The numerical solution of hyperbolic systems of partial differential equations in three independent variables

1960 ◽  
Vol 255 (1281) ◽  
pp. 232-252 ◽  
Keyword(s):  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Original Method ◽  
Plane Motion ◽  
Step Size ◽  
Independent Variables ◽  
Step Procedure ◽  
Dependent Variables ◽  
Derivatives Of ◽  
Unknown Point

An original method of integration is described for quasi-linear hyperbolic equations in three independent variables. The solution is constructed by means of a step-by-step procedure, employing difference relations along four bicharacteristics and one time-like ordinary curve through each point. From these difference relations the derivatives of the dependent variables at the unknown point are eliminated. The solution at any point can then be com­puted, with an error proportional to the step size cubed, without referring to conditions outside its domain of dependence. The application of the method to the systems of equations governing unsteady plane motion and steady supersonic flow of an inviscid, non-conducting fluid is discussed in detail. As an example of the use of the method, the flow over a particular delta-shaped body has been computed.

scholarly journals Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
F. M. Mahomed ◽  
A. Qadir ◽  
A. Ramnarain
Keyword(s):  
Hyperbolic Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Integration Theory ◽  
Equivalence Transformations ◽  
Complex Scalar ◽  
Hyperbolic Pdes ◽  
Independent Variables ◽  
Dependent Variables ◽  
Two Independent Variables ◽  
Linear Hyperbolic Equations

In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs) in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE) into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revisit semi-invariants under equivalence transformations of the dependent variables for systems of two linear hyperbolic PDEs in two independent variables when such systems correspond to scalar complex linear hyperbolic equations in two independent variables, using the above-mentioned splitting procedure. The semi-invariants under linear changes of the dependent variables deduced for this class of hyperbolic linear systems correspond to the complex semi-invariants of the complex scalar linear hyperbolic equation. We show thatthe adjoint factorization corresponds precisely to the complex splitting. We also study the reductions and the inverse problem when such systems of two linear hyperbolic PDEs arise from a linear complex hyperbolic PDE. Examples are given to show the application of this approach.

Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems

1982 ◽  
Vol 104 (1) ◽  
pp. 247-255 ◽  
Author(s):  
R. A. Wehage ◽  
E. J. Haug
Keyword(s):  
Differential Equations ◽  
Gaussian Elimination ◽  
Equations Of Motion ◽  
Influence Coefficient ◽  
Variable Order ◽  
Total System ◽  
Step Size ◽  
Integration Algorithm ◽  
Independent Variables ◽  
Dependent Variables

This paper presents a computer-based method for formulation and efficient solution of nonlinear, constrained differential equations of motion for mechanical systems. Nonlinear holonomic constraint equations and differential equations of motion are written in terms of a maximal set of Cartesian generalized coordinates, to facilitate the general formulation of constraints and forcing functions. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent variables, and constructs an influence coefficient matix relating variations in dependent and independent variables. This information is employed to numerically construct a reduced system of differential equations of motion whose solution yields the total system dynamic response. A numerical integration algorithm with positive-error control, employing a predictor-corrector algorithm with variable order and step size, is developed that integrates for only the independent variables, yet effectively determines dependent variables. Numerical results are presented for planar motion of two tracked vehicular systems with 13 and 24 degrees of freedom. Computational efficiency of the algorithm is shown to be an order of magnitude better than previously employed algorithms.

ANALISA PENGARUH IKLIM ORGANISASI DAN KOMPETENSI TERHADAP KINERJA PEGAWAI PT HUTAMA KARYA

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Erik Wardhana, MM.
Keyword(s):  
Organizational Climate ◽  
Employee Performance ◽  
Sampling Technique ◽  
Simple Random Sampling ◽  
Free Variable ◽  
Independent Variables ◽  
Dependent Variables ◽  
Correlational Approach ◽  
Survey Research Methods ◽  
The Relationship

This study entitled "Analysis of Effect of Climate Organization and Competence Againt Employee PT. Hutama Karya ". The purpose of this study was to obtain information on the relationship between the free variable that organizational climate (X1) and competence (X2) with the dependent variable is employee performance (Y), either partially or simultaneously, This study used survey research methods with the correlational approach and predictive, which aims for the relationship and influence between independent and dependent variables. The sampling technique can be done randomly (simple random sampling) of 852 employees, which is considered to resprentatif is 89 people. And to solve problems, to analyze and examine the relationship and influence between the independent variables on the dependent variable used models kausalistik through regression analysis with SPSS 14.0

PENGARUH PERSONAL BACKGROUND, POLITICAL BACKGROUND DAN PENGEATAHUAN DEWAN TENTANG ANGGARAN TERHADAP PERAN DPRD DALAM PENGAWASAN KEUANGAN DAERAH

2008 ◽  
Author(s):  
Yesi Mutia Basri ◽  
Rosliana Rosliana
Keyword(s):  
Multivariate Analysis ◽  
Significant Influence ◽  
Political Activity ◽  
Primary Data ◽  
Financial Control ◽  
Independent Variables ◽  
Dependent Variables ◽  
Political Background ◽  
Activity Dependent

This research aim to examine the influence of personal background, political background, and council budget knowledge towards the role of DPRD on region financial control. This research is motivated by the fact that individual background will effect to individual behavior on political activity. Dependent variables in this research are personal background, political background, and council budges knowledge towards the role of DPRD on region financial control Independent variables are the role of DPRD on region financial control in planning, implementing, and responsibility steps. The data in this research consist of primary data that taken from questionnaires distributed directly to respondents. The collected are from 34 Respondents that members of DPRD at Pekanbaru. Hypothesis of this research are examine by using Multivariate Analysis of Variances (MANOVA). The result of this research HI personal background political background and budget knowledge have significant influence toward the role of DPRD on region financial control in planning steps.H2 personal background, politico I background and budget knowledge have no significant influence toward the role of DPRD on region financial control in Implementing steps. H3 personal background political background and budget knowledge have no significant influence toward the role of DPRD on region financial control in Controlling steps.

scholarly journals Weight Feedback-Based Harmonic MDG-Ensemble Model for Prediction of Traffic Accident Severity

2021 ◽  
Vol 11 (11) ◽  
pp. 5072
Author(s):  
Byung-Kook Koo ◽  
Ji-Won Baek ◽  
Kyung-Yong Chung
Keyword(s):  
Traffic Accidents ◽  
Average Rate ◽  
Modern Society ◽  
Rate Of Change ◽  
Weighted Voting ◽  
Independent Variables ◽  
Dependent Variables ◽  
Accident Severity ◽  
Harmonic Average ◽  
Bagging Method

Traffic accidents are emerging as a serious social problem in modern society but if the severity of an accident is quickly grasped, countermeasures can be organized efficiently. To solve this problem, the method proposed in this paper derives the MDG (Mean Decrease Gini) coefficient between variables to assess the severity of traffic accidents. Single models are designed to use coefficient, independent variables to determine and predict accident severity. The generated single models are fused using a weighted-voting-based bagging method ensemble to consider various characteristics and avoid overfitting. The variables used for predicting accidents are classified as dependent or independent and the variables that affect the severity of traffic accidents are predicted using the characteristics of causal relationships. Independent variables are classified as categorical and numerical variables. For this reason, a problem arises when the variation among dependent variables is imbalanced. Therefore, a harmonic average is applied to the weights to maintain the variables’ balance and determine the average rate of change. Through this, it is possible to establish objective criteria for determining the severity of traffic accidents, thereby improving reliability.

scholarly journals A Student’s Guide to the Classification and Operationalization of Variables in the Conceptualization and Design of a Clinical Study: Part 1

2021 ◽  
Vol 43 (2) ◽  
pp. 177-179 ◽  
Author(s):  
Chittaranjan Andrade
Keyword(s):  
Clinical Study ◽  
Significant Relationship ◽  
Research Experience ◽  
Process Variables ◽  
Know How ◽  
Independent Variables ◽  
Cause And Effect ◽  
Confounding Variables ◽  
Dependent Variables ◽  
The Relationship

Students without prior research experience may not know how to conceptualize and design a study. This article explains how an understanding of the classification and operationalization of variables is the key to the process. Variables describe aspects of the sample that is under study; they are so called because they vary in value from subject to subject in the sample. Variables may be independent or dependent. Independent variables influence the value of other variables; dependent variables are influenced in value by other variables. A hypothesis states an expected relationship between variables. A significant relationship between an independent and dependent variable does not prove cause and effect; the relationship may partly or wholly be explained by one or more confounding variables. Variables need to be operationalized; that is, defined in a way that permits their accurate measurement. These and other concepts are explained with the help of clinically relevant examples.

scholarly journals The Effect of Older Adults’ Volunteering on Relational Satisfaction

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 408-408
Author(s):  
Meeryoung Kim
Keyword(s):  
Older Adults ◽  
Life Satisfaction ◽  
Target Population ◽  
Demographic Variables ◽  
Retirement Age ◽  
Relational Satisfaction ◽  
Human Relations ◽  
Independent Variables ◽  
Dependent Variables ◽  
Overall Life Satisfaction

Abstract Longevity is increasing in what is called the centenarian society. However, the average retirement age of Korea is the lowest among OECD countries. Because of increasing longevity, older adults need activities after retirement. Volunteering can be a substitute that allows Korean older adults to find a social identity. This study examined older adults’ volunteering and how many kinds of volunteering affected relational satisfaction differently. This study used the 6th additional wave of the Korean Retirement and Income Study (2016). The target population of this study was ages over 60 and the sample size was 280. For data analysis, multiple regressions were used. Demographic variables were controlled. As for independent variables, reasons for volunteering whether they were motivated for self or for others were used. For dependent variables, relational satisfaction, such as family, human relation and overall life satisfaction was used. Volunteers’ health is an important factor for relational satisfaction. If volunteering was self-motivated, satisfaction of both family and human relations were negatively affected. Reason for others also affected satisfaction of family and human relations negatively. Volunteering initiated by others increased satisfaction of family and human relations. Doing more than one kind of volunteering affected both satisfaction of family and human relations. For overall life satisfaction, the effect of volunteering for oneself was lower than other reasons. These findings implied that reasons for volunteering affected relational satisfaction differently. In addition, the activities of volunteering, such as taking part in one or more had different effects.

Control of Volumetric Properties of Hot-Mix Asphalt by Field Management

1996 ◽  
Vol 1543 (1) ◽  
pp. 125-131
Author(s):  
Prithvi S. Kandhal ◽  
Kee Y. Foo ◽  
John A. D'Angelo
Keyword(s):  
Hot Mix Asphalt ◽  
Linear Regression Analysis ◽  
Volumetric Properties ◽  
Production Test ◽  
Independent Variables ◽  
Dependent Variables ◽  
Preceding Work ◽  
Multiple Variable ◽  
Asphalt Content ◽  
Variable Analysis

Significant differences in the volumetric properties of laboratory-designed and plant-produced hot-mix asphalt (HMA) generally exist as demonstrated by FHWA Demonstration Project No. 74. The volumetric properties include voids in the mineral aggregate (VMA) and voids in the total mix (VTM). Guidelines for HMA contractors are needed to reconcile these differences and maintain control of volumetric properties during HMA production. The HMA mix design and field production test data (such as asphalt content, gradation, and volumetric properties) from 24 FHWA demonstration projects were entered into a data base and statistically analyzed. The objective was to identify and, if possible, quantify the independent variables (such as asphalt content and the percentages of material passing the No. 200 and other sieves) that significantly affect dependent variables VMA and VTM. The statistical analysis methods consisted of correlation analysis, stepwise multiple-variable analysis, and linear-regression analysis. On the basis of preceding work, guidelines have been developed for HMA contractors to reconcile the differences between the volumetric properties of the job mix formula and the produced HMA mix.

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.

scholarly journals Changes in Incisor Third-Order Inclination Resulting from Vertical Variation in Lingual Bracket Placement

2009 ◽  
Vol 79 (4) ◽  
pp. 747-754 ◽  
Author(s):  
Michael Knösel ◽  
Klaus Jung ◽  
Liliam Gripp-Rudolph ◽  
Thomas Attin ◽  
Rengin Attin ◽  
...  
Keyword(s):  
Null Hypothesis ◽  
Interindividual Variation ◽  
Occlusal Plane ◽  
Third Order ◽  
Vertical Variation ◽  
Independent Variables ◽  
The Third ◽  
Dependent Variables ◽  
Incisor Inclination ◽  
The Impact

Abstract Objective: To test the null hypothesis that third-order measurements are not correlated to lingual incisor features seen on radiographs. Material and Methods: The lateral headfilms of 38 untreated, norm-occlusion subjects without incisor abrasions or restorations were used for third-order measurements of upper and lower central incisors and assessment of the inclination of four sites suitable for lingual bracket placement with reference to the occlusal plane perpendicular. Lingual sections were determined by the tangents at the incisal fossa (S1), at the transition plateau between incisal fossa and the cingulum (S2), by a constructed line reaching from the incisal tip to the cingulum (S3), and by a tangent at the cingulum convexity (S4). Third-order angles were also assessed on corresponding dental casts using an incisor inclination gauge. Regression analysis was performed using the third-order measurements of both methods as the dependent variables and the inclination of the lingual enamel sections (S1, S2, S3, S4) as the independent variables. Results: The null hypothesis was rejected. For the most common bracket application sites located on the lingual shovel (S1 and S2), third-order inclination changes of 0.4–0.7 degrees are expected for each degree of change in the inclination of the lingual surface. The impact of bracket placement errors on third-order angulation is similar between sections S1 and S2 and the cingulum convexity (S4). Section S3 proved to be least affected by interindividual variation. Conclusion: The third-order measurements are correlated to lingual incisor features. Accordingly, third-order changes resulting from variation in lingual bracket placement can be individually predicted from radiographic assessments.

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