Dissertations / Theses on the topic 'Parabolic law of Fuller'

La production de l’huile de palme génère plusieurs déchets dont les coques de noix de palmistes (CNP). Face à l’épuisement des ressources naturelles, utilisables en technique routière, la valorisation des déchets agricoles comme les coques de noix de palmiste constitue une solution alternative d’avenir pour les pays producteurs du palmier à huile. Cette thèse étudie l’utilisation des coques de noix de palmiste comme agrégat grossier dans la formulation des composites, proposables comme matériaux de couches d’assises des chaussées à faible trafic. La première partie du manuscrit traite de l’élaboration des mélanges des coques de noix de palmiste et de la terre de barre (terre latéritique abondante dans le sud du Bénin) pour une utilisation en couche de fondation. Les proportions volumiques de chaque composite sont déterminées par la loi parabolique de Fuller-Thompson. Au laboratoire, les essais géotechniques sur le sol latéritique et sur les composites ont montré que l’ajout de 61% des CNP à la terre de barre augmente l’indice CBR de 76% à 95% de l’optimum Proctor Modifié. L’ajout de 15% de sable lagunaire dans la formulation a permis de réduire la plasticité de 29%. Ainsi, le composite (39 % de sol latéritique + 61 % de CNP) avec un indice CBR égal à 30 et le composite (45 % de sol latéritique, 40 % de CNP et 15 % de sable de lagune) avec un indice CBR égal à 41 sont utilisables en couche de fondation des routes à faible trafic. La deuxième partie est consacrée au remplacement dans un béton bitumineux semi grenu 0/10 utilisable en couche de roulement des gros granulats classiques par les coques de noix de palmiste. Les différentes compositions granulaires sont obtenues par le modèle d’empilement compressible de De Larrard. La tenue à l’eau, étudiée à travers l’essai de Duriez montre que les CNP peuvent remplacer les granulats grossiers dans les enrobés des chaussées à faible trafic. La valorisation des coques de noix de palmistes en technique routière, constitue une grosse solution technico- économique dans le désenclavement des milieux ruraux des pays tropicaux et surtout pour le transport des produits des zones de production vers celles de transformation et de consommation
The production of palm oil generates several wastes including palm kernel shells (PKS). Facing the depletion of natural resources that can be used in pavement construction, the recovery of agricultural waste such as palm kernel shells is an alternative solution for the future for oil palm producing countries. This thesis studies the use of palm kernel shells as coarse aggregate in the formulation of composites materials. The latter can be used as subbase course materials for low-traffic pavements. The first part of the manuscript deals with the production of mixtures of palm kernel shells and lateritic soil (lateritic soil abundant in the south of Benin) for use as a foundation layer. Parabolic law of Fuller-Thompson is utilized to determine the volume proportions of each composite. In the laboratory, geotechnical experiments on lateritic soil and on composites have shown that the addition of 61% PKS increases the CBR index from 76% to 95% of the Modified Proctor optimum. The addition of 15% lagoon sand in the formulation decreases the plasticity by 29%. Thus, the composites with a CBR index of 30 (39% lateritic soil + 61% PKS) and 41 (45% lateritic soil, 40% PKS and 15% lagoon sand) can be used in the foundation layer for low traffic roads. The second part focuses on the substitution of the traditional coarse aggregates by palm kernel shells in a semi-grained bituminous concrete 0/10. This type of asphalt is usable in surface wearing course. The different granular compositions are obtained by the compressible stacking model of De Larrard. The moisture resistance, studied through the Duriez test, shows that PKS can be a good alternative of coarse aggregates in lightly trafficked pavement mixes. The valorization of palm kernel shells in transportation technology is a major technical and economical solution to provide a better access to the rural areas in tropical countries. Especially, it can be useful for the transport of products from production areas to those of processing and consumption

O presente trabalho tem como finalidade demonstrar a relação entre Antropologia Filosófica e Direito a partir de duas correntes caracterizadas como antagônicas e seus respectivos expoentes: o personalismo de Lon Fuller e o economicismo de Richard Posner. Para tal, procuraremos primeiramente delimitar os conceitos com os quais trabalharemos: Antropologia Filosófica, Direito, Personalismo e Economicismo. Em seguida, apresentaremos os autores, centrando-nos principalmente na fundamentação jurídica de seu pensamento e na repercussão prática de suas teorias para evidenciar em que medida a base antropológica influencia a concepção de Direito e a ordem social. Concluiremos destacando a necessidade do conhecimento antropológico na formação jurídica no sentido de facilitar a compreensão das diversas teorias e sua consonância com os fins do Direito.
The present work aims to demonstrate the relation between Philosophical Anthropology and Law through two antagonic mainstreams and respective exponents: Lon Fuller´s personalism and the economicism of Richard Posner. For this goal, we will first offer the concepts we will be dealing with: Philosophical Anthropology, Law, Personalism and Economicism. Then, we will present the authors, mainly focusing on the legal fundamentals of their thought and practical repercussions of the theories in order to evidence how anthropological basis influence the conception of Law and the social order. To conclude, we will highlight the necessity of anthropological knowledge in legal education to facilitate the comprehension of different theories and its consonance with the ends of Law.

Criminology and legal philosophy still have much to gain from the exchange of ideas. However, attention must be paid to how this exchange is being made and what is being transferred. This project attempts to examine a currently unacknowledged exchange between the disciplines; that of an historicist, logos-centric method of knowledge production. Specifically, using a refashioned dialectic method, the debate between H.L.A. Hart and Lon L. Fuller will be compared and contrasted with Robert Agnew’s representation of criminology. This will give some clarity to the different ways by which the disciplines (re)produce knowledge. Importantly, the process of (re)production detailed here is characterized by a (dis)unity between how the disciplines rhetorically justify their methodology and the actual analyses being produced. To give this process colour, it will be examined in relation to criminology’s crisis. Ultimately, the analysis presented here raises doubts about the truthfulness of legal philosophical and criminological knowledge produced in this way.

This thesis investigates whether English law ought to be further developed to provide fuller protection for the privacy of the corporation. As an essential preliminary step, the thesis first explores the concept of privacy in general – privacy interests, definitions of privacy, rationales of privacy; and then proceeds to formulate a concept of privacy for the corporation. The thesis advances to consider the level of protection of the privacy of the corporation in English law, and finds that only a limited level of protection is provided – in broadcasting matters – by the Broadcasting Act 1996. The thesis then proceeds to critically examine whether the extended action for breach of confidence which protects an individual's privacy can and ought to be further developed to provide protection for the corporation’s privacy, and argues that the corporation’s privacy can and ought to be so developed. The thesis also investigates whether, in the alternative, the corporation’s privacy would be more suitably protected if it were developed as a property right under Article 1 of Protocol 1 ECHR, and finds that Article 1 of Protocol 1 would not suitably protect the corporation’s privacy. Instead, the thesis upholds the extended action for breach of confidence as a more natural and suitable home for the protection of the privacy of the corporation in English law. The thesis concludes with recommendations on the structural framework for the proposed protection of the corporation’s privacy under the extended action for breach of confidence. This research is undertaken primarily through doctrinal analysis; it analyses English Courts’ jurisprudence, the European Court of Human Rights jurisprudence, as well as the jurisprudence of the Court of Justice of the European Union where it concerns the administration of Article 8 ECHR. Theoretical arguments are also engaged in when it comes to defining and justifying the protection of the corporation’s privacy.

This study focused on a numerical second law analysis and optimisation of a receiver tube op- erating in a parabolic trough solar collector for small-scale application. The receiver functioned in a Rankine cycle. The focus was on entropy generation minimisation in the receiver due to the high quality exergy losses in this component. Water functioned as the working uid and was heated from ambient conditions (liquid) to a superheated state (vapour), consequently, the receiver tube was subject to both single phase as well as two-phase ow. Entropy generation in the receiver tube was mainly due to nite temperature di erences as well as uid friction. The contribution of each of these components was investigated. Geometrical as well as operating conditions were investigated to obtain good guidelines for receiver tube and plant design. An operating pressure in the range of 1 MPa (Tsat = 180 C) to 10 MPa (Tsat = 311 C) was considered. Furthermore a mass ow range of 0:15 kg=s to 0:4 kg=s was investigated. Results showed that beyond a diameter of 20 mm, the main contributor to the entropy generation was the nite temperature di erences for most conditions. Generally, operating pressures below 3 MPa showed bad performance since the uid friction component was too large for small operating pressures. This phenomenon was due to long two-phase lengths and high pressure drops in this region. The nite temperature di erence component increased linearly when the tube diameter was increased (due to the increase in exposed area) if the focused heat ux was kept constant. However, the uid friction component increased quadratically when the diameter was reduced. In general when the concentration ratio was increased, the entropy generation was decreased. This was due to more focused heat on each section of the receiver pipe and, in general, resulted in shorter receiver lengths. Unfortunately, there is a limit to the highest concentration ratio that can be achieved and in this study, it was assumed to be 45 for two-dimensional trough technology. A Simulated Annealing (SA) optimisation algorithm was implemented to obtain certain optimum parameters. The optimisation showed that increasing the diameter could result in a decrease in entropy generation, provided that the concentration ratio is kept constant. However, beyond a certain point gains in minimising the entropy generation became negligible. Optimal operating pressure would generally increase if the mass ow rate was increased. Finally, it was seen that the highest operating pressure under consideration (10 MPa) showed the best performance when considering the minimisation of entropy in conjunction with the maximisation of the thermodynamic work output.
Dissertation (MEng)--University of Pretoria, 2014.
tm2015
Mechanical and Aeronautical Engineering
MEng
Unrestricted

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Thesis (Ph. D.)--Georgia State University, 2008.
Title from file title page. Wendy Venet, committee chair; Glenn Eskew, Charles Steffen , committee members. Electronic text ( 284 p.) : digital, PDF file. Description based on contents viewed October 9, 2008. Includes bibliographical references (p. 269-284).

On etudie les systemes hyperboliques de lois de conservation en dimension un d'espace, en particulier ce qu'il reste d'une condition aux limites de dirichlet, de neumann ou melee, posee pour une perturbation parabolique du systeme, lorsque le cfficient de diffusion tend vers zero. De telles perturbations ont en general un sens physique dans le probleme qu'on etudie, elles modelisent en effet les effets de dissipation. Dans un premier temps, on montre que les limites de deux problemes differents pour l'equation de burgers, que joseph et le floch avaient decrites par des formules complexes, sont en fait egales. Il s'agit d'un probleme scalaire. Pour des systemes, la couche limite qui se forme dans le cas ou le bord n'est pas caracteristique (le cas caracteristique serait analogue au probleme, toujours ouvert, de la convergence de navier-stokes vers euler dans un domaine borne) est decrite. Par une methode d'energie, on demontre la validite du developpement asymptotique sur un intervalle de temps fini, anterieur a la formation des chocs. Dans le cas du p-systeme notamment, la condition aux limites residuelle est explicitee

Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles (EDP) non-linéaires stochastiques. Nous nous intéressons à des EDP paraboliques et hyperboliques que l’on perturbe stochastiquement au sens d’Itô. Il s’agit d’introduire l’aléatoire via l’ajout d’une intégrale stochastique (intégrale d’Itô) qui peut dépendre ou non de la solution, on parle alors de bruit multiplicatif ou additif. La présence de la variable de probabilité ne nous permet pas d’utiliser tous les outils classiques de l’analyse des EDP. Notre but est d’adapter les techniques connues dans le cadre déterministe aux EDP non linéaires stochastiques en proposant des méthodes alternatives. Les résultats obtenus sont décrits dans les cinq chapitres de cette thèse : Dans le Chapitre I, nous étudions une perturbation stochastique des équations de Barenblatt. En utilisant une semi- discrétisation implicite en temps, nous établissons l’existence et l’unicité d’une solution dans le cas additif, et grâce aux propriétés de la solution nous sommes en mesure d’étendre ce résultat au cas multiplicatif à l’aide d’un théorème de point fixe. Dans le Chapitre II, nous considérons une classe d’équations de type Barenblatt stochastiques dans un cadre abstrait. Il s’agit là d’une généralisation des résultats du Chapitre I. Dans le Chapitre III, nous travaillons sur l’étude du problème de Cauchy pour une loi de conservation stochastique. Nous montrons l’existence d’une solution par une méthode de viscosité artificielle en utilisant des arguments de compacité donnés par la théorie des mesures de Young. L’unicité repose sur une adaptation de la méthode de dédoublement des variables de Kruzhkov.. Dans le Chapitre IV, nous nous intéressons au problème de Dirichlet pour la loi de conservation stochastique étudiée au Chapitre III. Le point remarquable de l’étude repose sur l’utilisation des semi-entropies de Kruzhkov pour montrer l’unicité. Dans le Chapitre V, nous introduisons une méthode de splitting pour proposer une approche numérique du problème étudié au Chapitre IV, suivie de quelques simulations de l’équation de Burgers stochastique dans le cas unidimensionnel
This thesis deals with the mathematical field of stochastic nonlinear partial differential equations’ analysis. We are interested in parabolic and hyperbolic PDE stochastically perturbed in the Itô sense. We introduce randomness by adding a stochastic integral (Itô integral), which can depend or not on the solution. We thus talk about a multiplicative noise or an additive one. The presence of the random variable does not allow us to apply systematically classical tools of PDE analysis. Our aim is to adapt known techniques of the deterministic setting to nonlinear stochastic PDE analysis by proposing alternative methods. Here are the obtained results : In Chapter I, we investigate on a stochastic perturbation of Barenblatt equations. By using an implicit time discretization, we establish the existence and uniqueness of the solution in the additive case. Thanks to the properties of such a solution, we are able to extend this result to the multiplicative noise using a fixed-point theorem. In Chapter II, we consider a class of stochastic equations of Barenblatt type but in an abstract frame. It is about a generalization of results from Chapter I. In Chapter III, we deal with the study of the Cauchy problem for a stochastic conservation law. We show existence of solution via an artificial viscosity method. The compactness arguments are based on Young measure theory. The uniqueness result is proved by an adaptation of the Kruzhkov doubling variables technique. In Chapter IV, we are interested in the Dirichlet problem for the stochastic conservation law studied in Chapter III. The remarkable point is the use of the Kruzhkov semi-entropies to show the uniqueness of the solution. In Chapter V, we introduce a splitting method to propose a numerical approach of the problem studied in Chapter IV. Then we finish by some simulations of the stochastic Burgers’ equation in the one dimensional case

This study analyses the way that legal positivists from HLA Hart onwards have responded to Lon L Fuller’s challenge to positivism from the idea of the rule of law. The main thesis is that Hart and contemporary legal positivists working in the Hartian tradition have yet to adequately respond to Fuller’s Challenge. I argue that the reason for this is the approach they take to dealing with Fuller’s principles of the rule of law, which either (i) proceeds on the basis of the positivist perspective without engaging with Fuller’s wider anti-positivist arguments, or else (ii) accepts Fuller’s claim that the rule of law is part of our concept of law but does not acknowledge any effect of this on what determines legal validity (the content of legal norms). In both cases, I argue that tensions and problems result from a lack of engagement with Fuller’s anti-positivism. On the one hand, positivists have failed to show why their account of the nature of law better reflects our understanding of law than Fuller’s. On the other, the concessions that positivists have made to Fuller’s arguments are often detached from other elements in their theories, raising the question of whether the positivist response to Fuller is coherent. In addition, by closely analysing the major positivist accounts of the rule of law, this study challenges a number of orthodox interpretations that confuse our understanding of the positivist response to Fuller. I show that most positivists accept that there is something morally valuable about a legal system’s conformity to the principles of the rule of law, and that there is always some kind of at least minimal conformity to those principles in any legal system. By noticing what concessions positivists have made to Fuller’s understanding of the rule of law, I aim to both (i) shift the debate to the remaining disputes with the Hartian positivists, particularly on issues such as the ‘derivative approach’ and the ‘validity Social thesis’, and (ii) identify areas of fruitful engagement with Fuller, such as the question of judges’ moral obligations to law.

This thesis discusses and develops one approach to solve parabolic partial differential equations with random input data. The stochastic problem is firstly transformed into a parametrized one by using finite dimensional noise assumption and the truncated Karhunen-Loeve expansion. The approach, Monte Carlo discontinuous Galerkin (MCDG) method, randomly generates $M$ realizations of uncertain coefficients and approximates the expected value of the solution by averaging M numerical solutions. This approach is applied to two numerical examples. The first example is a two-dimensional parabolic partial differential equation with random convection term and the second example is a benchmark problem coupling flow and transport equations. I first apply polynomial kernel principal component analysis of second order to generate M realizations of random permeability fields. They are used to obtain M realizations of random convection term computed from solving the flow equation. Using this approach, I solve the transport equation M times corresponding to M velocity realizations. The MCDG solution spreads toward the whole domain from the initial location and the contaminant does not leave the initial location completely as time elapses. The results show that MCDG solution is realistic, because it takes the uncertainty in velocity fields into consideration. Besides, in order to correct overshoot and undershoot solutions caused by the high level of oscillation in random velocity realizations, I solve the transport equation on meshes of finer resolution than of the permeability, and use a slope limiter as well as lower and upper bound constraints to address this difficulty. Finally, future work is proposed.

This project, overall, involves a theory of law as dimensions. Throughout the history of the study of law, many different theoretical paradigms have emerged proffering different and competing ways to answer the question ‘what is law’? Traditionally, many of these paradigms have been at irreconcilable odds with one another. Notwithstanding this seeming reality, the goal of this project was to attempt to take three of the leading paradigms in legal theory and provide a way to explain how each might fit into a single coherent theory of law. I set out to accomplish this by drawing on the field of theoretical physics and that field’s use of spatial dimensions in explaining various physical phenomena. By engaging in a dimensional analysis of law, I found that I was able to place each paradigm within its own dimension with that dimension being defined by a specific element of time, and in doing so much of the conflict between the paradigms came to be ameliorated. The project has been divided into two main parts. PART I discusses the fundamentals of legal theory (Chapter 1) and the fundamentals of dimensions (Chapter 2). These fundamentals provide a foundation for a dimensional analysis of law which takes place throughout PART II. In Chapter 3, I argue that the three fundamental theses of Positivism coalesce with the 1st-dimension of law, which is defined as law as it exists at any one point in time. From there, I argue in Chapter 4 that the 2nd-dimension of law, being law as it exists between two points in time (i.e. when cases are adjudicated), is characterized by Pragmatism. I then turn, in Chapter 5, to argue that the 3rd-dimension of law, being law as it exists from the very first point in legal time to the ever changing present day, coalesces with the fundamental theses of Naturalism. Ultimately then, I argue that a theory of law as dimensions, through the vantage points of the specific elements of time, provides a more complete account of the nature of law.

This project uses Michel Foucault’s underdeveloped notion of “tolerated illegality” as a departure point for two converging inquiries. The first analyzes, and then critiques, dominant legal logics and values. This part argues that traditional legal philosophers exhibit a “disagreement without difference,” generally concurring that legal certainty and predictability enhance agency. Subsequently, this section critiques “formal legal” logic by linking it to science envy (specifically the desire for certainty and predictability), and highlighting its agency- limiting effects (e.g. the violence of law en-force-ment). The second part examines multiple dimensions of tolerated illegality, exploring the permutations of this complex socio-legal phenomenon. Here the implications of tolerated illegality are mapped across different domains, ranging from the dispossession of Indigenous peoples of their lands, to the latent ideologies embedded in superhero shows. This section also examines the idea of liberal “tolerance,” as well as the themes of power, domination, politics, bureaucracy, and authority. Ultimately, this project demonstrates that it is illuminating to study legality and (tolerated) illegality in tandem because although analyses of “formal legality” provide helpful analytical texture, the polymorphous and entangled nature of tolerated illegality makes clear just how restricted and artificial strict analyses of legality can be.
Graduate

Le présent mémoire est consacré à l'étude des chevauchements entre revendications territoriales autochtones. On s'y interroge sur l’origine et l’évolution de ces chevauchements ainsi que sur les mécanismes qui pourraient être employés pour trouver des solutions acceptables pour toutes les parties. Notre étude retrace d'abord l'évolution du critère d’exclusivité élaboré par les politiques et décisions judiciaires canadiennes relativement à l’octroi du titre autochtone, concluant que ce critère d’exclusivité est devenu un enjeu déterminant dans l’élaboration d’une solution relative aux chevauchements entre revendications territoriales. En observant la manière dont les différents paliers de gouvernement ont échoué dans leurs tentatives de solutionner les enjeux de chevauchement, nous constatons que les traditions juridiques autochtones doivent être intégrées à la résolution des conflits et à l’interprétation du critère d’exclusivité. Ceci exige de percevoir l’institution juridique de la résolution de conflits selon une certaine vision du droit. Nous utilisons ici celle de Lon Fuller, qui présente une approche permettant de réconcilier plusieurs traditions juridiques. Notre étude nous conduit à proposer le système du Indigenous Legal Lodge comme mécanisme de résolution de conflit permettant aux autochtones de faire appel à leurs traditions juridiques dans la résolution des chevauchements, permettant ainsi de réconcilier ces traditions diverses.
This thesis is dedicated to the study of overlapping aboriginal land claims. We question the origin and evolution of these overlaps and study the mechanisms which could be used in order to determine a solution acceptable to all parties. Our study first discusses the evolution of the exclusivity criterion developed in Canadian policy and case law relating to the granting of an aboriginal title, concluding that the criterion of exclusivity has become a defining issue in the development of a solution to overlaps between land claims. By observing the failures of the various levels of government in their attempts to develop solutions to overlapping claims, we find that Aboriginal legal traditions must be integrated into conflict resolution and be used when interpreting the exclusivity criterion. This requires us to perceive conflict resolution, as a legal institution, according to a certain understanding of the law. We use Lon Fuller’s vision, who presents an approach for reconciling various legal traditions. Our study brings us to propose the Indigenous Legal Lodge as a conflict resolution mechanism enabling Aboriginal groups to call upon their own legal traditions in resolving overlaps and to reconcile their differing traditions.

American jurisprudence currently applies two incompatible validity standards to determine which laws are enforceable. The natural law tradition evaluates validity by an uncertain standard of divine law, and its methodology relies on contradictory views of human reason. Legal positivism, on the other hand, relies on a methodology that commits the analytic fallacy, separates law from its application, and produces an incomplete model of law. These incompatible standards have created a schism in American jurisprudence that impairs the delivery of justice. This dissertation therefore formulates a new standard for legal validity. This new standard rejects the uncertainties and inconsistencies inherent in natural law theory. It also rejects the narrow linguistic methodology of legal positivism. In their stead, this dissertation adopts a pragmatic methodology that develops a standard for legal validity based on actual legal experience. This approach focuses on the operations of law and its effects upon ongoing human activities, and it evaluates legal principles by applying the experimental method to the social consequences they produce. Because legal history provides a long record of past experimentation with legal principles, legal history is an essential feature of this method. This new validity standard contains three principles. The principle of reason requires legal systems to respect every subject as a rational creature with a free will. The principle of reason also requires procedural due process to protect against the punishment of the innocent and the tyranny of the majority. Legal systems that respect their subjects' status as rational creatures with free wills permit their subjects to orient their own behavior. The principle of reason therefore requires substantive due process to ensure that laws provide dependable guideposts to individuals in orienting their behavior. The principle of consent recognizes that the legitimacy of law derives from the consent of those subject to its power. Common law custom, the doctrine of stare decisis, and legislation sanctioned by the subjects' legitimate representatives all evidence consent. The principle of autonomy establishes the authority of law. Laws must wield supremacy over political rulers, and political rulers must be subject to the same laws as other citizens. Political rulers may not arbitrarily alter the law to accord to their will. Legal history demonstrates that, in the absence of a validity standard based on these principles, legal systems will not treat their subjects as ends in themselves. They will inevitably treat their subjects as mere means to other ends. Once laws do this, men have no rest from evil.