On the topologies induced by a cone

Let $A$ be a commutative and unital $\mathbb{R}$-algebra, and $M$ be an Archimedean quadratic module of $A$. We define a submultiplicative seminorm $\|\cdot\|_M$ on $A$, associated with $M$. We show that the closure of $M$ with respect to $\|\cdot\|_M$-topology is equal to the closure of $M$ with respect to the finest locally convex topology on $A$. We also compute the closure of any cone in $\|\cdot\|_M$-topology. Then we omit the Archimedean condition and show that there still exists a lmc topology associated to $M$, pursuing the same properties

Lower Bounds for a Polynomial on a basic closed semialgebraic set using geometric programming

$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$. The paper shows that there is an algorithm for computing such a lower bound, based on geometric programming, which applies in a large number of cases. The algorithm extends and generalizes earlier algorithms of Ghasemi and Marshall, dealing with the case $m=0$, and of Ghasemi, Lasserre and Marshall, dealing with the case $m=1$ and $g_1= M-(x_1^d+\cdots+x_n^d)$. Here, $d$ is required to be an even integer $d \ge \max\{2,\deg(f)\}$. The algorithm is implemented in a SAGE program developed by the first author. The bound obtained is typically not as good as the bound obtained using semidefinite programming, but it has the advantage that it is computable rapidly, even in cases where the bound obtained by semidefinite programming is not computable

Quest/ion of Identities in African American Feminist Postmodern Drama: A Study of Selected Plays by Suzan-Lori Parks

Innovative and unconventional, Pulitzer Prize-winning playwright Suzan-Lori Parks belongs to the continuum of African American playwrights who have contributed to the quest/ion – the quest for and question – of identities for African Americans. Her plays are sites in which the quest/ion of identities for African Americans is pursued, raised and enacted. She makes use of both page and stage to emphasize the exigency of reshaping African Americans’ identities through questioning the dominant ideologies and metanarratives, delegitimizing some of the prevailing stereotypes imposed on them, drawing out the complicity of the media in perpetuating racism, evoking slavery, lynching and their aftereffects, rehistoricizing African American history, catalyzing reflections on the various intersections of sex, race, class and gender orientations, and proffering alternative perspectives to help readers think more critically about issues facing African Americans. In my dissertation, I approach three plays by Parks – The Death of the Last Black Man in the Whole Entire World (1990), Venus (1996) and Fucking A (2000) – from the standpoints of postmodern drama and African American feminism with a focus on the terrains that reflect the quest/ion of identities for African Americans, especially African American women. I argue that postmodern drama and African American feminism provide the ground for Parks to promote the development of a political agenda in order to call into question a number of dominant ideologies and metanarratives with regard to African Americans and draw upon the roles of those metanarratives as a powerful apparatus of racial and sexual oppressions. I also explore how Parks engages with postmodern drama and African American feminism to incorporate her own mininarratives in the dominant discourses. I argue that Parks in these plays uses postmodern drama and African American feminism to encourage reflections on intersectionality in order to reveal the concerns of African Americans, particularly African American women. Her plays challenge the dominant order of hierarchy and patriarchy, while in some cases urging unity and solidarity between African American men and women by showing how unity and solidarity can help them confront race, class and gender oppressions. Furthermore, I discuss how the utilization of postmodern techniques and devices helps Parks to transform the conventional features of playwriting, to create incredulity toward the dominant systems of oppression and to incorporate her mininarratives within the context of dominant discourses.Innovatiivinen ja ennakkoluuloton Pulitzer-palkittu näytelmäkirjailija Suzan-Lori Parks kuuluu niiden afroamerikkalaisten kirjailijoiden jatkumoon, jotka ovat pyrkineet haastamaan ja uudelleen määrittelemään afroamerikkalaista identiteettiä. Hän on näytelmiensä kautta sekä tekstuaalisesti että draamallisesti korostanut afroamerikkalaisen identiteetin uudelleen määrittelyn tarvetta kyseenalaistamalla valtaideologioita ja suuria kertomuksia, purkamalla afroamerikkalaisia koskevien stereotypioiden perusteita, sekä osoittamalla median rasismia ylläpitävää valtaa. Hän on tuonut esiin orjuuden ja lynkkausten jälkivaikutuksia, kirjoittanut uudelleen afroamerikkalaisten historiaa ja virittänyt pohdintoja sosiaalisen ja biologisen sukupuolen, rodun ja luokan erilaisista intersektionaalisista vaikutuksista. Näin hän on tarjonnut lukijoille vaihtoehtoisia tapoja ajatella kriittisesti afroamerikkalaisten kohtaamia ongelmia. Väitöskirjassani analysoin Parksin kolmea näytelmää – The Death of the Last Black Man in the Whole Entire World (1990), Venus (1996) and Fucking A (2000) – postmodernin draaman ja afroamerikkalaisen feminismin näkökulmista, keskittyen seikkoihin, jotka heijastavat afroamerikkalaisten, erityisesti naisten identiteettikysymyksiä. Väitän, että postmoderni draama ja afroamerikkalainen feminismi tarjoavat Parksille keinoja edistää poliittista ohjelmaa, jonka avulla voi kyseenalaistaa erilaisia valtaideologioita ja afroamerikkalaisia koskevia suuria kertomuksia sekä osoittaa näiden suurten kertomusten merkittävää roolia rodullisessa ja sukupuolisessa alistamisessa. Analysoin myös sitä, miten Parks soveltaa postmodernia draamaa ja afroamerikkalaista feminismiä tuodakseen hallitsevaa diskurssiin omia pienoiskertomuksiaan. Väitän että näytelmissään Parks käyttää juuri näitä keinoja motivoidakseen pohdintoja intersektionaalisuudesta ja nostaakseen esiin afroamerikkalaisten, erityisesti naisten ongelmia. Hänen näytelmänsä yhtäältä haastavat hallitseva hierarkkisen ja patriarkaalisen järjestyksen ja toisaalta kannustavat afroamerikkalaisia sukupuolen ylittävään yhtenäisyyteen ja keskinäiseen solidaarisuuteen osoittamalla, miten yhtenäisyys voi auttaa vastustamaan rotu-, luokka- ja sukupuolisortoa. Pohdin lisäksi sitä, miten postmodernien tekniikoiden ja menetelmien hyödyntäminen tarjoaa Parksille keinoja muokata näytelmäkirjoituksen perinnettä, horjuttaa hallitsevien sortojärjestelmien varmuutta ja tuoda omia pienoiskertomuksiaan hallitsevan diskurssin rinnalle.Siirretty Doriast

Quest/ion of Identities in Suzan-Lori Parks’s Post-revolutionary Drama

Inspired both by the Black Arts Movement and the postmodern revolt against it, Parks has concentrated on crafting provocative plays that represent and emphasize the concerns and quest/ion of identities for African Americans. In the present essay, I argue that Parks is interested in questioning the former constructed racial boundaries of blackness and revolutionary ideologies of the Black Arts Movement without turning a blind eye to the concerns of African American community. I show that Parks attempts to escape the traditions of the Black Arts Movement, which depended on conventions of narrative realism and straightforward language to transmit its revolutionary messages. My goal is to show how Parks’s plays make use of postmodern aesthetics and paradigms to transform the conventional features of playwriting, create indeterminacies toward dominant systems of oppression and raise the quest/ion of identities for African Americans in a post-revolutionary manner

Polynomial Optimization and the Moment Problem

There are a wide variety of mathematical problems in different areas which are classified under the title of Moment Problem. We are interested in the moment problem with polynomial data and its relation to real algebra and real algebraic geometry. In this direction, we consider two different variants of moment problem. The first variant is the global polynomial optimization problem, i.e., finding the minimum of a polynomial f in R[X1,...,Xn] on R^n. It is known that this problem is NP-hard. One of the most successful approaches to this problem is semidefinite programming (SDP), which gives a polynomial time method to approximate the largest real number $r$ such that f-r is a sum of squares of polynomials. But current implementations of SDP are not able to minimize polynomials in rather small number of variables (>6) of degree >8. We make use of a result due to Hurwitz, to give a criterion in terms of coefficients of a polynomial to be a sum of squares. Then, using this criterion, we introduce a much faster method to approximate a lower bound, in this case using geometric programming. The second variant is where we wish to determine when a given multi-sequence of reals comes from a Borel measure supported on a given subset K of R^n. This is the so called K-Moment Problem. Using Jacobi's Theorem for archimedean quadratic modules, we generalize a result of Berg et al. which states that the closure of the cone sums of squares in a weighted l1-topology consists of nonnegative polynomials on a hypercube. Then we substitute l1-topology with a locally convex topology tau, sums of squares by a cone C and the hypercube by a closed set K, and study the relation between closure of C in tau and nonnegative polynomials on K to solve the moment problem for a tau-continuous linear functional on R[X1,...,Xn]. We investigate the moment problem for weighted lp-continuous psd functionals and coefficientwise convergence topology on R[X1,...,Xn]. Then, we fix a set K, and find an appropriate locally convex topology tau, such that sums of 2d powers, solves the K-moment problem for tau-continuous linear functionals. In other words, we prove that a tau-continuous linear functional nonnegative on sums of 2d powers is representable by a Borel measure on K