in this paper, we use petrov-galerkin elements such as continuous and discontinuous lagrange-type k-0 elements and hermite-type 3-1 elements to find an approximate solution for linear fredholm integro-differential equations on $[0,1]$. also we show the efficiency of this method by some numerical examples

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, study (p,q)-Hermite–Hadamard multiple integrals. Many results given in paper provide extensions others previous research.

Abstract We prove the Kobayashi—Hitchin correspondence and approximate for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a manifold g Gauduchon metric X, bundle −polystable only it −Hermite-Einstein, , then −semistable −Hermite-Einstein.

We define S to be the set of those φ ∈ C∞(R,C) such that pn(φ) < ∞ for all n ≥ 0. S is a complex vector space and each pn is a norm, and because each pn is a norm, a fortiori {pn : n ≥ 0} is a separating family of seminorms. With the topology induced by this family of seminorms, S is a Fréchet space. As well, D : S → S defined by (Dφ)(x) = φ′(x), x ∈ R 1http://individual.utoronto.ca/jordanbell/...

In this paper we extend some recent results on moment identities, Hermite polynomials, and measure invariance properties on the Wiener space, to the setting of path spaces over Lie groups. In particular we prove the measure invariance of transformations having a quasi-nilpotent covariant derivative via a Girsanov identity and an explicit formula for the expectation of Hermite polynomials in the...

This paper considers the problem of transforming a triangular integer input matrix to canonical Hermite and Smith normal form. We provide algorithms and prove deterministic running times for both transformation problems that are linear (hence optimal) in the matrix dimension. The algorithms are easily implemented, assume standard integer multiplication, and admit excellent performance in practi...

This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator cal...

Invariants to image scaling composed of Gaussian–Hermite moments are introduced in this paper for the first time. To achieve the invariance, we propose to modulate the Gaussian–Hermite polynomial basis using variable parameter σ, the value of which depends on the input image. The scaling invariance property can be coupled with the rotation invariance presented earlier. This approach is applicab...