scholarly journals Stable Analysis of Solution Set for System of Quasivariational Relations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lefeng Shi ◽  
Zhe Yang
Keyword(s):  
Baire Category ◽  
Solution Set ◽  
Stability Of Solutions ◽  
Essential Component ◽  
Essential Stability ◽  
Essential Components ◽  
Quasivariational Inclusions

The essential stability of solutions for system of quasivariational relations is studied. We show that most of systems of quasivariational relations are essential (in the sense of Baire category) and that, for any system of quasivariational relations, there exists at least one essential component of its solution set. As applications, the existence of essential components of solution set for systems of KKM problems and systems of quasivariational inclusions is obtained.

scholarly journals A note of stability of weakly efficient solution set for optimization with set-valued maps

2003 ◽  
Vol 16 (3) ◽  
pp. 267-273
Author(s):  
Luo Qun
Keyword(s):  
Efficient Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Baire Category ◽  
Efficient Solutions ◽  
Solution Set ◽  
Weakly Efficient Solution ◽  
Solution Sets ◽  
Essential Components ◽  
Efficient Solution Set

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set .

scholarly journals Essential Components of Melanoma Histopathological Reporting: The Surgical Oncologist’s Perspective

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Vinka Nurdjaja ◽  
Masato Yozu ◽  
Jon A. Mathy
Keyword(s):  
Treatment Planning ◽  
International Collaboration ◽  
Cutaneous Melanoma ◽  
Clinical Relevance ◽  
Critical Role ◽  
Management Plan ◽  
Primary Cutaneous Melanoma ◽  
Essential Component ◽  
Essential Components ◽  
Cancer Reporting

Histopathological reporting plays a critical role in guiding the surgical oncologist’s management plan in treatment of primary cutaneous melanoma. The International Collaboration on Cancer Reporting (ICCR) espouses various components of structured histopathological reporting as “essential” or “recommended.” From a surgical oncologist’s perspective, we discuss the clinical relevance of each essential component, as well as prognostic and treatment implications with regard to treatment planning.

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