Search results for "Differential calculus"

Multi-State System in human reliability analysis

2009

Application of mathematical model of Multi-State System for human reliability analysis is considered in the paper. This paper describes new method for estimation of changes of more than one component states and they influence to Multi-State System reliability by Dynamic Reliability Indices. The Multi-State System failure is considered depending on decrease of some system component efficiency and the Multi-State System repair is declared depending on replacement of some failed components. The mathematical approach of Logical Differential Calculus is used for analysis of the Multi-State System reliability change that is caused by modifications of some system components states.

An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds

2003

For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…

The expansion $\star$ mod $\bar{o}(\hbar^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization

2019

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 w…

A technique for the dynamic identification of civil systems

2012

A statistical moments based approach for the dynamic identification of civil structures

2012

In recent years, interest in developing identification techniques that are valid in the case of unmeasured input has increased. In this field some interesting parametric approaches have been proposed. Nevertheless, the improvement of the available techniques or the formulation of new techniques is desirable. In this paper a time domain dynamic identification approach based on the statistical moments of the response of civil structures under base random excitations is discussed. Two types of models are used: the classically damped models characterized by mass proportional damping and the so-called “potential models” which are non linear in damping and stiffness. By applying the Itô different…

On Limiting Fréchet ε-Subdifferentials

1998

This paper presents an e-sub differential calculus for nonconvex and nonsmooth functions. We extend the previous work by Jofre et all to the case where the functions are lower semicontinuous instead of locally Lipschitz.

What is Differential Stochastic Calculus?

1999

Some well known concepts of stochastic differential calculus of non linear systems corrupted by parametric normal white noise are here outlined. Ito and Stratonovich integrals concepts as well as Ito differential rule are discussed. Applications to the statistics of the response of some linear and non linear systems is also presented.

Geometric Aspects of Thermodynamics

2016

This chapter deals with mathematical aspects of thermodynamics most of which will be seen to be primarily of geometrical nature. Starting with a short excursion to differentiable manifolds we summarize the properties of functions, of vector fields and of one-forms on thermodynamic manifolds. This summary centers on exterior forms over Euclidean spaces and the corresponding differential calculus. In particular, one-forms provide useful tools for the analysis of thermodynamics. A theorem by Caratheodory is developed which is closely related to the second law of thermodynamics. The chapter closes with a discussion of systems which depend on two variables and for which there is an interesting a…