scholarly journals Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ismail Kucuk ◽  
Kenan Yildirim
Keyword(s):  
Maximum Principle ◽  
Space Dimension ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Distributed Parameter ◽  
Hyperbolic Partial Differential Equation ◽  
The Maximum Principle ◽  
Convexity Assumptions ◽  
Necessary And Sufficient ◽  
One Space Dimension

The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality.

Necessary and sufficient conditions for optimal controls in viscous flow problems

1994 ◽  
Vol 124 (2) ◽  
pp. 211-251 ◽  
Author(s):  
H. O. Fattorini ◽  
S. S. Sritharan
Keyword(s):  
Maximum Principle ◽  
Viscous Flow ◽  
Sufficient Conditions ◽  
Optimal Controls ◽  
The Maximum Principle ◽  
Flow Problems ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Necessary And Sufficient ◽  
The Pontryagin Maximum Principle

A class of optimal control problems in viscous flow is studied. Main results are the Pontryagin maximum principle and the verification theorem for the Hamilton–Jacobi–Bellman equation characterising the feedback problem. The maximum principle is established by two quite different methods.

scholarly journals Maximum principle and existence of solutions for non necessarily cooperative systems involving Schrödinger operators

2008 ◽  
Vol 58 (5) ◽  
Author(s):  
H. Serag ◽  
A. Qamlo
Keyword(s):  
Maximum Principle ◽  
Existence Of Solutions ◽  
Schrödinger Operators ◽  
Sufficient Conditions ◽  
Cooperative Systems ◽  
Schrodinger Operators ◽  
The Maximum Principle ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient ◽  
Generalized Maximum Principle

AbstractIn this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gf q-positivity) for non cooperative systems.

Some generalized characters associated to a transitive permutation group

2020 ◽  
Vol 23 (3) ◽  
pp. 393-397
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Frobenius Group ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Transitive Permutation Group ◽  
Point Stabilizer ◽  
Necessary And Sufficient ◽  
Regular Character ◽  
Permutation Character

AbstractLet G be a finite transitive permutation group of degree n, with point stabilizer {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character {\psi_{t}=\rho_{G}-t(\pi-1_{G})}, where {\rho_{G}} is the regular character of G and {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that {\psi_{t}} is a character of G. A necessary condition is that {t\leq\min\{n-1,\lvert H\rvert\}}, and it turns out that {\psi_{t}} is a character of G for {t=n-1} resp. {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

A NOTE ON INEQUALITY CONSTRAINTS IN THE GARCH MODEL

2008 ◽  
Vol 24 (3) ◽  
pp. 823-828 ◽  
Author(s):  
Henghsiu Tsai ◽  
Kung-Sik Chan
Keyword(s):  
Generating Function ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Conditional Variance ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Economic Statistics ◽  
Absolute Monotonicity ◽  
Necessary And Sufficient ◽  
The Garch Model

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(p,q) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(p,q) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH(p,q) models with p ≥ 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for p ≥ 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.

scholarly journals Square roots in finite full transformation semigroups

1982 ◽  
Vol 23 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Mary Snowden ◽  
J. M. Howie
Keyword(s):  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Square Root ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Square Roots ◽  
Finite Set ◽  
Necessary And Sufficient

Let X be a finite set and let (X) be the full transformation semigroup on X, i.e. the set of all mappings from X into X, the semigroup operation being composition of mappings. This paper aims to characterize those elements of (X) which have square roots. An easily verifiable necessary condition, that of being quasi-square, is found in Theorem 2, and in Theorems 4 and 5 we find necessary and sufficient conditions for certain special elements of (X). The property of being compatibly amenable is shown in Theorem 7 to be equivalent for all elements of (X) to the possession of a square root.

scholarly journals On hyperbolic systems with entropy velocity covariant under the action of a group

2015 ◽  
Vol 12 (04) ◽  
pp. 763-785
Author(s):  
François Dubois
Keyword(s):  
Conservation Laws ◽  
Space Dimension ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Space Time ◽  
Systems Of Conservation Laws ◽  
Time Transformations ◽  
One Space Dimension

For hyperbolic systems of conservation laws in one space dimension endowed with a mathematical entropy, we define the notion of entropy velocity and we give sufficient conditions for such a system to be covariant under the action of a group of space-time transformations. These conditions naturally introduce a representation of the group in the space of states. We construct such hyperbolic systems from the knowledge of data on the manifold of null velocity. We apply these ideas for Galileo, Lorentz, and circular groups and, in particular, focus on nontrivial examples of [Formula: see text] systems of conservation laws.

scholarly journals Application of a Theorem in Stochastic Models of Elections

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Norman Schofield ◽  
Christopher Claassen ◽  
Ugur Ozdemir ◽  
Alexei Zakharov
Keyword(s):  
Formal Model ◽  
Sufficient Conditions ◽  
The United States ◽  
Character Trait ◽  
Necessary Condition ◽  
Presidential Candidates ◽  
Sufficient Conditions For Convergence ◽  
The Difference ◽  
Centripetal Effect ◽  
Necessary And Sufficient

Previous empirical research has developed stochastic electoral models for Israel, Turkey, and other polities. The work suggests thatconvergence to an electoral center(often predicted by electoral models) is a nongeneric phenomenon. In an attempt to explain nonconvergence, a formal model based onintrinsic valenceis presented. This theory showed that there are necessary and sufficient conditions for convergence. The necessary condition is that a convergence coefficientcis bounded above by the dimensionwof the policy space, while a sufficient condition is that the coefficient is bounded above by 1. This coefficient is defined in terms of the difference in exogenous valences, the “spatial coefficient”, and the electoral variance. The theoretical model is then applied to empirical analyses of elections in the United States and Britain. These empirical models include sociodemographic valence and electoral perceptions of character trait. It is shown that the model implies convergence to positions close to the electoral origin. To explain party divergence, the model is then extended to incorporate activist valences. This extension gives a first-orderbalance conditionthat allows the party to calculate the optimal marginal condition to maximize vote share. We argue that the equilibrium positions of presidential candidates in US elections and by party leaders in British elections are principally due to the influence of activists, rather than the centripetal effect of the electorate.

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