a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

We construct the Neveu-Schwarz sector of heterotic string field theory using the large Hilbert space of the superghosts and the multi-string products of bosonic closed string field theory. No picture-changing operators are required as in Wess-Zumino-Witten-like open superstring field theory. The action exhibits a novel kind of nonpolynomiality: in addition to terms necessary to cover missing re...

In this paper, we introduce operator s-convex functions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

We consider the minimization of convex functionals on a real Hilbert space. The requisite theory is reviewed, and concise proofs of the relevant results are given.

The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.

Abstract. We find a local (d + 1)× (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × d RiemannHilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polyno...