Explicit form of the modular equation.

1978 ◽  
Vol 1978 (299-300) ◽  
pp. 185-200 ◽  
Keyword(s):  
Explicit Form ◽  
Modular Equation

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

ENDOGENOUS GROWTH MODEL WITH HUMAN CAPITAL ON THE CIRCLE

2020 ◽  
pp. 4-9
Author(s):  
А.В. Королев
Keyword(s):  
Human Capital ◽  
Spatial Structure ◽  
Endogenous Growth ◽  
Explicit Form ◽  
Growth Model ◽  
Main Attention ◽  
Endogenous Growth Model ◽  
Central Plan ◽  
Special Case

В статье рассматривается модель эндогенного роста с человеческим капи-талом на простой пространственной структуре (окружности). Особое вни-мание уделено специальному случаю - комбинации параметров, при кото-рой удаётся получить решение задачи центрального планировщика на окружности в явном виде, что другим авторам не удавалось. In this article the endogenous growth model with human capital on the simple spatial structure (the circle) is considered. We pay main attention to a special case of a combination of parameters for which we were able to solve the central plan-ner problem on the circle in an explicit form, which other authors did not suc-ceed to do.

Determination of rate constants of redox reactions of second order from current-less potential-time curves by a simplified graphical-numerical method

1983 ◽  
Vol 48 (5) ◽  
pp. 1358-1367 ◽  
Author(s):  
Antonín Tockstein ◽  
František Skopal
Keyword(s):  
Numerical Method ◽  
Explicit Form ◽  
Rate Constant ◽  
Optimization Algorithm ◽  
Rate Constants ◽  
Redox Reactions ◽  
Second Order ◽  
Wide Region ◽  
Recurrent Formula

A method for constructing curves is proposed that are linear in a wide region and from whose slopes it is possible to determine the rate constant, if a parameter, θ, is calculated numerically from a rapidly converging recurrent formula or from its explicit form. The values of rate constants and parameter θ thus simply found are compared with those found by an optimization algorithm on a computer; the deviations do not exceed ±10%.

scholarly journals Bayesian credibility premium with GB2 copulas

2020 ◽  
Vol 8 (1) ◽  
pp. 157-171 ◽  
Author(s):  
Himchan Jeong ◽  
Emiliano A. Valdez
Keyword(s):  
Probability Measure ◽  
Explicit Form ◽  
Insurance Premium ◽  
Response Variable ◽  
Generalized Pareto ◽  
Special Case ◽  
Change Of Probability Measure

AbstractFor observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

2018 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
Jean-Claude Ndogmo
Keyword(s):  
Explicit Form ◽  
Nonlinear Equations ◽  
Variational Principles ◽  
Symmetry Algebra ◽  
First Integrals ◽  
Maximal Symmetry ◽  
General Order ◽  
Linear And Nonlinear ◽  
Variational Symmetries ◽  
Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

scholarly journals Color-kinematic duality in ABJM theory without amplitude relations

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750002
Author(s):  
Allic Sivaramakrishnan
Keyword(s):  
Gauge Group ◽  
Explicit Form ◽  
Tree Level ◽  
Abjm Theory ◽  
Gauge Freedom

We explicitly show that the Bern–Carrasco–Johansson color-kinematic duality holds at tree level through at least eight points in Aharony–Bergman–Jafferis–Maldacena theory with gauge group [Formula: see text]. At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.

PARTON RECOMBINATION IN CLASSICAL CASCADE

1990 ◽  
Vol 05 (28) ◽  
pp. 2377-2383 ◽  
Author(s):  
A. V. BATUNIN ◽  
O. P. YUSHCHENKO
Keyword(s):  
Explicit Form ◽  
Heavy Ion Collisions ◽  
Charged Particles ◽  
Heavy Ion ◽  
Considerable Decrease ◽  
High Energies ◽  
Ion Collisions ◽  
Parton Cascade ◽  
Energy Formula ◽  
The Mean

An equation for parton multiplicity in cascade with the recombination 1 → 2 ⊕ 2 → 1 is derived from a Kolmogorov-Chapman equation and solved. An evolution parameter τ of the cascade depends on the c.m. energy [Formula: see text]; an explicit form of the dependence is obtained from the condition that the mean multiplicity of charged particles in pp, [Formula: see text] collisions be reproduced. A considerable decrease in the mean multiplicity in heavy-ion collisions per pair of the colliding nucleons at high energies is predicted and compared to the parton cascade with no recombination.

scholarly journals Fine Spectra of Tridiagonal Symmetric Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Altun
Keyword(s):  
Explicit Form ◽  
Resolvent Operator ◽  
Sequence Spaces ◽  
Symmetric Matrices ◽  
Infinite Matrices ◽  
Banded Matrices ◽  
Lower Triangular ◽  
The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

Inequalities and infinite product formula for Ramanujan generalized modular equation function

2017 ◽  
Vol 46 (1) ◽  
pp. 189-200 ◽  
Author(s):  
Miao-Kun Wang ◽  
Yong-Min Li ◽  
Yu-Ming Chu
Keyword(s):  
Infinite Product ◽  
Product Formula ◽  
Modular Equation
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