Salma Charfi

Riesz Basis Property of Families of Nonharmonic Exponentials and Application to a Problem of a Radiation of a Vibrating Structure in a Light Fluid

This article deals with the Riesz basis property of families of nonharmonic exponentials. The exponents coincide with the eigenvalues of a specific perturbation of a closed linear operator. The key idea of this work is based on the estimate given by Nagy [6] using the spectral analysis method. Furthermore, it is also shown that the system of a sequence of exponentials families of the operator forms a Riesz basis in L 2(0, T), T > 0, where K is the integral operator with kernel the Hankel function of the first kind and order 0.

On a Riesz basis of finite-dimensional invariant subspaces and application to Gribov operator in Bargmann space

Abstract In this paper, we are mainly concerned with a new class of unbounded perturbations of unbounded normal operators. We give a description of the changed spectrum and we establish different conditions in terms of the spectrum to prove the existence of Riesz basis of finite-dimensional invariant subspaces of generalized eigenvectors. The obtained results are of importance for application to a non-self-adjoint Gribov operator in Bargmann space.

On the Time Asymptotic Behavior of a Transport Operator with Diffuse Reflection Boundary Condition

This article is concerned with the spectral properties of a transport operator with diffuse reflection boundary condition arising in L 1-spaces. Furthermore, a practical way to study asymptotic behavior of the solution of the transport operator without restriction on the initial data is given.

Reduction in CABAC encoding time of the HEVC

As time is important in coding video, this paper presents an optimization method to reduce encoding time of CABAC with respect to the compression rate, delivering the same video quality. This method is based on the statistics of the context models of syntax elements which have a higher number of contexts than others to be compelled in order to reduce their number and thus saving encoding time. In fact, we are interested in residual syntax elements which represents 65% of total number of models. This work is innovative since this idea was not dealt with before. Many simulations are done covering different settings of syntax elements for a variety of video sequences, using two configurations with two quantized parameters QP.

On the time asymptotic behavior of a transport operator with bounce-back boundary condition

This paper deals with the spectral properties of multidimensional transport equations with bounce-back boundary conditions arising in L p -spaces \((1 \leq p <\infty )\). These properties are closely related to the large dependent solutions of transport equations. An adequate assumption allows us to investigate the uniform stability of solutions for the Cauchy problem without restriction on the initial data.

On a characterization of the S-essential spectra of the sum and the product of two operators and application to a transport operator

Abstract In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S -essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L 1 ([– a, a ] × [–1, 1]) ( a > 0).

Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation

This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.