In this study, we investigate the eigenvalues and eigenvectors of a quadratic pencil of q-difference equations. The results obtained are then used to solve the corresponding system of differential equations with boundary and initial conditions and zero conditions at infinity. AMS Subject Classifications: 39A10.

The inverse spectral problem for the second-order differential pencil with quadratic dependence on parameter is studied. We obtain sufficient conditions global solvability of problem, prove its local and stability. considered in general case complex-valued coefficients arbitrary eigenvalue multiplicities. Studying stability, we take possible splitting multiple eigenvalues under a small perturba...

In this paper, we study the problem on small motions of two Oldroyd viscoelastic incompressible fluids contained in a fixed vessel. By means operator approach, reduce original initial-boundary to Cauchy for an operator-differential equation Hilbert space and prove well-posed solvability arbitrary time interval. We deduce normal oscillations considered hydraulic system (the Krein generalized pen...

A first-order partial differential equation with constant irreversible coefficients in a Banach space is considered. In the particular case of finite-dimensional space, initial-boundary-value problem matrix has no solution; hence, we pose Showalter-type conditions. Due to regularity operator pencil, splits into equations subspaces and given conditions lead initial subspaces. solution constructe...

Der Beitrag befasst sich mit einer Diskussion von Mode und Nachhaltigkeit in der Informationsund Kommunikationstechnik (IKT) am Beispiel des Eingabestifts (englisch Stylus oder Touch Pen). Die wechselhafte Entwicklungsgeschichte des Eingabestifts wirft die Frage auf, ob es sich beim Eingabestift um ein nachhaltiges Bedienkonzept der IKT handelt oder ggf. nur um eine (wiederkehrende) Modeerschei...

High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish...

We study Fredholmness of nonlocal boundary value problems for fourth order elliptic differential-operator equations in UMD Banach spaces. The main condition is given in terms of R-boundedness of some families of bounded operators generated by inverse of the characteristic operator pencil of the equation. Then we prove an isomorphism of the problem on the semi-axis, for some special boundary con...

The study evaluated the comparability of two versions of a certification test: a paperand-pencil test (PPT) and computer-based test (CBT). An effect size measure known as Cohen’s d and differential item functioning (DIF) analyses were used as measures of comparability at the test and item levels, respectively. Results indicated that the effect sizes were small (d < 0.20) and not statistically s...

A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available PENCIL CODE is validated with the focus on hydrogen combustion. This is the first open source DNS code with detailed chemistry available. An attempt has been made to present, for the first time, the full set of evolution and auxiliary equ...

A new laser differential confocal lens refractive index measurement is proposed, which uses the absolute zero of the differential confocal axial intensity curve to precisely identify the positions of the objective when the measurement pencil is focused on the vertex of the test lens and the reflector with or without the test lens in the measurement light-path, and then uses aberration compensat...