Age-period-cohort analysis in the 1870s: Diagrams, stereograms, and the basic differential equation

2011 ◽  
Vol 39 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Niels Keiding
Keyword(s):  
Differential Equation ◽  
Cohort Analysis ◽  
Basic Differential Equation

Das effektive Trägheitsmoment im quantenmechanischen Dreikörperproblem

1970 ◽  
Vol 25 (3) ◽  
pp. 317-321 ◽  
Author(s):  
H. Letz ◽  
H. Ruder ◽  
H. Volz
Keyword(s):  
Differential Equation ◽  
Rotational Motion ◽  
Body Problem ◽  
Exact Expression ◽  
Frame Of Reference ◽  
Wave Functions ◽  
Effective Moment ◽  
Variational Calculations ◽  
Basic Differential Equation ◽  
Effective Moment Of Inertia

The method of "specific decoupling", as described in two earlier papers, is applied to special forms of wave functions of the 3-body-problem. The internal frame of reference, connected with a collective rotational motion of the system, is determined by solution of the basic differential equation. An exact expression for the effective moment of inertia is given and evaluated. The results confirm the validity of former variational calculations

Diffusion Dialysis of Sulfuric Acid in a Batch Cell

1994 ◽  
Vol 59 (9) ◽  
pp. 1971-1982 ◽  
Author(s):  
Zdeněk Palatý ◽  
Alena Žáková
Keyword(s):  
Differential Equation ◽  
Sulfuric Acid ◽  
Sulfuric Acid Concentration ◽  
Geometrical Arrangement ◽  
Modified Method ◽  
Basic Differential Equation ◽  
Diffusion Dialysis ◽  
The Given ◽  
Dialysis Cell ◽  
Batch Cell

The paper deals with the diffusion dialysis of sulfuric acid into water in a batch cell with a Neosepta-AFN anionselective membrane. The transport of sulfuric acid through the membrane has been quantified with respect to the dissociation of the acid by the dialysis coefficients for HSO4- and SO42- ions. These coefficients have been determined by numerical integration of the basic differential equation describing the time dependence of sulfuric acid concentration in the dialysis cell with subsequent optimization of dialysis coefficients. Moreover, the membrane permeability coefficients for HSO4- and SO42- ions and nondissociated sulfuric acid have been determined by the modified method of the Wilson diagram using the data about mass transfer in liquid for the given geometrical arrangement of cell.

scholarly journals Calculating university education model based on finite element fractional differential equations and macro-control analysis

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Caijuan Li ◽  
Nawaf Alhebaishi ◽  
Mohammed Alaa Alhamami
Keyword(s):  
Differential Equation ◽  
College Education ◽  
University Education ◽  
Control Analysis ◽  
Basic Model ◽  
Theory Of Education ◽  
Differential Equation Models ◽  
Basic Differential Equation ◽  
Fractional Differential ◽  
Education Model

Abstract Firstly, based on the charging theory of ‘education cost-sharing,’ under appropriate assumptions, two basic differential equation models are proposed to describe the problem of college education charges; secondly, through qualitative analysis of the basic model, it is concluded that colleges and universities maintain or impose several conditions for stabilising its education fees; finally, through the analysis of two basic models in three unique models under three situations, some new conclusions and suggestions on the macro-control of college education fees and enrolment scale are given. Also, three extended differential equation models are proposed.

scholarly journals Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
H. Panahi ◽  
M. Baradaran
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Representation Theory ◽  
Exact Solutions ◽  
Lie Algebra ◽  
Algebraic Approach ◽  
Spherically Symmetric ◽  
Exact Solvability ◽  
Enveloping Algebra ◽  
Basic Differential Equation

We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra ofsl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory ofsl(2)Lie algebra.

G M (1,1) Optimization Model Re-Optimization

2012 ◽  
Vol 538-541 ◽  
pp. 2543-2547
Author(s):  
Yao Chen
Keyword(s):  
Differential Equation ◽  
Optimization Model ◽  
High Growth ◽  
Solution Algorithm ◽  
Grey Model ◽  
Practical Application ◽  
Simulation Accuracy ◽  
Growth Series ◽  
Gray Prediction ◽  
Basic Differential Equation

On the base of the basic differential equation, a new GM (1,1) model applying to non-homogenous index series was established by optimizing the background of original differential equation. Meanwhile, solution algorithm and efficiency of the optimization model was presented and verified in the paper respectively. The results showed that this nonlinear discrete gray prediction model significantly improves the simulation accuracy and is suitable for the non-homogeneous high-growth series. Therefore, our research has certain theory significance and the practical application value for simulation of grey model.

Analisis Persepsi Mahasiswa Terhadap Modul Persamaan Diferensial Dasar

2019 ◽  
Vol 2 ◽  
Author(s):  
Sudiyah Anawati ◽  
Idha Isnaningrum
Keyword(s):  
Differential Equation ◽  
Student Perceptions ◽  
Random Sampling ◽  
Sampling Method ◽  
Sampling Technique ◽  
Data Interpretation ◽  
Study Groups ◽  
Research Data ◽  
Basic Differential Equation ◽  
The Subject

Abstract. The purpose of this study was to find and analyze empirically about student perceptions of basic differential equation modules. The subject of this study was students of mathematics education programs who took the subject of basic differential equations. A total of 60 study samples were divided into two study groups of 30 students each. The sampling technique in this study was a non random sampling technique, namely the pusposive sampling method. Sampling is tailored to the purpose of the study and based on the subjective judgment of the researcher and on certain characteristics that are considered to have relevance to the characteristics of the population that were previously known with certain considerations. Data collection techniques were used through the dissemination of student perceptions instruments towards the Basic Differential Equation module. The collection of research data using a questionnaire. Judging from the recapitulation of the results of data interpretation, it can be concluded that the results of the study are categorized as Good. From the recapitulation of the results of the data obtained there are 8% very good categories, 60% good categories, 32% enough categories, 0% categorized as poor, and 0% categorized as very opor. Keywords: Perception, Students, Differential Equation Modules

scholarly journals Basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas

2005 ◽  
Vol 54 (12) ◽  
pp. 5534
Author(s):  
Bian Bao-Min ◽  
He An-Zhi ◽  
Li Zhen-Hua ◽  
Yang Ling ◽  
Zhang Ping ◽  
...  
Keyword(s):  
Differential Equation ◽  
Ideal Gas ◽  
Nonsteady Flow ◽  
One Dimensional ◽  
Basic Differential Equation ◽  
Self Similar

scholarly journals Differential Equation Models for Education Charges of Universities in China and the Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Minhang Liu ◽  
Hua Su
Keyword(s):  
Higher Education ◽  
Differential Equation ◽  
Qualitative Analysis ◽  
University Education ◽  
Social Concern ◽  
Differential Equation Models ◽  
Basic Differential Equation ◽  
State Investment ◽  
The Cost ◽  
The University

In recent years, with the expansion of university enrollment in China, the cost of running a school is getting higher and higher. Under the circumstance of insufficient state investment in higher education, the education charge paid by students has become an important source of the university income. It has become a hot topic of social concern to formulate a reasonable charging model to enable more students to enter higher education institutions. In this paper, we mainly put forward the basic differential equation models describing the problem of higher education charges in China. Through the qualitative analysis of these two basic models, we draw several conditions for universities to maintain or stabilize their education charges and give some suggestions on macrocontrol of university education charges in China.

Buckling Under Locally Hydrostatic Pressure

1946 ◽  
Vol 13 (3) ◽  
pp. A198-A200
Author(s):  
G. H. Handelman
Keyword(s):  
Differential Equation ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Pressure Distribution ◽  
Buckling Loads ◽  
The Third ◽  
Basic Assumptions ◽  
Basic Differential Equation ◽  
Discrete Values ◽  
Definition Of

Abstract The instability of a simple pin-supported beam when subject to a locally hydrostatic pressure distribution, the intensity of which is a function of distance along the beam only, is discussed in this paper. In particular, the pressure is assumed to follow a polynomial law given by Equation [1]. The problem, basic assumptions, and precise definition of locally hydrostatic pressure are stated in the first section of the paper. The second section contains a discussion of the equations of equilibrium from which the basic differential equation is derived. The solutions of this differential equation satisfy the boundary conditions only for certain discrete values of the parameters involved, and these values in turn define the buckling loads. In the third section the buckling loads are tabulated for several cases in comparison with the buckling loads for the same beam subject only to an end thrust. The appendix contains a mathematical discussion of the solution of the basic differential equation and a derivation of the formula for the buckling loads.

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