Necessary and sufficient conditions for stability of switched Hamiltonian systems with multiple equilibria

2013 ◽  
Author(s):  
Liying Zhu
Keyword(s):  
Hamiltonian Systems ◽  
Multiple Equilibria ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

scholarly journals KÄHLER POLARIZATION AND WICK QUANTIZATION OF HAMILTONIAN SYSTEMS SUBJECT TO SECOND-CLASS CONSTRAINTS

2002 ◽  
Vol 17 (02) ◽  
pp. 121-129
Author(s):  
S. L. LYAKHOVICH ◽  
A. A. SHARAPOV
Keyword(s):  
Hamiltonian Systems ◽  
Deformation Quantization ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class Constraint ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Dirac Brackets ◽  
Necessary And Sufficient ◽  
Constraint Surface

The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) Kähler manifold. The deformation quantization for such systems is mentioned resulting in the Wick-type symbols for the respective Dirac brackets.

scholarly journals Accountability and Information in Elections

2017 ◽  
Vol 9 (2) ◽  
pp. 95-138 ◽  
Author(s):  
Scott Ashworth ◽  
Ethan Bueno de Mesquita ◽  
Amanda Friedenberg
Keyword(s):  
Multiple Equilibria ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Voter Behavior ◽  
Institutional Reforms ◽  
Trade Off ◽  
Institutional Variation ◽  
Necessary And Sufficient

Elections are thought to improve voter welfare through two channels: effective accountability (i.e., providing incentives for politicians to take costly effort) and electoral selection (i.e., retaining politicians with characteristics voters value). We show that there may be a trade-off between these two channels. Higher levels of effective accountability may hinder the voters' ability to learn about the politicians. In turn, this may hinder electoral selection and be detrimental to voter welfare. This is because increasing effective accountability directly impacts how informative governance outcomes are about an incumbent's type. We show that, if politicians' effort and type are local substitutes (resp. complements) in the production of governance outcomes, an increase in effective accountability corresponds to a decrease (resp. increase) in Blackwell (1951) informativeness. We also show that effective accountability can vary even absent institutional variation. In particular, we provide necessary and sufficient conditions for there to be multiple equilibria that differ in terms of both effective accountability and electoral selection. Overall, our findings have implications for voter behavior, the efficacy of institutional reforms, and voter welfare. (JEL D72, D83)

A Note on the Bogdanov–Takens Bifurcation in the Romer Model with Learning by Doing

2017 ◽  
Vol 27 (01) ◽  
pp. 1750002
Author(s):  
Giovanni Bella
Keyword(s):  
Endogenous Growth ◽  
Multiple Equilibria ◽  
Sufficient Conditions ◽  
Learning By Doing ◽  
Necessary And Sufficient Conditions ◽  
Poverty Trap ◽  
Bifurcation Theorem ◽  
Necessary And Sufficient

This paper is aimed at describing the whole set of necessary and sufficient conditions for the emergence of multiple equilibria and global indeterminacy in the standard endogenous growth framework with learning by doing. The novelty of this paper relies on the application of the original Bogdanov–Takens bifurcation theorem, which allows us to characterize the full dynamics of the model, and determine the emergence of an unavoidable poverty trap.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

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