The problem of calculating the lower confidence limit for the reliability function and the other main indices, such as the mean time to failure (mean lifetime) and the guaranteed (gamma-percentile) lifetime of a syste...
详细信息
The problem of calculating the lower confidence limit for the reliability function and the other main indices, such as the mean time to failure (mean lifetime) and the guaranteed (gamma-percentile) lifetime of a system based on the reliability test results has been considered. The problem is solved under the general nonparametric assumption of the monotonically increasing failure intensity function (aging) of a system. A series of expressions for the lower confidence limits of the aforementioned main reliability indices has been derived.
In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. W...
详细信息
In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasing norm-bounded sequence has a limit. We supply a counterexample, which shows that this property is essential and give a modification of obtained results for the space C(T), which does not possess this property.
We consider the Cauchy problem with a non-negative continuous initial function for the equation u(t) = (u(m))(xx) + c(u(n))(x), where m > 1, m greater than or equal to n greater than or equal to 1, and c is a posit...
详细信息
We consider the Cauchy problem with a non-negative continuous initial function for the equation u(t) = (u(m))(xx) + c(u(n))(x), where m > 1, m greater than or equal to n greater than or equal to 1, and c is a positive constant. We prove a number of existence and uniqueness theorems for generalized solutions increasing at infinity for this Cauchy problem;we also investigate the behaviour of these solutions for large values of the time.
Let A, B, X, and Y be nxn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\od...
详细信息
Let A, B, X, and Y be nxn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n\times n$\end{document} complex matrices such that A is self-adjoint, B >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$B\geq 0$\end{document}, +/- A <= B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\pm A\leq B$\end{document}, max(parallel to X parallel to 2,parallel to Y parallel to 2)<= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\max ( \Vert X \Vert <^>{2}, \Vert Y \Vert <^>{2} ) \leq 1$\end{document}, and let f be a nonnegative increasing convex function on [0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[ 0,\infty ) $\end{document} satisfying f(0)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f(0)=0$\end{document}. Then 2sj(f(|XAY & lowast;|))<= max{parallel to X parallel to 2,parallel to Y parallel to 2}sj(f(B+A)circle plus f(B-A))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{was
We study the space of all continuous and increasing self mappings of a real interval [a, b], where a < b are real numbers, equipped with the topology of uniform convergence. We show, in particular, that most such f...
详细信息
We study the space of all continuous and increasing self mappings of a real interval [a, b], where a < b are real numbers, equipped with the topology of uniform convergence. We show, in particular, that most such functions have infinitely many different fixed points.
The onset of symptoms was gradual 5 months earlier, and symptoms were aggravated during the 2 months before his visit to my facility. The patient reported that he had increased his running intensity before the onset o...
详细信息
The onset of symptoms was gradual 5 months earlier, and symptoms were aggravated during the 2 months before his visit to my facility. The patient reported that he had increased his running intensity before the onset of his symptoms. The patient had no previous history of right knee disorders but had a reconstruction of his left anterior cruciate ligament 6 years 'before the clinic visit. No diagnostic studies were performed before the surgeon established the diagnosis.
We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these fun...
详细信息
We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.
A function g between directed sets ='> and => is called ultimately increasing if for each sigma(1) is an element of Sigma there exists sigma(2) >=' sigma(1) such that sigma >=' sigma(2) double ...
详细信息
A function g between directed sets ='> and => is called ultimately increasing if for each sigma(1) is an element of Sigma there exists sigma(2) >=' sigma(1) such that sigma >=' sigma(2) double right arrow g(sigma) >= g(sigma(1)). A subnet of a net a defined on => [9] is nothing but a composition of the form a o g where g is ultimately increasing and g(Sigma) is a cofinal subset of Lambda. While even for linearly ordered sets, an increasing net defined on a cofinal subset of the domain need not have an increasing extension, in complete generality, it must have an ultimately increasing extension, and conversely when the domain is linearly ordered. Applications are given in the context of functions with values in a linearly ordered set equipped with the order topology - in particular, the extended real numbers. For example, we show that a real sequence < a(n)> converges to the supremum of its set of terms if and only if < a(n)> is the supremum of the ultimately increasing sequences that it majorizes.
暂无评论