Serap Bulut Civil Aviation College, Kocaeli University, Arslanbey Campus, 41285 İzmit-Kocaeli, Turkey Correspondence should be addressed to Serap Bulut, [email protected] Received 28 March 2012; Accepted 16 May 2012 Academic Editor: Hernando Quevedo Copyright q 2012 Serap Bulut. This is an open access article distributed under the Creative Commons Attribution License, which permits unr...

The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily and...

We prove an addition formula for Jacobi functions r ~' ~) (~17_~-~ ) analogous to the known addition formula for Jacobi polynomials. We exploit the positivity of the coefficients in the addition formula by giving the following application. We prove that the product of two Jacobi functions of the same argument has a nonnegative Fourier-Jacobi transform. This implies that the convolution structur...

We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic operator which cascades wavelet convolutions and modulus nonlinearities. It is derived from the pitch spiral, in that convolutions are successively performed in...

We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n + 1)-th order differential equation and give a simple method for obtaining the differential equation. Also we determine the exponents of the differential equation and derive a bound for the degree of the polynomials, whic...

While CNNs naturally lend themselves to densely sampled data, and sophisticated implementations are available, they lack the ability to efficiently process sparse data. In this work we introduce a suite of tools that exploit sparsity in both the feature maps and the filter weights, and thereby allow for significantly lower memory footprints and computation times than the conventional dense fram...

In this paper we give a randomized O(n logn)-time algorithm for the string matching with don't cares problem. This improves the Fischer-Paterson bound 10] from 1974 and answers the open problem posed (among others) by Weiner 30] and Galil 11]. Using the same technique, we give an O(n logn)-time algorithm for other problems, including subset matching and tree pattern matching 15, 21, 9, 7, 17] a...

We establish the unimodality and the asymptotic strong unimodality of the ordinary multinomials and give their smallest mode leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. We conclude giving the generating functions of the sequence of generalized ordinary multinomials and for an extension of the sequence of maximal probabilities ...

An extremal problem for the coefficients of sine polynomials, which are nonnegativein [0, π], posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér-Riesz representation of nonnegativegeneral trigonometric and cosine polynomials is proved for nonnegativesine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szegő are obtained ex...

Applying the coefficient inequalities of functions f(z) belonging to the subclasses SD(α, β) and KD(α, β) of certain analytic functions in the open unit disk U, two subclasses SD∗(α, β) and KD∗(α, β) are introduced. In this present paper, some interesting convolution properties of functions f(z) in the classes SD∗(α, β) and KD∗(α, β) are discussed by using Shwarz inequality. 2000 Mathematical S...