Approximating Positive Polynomials Using Sums of Squares

2003 ◽  
Vol 46 (3) ◽  
pp. 400-418 ◽  
Author(s):  
M. Marshall

AbstractThe paper considers the relationship between positive polynomials, sums of squares and the multi-dimensional moment problem in the general context of basic closed semi-algebraic sets in real n-space. The emphasis is on the non-compact case and on quadratic module representations as opposed to quadratic preordering presentations. The paper clarifies the relationship between known results on the algebraic side and on the functional-analytic side and extends these results in a variety of ways.

2016 ◽  
pp. 15
Author(s):  
Mariana Giaretto ◽  
Victoria Naffa

ResumenEn este trabajo analizamos las relaciones entre tomas de tierras y Estado, en elAlto Valle de Río Negro en Argentina. En un contexto general de especulacióninmobiliaria, por la que se encarecen los precios de alquileres y terrenos, y depolíticas de vivienda selectivas y acotadas, los sectores populares acceden aun espacio en la ciudad mediante tomas de tierras. Frente a estos conflictos,el Estado, en sus diferentes niveles y poderes, despliega una forma deintervención basada en la criminalización de las luchas por tierra y vivienda.Al mismo tiempo, el poder ejecutivo nacional crea la Secretaría de Acceso alHábitat, para posibilitar la intervención política orientada a la regularizaciónde los asentamientos. Sin embargo, esta intervención tiende a reinscribir laproblemática habitacional en el campo político, para reducirla a un conflicto“entre partes”, eludiendo la responsabilidad estatal.Desde un enfoque metodológico cualitativo, seleccionamos como referenteempírico el caso del asentamiento de Villa Obrera en Fiske, Menuco (Gral.Roca), y las técnicas de recolección de datos se basan en fuentes secundarias,como expedientes judiciales y normativa, y en fuentes primarias como son losrelatos de los protagonistas mediante entrevistas individuales y colectivas.Palabras clave: tomas de tierras, Estado, criminalización de los conflictos.Conflicts caused by land occupation and modesof State intervention: analysis of an experience ofAlto Valle in Río Negro (Argentina)AbstractThis paper analyzes the relationship between State and land occupation,at Alto Valle in Río Negro, Argentina. In a general context of real estatespeculation, where rents and land prices are expensive, and a policy ofselective and limited housing, popular sectors can have access to a spacein the city through land occupation. In front of these conflicts, the Statein its different levels and powers, displays a form of intervention basedon the criminalization of struggles for land and housing. At the sametime, the national executive creates the Secretariat of Access to Habitat,oriented to allow political intervention for the regularization of settlements.However, this intervention tends to re-register the housing problems in thepolitical arena, reducing it to a conflict “between parties” and eluding theresponsibility of the State.From a qualitative methodological approach, we selected as empirical referencethe case of the settlement of Villa Obrera in Fiske, Menuco (GeneralRoca). The techniques of data collection are based on secondary sources, suchas policy and legal records, and primary sources as the stories of protagoniststhrough individual and collective interviews.Keywords: land occupation, State, criminalization of conflicts.Conflitos sobre ocupações de terras e modos deintervenção do estado: análise de uma experiênciado Alto Valle do Rio Preto (Argentina)ResumoEste trabalho analisa as relações entre a posse de terra e o Estado, no AltoValle do Rio Preto, na Argentina. Num contexto geral da especulaçãoimobiliária, por qual se encarecem os preços do aluguel e das terras, e depolíticas de habitação seletivas e limitadas, os setores populares acedem aum espaço na cidade através de ocupações de terras. Frente a estes conflitos,o Estado, em seus diferentes níveis e poderes, desenvolve uma forma deintervenção com base na criminalização das lutas pela terra e vivenda. Aomesmo tempo, o poder executivo nacional cria a Secretaria de Acesso àHabitat para possibilitar à intervenção política orientada a regularização dosassentamentos. No entanto, esta intervenção tende a registrar os problemasde habitação no campo político, para reduzi-la a um conflito “entre aspartes”, iludindo a responsabilidade do Estado.A partir de uma abordagem metodológica qualitativa, foi selecionado comoreferência empírica o caso do Assentamento de Villa Obrera em Fiske,Menuco (Gral. Roca), e as técnicas de recolecção de dados são baseados emfontes secundárias, como expedientes judiciais e normativos, e em fontes primárias como são as histórias dos protagonistas através de entrevistasindividuais e coletivas.Palavras-chave: tomada de terras, Estado, criminalização dos conflitos.


Elenchos ◽  
2019 ◽  
Vol 40 (2) ◽  
pp. 383-400
Author(s):  
Manuel Mazzetti

Abstract The purpose of this paper is to identify the upholders of the thesis reported by Plutarch, De Stoicorum repugnantiis 23, aimed to reject Stoic determinism. A brief introduction will be devoted to the relationship between this text and the more general context of the Stoic philosophy. Then, I will take into account the objection against Stoic determinism raised by some anonymous philosophers: according to it, causal determinism would be inconsistent with the choice among indistinguishables. Chrysippus replied that if that choice were not determined, it would occur without causes; and this would be absurd. Then I will summarize the most likely hypotheses about the identification of Chrysippus’ opponents, and I will opt for Academics. Finally, I will try to conjecture the link between Plutarch’s passage and the debate among Stoics and Academics about indistinguishables, as we know it from other sources.


2017 ◽  
Vol 2019 (11) ◽  
pp. 3313-3375 ◽  
Author(s):  
Igor Klep ◽  
Scott McCullough ◽  
Klemen Šivic ◽  
Aljaž Zalar

Abstract A $\ast$-linear map $\Phi$ between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations $I_n\otimes \Phi$ are positive. In this article, quantitative bounds on the fraction of positive maps that are completely positive are proved. A main tool is the real algebraic geometry techniques developed by Blekherman to study the gap between positive polynomials and sums of squares. Finally, an algorithm to produce positive maps that are not completely positive is given.


1980 ◽  
Vol 32 (6) ◽  
pp. 1325-1332 ◽  
Author(s):  
J. A. Bondy ◽  
R. C. Entringer

The relationship between the lengths of cycles in a graph and the degrees of its vertices was first studied in a general context by G. A. Dirac. In [5], he proved that every 2-connected simple graph on n vertices with minimum degree d contains a cycle of length at least min{2d, n};. Dirac's theorem was subsequently strengthened in various directions in [7], [6], [13], [12], [2], [1], [11], [8], [14], [15] and [16].Our aim here is to investigate another aspect of this relationship, namely how the lengths of the cycles in a 2-connected graph depend on the maximum degree. Let us denote by ƒ(n, d) the largest integer k such that every 2-connected simple graph on n vertices with maximum degree d contains a cycle of length at least k. We prove in Section 2 that, for d ≧ 3 and n ≧ d + 2,


2018 ◽  
Vol 16 (1-2) ◽  
pp. 253-312
Author(s):  
David Durand-Guédy

AbstractThis article deals with the history of Isfahan during the five centuries between the arrival of the Turks and the beginning of the Safavid period. It attempts to identify the continuities and ruptures from three different perspectives: To what extent can we speak of an urban decline? What was the relationship of the Isfahanis with the imperial rulers? How did the general context impact the makeup and the organisation of the society? It appears that Isfahan demonstrated remarkable resilience over the period, and that it is only beginning with the Timurid period that we can speak of a decline. Likewise, there is remarkable continuity in the ways in which the local elites collaborated with or resisted the imperial players. The role of the Ṣāʿid family, which held the cadial function over four centuries, is emblematic in this respect. Conversely, under special circumstances, the imperial players were able to exert great substantial influence on the local communities, and it is this political backing which explains the strengthening of the Hanafis in the sixth/twelfth century, and that of the Shiis in the following. One of the main accomplishments of this synthesis view of Isfahan history is that it assesses the effects of the Mongol domination relative to that of other periods.


Author(s):  
Mihai Putinar ◽  
Florian-Horia Vasilescu

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