Bangteng Xu

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Variational inequalities theory has been widely used in many fields, such as economics, physics, engineering, optimization and control, transportation [1, 4]. Like convexity to mathematical programming problem (MP), monotonicity plays an important role in solving variational inequality (VI). To investigate the variational inequality, many kinds of monotone(More)
Using covering numbers we prove that a standard real integral table algebra (A, B) with |B| ≥ 6 has a P-polynomial structure with respect to every b = 1 in B if and only if 2|B| − 1 is prime and (A, B) is exactly isomorphic to the Bose-Mesner algebra of the association scheme of the ordinary (2|B| − 1)-gon. Then we present an example showing that this(More)
Let G be a finite abelian group acting faithfully on a finite set X . The G-bentness and G-perfect nonlinearity of functions on X are studied by Poinsot and co-authors (Discret Appl Math 157:1848–1857, 2009; GESTS Int Trans Comput Sci Eng 12:1–14, 2005) via Fourier transforms of functions on G. In this paper we introduce the so-called G-dual set ̂X of X ,(More)
Hanaki [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] generalized many properties of characters of finite groups to characters of association schemes. In this paper we show that many of(More)
Let G, H be finite groups and let X be a finite G-set. G-perfect nonlinear functions from X to H have been studied in several papers. They have more interesting properties than perfect nonlinear functions from G itself to H. By introducing the concept of a (G,H)related difference family of X, we obtain a characterization of G-perfect nonlinear functions on(More)