Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third ...

Yang, R.J. Gu, L.
Published in
Structural and Multidisciplinary Optimization

Traditional reliability-based design optimization (RBDO) requires a double loop iteration process. The inner optimization loop is to find the most probable point (MPP) and the outer is the regular optimization loop to optimize the RBDO problem with reliability objectives or constraints. It is well known that the computation can be prohibitive when ...

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third ...

Farahmand, K.
Published in
Journal of Theoretical Probability

There is both mathematical and physical interest in the behaviour of the polynomial of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$a_0 + a_1 (_{\text{1}}^...

Medard, Muriel Tsitsiklis, John N. Bertsekas, Dimitri P. Abou Faycal, Ibrahim C. (Ibrahim Chafik)...

Modeling, quantification, and analysis of uncertainty. Formulation and solution in sample space. Random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. Interpretations, applications, and lecture demonstrations. Meets with graduate ...

Deshouillers, Jean-Marc Freiman, Gregory A. Yudin, Alexander A.
Published in
Journal of Theoretical Probability

We derive an upper bound for the concentration of the sum of i.i.d. random variables with values in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}^d$$ \end...

Gitman, Michael B. Trusov, Peter V. Fedoseev, Sergei A.
Published in
Korean Journal of Computational & Applied Mathematics

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

Rios Neto, Atair Pinto, Ricardo L. U. F.

A stochastic approach is proposed to generate a direct search procedure where errors in the constraints are inherently treated. The objective is to have the possibility of directly considering the relative accuracy in the satisfaction of constraints, when one is numerically solving a nonlinear constrained optimization problem. This is done by addin...