scholarly journals Finite-dimensional approximations of distributed RC networks

2014 ◽  
Vol 62 (2) ◽  
pp. 263-269 ◽  
Author(s):  
W. Mitkowski
Keyword(s):  
Spectral Properties ◽  
Dynamic Properties ◽  
Numerical Calculations ◽  
Electrical Networks ◽  
State Matrix ◽  
Finite Dimensional ◽  
Rc Networks

Abstract Spectral properties of ladder and spatial electrical networks are considered. Dynamic properties of the networks are characterised by eigenvalues of the Jacobi cyclic state matrix. The effective formulas for eigenvalues of appropriate uniform systems are given. Numerical calculations were made using MATLAB.

scholarly journals Finite-dimensional maps describing the dynamics of a logistic equation with delay

2019 ◽  
Vol 487 (6) ◽  
pp. 611-616
Author(s):  
S. D. Glyzin ◽  
S. A. Kashchenko
Keyword(s):  
Numerical Simulation ◽  
Equilibrium State ◽  
Stable Equilibrium ◽  
Dynamic Properties ◽  
Logistic Equation ◽  
Mathematical Ecology ◽  
Stable Equilibrium State ◽  
Finite Dimensional ◽  
Equation With Delay ◽  
Dynamics Of Populations

This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation and presented maps are widely used in problems of mathematical ecology as models of the dynamics of populations. The paper compares the dynamic properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.

scholarly journals Spectral Enclosures and Complex Resonances for General Self-Adjoint Operators

1998 ◽  
Vol 1 ◽  
pp. 42-74 ◽  
Author(s):  
E.B. Davies
Keyword(s):  
Spectral Properties ◽  
Linear Subspace ◽  
Adjoint Operator ◽  
Dimensional Linear Subspace ◽  
Finite Dimensional ◽  
Adjoint Operators ◽  
Computation Of Eigenvalues

AbstractThis paper considers a number of related problems concerning the computation of eigenvalues and complex resonances of a general self-adjoint operator H. The feature which ties the different sections together is that one restricts oneself to spectral properties of H which can be proved by using only vectors from a pre-assigned (possibly finite-dimensional) linear subspace L.

scholarly journals Products of Positive Operators

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Maximiliano Contino ◽  
Michael A. Dritschel ◽  
Alejandra Maestripieri ◽  
Stefania Marcantognini
Keyword(s):  
Positive Operator ◽  
Hilbert Spaces ◽  
Spectral Properties ◽  
Compact Operators ◽  
Positive Operators ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Special Classes

AbstractOn finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class $${\mathcal {L}^{+\,2}}$$ L + 2 of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in $${\mathcal {L}^{+\,2}}$$ L + 2 are developed, and membership in $${\mathcal {L}^{+\,2}}$$ L + 2 among special classes, including algebraic and compact operators, is examined.

Spectral Properties of Finite-dimensional Waveguide Systems

2015 ◽  
Vol 30 ◽  
pp. 670-692
Author(s):  
Nurhan Colakoglu ◽  
Peter Lancaster
Keyword(s):  
Spectral Properties ◽  
Real Spectrum ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Waveguide Type ◽  
Central Result ◽  
Expository Paper

This is a largely expository paper in which we study a finite dimensional model for gyroscopic/waveguiding systems. We study properties of the spectrum that play an important role when computing with such models. The notion of "waveguide type" is defined and explored in this context and Theorem 3.1 provides a form of the central result (due to Abramov) concerning the existence of real spectrum for such systems. The roles of semisimple/defective eigenvalues are discussed, as well as the roles played by eigenvalue "types" (or "Krein signatures"). The theory is illustrated with examples.

scholarly journals Symmetric Properties of Eigenvalues and Eigenfunctions of Uniform Beams

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2097
Author(s):  
Daulet Nurakhmetov ◽  
Serik Jumabayev ◽  
Almir Aniyarov ◽  
Rinat Kussainov
Keyword(s):  
Nondestructive Testing ◽  
Boundary Value Problems ◽  
Mechanical System ◽  
Spectral Properties ◽  
Variable Coefficient ◽  
Boundary Value ◽  
Variable Coefficients ◽  
Numerical Calculations ◽  
Eigenvalues And Eigenfunctions ◽  
Specific Variable

In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The novelty of the research is in consideration of the models with an arbitrary variable coefficient of foundation. Qualitative results that influence the symmetry of the coefficient of foundation on the spectral properties of the corresponding problems are obtained, for which specific variable coefficients of foundation are tested using numerical calculations. Three types of fixing at the ends are studied: clamped-clamped, hinged-hinged and free-free. The conditions of the stiffness and types of beam fixing have been found for the set of eigenvalues of boundary value problems on a full segment and can be represented as two groups of the eigenvalues of certain problems on a half segment. Such qualitative spectral properties of a mechanical system can contribute to the creation of various algorithms for nondestructive testing, which are widely used in technical acoustics.

Spectral properties of two parameter eigenvalue problems II

1987 ◽  
Vol 106 (1-2) ◽  
pp. 39-51 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Separable Hilbert Space ◽  
Asymptotic Properties ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Adjoint Operators ◽  
Bounded Below ◽  
Two Parameter

SynopsisWe consider eigenvalues λ =(λ1, λ2) ∈R2 for the problem W(λ)x = 0, x ≠ 0, x ∈ H, where W(λ) = R + λ1V1 + λ2V2), and R, V1, V2 are self-adjoint operators on a separable Hilbert space H, R being bounded below with compact resolvent and V1, V2 being bounded. The i-th eigencurve Z1 is the set of eigenvalues λ, for which the i-th eigenvalue (counted according to multiplicity and in increasing order) of W(λ) vanishes. We study monotonic and asymptotic properties of Zi, and we give formulae for any asymptotes that exist. Additional results are given in the finite dimensional case.

The distribution of antigen on the surface of RBL-2H3 rat basophilic leukemia cells observed by back-scattered electron imaging

1986 ◽  
Vol 44 ◽  
pp. 274-275
Author(s):  
R.F. Stump ◽  
J.R. Pfeiffer ◽  
JC. Seagrave ◽  
D. Huskisson ◽  
J.M. Oliver
Keyword(s):  
Cell Surface ◽  
Dynamic Properties ◽  
Leukemia Cells ◽  
Antigen Binding ◽  
Scattered Electron ◽  
Ige Receptor ◽  
Receptor Complexes ◽  
Rat Basophilic Leukemia Cells ◽  
Electron Imaging ◽  
Basophilic Leukemia

In RBL-2H3 rat basophilic leukemia cells, antigen binding to cell surface IgE-receptor complexes stimulates the release of inflammatory mediators and initiates a series of membrane and cytoskeletal events including a transformation of the cell surface from a microvillous to a lamellar topography. It is likely that dynamic properties of the IgE receptor contribute to the activation of these responses. Fewtrell and Metzger have established that limited crosslinking of IgE-receptor complexes is essential to trigger secretion. In addition, Baird and colleagues have reported that antigen binding causes a rapid immobilization of IgE-receptor complexes, and we have demonstrated an apparent increase with time in the affinity of IgE-receptor complexes for antigen.

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