A new derivation of the counting formula for Young tableaux

A new very short proof of the counting formula for Young tableaux is given. Its equivalence with the hook formula is easy to establish.     

A simple derivation of a formula of Furstenberg and Tzkoni

It is shown that an integral geometric formula concerningn-dimensional ellipsoids, due to Furstenberg and Tzkoni, is a corollary of a classical formula of Blaschke and Petkantschin.     

A new derivation of Painlevé hierarchies

We give a new derivation of two Painlevé hierarchies. This is done by extending the accelerating-wave reductions of the Korteweg-de Vries and dispersive water wave equations to their respective hierarchies. We also consider the extension of this reduction of Burgers equation to the Burgers hierarchy.     

The Euler-Maclaurin sum formula for an inner derivation

An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in an inner derivation as the difference between a summation operator and an inner antiderivation, on a closed subalgebra of a Banach algebra.     

Another derivation of the local double logarithmic reconstruction formula

In [1] Artebrant and Schroll presented a finite volume method for hyperbolic conservation laws of 3rd order accuracy with no limiter and no special shock treatment. The method is based on local reconstruction of a double logarithmic function from cell averages on a 3-point stencil. Results shown in [1] make it appear very attractive and highly efficient. The derivation of the reconstrucion formula however starts with a relativ complex expression in some way anticipating the final result. In the following a more lucid one is shown proceeding from scratch and permitting symmetries to be clearly seen. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A remark to a paper of Kato and Ikebe

This paper deals with Schrödinger operators as they were treated by Kato - Ikebe [3]. It is shown that every element of the domain of definition of the adjoint of such an operator has locally square integrable distributional derivatives up to the order 2. For this the potential of the Schrödinger operator must fulfil a local Stummel condition; if the potential is only locally square integrable a somewhat weaker statement is possible for three dimensions (see remark 2 at the end of this paper).     

A new proof of Suzuki's formula

We give a different proof of a formula of Suzuki and its strengthening by Zaidenberg for the topological Euler characteristic of an affine surface fibered over a curve. We deduce this formula using the ideas for the proof of an analogous formula for a proper morphism.     

A new formula for winding number

We give a new formula for the winding number of smooth planar curves and show how this can be generalized to curves on closed orientable surfaces. This gives a geometric interpretation of the notion of winding number due to B. Reinhart and D.R.J. Chillingworth.     

A new derivation of eigenvalue inequalities for the multinomial distribution

We consider the covariance matrix of the multinomial distribution. We suggest a new derivation of inequalities for the eigenvalues of this matrix using a classical result on the product of two positive semi-definite matrices.     

A new look at Jarvis' distribution formula

Starting from the well-known transformation law for the Klein functions, we give a proof of a fairly general multiplicative distribution formula for the Siegel functions associated to isogenous complex lattices. This formula has as an immediate consequence the remarkable distribution formula proved by Jarvis in 2000 on the occasion of Rolshausen's thesis on the second K-group of an elliptic curve.     

A new approach to the credibility formula

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.     

A new derivation of Frisch's algorithm for calculating vertex-pair connectivity

In this paper we give a new and conceptually simple version of Frisch's algorithm for calculating the vertex connectivity of a graph. We show how this algorithm is obtained immediately from the Ford and Fulkerson labelling algorithm by using a 2-ply scanning step. Data structures are introduced which lead to efficiencies in execution, and the final algorithm is presented in a go-to-less notation.This work was supported in part by U.S. Army Research Office, Durham under contract DA HC04 69 C 0012, and NSF Grant GJ-965.     

Numerical integration over a disc. A new Gaussian quadrature formula

Summary. We construct a quadrature formula for integration on the unit disc which is based on line integrals over distinct chords in the disc and integrates exactly all polynomials in two variables of total degree . Received August 8, 1996 / Revised version received July 2, 1997     

A new proof of the Herbert multiple-point formula

We prove the Herbert multiple-point formula modulo 2-torsion using the method of the universal immersion. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 107–116, 2005.     

A new theoretical derivation of NFFT and its implementation on GPU

An efficient calculation of NFFT (nonequispaced fast Fourier transforms) is always a challenging task in a variety of application areas, from medical imaging to radio astronomy to chemical simulation. In this article, a new theoretical derivation is proposed for NFFT based on gridding algorithm and new strategies are proposed for the implementation of both forward NFFT and its inverse on both CPU and GPU. The GPU-based version, namely CUNFFT, adopts CUDA (Compute Unified Device Architecture) technology, which supports a fine-grained parallel computing scheme. The approximation errors introduced in the algorithm are discussed with respect to different window functions. Finally, benchmark calculations are executed to illustrate the accuracy and performance of NFFT and CUNFFT. The results show that CUNFFT is not only with high accuracy, but also substantially faster than conventional NFFT on CPU.