The Functional Argument

AbstractIn this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

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The Functional Argument

Legal Directives and Practical Reasons ◽

10.1093/oso/9780199659876.003.0007 ◽

2018 ◽

pp. 97-132

Author(s):

Noam Gur

Keyword(s):

Collective Action ◽

Practical Reasoning ◽

Pivotal Role ◽

Reasons For Action ◽

Intended Function ◽

Guiding Function ◽

Functional Argument ◽

Relevant Consideration

This chapter discusses law’s capacity to fulfil its conduct-guiding function within different frameworks of practical reasoning. A functional argument of Raz is initially presented: according to this argument, authorities—including legal authorities—would not be able to fulfil their intended function if their directives operated as reasons for action that compete with opposing reasons in terms of their weight, rather than as pre-emptive reasons (Section 6.1). Several grounds for this argument are considered and found to be inadequate (Section 6.2). The spotlight is then directed onto another relevant consideration: law’s structural suitability to counteract several situational biases operative in contexts of individual and collective action (Sections 6.3.1–6.3.5). It is argued that law’s pivotal role in addressing practical problems linked with those biases strongly militate against the weighing model (Sections 6.3.6). Finally, the implications of those biases for the pre-emption thesis are discussed (Sections 6.3.7).

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A Note on an Oscillation Criterion for an Equation with a Functional Argument

Canadian Mathematical Bulletin ◽

10.4153/cmb-1968-071-2 ◽

1968 ◽

Vol 11 (4) ◽

pp. 593-595 ◽

Cited By ~ 36

Author(s):

Paul Waltman

Keyword(s):

Oscillatory Solution ◽

Oscillation Criterion ◽

All Solutions ◽

Image Position ◽

Functional Argument ◽

Oscillation Of Solutions

It might be thought that, as far as the oscillation of solutions is concerned, the behaviour ofandwould be the same as long as t - α(t) → ∞ as t→∞. To motivate the theorem presented in this note, we show first that this is not the case. Consider the above equation with α(t) = 3t/4, a(t) = l/2t2 i.e.This equation has the non-oscillatory solution y(t) = t1/2 although all solutions ofare oscillatory [1, p. 121].

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Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument

Georgian Mathematical Journal ◽

10.1515/gmj.2000.373 ◽

2000 ◽

Vol 7 (2) ◽

pp. 373-378

Author(s):

Aiqin Qi ◽

Yansheng Liu

Keyword(s):

Differential Equations ◽

Periodic Boundary ◽

Boundary Value ◽

Upper And Lower Solutions ◽

Initial Value ◽

First Order ◽

Monotone Iterative ◽

Periodic Boundary Value Problems ◽

Functional Argument ◽

First Order Differential Equations

Abstract This paper is concerned with periodic boundary value problems involving first order differential equations with functional arguments. The main feature of the paper is that the existence of maximal and minimal solutions is obtained by constructing sequences of upper and lower solutions of the initial value problems and not by establishing the comparison principle.

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L'évolution des rapports entre le droit canadien et le droit international un demi-siècle après l'affaire des conventions internationales de travail

Canadian Yearbook of international Law/Annuaire canadien de droit international ◽

10.1017/s0069005800003210 ◽

1988 ◽

Vol 25 ◽

pp. 301-324

Author(s):

A.L.C. De Mestrall

Keyword(s):

International Law ◽

Constitutional Amendment ◽

English Canada ◽

Supreme Court Of Canada ◽

Exclusive Jurisdiction ◽

The Supreme Court ◽

The Government ◽

Government Of Canada ◽

Droit International ◽

Functional Argument

SummaryThis article reviews the suggestion implicit in two recent obiter dicta of the Supreme Court of Canada and the widely held view in English Canada that the Labour Conventions Reference was wrongly decided, and that parliament should have exclusive jurisdiction to implement any treaty. It is argued that reversal of this rule would constitute a fundamental change in the nature of the Canadian federal system; is not warranted by any functional argument and has never been requested by the principal interested party, namely the government of Canada. It is also argued that the only proper way to make such a change is by way of formal constitutional amendment. Given the existence of a host of treaties covering every imaginable field of human conduct, a blank cheque to parliament to implement any treaty would in effect constitute one of the most major changes of the Constitution in our hutory. Among the problems considered is that of the extreme fluidity of the concept of a treaty in international law. The author suggests that other avenues exist for the expansion of federal legislative jurisdiction to implement treaties in the field of international trade if this is necessary.

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IS FINNIS WRONG?

Legal Theory ◽

10.1017/s1352325208070109 ◽

2007 ◽

Vol 13 (3-4) ◽

pp. 257-283 ◽

Cited By ~ 6

Author(s):

Veronica Rodriguez-Blanco

Keyword(s):

Practical Reason ◽

Third Reich ◽

Customary Law ◽

Theoretical Research ◽

Ethical Perspective ◽

Central Case ◽

The Third Reich ◽

The Concept Of Law ◽

Functional Argument ◽

Concept Of Law

Judges and lawyers believe that international law, customary law, and legal systems such as the Third Reich or apartheid law in South Africa are law. But how do we explain the fact that there is one concept of law when there are different conceptions of law with a variety of different features? Finnis, inspired by the Aristotelian notion of central case, adumbrates the idea that the concept of law might be unified by a primary concept which is the concept of “law as practical reason”; that is, law conceived from an ethical perspective. He advances two arguments to defend his methodology: the conceptual and the functional. Contra Finnis, the paper shows that neither the conceptual nor the functional argument can successfully support the view that “law as practical reason” is the central case of the concept of law. The study clarifies the Aristotelian notion of central case and illustrates the mistaken application of this notion to the concept of law. However, we also argue that Finnis's insight–the idea that all the different conceptions of law might be unified for the purposes of theoretical research–is fundamental and appealing. This paper aims to reconstruct Finnis's insight through the model of core resemblance. The result is that the different conceptions of law can be unified by resemblance to the concept of “law as practical reason,” though there is no identity among the different conceptions of law.

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