The SC property of an expected residual function arising from stochastic complementarity problems

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization problem which minimizes an expected residual function defined by an NCP function. In this work, we show that the expected residual function defined by the Fischer–Burmeister function is an View the MathML source" title="View the MathML source" align="absbottom" border="0" height=13 width="24"/> function.     

Majorization of regular measures and weights with finite and positive critical exponent

For the sets View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si1.gif">, 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si5.gif"> there exists View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si6.gif"> such that dμ/dν?1. A corresponding principle holds for the sets View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si8.gif">, p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si12.gif">: For every View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si13.gif"> there exists View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07008505-si14.gif"> such that w?ω.     

A remark on Andrews-Askey integral

In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07013297-si1.gif"> transformation formula.     

Precoloring extension on unit interval graphs

In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs.     

Condensed Cramer rule for some restricted quaternion linear equations

In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature.     

Remarks on the formula for γ-interior

The paper presents a formula for the γ-interior of a set under special conditions for View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X04002252-si1.gif">, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89-93]. There are also some applications.     

Weighted estimates for a class of multilinear fractional type operators

In this paper, a class of multiple fractional type weights View the MathML source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0022247X09006763-si1.gif"> is defined as

View the MathML source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0022247X09006763-si2.gif">     

Generalized Navier-Stokes equations with initial data in local Q-type spaces

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of View the MathML source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0022247X10002969-si1.gif">. This result applies to the usual incompressible Navier-Stokes equations.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si1.gif"> summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si2.gif"> and Dougall's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si3.gif"> summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si4.gif"> summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.