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 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 On the adjacency dimension of graphs

2016 ◽  
Vol 10 (1) ◽  
pp. 102-127 ◽  
Author(s):  
A. Estrada-Moreno ◽  
Y. Ramírez-Cruz ◽  
J.A. Rodríguez-Velázquez
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Arbitrary Graph ◽  
Necessary And Sufficient

In this article we study the problem of finding the k-adjacency dimension of a graph. We give some necessary and sufficient conditions for the existence of a k-adjacency basis of an arbitrary graph G and we obtain general results on the k-adjacency dimension, including general bounds and closed formulae for some families of graphs.

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.

Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

2020 ◽  
Vol 22 (03) ◽  
pp. 2050001
Author(s):  
Natalia Naumova
Keyword(s):  
Sufficient Conditions ◽  
Existence Results ◽  
Simple Games ◽  
Bargaining Set ◽  
Tu Games ◽  
Restricted Cooperation ◽  
Generalized Kernel ◽  
Existence Conditions ◽  
Necessary And Sufficient ◽  
Bargaining Sets

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions [Formula: see text] and can use coalitions from [Formula: see text]. Necessary and sufficient conditions on [Formula: see text], [Formula: see text] that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game [Formula: see text] with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if [Formula: see text] and [Formula: see text]. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author. For monotonic [Formula: see text], the condition on [Formula: see text] for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for [Formula: see text].

scholarly journals On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side

1996 ◽  
Vol 9 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Michael V. Basin
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Unbounded Operator ◽  
Infinite Dimensional ◽  
Regular Functions ◽  
Right Hand ◽  
Equivalent Equation ◽  
Vector Distribution ◽  
Existence Conditions ◽  
Necessary And Sufficient

An infinite-dimensional differential equation in vector distribution in a Hilbert space is studied in case of an unbounded operator and discontinuous regular functions in a right-hand side. A unique solution (vibrosolution) is defined for such an equation, and the necessary and sufficient existence conditions for a vibrosolution are proved. An equivalent equation with a measure, which enables us to directly compute jumps of a vibrosolution at discontinuity points of a distribution function, is also obtained. The application of the obtained results to control theory is discussed in the conclusion.

scholarly journals State-Burst Feedback Control for Fault Recovery of Input/State Asynchronous Sequential Machines

2021 ◽  
Vol 11 (21) ◽  
pp. 9790
Author(s):  
Jung-Min Yang ◽  
Seong-Jin Park ◽  
Seong Woo Kwak
Keyword(s):  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Controller Synthesis ◽  
Input State ◽  
Transient Faults ◽  
Design Flexibility ◽  
Sequential Machines ◽  
Control Scheme ◽  
Existence Conditions ◽  
Necessary And Sufficient

Static corrective controllers are more efficient than dynamic ones since they consist of only logic elements, whereas their existence conditions are more restrictive. In this paper, we present a static corrective control scheme for fault diagnosis and fault tolerant control of input/state asynchronous sequential machines (ASMs) vulnerable to transient faults. The design flexibility of static controllers is enlarged by virtue of using a diagnoser and state bursts. Necessary and sufficient conditions for the existence of a diagnoser and static fault tolerant controller are presented, and the process of controller synthesis is addressed based on the derived condition. Illustrative examples on practical ASMs are provided to show the applicability of the proposed scheme.

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