The main purpose of this study is to estimate the step heat fluxes applied to the wall of a two-dimensional symmetric channel with turbulent flow. For inverse analysis, conjugate gradient method with adjoint problem is used. In order to calculate the flow field,   two equation model is used. In this study, adjoint problem is developed to conduct an inverse analysis of heat transfer in a channel...

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the n-dimensional radial momentum operator is not self-adjoint and has no selfadjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on L[(0,∞), dr] which is n...

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl–Titchmarsh half-line m-coefficients (and 2 ...

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L = A +V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the operator angles betw...

1 Definition of the Adjoint Let V be a complex vector space with an inner product < , and norm , and suppose that L : V → V is linear. If there is a function L * : V → V for which Lx, y = x, L * y (1.1) holds for every pair of vectors x, y in V , then L * is said to be the adjoint of L. Some of the properties of L * are listed below. Proof. Introduce an orthonomal basis B for V. Then find the m...

In this paper, we examine the semiclassical behavior of scattering data a non-self-adjoint Dirac operator with fairly smooth—but not necessarily analytic—potential decaying at infinity. particular, using ideas and methods from work Langer Olver [Philos. Trans. R. Soc. London, Ser. A 278(1279), 137–174 (1975)], provide rigorous analysis coefficients, Bohr–Sommerfeld condition for location eigenv...

‎in this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎the equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...

The symmetric Al-Salam and Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christi...