scholarly journals Strongly essential set of vector Ky Fan's points problem and its applications

2021 ◽  
Vol 6 (4) ◽  
pp. 3160-3176
Author(s):  
Dejin Zhang ◽  
◽  
Shuwen Xiang ◽  
Xicai Deng ◽  
Yanlong Yang ◽  
...  
Keyword(s):  
Essential Set

scholarly journals Diagrams and Essential Sets for Signed Permutations

10.37236/8106 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
David Anderson
Keyword(s):  
Schubert Variety ◽  
Signed Permutation ◽  
Signed Permutations ◽  
Degeneracy Locus ◽  
Essential Set ◽  
Diagrammatic Method ◽  
Essential Sets ◽  
Rank Conditions ◽  
Theoretic Version

We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations.  In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation.  Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.

scholarly journals Unifying Class-Based Representation Formalisms

1999 ◽  
Vol 11 ◽  
pp. 199-240 ◽  
Author(s):  
D. Calvanese ◽  
M. Lenzerini ◽  
D. Nardi
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Finite Model ◽  
Functional Dependencies ◽  
Semantic Data ◽  
Representation Systems ◽  
Frame Systems ◽  
Essential Set

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains. We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models. As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available. The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning. A notable feature of our proposal is that reasoning in both cases is decidable. We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms.

Modeling the Soft Skills of Green Procurement Professionals using Interpretive Structural Modeling Approach

2016 ◽  
pp. 120-131 ◽  
Author(s):  
Surajit Bag
Keyword(s):  
Human Resource ◽  
Soft Skills ◽  
Structural Modeling ◽  
Human Resource Managers ◽  
Interpretive Structural Modeling ◽  
Green Procurement ◽  
Modeling Approach ◽  
Hard Skills ◽  
Resource Managers ◽  
Essential Set

Green procurement demands a creative attitude and innovation oriented culture which is still missing in many organizations. It is noted that most of the procurement professionals lack essential soft skills which are more important than hard skills. Human resource managers need to develop appropriate teaching methodologies for procurement professionals to enhance the essential soft skills. The purpose of this study is to identify the essential set of soft skills required for green procurement practices. Interpretive structural modeling approach was applied to find the interrelationships. This study also provides deep insight to human resource managers and will be helpful in developing training programs for procurement professionals.

scholarly journals The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qi-Qing Song
Keyword(s):  
Equilibrium Problem ◽  
Existence Result ◽  
Quasi Equilibrium ◽  
Topological Order ◽  
Stability Of Solutions ◽  
Maximal Elements ◽  
Quasiequilibrium Problems ◽  
Existence And Stability ◽  
Essential Set ◽  
Vector Quasiequilibrium Problems

In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem.

scholarly journals Rough sets in graphs using similarity relations

2022 ◽  
Vol 7 (4) ◽  
pp. 5790-5807
Author(s):  
Imran Javaid ◽  
◽  
Shahroz Ali ◽  
Shahid Ur Rehman ◽  
Aqsa Shah
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Membership Functions ◽  
Similarity Relations ◽  
Complete Bipartite Graphs ◽  
Essential Set ◽  
Essential Sets ◽  
Necessary And Sufficient ◽  
Clustering Criterion

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

scholarly journals On the essential set of function algebras

1968 ◽  
Vol 44 (10) ◽  
pp. 1000-1002
Author(s):  
Hiroshi Ishikawa ◽  
Jun Tomiyama ◽  
Junzo Wada
Keyword(s):  
Function Algebras ◽  
Essential Set

On the Extreme Points of Quotients of L∞ by Douglas Algebras

1984 ◽  
Vol 27 (4) ◽  
pp. 517-522 ◽  
Author(s):  
Waleed Deeb ◽  
Rahman Younis
Keyword(s):  
Unit Ball ◽  
Blaschke Product ◽  
Best Approximation ◽  
Extreme Points ◽  
Douglas Algebra ◽  
Essential Set ◽  
Douglas Algebras

AbstractLet B be a Douglas algebra which admits best approximation. It will be shown that the following are equivalent: (1) The unit ball of (L∞/B) has no extreme points; (2) For any Blaschke product b with , there exists h ∈ B such that and h|E≢0, where E is the essential set of B.It will also be proven that if B⊇H∞+C and its essential set E contains a closed Gδ set, then the unit ball of (L∞/B) has no extreme points. Many known results concerning this subject will follow from these results.

Challenges of Learning Analytics Execution in the Educational System

2018 ◽  
pp. 28-40
Author(s):  
Manoj Kumar Singh
Keyword(s):  
Higher Education ◽  
Educational System ◽  
Learning Analytics ◽  
First Century ◽  
Teachers And Students ◽  
Twenty First Century ◽  
Essential Set ◽  
Educational Enterprise ◽  
Education Stakeholders

Education for the twenty-first century continues to promote discoveries in the field through learning analytics. The problem is that the rapid embrace of learning analytics diverts educators' attention from clearly identifying requirements and implications of using learning analytics in higher education. Learning analytics is a promising emerging field, yet higher education stakeholders need to become further familiar with issues related to the use of learning analytics in higher education. This chapter addresses the above problem and design of learning analytics implementations: the practical shaping of the human tactics involved in taking on and using analytic equipment, records, and reviews as part of an educational enterprise. This is an overwhelming but equally essential set of design choices from the ones made within the advent of the learning analytics structures themselves. Finally, this chapter's implications for learning analytics teachers and students and areas requiring further studies are highlighted.

Implications of Supply Chain Management on the Connection between Business Performance and Enterprise Resource Planning Framework

2020 ◽  
pp. 101-108
Author(s):  
Ying Zhang ◽  
Zakaria Fareed
Keyword(s):  
Supply Chain ◽  
Supply Chain Management ◽  
Enterprise Resource Planning ◽  
Structural Equation ◽  
Business Performance ◽  
Resource Planning ◽  
Chain Management ◽  
Fundamental Information ◽  
Planning Framework ◽  
Essential Set

Enterprise Resource Planning (ERP) and Supply Chain Management (SCM) are the two fundamental Information Technology (IT) investment advancements that businesses are resorting to in the modern age. These are the advancements and options which are known to be essential in literature as a contributing fact to the enhancement of Business Performance (BP). In that regard, the main purpose of this contribution is to evaluate the adoption of ERP and its effects of BP through the option of SCM. This paper presents a novel model that applies enterprise resource planning with the option of SCM to effectively optimize BP in the competitive world. The structural equation framework is thus fundamental for testing of the model and how its fits the level of the four projected research hypotheses. The essential set of data for this analysis was gathered from companies in Malaysia. The findings in this research have been supported using empirical evidences, availability of positive factors of ERP for the option of supply chain ultimately amounts to enhanced BP.

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