Norm Duality Research Articles

LA PERSPECTIVA DE GENERO EN LAS COSTUMBRES JURIDICAS DE LA POBLACION ORIGINARIA DE LA REGION PUNO

La perspectiva de género, en la construcción de una sociedad más igualitaria, no sólo es preocupación de la teoría y del debate político, ha sido incorporada en nuestra legislación y en las políticas públicas. La identificación de diversas brechas de género que se visibilizan como situaciones de desigualdad entre hombres y mujeres, en diversos espacios de desarrollo de las personas, constituye una realidad que se ha cuestionado. Es por ello que, al respecto, se ha generado preocupación del Estado y como resultado es la existencia de una inequívoca política de Estado sobre la igualdad de género. Así, se ha promulgado un marco normativo para la plasmación gradual de la igualdad entre hombres y mujeres. En diversos sectores del estado la aplicación de la perspectiva de género resulta un imperativo. Si bien esto resulta plausible, es también cierto que existe otro marco normativo que no es el oficial, y que regula con mucha eficacia la vida de las personas. Nos referimos al Derecho consuetudinario que se gesta sobre todo en las poblaciones originarias. Las costumbres constituyen un medio como se van construyendo de manera dinámica y sostenida las realidades sociales, las realidades jurídicas. Ante la dualidad de normas que regula las interrelaciones en el mundo andino, esto es, las normas legales oficiales y aquellas que provienen del Derecho Consuetudinario, es importante abordar esta temática en el derecho consuetudinario para verificar si esa dinámica normativa asume en su construcción y aplicación a la perspectiva de género. En la presente investigación, que en realidad es un fragmento de una de mayor dimensión, se busca determinar si en las costumbres jurídicas que moldean el derecho consuetudinario en las poblaciones originarias de la Región Puno se aplica la perspectiva de género, en la búsqueda de la igualdad entre hombres y mujeres.
 Respecto a la metodología, se trata de una investigación de tipo descriptivo, pues es un trabajo de campo de carácter interpretativo. Para el proceso interpretativo-analítico se utilizó el método fenomenológico-hermenéutico, pues el propósito es comprender, interpretar, profundizar en los significados desde el punto de vista del actor y establecer relaciones entre los significados y el contexto. La técnica de análisis será el Análisis Cualitativo, para recabar información que se focaliza en la entrevista. Para la selección de la muestra se consideró a informantes claves representativos de las poblaciones originarias de nuestra región, jueces de paz no letrados, autoridades comunales, ronderos y ronderas, tanto de la zona quechua como aymara de la Región Puno.
 
 Las conclusiones arribadas demuestran que en la Región de Puno, se manifiesta rezagos de una cultura de tipo patriarcal con predominio de los hombres sobre las mujeres determinando a partir de ello relaciones de desigualdad que no permiten el desarrollo de las mujeres y que estas asuman responsabilidades para las cuales cuentan con capacidades suficientes; sin embargo, en los últimos tiempos se ha venido gestando un cambio en la forma de entender la relación entre hombres y mujeres, y se está propiciando una mayor participación de las mujeres en el desarrollo familiar y social, lo que importa la aplicación paulatina de la perspectiva de género en la construcción de las realidades sociales y jurídicas. Los resultados obtenidos en la investigación podrían contribuir a generar nuevos estudios referidos al género y derecho consuetudinario, a la interculturalidad.

Enkapsis and the Development of Customary International Law: An Encyclopedic Approach to Inter-Legality

This essay draws from the work of the late Dutch Christian philosopher Herman Dooyeweerd (1894-1977), former chair of jurisprudence and the history of Dutch law at the Vrije Universiteit Amsterdam (1926-1964), to construct an account of customary international law. His little known Encylopedia of the Science of Law (ESL) not only presages by about a century but, in my view, also offers an engaging framework for studying and understanding what is now being called ‘the challenge of inter-legality,’ or the question of a ‘plurality of legalities,’ where ‘the law surfaces as the composite legal nature of the issue under scrutiny,’ and where a certain resilient and reflexive ‘material interconnectedness’ ‘among functional fields’ arises from ‘the overlapping among regimes and orders,’ which are also self-referential and coherent in themselves. Rejecting an account of the state as the sole lawmaker, he proffers a pluralist ontology founded on the philosophical principle sovereinteit in eigen kring (sphere sovereignty) as a source of diverse structural-material principles for legal or jural positivization. Here, there are three inter-related elements: first, is his notion of individuality-structures (entities), which give rise to law unique to their particular practice or sphere (entities as rule complexes, each sovereign in its own orbit, exhibiting a differentiated responsibility unique to its nature). Second is the various ways in which they engage in relations of enkapsis or enkaptic interlacements – resulting in complex intertwinements of the formal and the material sources of law with profound implications on the private-public (law) distinction. Third is his modal theory of the jural aspect, which is one of the irreducible yet interconnected universal multi-dimensional modes or aspects of reality, and through which entities and enkapses are viewed and understood as legal phenomena. In summary, his theory of the sources of law states: All law displaying the typical individuality structure of a particular community of inter-individual or inter-communal relationship, in principle falls within the material-jural sphere of competence of such a societal orbit, and is only formally connected (in its genetic form) with spheres of competence of other societal orbits. Through enkapsis, different sources of law display a mutual interrelationship that bind and limit without altogether canceling one another. For Dooyweerd, insight into the nature of enkapsis, appears to be of fundamental importance for the theory of human society because, in current conceptions, the difference in principle between sphere sovereignty and autonomy is consistently misunderstood. This insight has a fundamental bearing on any theory of the sources of law, because it is only by making a sharp distinction between the internal sphere sovereignty of radically different societal structures (such as for example, state, church, and business organization) and the autonomy of parts of one and the same societal whole (such as, for example, municipality and province within the state) can proper jural insight be obtained into the mutual relationship of the original material spheres of competence with respect to the area of law formation. Thus, a formal source or genetic form of law posivitizing jural principles may be an original source of law in one sphere of competence but may be a derived source of law in another. Applying his theory, customary international law is a formal source of law; that is, a genetic form or mode of generating international law. But its material bases may lie in the particular enkaptic interlacements involved. Further, as a formal source exhibiting the duality of norms in international law, a treaty may be a codification of norms that exist independently as custom, but it may at the same time display a multi-layered interlacement of structural-material principles from various sources.

Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets

In this paper, the problem of computing the projection, and therefore the minimum distance, from a point onto a Minkowski sum of general convex sets is studied. Our approach is based on the minimum norm duality theorem originally stated by Nirenberg and the Nesterov smoothing techniques. It is shown that projection points onto a Minkowski sum of sets can be represented as the sum of points on constituent sets so that, at these points, all of the sets share the same normal vector which is the negative of the dual solution. The proposed NESMINO algorithm improves the theoretical bound on number of iterations from $O(\frac{1}{\epsilon})$ by Gilbert [SIAM J. Contr., vol. 4, pp. 61--80, 1966] to $O\left(\frac{1}{\sqrt{\epsilon}}\ln(\frac{1}{\epsilon})\right)$, where $\epsilon$ is the desired accuracy for the objective function. Moreover, the algorithm also provides points on each component sets such that their sum is equal to the projection point.

Norm duality and the cross norm criteria for quantum entanglement

We use duality techniques to prove and generalize the cross norm and computable cross norm criteria for separability of quantum states. While the original proof of the cross norm criterion is long and involved, our new proof is short and elementary. Furthermore, our proof generalizes naturally to arbitrary Schmidt number. We also use these techniques to generalize the computable cross norm criterion to arbitrary Schmidt number and prove some results of independent interest along the way.

A New Class of Minimum Norm Duality Theorems

In this paper we derive new duality results on the width and the length of symmetrical convex bodies. Let K be a symmetrical convex body in $R^m$ and let $\|\cdot\|$ be some (arbitrary) norm on $R^m$. The width of K is obtained by searching for the smallest “sandwich” (or “slab”) that contains K. It is shown that the dual problem has the following form: Find the largest diameter of a norm ball that is contained in K. Indeed, the diameter of a maximal norm ball equals the width of the smallest sandwich. Moreover, the solutions of the two problems obey certain alignment relations. The length of K is found by searching the largest “sandwich” that contains K. The last problem is closely related to the “maximal chord problem” whose optimal value is called the “diameter” of K. In this case the dual problem is to find the smallest norm ball that contains K. It is proved that the diameter of the smallest norm ball equals the diameter (the length) of K, and that primal and dual solutions satisfy certain alignment relations. Part of the results remain valid for more general convex sets.

A New and Self-Contained Proof of Borwein’s Norm Duality Theorem

Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be relaxed.

The distance between two convex sets

In this paper we explore the duality relations that characterize least norm problems. The paper starts by presenting a new Minimum Norm Duality (MND) theorem, one that considers the distance between two convex sets. Roughly speaking the new theorem says that the shortest distance between the two sets is equal to the maximal “separation” between the sets, where the term “separation” refers to the distance between a pair of parallel hyperplanes that separates the two sets. The second part of the paper brings several examples of applications. The examples teach valuable lessons about the role of duality in least norm problems, and reveal new features of these problems. One lesson exposes the polar decomposition which characterizes the “solution” of an inconsistent system of linear inequalities. Another lesson reveals the close links between the MND theorem, theorems of the alternatives, steepest descent directions, and constructive optimality conditions.

Dedovshchina as an Element of the «Small Society» : Evidence From Russia and Other Countries.

Dedovshchina is considered as a by-product of a particular institutional organization, the «small» society. Non differentiation of the spheres of everyday life, personalized relationships, imperfect control of violence, duality of norms and the imposed authority characterize the «small» society. Dedovshchina consists in orienting the violence generated on everyday basis towards replacement victims or the victims that can be sacrificed. The «small» society produces phenomena similar to dedovshchina everywhere where it exists, in Russia as well as in the West. In the context of the Russian army, first-year soldiers transforms into replacement victims of the violence resulting from learning obedience as a centerpiece of the military service.

Theorems of the Alternative and Duality

This paper investigates the relations between theorems of the alternative and the minimum norm duality theorem. A typical theorem of the alternative is associated with two systems of linear inequalities and/or equalities, a primal system and a dual one, asserting that either the primal system has a solution, or the dual system has a solution, but never both. On the other hand, the minimum norm duality theorem says that the minimum distance from a given point z to a convex set \(\mathbb{K}\) is equal to the maximum of the distances from z to the hyperplanes separating z and \(\mathbb{K}\). We consider the theorems of Farkas, Gale, Gordan, and Motzkin, as well as new theorems that characterize the optimality conditions of discrete l1-approximation problems and multifacility location problems. It is shown that, with proper choices of \(\mathbb{K}\), each of these theorems can be recast as a pair of dual problems: a primal steepest descent problem that resembles the original primal system, and a dual least–norm problem that resembles the original dual system. The norm that defines the least-norm problem is the dual norm with respect to that which defines the steepest descent problem. Moreover, let y solve the least norm problem and let r denote the corresponding residual vector. If r=0, which means that z ∈ \(\mathbb{K}\), then y solves the dual system. Otherwise, when r≠0 and z ∉ \(\mathbb{K}\), any dual vector of r solves both the steepest descent problem and the primal system. In other words, let x solve the steepest descent problem; then, r and x are aligned. These results hold for any norm on \(\mathbb{R}^n \). If the norm is smooth and strictly convex, then there are explicit rules for retrieving x from r and vice versa.

Derivation of duality in mathematical programming and optimization theory

Consider the primal problem to minimize a function over a set of feasible solutions in Euclidean space. This paper derives a general dual problem directly from this primal problem. It shows that the Lagrangian, conjugate and Johri's formulations of duality in nonlinear programming, the linear programming duality, and the minimum norm duality principle in optimization theory are all special cases of this general duality formulation. This explains the duality — why two seemingly different problems provide the same answer — by showing that there really is no duality but that the dual problems are just different forms of the primal problem. All these results are derived in a simple, intuitive, unified manner.

Duality via halfspaces

This note shows that half spaces play a very special role in the development of duality. In addition to the minimum norm duality, the duality in linear programming, and Wolfe's and Johri's formulations in nonlinear programming can all be derived via half spaces by following an identical five step procedure.

The foundation of quantum theory and noncommutative spectral theory: Part II

The present paper comprises Sects. 5–8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having layed down the foundations in the first part of this work (which appeared in the last issue of this journal and comprises Sects. 0–4), we arrived at a dual pair 〈Y, M〉 consisting of abase norm space Y and anorder unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. (2,3) In this part we add to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and enable us to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9).

Norm duality for convex processes and applications

One can associate two norms with a Banach space convex process. These norms are dual to each other and the norm of a process agrees with the dual norm of its adjoint. This norm duality provides an extremely general and simple way of establishing surjectivity or boundedness properties of homogeneous (linear or convex) inequality systems.

Applications of the Hahn-Banach Theorem in Approximation Theory

Applications of the Hahn-Banach Theorem in Approximation Theory