Necessary and sufficient existence conditions for a boundary control of vibrations of a string and a spherical layer for small times

2011 ◽  
Vol 47 (5) ◽  
pp. 746-757
Author(s):  
S. A. Sergeev
Keyword(s):  
Boundary Control ◽  
Spherical Layer ◽  
Small Times ◽  
Existence Conditions ◽  
Necessary And Sufficient

scholarly journals BOUNDARY CONTROL PROBLEM FOR ONE DEGENERATE HIBERBOLIC EQUATION

2019 ◽  
pp. 19-27
Author(s):  
А.Х. Аттаев
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Sufficient Conditions ◽  
Analytical Form ◽  
Cauchy Data ◽  
Boundary Control Problem ◽  
Order Hyperbolic Equation ◽  
Boundary Controls ◽  
Necessary And Sufficient ◽  
Second Order Hyperbolic Equation

В работе изучается задача граничного управления для вырождающегося гиперболического уравнения второго порядка. Установлены необходимые и достаточные условия управляемости данными Коши за минимальный промежуток времени. Граничные управления предъявлены в явном аналитическом виде. The paper studies the boundary control problem for a degenerate second-order hyperbolic equation. Necessary and sufficient conditions are established for minimal time controllability over Cauchy data. Boundary controls are presented in an explicit analytical form.

scholarly journals The Combinatorial Geometry of Stresses in Frameworks

2020 ◽  
Vol 65 (1) ◽  
pp. 43-89
Author(s):  
Oleg Karpenkov
Keyword(s):  
Combinatorial Geometry ◽  
Arbitrary Graph ◽  
Existence Conditions ◽  
Straight Segments ◽  
Necessary And Sufficient

AbstractConsider a realization of a graph in the space with straight segments representing edges. Let us assign a stress for every its edge. In case if at every vertex of the graph the stresses sum up to zero, we say that the realization is a tensegrity. Some realizations possess non-zero tensegrities while the others do not. In this paper we study necessary and sufficient existence conditions for tensegrities in the plane. For an arbitrary graph we write down these conditions in terms of projective “meet-join” operations.

scholarly journals On Disturbance Decoupled Observers for a Class of Bilinear Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 371-377 ◽  
Author(s):  
M. Zasadzinski ◽  
H. Rafaralahy ◽  
C. Mechmeche ◽  
M. Darouach
Keyword(s):  
Fault Detection ◽  
Linear System ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Necessary And Sufficient Conditions ◽  
Observer Design ◽  
Unknown Inputs ◽  
Existence Conditions ◽  
Error Dynamics ◽  
Necessary And Sufficient

In this paper, the class of bilinear systems subjected to unknown inputs for which there exists a disturbance decoupled observer with linear error dynamics is characterized. It is shown that the design of this kind of observer is equivalent to the design of a disturbance decoupled observer for a linear system. This result simplifies considerably the observer design compared to those proposed in the literature, and the observer existence conditions can be easily deduced. As a corollary of this result, necessary and sufficient conditions for the existence of disturbance decoupled linear observers for bilinear systems subjected to unknown inputs are derived. This approach is extended to the fault detection of bilinear systems.

scholarly journals Existence conditions for a class of modular subgroups of genus zero

2002 ◽  
Vol 66 (3) ◽  
pp. 517-525
Author(s):  
Joachim A. Hempel
Keyword(s):  
Rational Function ◽  
Finite Index ◽  
Modular Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Genus Zero ◽  
Existence Conditions ◽  
Necessary And Sufficient

Every subgroup of finite index of the modular groupPSL(2, ℤ) has asignatureconsisting of conjugacy-invariant integer parameters satisfying certain conditions. In the case of genus zero, these parameters also constitute a prescription for the degree and the orders of the poles of a rational functionFwith the property:Functions correspond to subgroups, and we use this to establish necessary and sufficient conditions for existence of subgroups with a certain subclass of allowable signatures.

Existence conditions for two-parameter eigenvalue problems

1981 ◽  
Vol 91 (1-2) ◽  
pp. 15-30 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne ◽  
Lawrence Turyn
Keyword(s):  
Hilbert Spaces ◽  
Eigenvalue Problems ◽  
Sufficient Conditions ◽  
Compact Resolvent ◽  
Existence Conditions ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Adjoint Operators ◽  
Bounded Below ◽  
Two Parameter

SynopsisWe discuss necessary and sufficient conditions for the existence of eigentuples λ=(λl,λ2) and eigenvectors x1≠0, x2≠0 for the problem Wr(λ)xr = 0, Wr(λ)≧0, (*), where Wr(λ)= Tr + λ1Vr2, r=1,2. Here Tr and Vrs are self-adjoint operators on separable Hilbert spaces Hr. We assume the Vrs to be bounded and the Tr bounded below with compact resolvent. Most of our conditions involve the conesWe obtain results under various conditions on the Tr, but the following is typical:THEOREM. If (*) has a solution for all choices ofT1, T2then (a)0∉ V1UV2,(b)V1∩(—V2) =∅ and (c) V1⊂V2∪{0}, V2⊈V1∪{0}. Conversely, if (a) and (b) hold andV1⊈V2∪∩{0}, V2⊈ then (*) has a solution for all choices ofT1, T2.

scholarly journals Optimal boundary control problems of retarded parabolic systems

2013 ◽  
Vol 23 (3) ◽  
pp. 261-279 ◽  
Author(s):  
Adam Kowalewski ◽  
Anna Krakowiak
Keyword(s):  
Neumann Problem ◽  
Boundary Control ◽  
Sufficient Conditions ◽  
Parabolic Systems ◽  
Control Problems ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems ◽  
The Neumann Problem ◽  
Necessary And Sufficient

Abstract Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

scholarly journals On the Existence Conditions for Balanced Fractional $2^{m}$ Factorial Designs of Resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$ with $N<\nu_{\ell}(m)$

2016 ◽  
Vol 5 (4) ◽  
pp. 84
Author(s):  
Yoshifumi Hyodo ◽  
Masahide Kuwada ◽  
Hiromu Yumiba
Keyword(s):  
Factorial Design ◽  
Higher Order ◽  
Sufficient Condition ◽  
Factorial Designs ◽  
Necessary And Sufficient Condition ◽  
Main Effect ◽  
Existence Conditions ◽  
Necessary And Sufficient ◽  
Factorial Effects

We consider a fractional $2^{m}$ factorial design derived from a simple array (SA) such that the $(\ell+1)$-factor and higher-order interactions are assumed to be negligible, where $2\ell\le m$. Under these situations, if at least the main effect is estimable, then a design is said to be of resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$. In this paper, we give a necessary and sufficient condition for an SA to be a balanced fractional $2^{m}$ factorial design of resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$ for $\ell=2,3$, where the number of  assemblies is less than the number of non-negligible factorial  effects. Such a design is concretely characterized by the suffixes of the indices of an SA.

scholarly journals Homoclinic and heteroclinic solutions to a hepatitis C evolution model

2018 ◽  
Vol 16 (1) ◽  
pp. 1537-1555 ◽  
Author(s):  
Tadas Telksnys ◽  
Zenonas Navickas ◽  
Romas Marcinkevicius ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Evolution Model ◽  
Coupling Coefficients ◽  
Heteroclinic Solutions ◽  
Existence Conditions ◽  
Generalized Differential ◽  
Necessary And Sufficient ◽  
Appl Math ◽  
Topological Sense

AbstractHomoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.

Sign in / Sign up

Export Citation Format

Share Document