This work presents the application of recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all lower-order (i.e., first-, second-, third-, fourth-order) adjoint sensitivities analysis methodologies. model comprises nonlinear response, uncertain par...

Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply...

A class of non-self-adjoint fourth order differential operators with general separated boundary conditions in Weyl’s limit circle case is studied. The dissipation property of the considered operators in L2[a,b) is proven by analysis and by using the characteristic determinant, the completeness of the system of eigenfunctions and associated functions of these dissipative operators also be proven...

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation or the corresponding modified version play an important role in the study of the interface movements. In this work, we use the free software MAXIMA program symmgrp2009.max derived by W. Heremann to calculate the determining equations for the classical symm...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...