1,720,975 research outputs found
(n+1)-Families of Sets in General Position
No full textA family of sets in R n is said to be in general position if any m--flat, 0 m n \Gamma 1; intersects at most m+ 1 members of the family. Using the Fan-- Glicksberg--Kakutani fixed point theorem, we prove that if fA 1 ; A 2 ; : : : ; A n+1 g is a family of compact convexly connected sets then for any proper subset I of f1; 2; : : : ; n+1g; there exists exactly one hyperplane H which separates strictly the sets [fA i : i 2 Ig and [fA j : j 2 f1; 2; \Delta \Delta \Delta ; n + 1g n Ig and satisfies d(A 1 ; H) = d(A 2 ; H) = \Delta \Delta \Delta = d(A n+1 ; H)
Compatibility of some systems of inequalities
Get PDFIn this paper, necessary and sufficient conditions for the compatibility of some systems of quasi-convex, or convex inequalities are established. Finally a new proof for a theorem of Shioji and Takahashi (1988) [10] is given
Alternative principles and their applications
No full textKakutani map, Fixed point, Matching theorem, Analytic alternative, Minimax inequality, 54H25, 54C60, 49J35, 52A07,
Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization
No full textGoing Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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