
Stochastic modelling and simulation of PTEN regulatory networks with miRNAs and ceRNAs
Full text linkIn this work, three genetic regulatory networks are considered, that model the post–transcriptional regulation of the PTEN onco suppressor gene, mediated by microRNAs and competitive endogenous RNAs, in glioblastoma multiforme, the most severe of brain tumours. We simulate solutions of the resulting stochastic differential systems and discuss the effects of this miRNA-fashioned regulation on PTEN expression
Trinomial equation: the Hypergeometric way.
Full text linkThis paper is devoted to the analytical treatment of trinomial equations of the form y^n + y = x, where y is the unknown and x∈C is a free parameter. It is well-known that, for degree n≥5, algebraic equations cannot be solved by radicals; nevertheless, roots are described in terms of univariate hypergeometric or elliptic functions. This classical piece of research was founded by Hermite, Kronecker, Birkeland, Mellin and Brioschi, and continued by many other Authors. The approach mostly adopted in recent and less recent papers on this subject (see [1,2] for example) requires the use of power series, following the seminal work of Lagrange [3]. Our intent is to revisit the trinomial equation solvers proposed by the Italian mathematician Davide Besso in the late nineteenth century, in consideration of the fact that, by exploiting computer algebra, these methods take on an applicative and not purely theoretical relevance
Molecular and Mathematical Biology, Chemistry, Medicine and Medical Statistics, Bioinformatics and Numerical Analysis - ISBN:9788833690759. In SERIES IN APPLIED SCIENCES
No full textSeries in Advanced Sciences is devoted to Mathematical Modelling, Numerical and Data Analysis, in particular, with applications to Biology, Biotechnology and Medicine
Analisi di un Algoritmo Vettoriale per la Ricostruzione di Immagini in Tomografia
No full textIl presente articolo riassume le caratteristiche principali di un algoritmo vettoriale per la ricostruzione di immagini da proiezioni tomografiche.
Partendo da un'analisi dell'algoritmo di Proiezione all'Indietro Filtrata, viene costruita una nuova routine che esegue il filtraggio delle proiezioni tramite una particolare funzione filtro.
I risultati vengono quindi testati mediante la simulazione di un problema tomografico, implementato e risolto sul processore vettoriale CRAY X-MP/48
Runtime complexity estimation for accurate solution of linear systems
No full textAn established idea for the accurate solution of linear systems is to use iterative refinement. More recently it has been shown that a modification of iterative refinement can be advantageous for high precision computation. In this work we describe a simplified complexity analysis that reliably shows when an iterative solution procedure is advantageous over a direct solution method. The analysis involves an estimate of the condition number of a matrix
and is efficient enough to be used for automatic method selection at runtime in a linear solver. We also introduce a scaling technique that is advantageous when solving for the solution and correction steps using machine precision. Numerical experiments, using an implementation developed in the Mathematica kernel, are provided to confirm the theory that has been presented
Two approaches for evaluating the period function of some Hamiltonian systems
No full textThe theory of nonlinear oscillators is an extremely active field of contemporary research, given the vastness of the phenomena modelled through nonlinear differential equations with periodic solutions. In particular, the period function associated with Hamiltonian systems has been the subject of an outstanding piece of research.
Our contribution, here, concerns oscillatory systems ruled by odd–degree polynomial restoring forces. We present two approaches for the symbolic approximation of the energy–period function: one based on asymptotic expansions of the period function, and the other through the approximation obtained using fifth–order Chebyshev polynomials of the restoring force and the consequent closed–form solution of the approximate equation. The obtained approximation
quality is verified through different comparison methods illustrated in this chapter
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