The Necessary Condition of the First Order in the Case of Two or More Variables, Without Constraints

1966 ◽  
pp. 27-36
Author(s):  
Ragnar Frisch
Keyword(s):  
Necessary Condition ◽  
First Order

Coercion and the Nature of Law

2020 ◽  
Author(s):  
Kenneth Einar Himma
Keyword(s):  
Conceptual Analysis ◽  
Existence Condition ◽  
Necessary Condition ◽  
First Order ◽  
Normative System ◽  
Motivating Reasons

COERCION AND THE NATURE OF LAW argues that it is a conceptually necessary condition for something to count as a system of law according to our conceptual practices that it authorizes the imposition of coercive sanctions for violations of some mandatory norms governing non-official behavior (the Coercion Thesis). The book begins with an explication of the modest approach to conceptual analysis that is deployed throughout. The remainder of the book is concerned to show that an institutional normative system is not reasonably contrived to do anything that law must be able to do for us to make sense of why we adopt systems of law to regulate non-official behavior unless we assume that mandatory norms governing that behavior are backed by the threat of a sovereign; an institutional normative system that satisfies every other plausible existence condition for law is not reasonably contrived to give rise to either objective or subjective first-order motivating reasons to comply with mandatory norms governing non-official behavior unless they are backed by the threat of a coercive sanction. Law’s presumed conceptual normativity can be explained only by the Coercion Thesis.

A Difference Method for Plane Problems in Magnetoelastodynamics

1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Difference Method ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Symmetric Hyperbolic System ◽  
Von Neumann ◽  
First Order ◽  
Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

FEEDBACK LOOPS, STABILITY AND MULTISTATIONARITY IN DYNAMICAL SYSTEMS

1995 ◽  
Vol 03 (02) ◽  
pp. 409-413 ◽  
Author(s):  
ERIK PLAHTE ◽  
THOMAS MESTL ◽  
STIG W. OMHOLT
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Negative Feedback ◽  
Feedback Loop ◽  
Feedback Loops ◽  
Necessary Condition ◽  
Negative Feedback Loop ◽  
Positive Feedback Loop ◽  
First Order ◽  
First Order Differential Equations

By fairly simple considerations of stability and multistationarity in nonlinear systems of first order differential equations it is shown that under quite mild restrictions a negative feedback loop is a necessary condition for stability, and that a positive feedback loop is a necessary condition for multistationarity.

A comparative study of two-phase flow models relevant to bubble column dynamics

1999 ◽  
Vol 394 ◽  
pp. 73-96 ◽  
Author(s):  
P. D. MINEV ◽  
U. LANGE ◽  
K. NANDAKUMAR
Keyword(s):  
Bubble Column ◽  
Bubbly Flows ◽  
Necessary Condition ◽  
Qualitative Behaviour ◽  
Two Phase ◽  
Weakly Nonlinear ◽  
Flow Models ◽  
First Order ◽  
Column Dynamics ◽  
Permanent Wave

Multiphase flow modelling is still a major challenge in fluid dynamics and, although many different models have been derived, there is no clear evidence of their relevance to certain flow situations. That is particularly valid for bubbly flows, because most of the studies have considered the case of fluidized beds. In the present study we give a general formulation to five existing models and study their relevance to bubbly flows. The results of the linear analysis of those models clearly show that only two of them are applicable to that case. They both show a very similar qualitative linear stability behaviour. In the subsequent asymptotic analysis we derive an equation hierarchy which describes the weakly nonlinear stability of the models. Their qualitative behaviour up to first order with respect to the small parameter is again identical. A permanent-wave solution of the first two equations of the hierarchy is found. It is shown, however, that the permanent-wave (soliton) solution is very unlikely to occur for the most common case of gas bubbles in water. The reason is that the weakly nonlinear equations are unstable due to the low magnitude of the bulk modulus of elasticity. Physically relevant stabilization can eventually be achieved using some available experimental data. Finally, a necessary condition for existence of a fully nonlinear soliton is derived.

Order of justice in queues of emerging markets

2020 ◽  
Vol 37 (6) ◽  
pp. 605-616
Author(s):  
Swagato Chatterjee
Keyword(s):  
Social Justice ◽  
Emerging Markets ◽  
Service Provider ◽  
Emerging Market ◽  
Social Systems ◽  
Service Evaluation ◽  
Necessary Condition ◽  
Content Type ◽  
Extant Literature ◽  
First Order

Purpose Extant literature on queuing has identified service queues as social systems where social justice is an important factor for service evaluation. First-order justice, defined as a first-come first-served (FCFS) process, has been found to be a necessary condition of social justice and positive evaluation. Second-order justice, defined as equal waiting time, has been found to be an additional factor which comes into play only when first-order justice is met. This paper aims to show that in the emerging market situation, the above definitions of justice and the order mentioned above does not work. Design/methodology/approach Instead of equal wait, the study has focused on equitable wait, i.e. waiting duration is in sync with the service needs. Three experiments have been performed to establish the hypotheses suggested. Findings FCFS is found not to be the necessary condition as it was in the extant literature and can be relaxed sometimes to get higher service evaluation by ensuring justice from the equitable wait. The study also portrays the interaction effects of the two types of social justice on service evaluation. Moreover, the impact of justice from equitable wait on service evaluations is found to be moderated by perceived personal connect of the service provider and the consumer, perceived importance of system and process and perceived ability of the service provider of capacity improvement and mediated by perceived control of service provider on providing the justice of equitable wait. Research limitations/implications The study contributes toward the understanding of social justice in service queues. It also contributes to the literature of attribution theory and consumer betrayal. Practical implications The study provides suggestions to retail managers in emerging markets to choose queue management strategies depending on the size of the retail shops and consumers’ expectations from them. Originality/value The study introduces the concept of justice from the equitable wait, which is original in the queuing literature to the best of the author’s knowledge. The study also finds a new order of justice in the emerging market scenario.

Linearization and Boundary Trajectories of Nonsmooth Control Systems

1988 ◽  
Vol 40 (3) ◽  
pp. 589-609 ◽  
Author(s):  
H. Frankowska ◽  
B. Kaśkosz
Keyword(s):  
Control System ◽  
Control Systems ◽  
Differential Inclusions ◽  
Necessary Condition ◽  
Time Interval ◽  
Control Pair ◽  
Smooth Control ◽  
First Order ◽  
Image Position ◽  
Nonsmooth Control Systems

This paper deals with boundary trajectories of non-smooth control systems and differential inclusions.Consider a control system(1.1)and denote by R(t) its reachable set at time t. Let (z, u*) be a trajectory-control pair. If for every t from the time interval [0, 1], z(t) lies on the boundary of R(t) then z is called a boundary trajectory. It is known that for systems with Lipschitzian in x right-hand side, z is a boundary trajectory if and only if z(1) belongs to the boundary of the set R(1). If z is not a boundary trajectory, that is, z(1) ∊ Int R(1) then the system is said to be locally controllable around z at time 1.A first-order necessary condition for boundary trajectories of smooth systems comes from the Pontriagin maximum principle, (see e.g. [12]).

Horn sentences in identity theory

1959 ◽  
Vol 24 (4) ◽  
pp. 306-310 ◽  
Author(s):  
K. I. Appel
Keyword(s):  
Direct Product ◽  
Identity Theory ◽  
Cartesian Product ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Index Set ◽  
First Order ◽  
Elementary Class ◽  
Necessary And Sufficient ◽  
Order Predicate Calculus

Horn [2] obtained a sufficient condition for an elementary class to be closed under direct product. Chang and Morel [1] showed that this is not a necessary condition. We will show that, if consideration is restricted to identity theory, that is, a first-order predicate calculus with equality but no other relation symbols or operation symbols, Horn's condition is necessary and sufficient.A model for identity theory consists of a non-empty domain A, but no relations or operations except equality. If I is an index set, and for each is a model for identity theory, then the direct product of the is a model for identity theory and has domain A, the cartesian product of the Ai.

scholarly journals A necessary condition ensuring the strong hyperbolicity of first-order systems

2019 ◽  
Vol 16 (01) ◽  
pp. 193-221
Author(s):  
Fernando Abalos
Keyword(s):  
Evolution Equations ◽  
Sufficient Conditions ◽  
Singular Values ◽  
Singular Value ◽  
Necessary Condition ◽  
Finite Conductivity ◽  
Charged Fluids ◽  
First Order ◽  
Value Decomposition ◽  
Necessary And Sufficient

We study strong hyperbolicity of first-order partial differential equations for systems with differential constraints. In these cases, the number of equations is larger than the unknown fields, therefore, the standard Kreiss necessary and sufficient conditions of strong hyperbolicity do not directly apply. To deal with this problem, one introduces a new tensor, called a reduction, which selects a subset of equations with the aim of using them as evolution equations for the unknown. If that tensor leads to a strongly hyperbolic system we call it a hyperbolizer. There might exist many of them or none. A question arises on whether a given system admits any hyperbolization at all. To sort-out this issue, we look for a condition on the system, such that, if it is satisfied, there is no hyperbolic reduction. To that purpose we look at the singular value decomposition of the whole system and study certain one parameter families ([Formula: see text]) of perturbations of the principal symbol. We look for the perturbed singular values around the vanishing ones and show that if they behave as [Formula: see text], with [Formula: see text], then there does not exist any hyperbolizer. In addition, we further notice that the validity or failure of this condition can be established in a simple and invariant way. Finally, we apply the theory to examples in physics, such as Force-Free Electrodynamics in Euler potentials form and charged fluids with finite conductivity. We find that they do not admit any hyperbolization.

scholarly journals Maximum principle and its extension for bounded control problems with boundary conditions

2004 ◽  
Vol 2004 (35) ◽  
pp. 1855-1879 ◽  
Author(s):  
Olga Vasilieva
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Second Order ◽  
Necessary Condition ◽  
Control Problems ◽  
Bounded Control ◽  
Singular Controls ◽  
Bounded Control Problems ◽  
The Maximum Principle ◽  
First Order

This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First-order necessary condition for optimality is obtained in the customary form of the maximum principle, and second-order necessary condition for optimality of singular controls is derived on the basis of second-order increment formula using the method of increments along with linearization approach.

Sign in / Sign up

Export Citation Format

Share Document