We give a generalization of the notion finite Blaschke products from perspective generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these relate to so-called Shapiro--Shields and shift-invariant subspaces generated by polynomials. Applying our results, show that only entire on weighted Hardy spaces over unit disk are multiples monomials, ex...

We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3D Lipschitz domains comprising square-integrable potentials and involving only weakly singular kernels. Generalized Garding inequalities are derived we establish that the obtained Fredholm of index zero. Their finite dimensional kernels characterized show their dimension is equal to number topological inva...

We study inexact Rayleigh quotient iteration (IRQI) for computing a simple interior eigenpair of the generalized eigenvalue problem Av = λBv, providing new insights into a special type of preconditioners with “tuning” for the efficient iterative solution of the shifted linear systems that arise in this algorithm. We first give a new convergence analysis of IRQI, showing that locally cubic and q...

We consider a full-duplex state-dependent relay channel with state non-causally available at only the relay. In the framework of cooperative wireless networks, some specific terminals can be equipped with cognition capabilities, i.e, the relay in our model. In the discrete memoryless (DM) case, we obtain inner and outer bounds on the capacity. The inner bound is obtained by a coding scheme at t...

Data from direct numerical simulations (DNS) of fully-developed turbulent channel flows subjected to a constant surface heat-flux are used to explore the scaling behaviours admitted by the mean thermal energy equation. Following the framework of Wei et al. (2005) [1,2], the analysis employs a theory based on the magnitude ordering of terms in the mean thermal energy equation of wall-bounded tur...

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

This paper deals with the modeling and control of a special class of single-link flexible arms. These arms consist of flexible massless structures having some masses concentrated at certain points of the beam. In this paper, the dynamic model of such flexible arms is dewloped and some of the control properties are deduced. A robust control scheme to remove the effects of friction in the joins i...

Convolutional neural networks have become a main tool for solving many machine vision and machine learning problems. A major element of these networks is the convolution operator which essentially computes the inner product between a weight vector and the vectorized image patches extracted by sliding a window in the image planes of the previous layer. In this paper, we propose two classes of su...

We investigate the influence of the inner profile of lens objects on gravitational lens statistics taking into account of the effect of magnification bias and both the evolution and the scatter of halo profiles. We take the dark halos as the lens objects and consider the following three models for the density profile of dark halos; SIS (singular isothermal sphere), the NFW (Navarro Frenk White)...

We study an inexact implicitly restarted Arnoldi (IRA) method for computing a few eigenpairs of generalized non-Hermitian eigenvalue problems with spectral transformation, where in each Arnoldi step (outer iteration) the matrix-vector product involving the transformed operator is performed by iterative solution (inner iteration) of the corresponding linear system of equations. We provide new pe...