scholarly journals On the differential equations of H. Lewy

1961 ◽  
Vol 2 (1) ◽  
pp. 11-16
Author(s):  
W. B. Smith-White
Keyword(s):  
Differential Equations ◽  
Special Form ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Image Position ◽  
Two Independent Variables

It is known that the theory of Cauchy's problem for differential equations with two independent variables is réducible to the corresponding problem for systems of quasi-linear equations. The reduction is carried further, by means of the theory of characteristics, to the case of systems of equations of the special form first considered by H. Lewy [1]. The simplest case is that of the pair of equationswhere the aii depend on z1 and z2. The problem to be considered is that of finding functions z1(x, y), z2(x, y) which satisfy (1) and which take prescribed values on x + y = 0.

scholarly journals Theoretical Prediction of Thermophysical Properties of Waste Beef Tallow Biodiesel

2020 ◽  
Author(s):  
Gokul Raghavendra Srinivasan ◽  
Ranjitha Jambulingam
Keyword(s):  
Molecular Weight ◽  
Beef Tallow ◽  
Linear Equations ◽  
Carbon Chain ◽  
Carbon Chain Length ◽  
Independent Variables ◽  
Degree Of Unsaturation ◽  
Carbon Molecules ◽  
Thermo Physical Properties ◽  
Two Independent Variables

In this present study, simple linear equations were developed for predicting the thermo-physical properties of beef tallow biodiesel by considering their molecular weight and number of double bonds as two independent variables. Interestingly, molecular weight signifies as a function of carbon chain length and number of carbon molecules in it whereas numbers of double bond signifies the degree of unsaturation.

scholarly journals Theoretical Prediction of Thermophysical Properties of Waste Beef Tallow Biodiesel

2020 ◽  
Author(s):  
Gokul Raghavendra Srinivasan ◽  
Ranjitha Jambulingam
Keyword(s):  
Molecular Weight ◽  
Beef Tallow ◽  
Linear Equations ◽  
Carbon Chain ◽  
Carbon Chain Length ◽  
Independent Variables ◽  
Degree Of Unsaturation ◽  
Carbon Molecules ◽  
Thermo Physical Properties ◽  
Two Independent Variables

In this present study, simple linear equations were developed for predicting the thermo-physical properties of beef tallow biodiesel by considering their molecular weight and number of double bonds as two independent variables. Interestingly, molecular weight signifies as a function of carbon chain length and number of carbon molecules in it whereas numbers of double bond signifies the degree of unsaturation.

scholarly journals Theoretical Prediction of Thermophysical Properties of Waste Beef Tallow Biodiesel

2019 ◽  
Author(s):  
Gokul Raghavendra Srinivasan ◽  
Ranjitha Jambulingam
Keyword(s):  
Molecular Weight ◽  
Beef Tallow ◽  
Linear Equations ◽  
Carbon Chain ◽  
Carbon Chain Length ◽  
Independent Variables ◽  
Degree Of Unsaturation ◽  
Carbon Molecules ◽  
Thermo Physical Properties ◽  
Two Independent Variables

In this present study, simple linear equations were developed for predicting the thermo-physical properties of beef tallow biodiesel by considering their molecular weight and number of double bonds as two independent variables. Interestingly, molecular weight signifies as a function of carbon chain length and number of carbon molecules in it whereas numbers of double bond signifies the degree of unsaturation.

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.

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