共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
A modification to a theorem in Ref. 1 and its proof are given. 相似文献
3.
In this paper, we derive an estimate for the G-subderivative of the value function associated with a perturbed optimization problem with differential inclusion constraints. We then apply this result to obtain a necessary condition for a solution to a bilevel dynamic problem. 相似文献
4.
We know that the Box dimension of f(x) ∈ C~1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1. 相似文献
5.
Dumitru Popa 《Positivity》2006,10(1):87-94
We introduce in a natural way the notion of measure with bounded variation with respect to a normed ideal of operators and
prove that for each maximal normed ideal of operators (, ), is true the following result: If U ∈ L(C(T,X), Y) with G the representing measure of U and G : Σ → ((X, Y),) has bounded variation, then U ∈ (C(T,X), Y). As an application of this result we prove that an injective tensor product of an integral operator with an operator belonging
to a maximal normed ideal of operators (,) belongs also to (, ). 相似文献
6.
Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional
approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated
that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating
subspaces consisting of piecewise constant functions. Algorithms based on a primal—dual framework that exploit the structure
of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images
with very high noise.
Accepted 29 March 1998 相似文献
7.
René Erlín Castillo Nelson Merentes Humberto Rafeiro 《Mediterranean Journal of Mathematics》2014,11(4):1069-1079
In this paper, we introduce bounded variation spaces in the Wiener sense with p-variable and study some of its basic properties. 相似文献
8.
利用Henstock积分,讨论了一类不连续系统有界变差解对参数的连续依赖性及其它相关性质. 相似文献
9.
In this paper we derive a multidimensional version of the rate conservation law (RCL) for càdlàg processes of bounded variation. These results are then used to analyze queueing models which have a natural multidimensional characterization, such as priority queues. In particular the RCL is used to establish certain conservation laws between the idle probabilities for such queues. We use the relations to provide a detailed analysis of preemptive resume priority queues with M/G inputs. Special attention is paid to the validity of the so-called reduced service rate approximation. 相似文献
10.
讨论了一类奇异摄动非线性分数阶时滞问题.首先利用奇异摄动方法求出了问题的外部解.再利用伸展变量法构造了问题在边界附近的两个边界层校正项,得出了所提问题的形式渐近解.最后,在合适的假设条件下,利用微分不等式理论证明了解的一致有效性,并给出了结论及未来的研究方向. 相似文献
11.
12.
13.
通过对K.J.Palmer ̄[4]中方法的改进,本文讨论了摄动系统有界解的存在性,得到了不同于[4]中的结果,并把改进了的方法运用到拟自治奇异摄动系统,得到了拟自治奇异摄动系统存在有界解的一个简洁的充分条件。本文的方法还提供了一个处理摄动项含小参数的方法。 相似文献
14.
S. Nobakhtian M. R. Pouryayevali 《Numerical Functional Analysis & Optimization》2013,34(11):1175-1189
We introduce a concept of generalized invexity for the nonsmooth continuous time optimization problems, namely, the concept of Karush-Kuhn-Tucker (KKT) invexity. Then, we prove that this notion is necessary and sufficient for global optimality of a KKT point. We also extend the notion of weak-invexity for nonsmooth continuous time optimization problems. Further, we show that weak-invexity is a necessary and sufficient condition for weak duality. 相似文献
15.
For parametrized Hamiltonian systems with an arbitrary, finite number of degrees of freedom, it is shown that secularly stable families of equilibrium solutions represent approximate trajectories for small (not necessarily Hamiltonian) perturbations of the original system. This basic result is further generalized to certain conservative, but not necessarily Hamiltonian, systems of differential equations. It generalizes to the conservative case a theorem due, in the dissipative case, to Tikhonov, to Gradshtein, and to Levin and Levinson. It justifies the use of physically motivated approximation procedures without invoking the method of averaging and without requiring nonresonance conditions or the integrability of the unperturbed Hamiltonian. 相似文献
16.
17.
18.
19.
Introduce the notation: $\mathbb{Z}$ is the set of integers, $\bar {\mathbb{Z}}={\mathbb{Z}} \cup \{-\infty, +\infty\},{\mathbb{R}}_+^2 =\{x=(x_1,x_2) \in {\mathbb{R}}^2; x_1>0,x_2>0\}$ , $g_{k,m} (x,\alpha,h)= \int\limits_0^1 {g_1 (\frac{(k+u)h_1 - x_1}{\alpha_1})g_2(\frac{(m+u)h_2 - x_2}{\alpha_2})}du$ , where $g_i :\mathbb{R} \to \mathbb{R},x \in \mathbb{R}^2 ,\alpha ,h \in \mathbb{R}_ + ^2 $ . Under certain conditions on the functions g 1, g 2, we prove that the system of functions $g_{k,m} (x,\alpha^(n), h^(n)) (k,m \in \bar {\mathbb{Z}})$ , where $\alpha ^{\left( n \right)} ,h^{\left( n \right)} \in \mathbb{R}_ + ^2 $ are arbitrary infinitesimal sequences, is complete in the space C $\mathbb{R}^2 $ of uniformly continuous bounded functions f equipped with the norm $||f|| = \mathop {\sup }\limits_{x \in \mathbb{R}^2 } |f(x)|$ . Starting with the functions g k,m , it is possible to construct a method for uniform approximating in $\mathbb{R}^2 $ any continuous function of bounded variation in the sense of Hardy. An error estimate is derived in terms of the second order moduli of continuity. Based on the obtained results, we discuss in detail the accuracy of uniform approximation of functions of several variables by linear functions. The error estimates are derived by using second order moduli of continuity. We pay a particular attention to sharpness of constants. Bibliography: 8 titles. 相似文献
20.
The first boundary value problem for a multidimensional parabolic differential equation with a small parameter ε multiplying all derivatives is studied. A complete (i.e., of any order with respect to the parameter) regularized asymptotics of the solution is constructed, which contains a multidimensional boundary layer function that is bounded for x = (x1, x2) = 0 and tends to zero as ε → +0 for x ≠ 0. In addition, it contains corner boundary layer functions described by the product of a boundary layer function of the exponential type by a multidimensional parabolic boundary layer function. 相似文献