Inversion formulas for q-Riemann-Liouville and q-Weyl transforms

We study fractional transforms associated with q-Bessel operator which is useful to inverse q-Riemann-Liouville and q-Weyl transforms.     

Extended arithmetic functions

The Ramanujan Journal - In this paper, we give an attempt to extend some arithmetic properties such as multiplicativity and convolution products to the setting of operator theory and we provide...     

New Studies on the Fock Space Associated to the Generalized Airy Operator and Applications

In this work, we introduce the Fock space \(F_\nu (\mathbb {C})\) associated to the Airy operator \(L_\nu \), and we establish Heisenberg-type uncertainty principle for this space. Next, we study the Toeplitz operators, the Hankel operators and the translation operators on this space. Furthermore, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator \(T{:}\,F_\nu (\mathbb {C})\rightarrow H\), where H be a Hilbert space. Finally, we come up with some results regarding the extremal functions, when T is the difference operator and the Dunkl-difference operator, respectively.     

Deformed Heisenberg algebra with reflection and <Emphasis Type="Italic">d</Emphasis>-orthogonal polynomials

This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d-orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1. The underlying algebraic framework allowed a systematic derivation of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.     

Experimental study of the airside performance of tube row spacing in finned tube heat exchangers

Almost all of the studies in dehumidifying coils are experimental studies. In this study, effect of tube regulation space on heat and mass transfer and friction factor for heat exchangers made from aluminum fins and cooper tubes are identified experimentally. External surface heat transfer coefficient, Colburn factor and friction factor was calculated by the help of the computer program by using experimental values done. After the diagrams investigated, with the decreasing of tube row spacing the external surface heat transfer in the dry surface and friction factor increased. If wet and dry surfaces are compared, Colburn and friction factor in wet surfaces is larger than Colburn and friction factor in dry surfaces.     

Second law analysis of the 2D laminar flow of two-immiscible,incompressible viscous fluids in a channel

The laminar and fully developed flows of two immiscible fluids confined in a thin slit of constant wall heat fluxes are analyzed in terms of entropy generations due to irreversibility of forced convection heat transfer. The governing equations are analytically derived using expressions for velocity distributions. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying irreversibility distribution ratio ϕ. It is found that the minimum entropy generation takes place at the dimensionless half transverse distance (ξ) of 0.3 for values of ϕ higher than zero. The entropy generation near the plate increases more rapidly in fluid I than in fluid II as viscous dissipation effects becomes more important. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N _S ) for two-immiscible incompressible flows in the slit.     

Admissibility results under some balanced loss functions for a functional regression model

We consider the problem of the nonparametric estimation in a functional regression model $Y=r(X)+\epsilon$, with Y a real random variable response and X representing a functional variable taking values in a semi-metric space. The aim of this note is to find conditions of admissibility of Stein-type estimators of such a model under a class of balanced loss functions. Our method is to compare the risk with that obtained in the case of a quadratic loss.     

Optimization of Combustion Efficiency Using a Fuel Composition Based on CH4 and/or H2

Russian Journal of Applied Chemistry - In this paper, we investigate the exergy analysis of the combustion chamber supplied by different fuel compositions based mainly on methane and/or hydrogen in...     

OPTIMIZATION APPROACH FOR THE MONGE-AMPèRE EQUATION

In this paper, we introduce and study a method for the numerical solution of the elliptic Monge-Ampère equation with Dirichlet boundary conditions. We formulate the Monge-Ampère equation as an optimization problem. The latter involves a Poisson Problem which is solved by the finite element Galerkin method and the minimum is computed by the conjugate gradient algorithm. We also present some numerical experiments.