If I is a (two-sided) ideal of ring R, we let $${\text {ann}}_l(I)=\{r\in R\mid rI=0\},$$ {ann}}_r(I)=\{r\in Ir=0\},$$ and {ann}}(I)={\text {ann}}_l(I)\cap {\text {ann}}_r(I)$$ be the left, right double annihilators. An said to an annihilator if $$I={\text {ann}}(J)$$ for some J (equivalently, {ann}}({\text {ann}}(I))=I$$ ). We study ideals Leavitt path algebras graph $$C^*$$ -algebras. Let $$L...

A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer parameters range where Hopf bifurcation occurs in corresponding incompressible system. The spectrum of linearized operator time periodic function space investigated detail near point when singular perturbation parameter small. resu...

Abstract This paper explores the possibility for summing Fourier series nonlinearly via Pythagorean harmonic mean. It reports on new results this summability with introduction of concepts like smoothing operator and semi-harmonic summation. The is demonstrated to be Kalman filtering linear summability, logistic processing linearized summability. An emerging direct inapplicability seismic-like s...

In this work we study the semi-discrete linearized Benjamin-Bona-Mahony equation (BBM) which is a model for propagation of one-dimensional, unidirectional, small amplitude long waves in non-linear dispersive media. particular, derive stability estimate yields unique continuation property. The proof based on Carleman finite difference approximation Laplace operator with boundary observation larg...

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms ...

<p style='text-indent:20px;'>The spectrum structure of the linearized Boltzmann operator has been a subject interest for over fifty years and inspected in space <inline-formula><tex-math id="M2">\begin{document}$ L^2\left( {\mathbb R}^d, \exp(|v|^2/4)\right) $\end{document}</tex-math></inline-formula> by B. Nicolaenko [<xref ref-type="bibr" rid="b27">27</x...

In the previous paper, we constructed a smooth branch of travelling waves for 2 dimensional Gross-Pitaevskii equation. Here, continue study this branch. We show some coercivity results, and deduce from them kernel linearized operator, spectral stability result, as well uniqueness result in energy space. particular, our proves non degeneracy these waves, which is key step classification construc...

We study the spectral stability of nonlinear Dirac operator in dimension $$1+1$$ , restricting our attention to nonlinearities form $$f(\left\langle \psi ,\beta \right\rangle _{\mathbb {C}^2}) \beta $$ . obtain bounds on eigenvalues for linearized around standing wave solutions $$e^{-i\omega t} \phi _0$$ For case power $$f(s)= s |s|^{p-1}$$ $$p>0$$ we a range frequencies $$\omega such that has ...

In this paper, we study an ill-posed, nonlinear inverse problem in heat conduction and hy-drology applications. In 2], the problem is linearized to give a linear integral equation, which is then solved by the Tikhonov method with the identity as the regularization operator. We prove in this paper that the resulting equation is well-condition and has clustered spectrum. Hence if the conjugate gr...