Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes

1960 ◽  
Vol 56 (4) ◽  
pp. 367-380 ◽  
Author(s):  
I. J. Good
Keyword(s):  
Stochastic Processes ◽  
Arbitrary Number ◽  
Branching Processes ◽  
Inverse Function ◽  
New Method ◽  
Independent Variables ◽  
Several Variables ◽  
Convenient Form ◽  
Enumeration Problems ◽  
Two Independent Variables

ABSTRACTA generalization to two independent variables of Lagrange's expansion of an inverse function was given by Stieltjes and proved rigorously by Poincaré. A new method of proof is given here that also provides a new and sometimes more convenient form of the generalization. The results are given for an arbitrary number of independent variables. Applications are pointed out to random branching processes, to queues with various types of customers, and to some enumeration problems.

ON THE CONVERGENCE OF DISCRETE PROCESSES WITH MULTIPLE INDEPENDENT VARIABLES

2017 ◽  
Vol 58 (3-4) ◽  
pp. 379-385
Author(s):  
N. ISHIMURA ◽  
N. YOSHIDA
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Stochastic Processes ◽  
Discrete Analogue ◽  
The Other ◽  
Standard Brownian Motion ◽  
Symmetric Random Walk ◽  
Independent Variables ◽  
Process Convergence ◽  
Two Independent Variables

We discuss discrete stochastic processes with two independent variables: one is the standard symmetric random walk, and the other is the Poisson process. Convergence of discrete stochastic processes is analysed, such that the symmetric random walk tends to the standard Brownian motion. We show that a discrete analogue of Ito’s formula converges to the corresponding continuous formula.

scholarly journals Construction Solutions of PDE in Parametric Form

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Alexandra K. Volosova ◽  
Konstantin Alexandrovich Volosov
Keyword(s):  
Exact Solutions ◽  
Unique Solution ◽  
Wide Class ◽  
New Method ◽  
Parametric Form ◽  
Algebraic Equations ◽  
Independent Variables ◽  
Linear Algebraic Equations ◽  
New Variables ◽  
Two Independent Variables

The new important property of wide class PDE was found solely by K. A. Volosov. We make an arbitrary replacement of variables. In the case of two independent variables , then it always gives the possibility of expressing all PDE second and more order as . This is a linear algebraic equations system with regards derivatives to old variables , on new variables . This system has the unique solution. In the case of three and more independent variables then it gives the possibility of expressing PDE second order as , if we do same compliment proposes. In the present paper, we suggest a new method for constructing closed formulas for exact solutions of PDE, then support on this important new property.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

Explaining Peaceful Change in Central and Eastern Europe

2020 ◽  
Author(s):  
Alexander Tabachnik ◽  
Benjamin Miller
Keyword(s):  
Eastern Europe ◽  
Central And Eastern Europe ◽  
State Capacity ◽  
The State ◽  
National Identities ◽  
Great Power ◽  
Soviet System ◽  
The Balkans ◽  
Independent Variables ◽  
Two Independent Variables

This chapter explains the process of peaceful change in Central and Eastern Europe following the demise of the Soviet system. It also explains the failure of peaceful change in the Balkans and some post-Soviet countries, such as the Ukrainian conflict in 2014. The chapter accounts for the conditions for peaceful change and for the variation between peaceful and violent change by the state-to-nation theory. The two independent variables suggested by the theory are the level of state capacity and congruence—namely the compatibility between state borders and the national identities of the countries at stake. Moreover, according to the theory, great-power engagement serves as an intervening variable and in some conditions, as explained in the chapter, may help with peaceful change.

scholarly journals New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Saima Rashid ◽  
Zareen A. Khan ◽  
S. D. Makharesh
Keyword(s):  
Time Scales ◽  
Legendre Transform ◽  
Independent Variables ◽  
Hilbert Type ◽  
Two Independent Variables ◽  
New Inequalities

AbstractIn this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

Online viewers’ choices over advertisement number and duration

2020 ◽  
Vol 14 (2) ◽  
pp. 215-238
Author(s):  
Stephen Nettelhorst ◽  
Laura Brannon ◽  
Angela Rose ◽  
Whitney Whitaker
Keyword(s):  
Exposure Time ◽  
Design Methodology ◽  
Persuasive Messages ◽  
Content Type ◽  
Independent Variables ◽  
Research Designs ◽  
Total Exposure Time ◽  
Online Simulations ◽  
Independent Variable ◽  
Two Independent Variables

Purpose The purpose of this study is to investigate online viewers’ preferences concerning the number and duration of video advertisements to watch during commercial breaks. The goal of the investigations was to assess whether online viewers preferred watching a fewer number of advertisements with longer durations or a greater number of advertisements with shorter durations. Design/methodology/approach Two studies used experimental research designs to assess viewers’ preferences regarding advertisements. These designs used two independent variables and one dependent variable. The first independent variable manipulated the type of choice options given to online viewers (e.g. one 60 s or two 30 s advertisements). The second independent variable manipulated when the choice was given to online viewers (i.e. at the beginning of the viewing experience or in the middle of the experience). The dependent variable measured viewers’ choices concerning their preferred advertisement option. Findings The results across both studies found that participants made choices that minimized total advertisement exposure time when possible. When minimizing total exposure time was not possible, participants made choices that minimized the number of exposures instead. Originality/value These investigations extend the literature on advertisement choice by examining online viewers’ preferences about the format of their advertising experience rather than the content of the persuasive messages themselves. In addition, these investigations provide value by investigating viewers’ responses to stimuli within realistic online simulations rather than abstract hypotheticals.

A resolution of the Euler operator II

1981 ◽  
Vol 89 (3) ◽  
pp. 501-510 ◽  
Author(s):  
Chehrzad Shakiban
Keyword(s):  
Calculus Of Variations ◽  
Differential Polynomials ◽  
Algebraic Proof ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Independent Variables ◽  
Several Variables ◽  
Euler Operator ◽  
Dependent Variables ◽  
Local Exactness

AbstractAn exact sequence resolving the Euler operator of the calculus of variations for partial differential polynomials in several dependent and independent variables is described. This resolution provides a solution to the ‘Inverse problem of the calculus of variations’ for systems of polynomial partial equations.That problem consists of characterizing those systems of partial differential equations which arise as the Euler-Lagrange equations of some variational principle. It can be embedded in the more general problem of finding a resolution of the Euler operator. In (3), hereafter referred to as I, a solution of this problem was given for the case of one independent and one dependent variable. Here we generalize this resolution to several independent and dependent variables simultaneously. The methods employed are similar in spirit to the algebraic techniques associated with the Gelfand-Dikii transform in I, although are considerably complicated by the appearance of several variables. In particular, a simple algebraic proof of the local exactness of a complex considered by Takens(5), Vinogradov(6), Anderson and Duchamp(1), and others appears as part of the resolution considered here.

Institutional Misconducts and Anxiety Levels Among Jailed Inmates

1980 ◽  
Vol 7 (2) ◽  
pp. 203-214 ◽  
Author(s):  
James L. Bonta ◽  
Geoff Nanckivell
Keyword(s):  
Anxiety Level ◽  
Demographic Differences ◽  
Independent Variables ◽  
History Of ◽  
Anxiety Levels ◽  
Two Independent Variables

The present investigation reports upon various aspects of incarceration within a jail setting. In the first study, variables that were associated with the occurrence of institutional misconducts were documented by comparing a group of inmates committing misconducts with inmates having no history of misconducts. A number of personal and demographic differences were observed between the groups, but no relationship between crowding and the occurrence of a misconduct was found. The second study investigated the effect of incarceration and sentencing upon the inmates' anxiety level. Sixty-one inmates formed four groups varying on two independent variables: pretest and sentence. Significant effects due to incarceration and sentencing were absent.

Sign in / Sign up

Export Citation Format

Share Document