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Normal martingales and polynomial families

H. Hammouch (2004)

Annales Polonici Mathematici

Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve...

Notes diverses

E. Catalan (1882)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

Rajkovic, Predrag M., Barry, Paul, Savic, Natasa (2012)

Mathematica Balkanica New Series

MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.

Numerical aspects of the identification of thermal characteristics using the hot-wire method

Vala, Jiří (2013)

Programs and Algorithms of Numerical Mathematics

The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions, neglecting...

On a Class of Generalized Elliptic-type Integrals

Garg, Mridula, Katta, Vimal, Kalla, S. (2001)

Serdica Mathematical Journal

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized...

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