摘要:

This paper presents a mathematical approach, based on the spectral analysis and Fourier transformation to derive the principle of uncertainty. The approach presented in this paper is found to be different from those appeared so far in the literature. It shows that the uncertainty principle is, in fact, an aliasing phenomenon and emerges merely from the quantization effect. The concept of ‘certainty’ is also introduced and discussed. It is shown that observation rates higher than the speed of a particle are the only possible approaches to the absence of uncertainty in the measurements of the observable quantities ofthe entity. This would imply that for particles travelling at the velocity of light, data acquisition rates higher than the speed of light should be required. Therefore, the uncertainty principle is related to the theory of relativity and exists so far as the velocity of light poses as an upperlimit universal constant. Otherwise, it would render to ‘certainty’ if our observation abilities could escalade at rates above the speed of light. This is to say that the uncertainty can be an inherent intrinsic property grounded in the universal speed limitation, which also subdues our observation abilities too; else demanding challenges on Einstein’s definition of simultaneity, and hence its consequences, has to be expected.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700260

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Let a system of the ordinary non-linear differential equations of the second order be a system of the linear algebraic equations with respect to the second derivatives. The set S where the principal determinant vanishes we call the singular set. We suppose that the system is defined on the set Γ and the first integral can be continuously prolongated on Γ ∪ S. The prolongation of the integral curve from Γ on Γ ∪ S, compatible with the prolongation of the first integral, is defined and studied in the case of mes S = 0 with respect to the Lebesgue measure.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700261

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this work, we shall introduce as well as study the problem of selective invariance and attractivity of sets given by multi-valued differential equations. Not as usual, from the control theory point of view, but here, we discuss it from the differential games view point from which this problem can be interpreted as a qualitative problem. One of our results can be applied to the game of pursuit and evasion in some formulations.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700262

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We will prove a theorem of existence and uniqueness for the quasi-static problem in linear viscoelasticity, with boundary conditions of Dirichlet, in which the function of Boltzmann Ġ is not summable and without the use of the hypothesis of the reversibility of time.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700263

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we are going to discuss some properties of euclidean m-simplices arising in a particular class of transformations. Furthermore a physical application to the epitaxial growth of crystals is given.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700264

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In the complex analysis the singular integral of Cauchy-type at the point of the curve of integration can be presented as a sum of the logarithmic part and of the rest F. As a rule the logarithmic part is defined in the Cauchy-sense of "value principal" (v.p.) and F is defined as a common integral (see Ref. [1, 4]) In this paper we define F also in the sense of v.p. For this definition the sufficient conditions of the continuous prolongation of F at the point of the curve of integration and on the whole curve are found. As consequences the Sokhotski formulas are conserved. The generalisation of the continuous prolongation on two complex variables is also possible [5]. Using the properties of this continuous prolongation we show that with respect to the supnorm. the space of the integrals of Cauchy type with the tmiformly bounded length of the curves is a complete space. if we limit us by the parametric curves of integration with the bounded second derivative.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700265

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper, a production lot size inventory model for deteriorating items with inventory-level dependent production and demand rate is developed. The production rate and demand both are dependent on the instantaneously level, and an alternative optimization technique is presented to derive an optimal production policy. The method is illustrated by a numerical example and a sensitivity analysis of the optimal solution with respect to parameters of the system is also carried out.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700266

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A zero-penalty stochastic control model and a new control policy for smuggling is proposed in which we let PN(b - c/t) be the probability that N (N≥1) units of a necessary similar product smuggle in a state at time t (t > 0) from place outside the state. We assume that in the time interval (t, t + dt) the probability for a unit of the product smuggle in from outside place is (b - c)dt where (b - c) > 0, is called the force of smuggling. The quantity PN(b - c/t) is called density of smuggling that obtained from the model by using smuggler as generator of smuggling. The control policy for smuggling is obtained from the density. The density of smuggling may also be used to make smuggling highly less as well as less profitable. A numerical example has shown that the chance for large-scale smuggling declines with the decline of force that causes smuggling.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700267

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

For the uniform partition, we prove that the second derivative at the point xiof the cubic spline (denoted by Mi) and the second central finite difference of the function u(xi) (denoted by δ2u(xi)/h2) approximate u"(xi) on the opposite side. By using this property, we introduce the number Cito be the average of Miand δ2u(xi)/h2and we can conclude that Cigives a better approximation to u"(xi). Finally, we use Ciin the numerical solution of second order PDEs. Numerical examples are given.

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700268

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0972-0502    

DOI:10.1080/09720502.1999.10700269

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor