scholarly journals Die ruimtelike vorm van 'n onelastiese, buigbare, geankerde kabel

1992 ◽  
Vol 11 (3) ◽  
pp. 94-101 ◽  
Author(s):  
T. P. Dreyer
Keyword(s):  
Unit Length ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Continuous Model ◽  
The Other ◽  
End Point ◽  
Non Linear ◽  
Linear Differential ◽  
The One ◽  
External Forces

Consider an inelastic, perfectly flexible cable with given external forces acting on the total length of the cable. The one end-point is fixed in the origin and the other end-point is anchored at a given point (a;b;c) in space. The resulting configuration of the cable in space can be modelled by a system of non-linear differential equations. In this article it is shown that this continuous model of the cable can always be solved in terms of an integral. In the special case of a constant (i.e. independent of the position on the cable) external force per unit length the solution is given explicitly in terms of three constants that describe the tension at the origin. These three constants are determined by the boundary values a, b and c at the other end-point, and must be calculated in general by a numerical procedure from the three resulting simultaneous non-linear equations. A few applications of this method are shown.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

scholarly journals A computational method for solving differential equations with quadratic nonlinearity by using Bernoulli polynomials

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 275-283
Author(s):  
Kubra Bicer ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Mean Value ◽  
Computational Method ◽  
Mean Value Theorem ◽  
Residual Functions ◽  
Non Linear ◽  
Linear Differential

In this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. Both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds.

scholarly journals The differential equations of ballistics

1933 ◽  
Vol 231 (694-706) ◽  
pp. 263-288
Keyword(s):  
Differential Equations ◽  
Applied Mathematics ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Pressure Index ◽  
Internal Ballistics ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The differential equations arising in most branches of applied mathematics are linear equations of the second order. Internal ballistics, which is the dynamics of the motion of the shot in a gun, requires, except with the simplest assumptions, the discussion of non-linear differential equations of the first and second orders. The writer has shown in a previous paper* how such non-linear equations arise when the pressure-index a in the rate-of-burning equation differs from unity, although only the simplified case of non-resisted motion was there considered. It is proposed in the present investigation to examine some cases of resisted motion taking the pressure-index equal to unity, to give some extensions of the previous work, and to consider, so far as is possible, the nature and the solution of the types of differential equations which arise.

scholarly journals Comparison Methods for Solving Non-Linear Sturm–Liouville Eigenvalues Problems

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1179 ◽  
Author(s):  
Kamel Al-Khaled ◽  
Ashwaq Hazaimeh
Keyword(s):  
Variational Iteration Method ◽  
The Other ◽  
Sinc Method ◽  
Linear System Of Equations ◽  
Non Linear ◽  
The Laplace Transform ◽  
Sturm Liouville ◽  
Linear Differential ◽  
Non Linear System ◽  
Adomian’S Polynomials

In this paper, we present a comparative study between Sinc–Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm–Liouville eigenvalue problem. In the Sinc method, the problem under consideration was converted from a non-linear differential equation to a non-linear system of equations, that we were able to solve it via the use of some iterative techniques, like Newton’s method. The other method under consideration is the VIM, where the VIM has been modified through the use of the Laplace transform, and another effective modification has also been made to the VIM by replacing the non-linear term in the integral equation resulting from the use of the well-known VIM with the Adomian’s polynomials. In order to explain the advantages of each method over the other, several issues have been studied, including one that has an application in the field of spectral theory. The results in solutions to these problems, which were included in tables, showed that the improved VIM is better than the Sinc method, while the Sinc method addresses some advantages over the VIM when dealing with singular problems.

Changing shape according to strength: Evidence from root allomorphy in Greek

2019 ◽  
Vol 36 (3) ◽  
pp. 553-574 ◽  
Author(s):  
Anthi Revithiadou ◽  
Giorgos Markopoulos ◽  
Vassilios Spyropoulos
Keyword(s):  
The Other ◽  
Activation Level ◽  
Vocabulary Item ◽  
Non Linear ◽  
The One ◽  
Surface Realization

Abstract In this article we examine patterns of root allomorphy in Greek that involve vowel alternations and propose a Generalized Non-linear Affixation (Bermúdez-Otero 2012) analysis according to which these alternations result from the competition between segments that belong, on the one hand, to the vocabulary items of roots and, on the other, to the exponents of functional heads (Voice/Aspect, n). More specifically, we claim that phonological entities have a gradient degree of presence in a structure, that is, are specified with a certain activation strength value underlyingly (Smolensky and Goldrick 2016). As a result, the surface realization of roots is determined by the relevant activation level of the exponents of functional heads they are eventually combined with. From all available exponents, the one that optimally complements the strength value of the vocabulary item of a given root will eventually surface. Our analysis is shown to be theoretically advantageous because it develops a strictly phonological account of allomorphy and, moreover, it captures the attested generalizations without resorting to extensive stem/span listing or to the application of phonologically unrestricted readjustment rules.

Hegel as a Theorist of Secularization

2013 ◽  
Vol 34 (2) ◽  
pp. 223-244
Author(s):  
Espen Hammer
Keyword(s):  
Philosophy Of Religion ◽  
The State ◽  
The Other ◽  
The Political ◽  
Adequate Account ◽  
Religious Development ◽  
End Point ◽  
Religious Thinking ◽  
The Absolute ◽  
The One

Hegel's philosophy of religion is characterized by what seems to be a deep tension. On the one hand, Hegel claims to be a Christian thinker, viewing religion, and in particular Christianity, as a manifestation of the absolute. On the other hand, however, he seems to view modernity as largely secular, devoid of authoritative claims to transcendence. Modernity is secular in the political sense of requiring the state to be neutral when it comes to matters of religion. However, it is also secular in the sense of there being no recourse to authoritative representations of a transcendent God. Drawing on Charles Taylor's view of secularization, the article focuses on the second strand of his religious thinking, exploring how Hegel can be thought of as a theorist of secularization. It is claimed that his dialectic of religious development describes a process of secularization. Ultimately, Hegel's system offers a view of the absolute as immanent, suggesting that an adequate account of religion will necessarily have to accept secularization as the end-point of spirit's development. This is how the tension between religion and secularization can be resolved.

scholarly journals Managerial Ownership, Board of Directors, Equity-based Compensation and Firm Performance: A Comparative Study between France and the United States

2017 ◽  
Vol 8 (1) ◽  
pp. 78-95 ◽  
Author(s):  
Mehdi Bouras ◽  
Mohamed Imen Gallali
Keyword(s):  
Firm Performance ◽  
Comparative Study ◽  
Board Of Directors ◽  
Ownership Structure ◽  
Corporate Performance ◽  
The Other ◽  
Managerial Ownership ◽  
Managerial Entrenchment ◽  
Non Linear ◽  
The One

Abstract The aim of this comparative study between the French and American markets, characterized by a different ownership structure is to examine the relationship between managerial ownership, the board of directors, the equity-based compensation and corporate performance. Regardless of the selected sample, we found on the one hand, a non-linear relationship between managerial ownership and firm performance and on the other hand, in the case of managerial entrenchment board of directors is a substitute for managerial ownership to solve the agency problem. In addition, stock-based compensation is non-linear function with managerial ownership, contrary to previous studies that assume a monotonous or non-significant relationship. The hypothesis of endogeneity is valid only in the American case. This result leads us to believe that the U.S. CEO has a preference to hold a large percentage of shares of firms that generate a good performance to neutralize capital market monitoring. Our study is exclusive in terms of the effect of managerial ownership on corporate performance in terms of comparison between two markets, characterized by a difference in ownership structure. We determine the impact of equity compensation on the one hand, the managerial ownership where all the studies assume either a monotone or neutral relationship between these two variables and on the other hand, the effect of board in the alignment or managerial entrenchment cases.

Dependence of stress-optical coefficients on the mechanical and optical properties of polymers

1973 ◽  
Vol 8 (4) ◽  
pp. 267-276 ◽  
Author(s):  
P S Theocaris
Keyword(s):  
Mechanical Properties ◽  
Refractive Index ◽  
Optical Properties ◽  
Internal Structure ◽  
The Other ◽  
Linear Region ◽  
Non Linear ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Behaviour ◽  
The One

The internal structure of the stress-optical coefficients, as they are related to various direct interferometric methods, has been analysed and the nature of their components studied. It is shown that the stress-optical coefficients are composed of two parts. The one part depends on the variation of the mechanical properties; the other is related to the variation of the refractive index of the polymer. The influence of the mechanical properties is considerable and comparable to the influence of the optical properties. The study of the mechanical and optical contributions to the values of the stress-optical coefficients included not only the linear, but also the non-linear viscoelastic behaviour of the polymers. It is concluded that the corresponding limits of linearity of these coefficients do not coincide. Furthermore, the influence of the mechanical properties on the stress-optical coefficients is increasing relatively to the influence of the optical properties in the non-linear region.

scholarly journals The motion of a stream of finite depth past a body

1915 ◽  
Vol 92 (636) ◽  
pp. 107-121
Keyword(s):  
Circular Cylinder ◽  
Ideal Fluid ◽  
Finite Depth ◽  
Resultant Force ◽  
The Other ◽  
Potential Motion ◽  
The One ◽  
External Forces

When a circular cylinder moves uniformly in an ideal fluid (i.e. frictionless and incompressible) at rest at infinity, the resultant force acting on it is zero, it no external forces act. This is however, only true when the motion is the usual potential motion. Supposing that in addition to the potential stream produced by the motion of the cylinder a circulation around it be considered, the velocity of the fluid is incresased on the one side, an decreased on the other, and this produces a force acting on the cylinder perpendicular to the direction of motion.

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