scholarly journals Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Ngai-Ching Wong ◽  
Jen-Chih Yao
Keyword(s):  
Minimization Problem ◽  
Hemivariational Inequality ◽  
The Other ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Mild Conditions ◽  
Other Hand ◽  
Well Posed ◽  
Special Case

The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed variational-hemivariational inequality and give some conditions under which the strongly mixed variational-hemivariational inequality is strongly well-posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational-hemivariational inequality and the well-posedness for the corresponding inclusion problem.

scholarly journals Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

2017 ◽  
Vol 48 (4) ◽  
pp. 345-364 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yung-Yih Lur ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Minimization Problem ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Reflexive Banach Spaces ◽  
Mild Conditions ◽  
Well Posed

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.

scholarly journals Well-posedness by perturbations of variational-hemivariational inequalities with perturbations

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 881-895 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Himanshu Gupta ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequalities ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Mild Conditions ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities ◽  
Well Posed ◽  
Special Case

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational inequalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational-hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

scholarly journals Well-Posedness by Perturbations for Variational-Hemivariational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Shu Lv ◽  
Yi-bin Xiao ◽  
Zhi-bin Liu ◽  
Xue-song Li
Keyword(s):  
Optimization Problem ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness

We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the well-posedness by perturbations for the corresponding inclusion problem.

scholarly journals On the well-posedness of differential quasi-variational-hemivariational inequalities

2020 ◽  
Vol 18 (1) ◽  
pp. 540-551 ◽  
Author(s):  
Jinxia Cen ◽  
Chao Min ◽  
Van Thien Nguyen ◽  
Guo-ji Tang
Keyword(s):  
Hilbert Spaces ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Well Posed

Abstract The goal of this paper is to discuss the well-posedness and the generalized well-posedness of a new kind of differential quasi-variational-hemivariational inequality (DQHVI) in Hilbert spaces. Employing these concepts, we explore the essential relation between metric characterizations and the well-posedness of DQHVI. Moreover, the compactness of the set of solutions for DQHVI is delivered, when problem DQHVI is well-posed in the generalized sense.

Analyses and Evaluation of Responses to Slowly Changing Dimensions in Data Warehouses

2011 ◽  
pp. 324-337
Author(s):  
Lars Frank ◽  
Christian Frank
Keyword(s):  
Data Warehouse ◽  
Concurrency Control ◽  
The Other ◽  
Data Warehouses ◽  
Other Hand ◽  
Star Schema ◽  
Dynamic Dimension ◽  
Special Case

A Star Schema Data Warehouse looks like a star with a central, so-called fact table, in the middle, surrounded by so-called dimension tables with one-to-many relationships to the central fact table. Dimensions are defined as dynamic or slowly changing if the attributes or relationships of a dimension can be updated. Aggregations of fact data to the level of the related dynamic dimensions might be misleading if the fact data are aggregated without considering the changes of the dimensions. In this chapter, we will first prove that the problems of SCD (Slowly Changing Dimensions) in a datawarehouse may be viewed as a special case of the read skew anomaly that may occur when different transactions access and update records without concurrency control. That is, we prove that aggregating fact data to the levels of a dynamic dimension should not make sense. On the other hand, we will also illustrate, by examples, that in some situations it does make sense that fact data is aggregated to the levels of a dynamic dimension. That is, it is the semantics of the data that determine whether historical dimension data should be preserved or destroyed. Even worse, we also illustrate that for some applications, we need a history preserving response, while for other applications at the same time need a history destroying response. Kimball et al., (2002), have described three classic solutions/responses to handling the aggregation problems caused by slowly changing dimensions. In this chapter, we will describe and evaluate four more responses of which one are new. This is important because all the responses have very different properties, and it is not possible to select a best solution without knowing the semantics of the data.

Selenosilane-Promoted Selective Mild Transformation of N-Thiophthalimides into Symmetric Disulfides

Synthesis ◽  
2019 ◽  
Vol 51 (08) ◽  
pp. 1819-1824 ◽  
Author(s):  
Caterina Viglianisi ◽  
Chiara Bonardi ◽  
Elena Ermini ◽  
Antonella Capperucci ◽  
Stefano Menichetti ◽  
...  
Keyword(s):  
The Other ◽  
Chemical Behavior ◽  
Simple Method ◽  
Mild Conditions ◽  
Other Hand ◽  
Dialkyl Disulfides

The reactivity of N-thiophthalimides with silyl chalcogenides is described. Treatment of N-thiophthalimides with bis(trimethylsilyl) sulfide [(Me3Si)2S] leads to the formation of a mixture of the corresponding disulfides and trisulfides. On the other hand, N-thiophthalimides react with bis(trimethylsilyl) selenide [(Me3Si)2Se] under TBAF catalysis to smoothly give variously substituted diaryl, divinyl, and dialkyl disulfides; formation of a selenotrisulfide (dithiaselane, RSSeSR) is rationalized as an intermediate. Exploiting the different chemical behavior of silyl chalcogenides, we have disclosed a novel, selective, and operationally simple method to access disulfides in good yields under mild conditions.

scholarly journals Stationarity as a path property

2019 ◽  
Vol 39 (2) ◽  
pp. 403-422
Author(s):  
Yi Shen ◽  
Tony S. Wirjanto
Keyword(s):  
Stochastic Process ◽  
Stationary Process ◽  
The Other ◽  
Mild Conditions ◽  
Other Hand ◽  
Distributional Property ◽  
Shift Invariance ◽  
Stationarity Test ◽  
Path Property ◽  
Almost All

Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

scholarly journals Partial differential hemivariational inequalities

2018 ◽  
Vol 7 (4) ◽  
pp. 571-586 ◽  
Author(s):  
Zhenhai Liu ◽  
Shengda Zeng ◽  
Dumitru Motreanu
Keyword(s):  
Evolution Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Upper Semicontinuity ◽  
Solution Set ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Partial Differential ◽  
New Class

AbstractThe aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories.

Continuidad y discontinuidad en la transmisión de las palabras patrimoniales competidas por arabismos: oliva y aceituna, olio y aceite, olivo y aceituno

2021 ◽  
Vol 66 (4) ◽  
pp. 69-80
Author(s):  
Mihai Enăchescu ◽  
Keyword(s):  
Spanish Language ◽  
Corpus Analysis ◽  
The Other ◽  
Other Hand ◽  
The Common ◽  
Lexical Substitution ◽  
Restricted Use ◽  
Special Case ◽  
Continuity And Discontinuity

Continuity and Discontinuity in the Transmission of Spanish Inherited Words Competed by Arabisms: oliva and aceituna, olio and aceite, olivo and aceituno. The loss and replacement of Arabisms by Latin loanwords was a frequent phenomenon between the sixteenth and the seventeenth centuries; the opposite movement, the replacement of an inherited word by an Arabism is far less frequent. Oliva, an inherited word, is competed by the Arabism aceituna; currently the common name for the fruit in the Hispanic world is aceituna, and oliva has a restricted use to the phrase aceite de oliva or to refer to a colour. Similarly, the inherited word olio will be replaced by aceite, and with a specialized meaning will be eliminated by the euphuism óleo, its etymological doublet. On the other hand, olivo prevails over aceituno and represents a special case of continuity in this lexical family. The research will be carried out in two directions: first, I will analyse the old academic dictionaries and other specialized dictionaries and glossaries from the fifteenth-twentieth centuries. Second, I will conduct a corpus analysis, based on the diachronic corpora available for the Spanish language. This study will try to answer the questions how? and why? of these neological movements of vocabulary. Keywords: inherited words, Arabisms, oliva, aceituna, lexical substitution

scholarly journals Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Min Ling ◽  
Weimin Han
Keyword(s):  
Stokes Equations ◽  
Normal Component ◽  
Numerical Algorithms ◽  
Hemivariational Inequality ◽  
Navier Stokes ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Solution Existence And Uniqueness ◽  
Stationary Navier Stokes Equations

AbstractThis paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.

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