Search results for "Trigonometri"
showing 10 items of 38 documents
Comments on “Mean velocity and turbulent characteristics of flow over half-cycle cosine sharp-crested weirs” by Salehi S., Esmaili K., Azimi A.H.
2019
Abstract In this paper the stage-discharge equation of a half-cycle cosine weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationships are estimated using the results of the experimental runs by Salehi et al..
On Carlson"s and Shafer"s inequalities
2014
In this paper the authors re ne the Carlson"s inequalities for inverse cosine function, and the Shafer"s inequalities for inverse tangent function.
On some inequalities for the identric, logarithmic and related means
2015
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
Relevansen av trigonometri : En studie i to deler på relevansen av trigonometri for elever på videregående skole
2017
Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2017 The topic of this master’s thesis is the relevance of mathematics, especially the relevance of trigonometry. Many students ask the question “why do I need to learn about this”. The aim of this study was to give the students an answer to this question. In the research literature, I found that this question has to do with relevance, and that relevance is a connection between people, an activity and future goals. In particular, one needs to question: relevance of what? relevance according to whom? relevance for whom? And relevance to what end? The empirical part of my research consisted of two studies. In Study 1 the purpose …
Spectral Approach to Equivalent Statistical Quadratization and Cubicization Methods for Nonlinear Oscillators
2003
Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian…
Millimeter-Scale and Billion-Atom Reactive Force Field Simulation on Sunway Taihulight
2020
Large-scale molecular dynamics (MD) simulations on supercomputers play an increasingly important role in many research areas. With the capability of simulating charge equilibration (QEq), bonds and so on, Reactive force field (ReaxFF) enables the precise simulation of chemical reactions. Compared to the first principle molecular dynamics (FPMD), ReaxFF has far lower requirements on computational resources so that it can achieve higher efficiencies for large-scale simulations. In this article, we present our efforts on scaling ReaxFF on the Sunway TaihuLight Supercomputer (TaihuLight). We have carefully redesigned the force analysis and neighbor list building steps. By applying fine-grained …
Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique
2003
This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation o…
Indefinite integrals of some special functions from a new method
2015
A substantial number of indefinite integrals of special functions are presented, which have been obtained using a new method presented in a companion paper [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. The method was originally derived from the Euler–Lagrange equations but an elementary proof is also presented in [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. Sample results are presented here for Bessel functions, Airy functions and hypergeometric functions. More extensive results are given for th…
Pseudo-Abelian integrals along Darboux cycles
2008
We study polynomial perturbations of integrable, non-Hamiltonian system with first integral of Darboux-type with positive exponents. We assume that the unperturbed system admits a period annulus. The linear part of the Poincare return map is given by pseudo-Abelian integrals. In this paper we investigate analytic properties of these integrals. We prove that iterated variations of these integrals vanish identically. Using this relation we prove that the number of zeros of these integrals is locally uniformly bounded under generic hypothesis. This is a generic analog of the Varchenko-Khovanskii theorem for pseudo-Abelian integrals. Finally, under some arithmetic properties of exponents, the p…
Eine Neue Rechnung zur Röntgenkleinwinkelstreuung an Fadenmolekulen. Die Ermittlung der Segmentgestalt
1967
The scattering function of chain molecules in the x-ray small-angle range depends on the shape of the segments. For instance, one obtains quite different scattering curves from solutions of isotactic and syndiotactic poly(methyl methacrylate) (PMMA) in the same solvent. From several models of statistically coiled polymer chains, the scattering functions were calculated with the aid of the Monte Carlo method. Again, a considerable difference between the functions obtained is observed. If the curvature of a thread varies statistically from one point to another, the mean curvature can be determined from the scattering function. A suitable measure for the mean curvature is the persistence lengt…