Uniqueness of certain polynomials constant on a line

We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let $p(x,y)$ be a polynomial of degree $d$ with $N$ positive coefficients and no negative coefficients, such that $p=1$ when $x+y=1$. A sharp estimate $d \leq 2N-3$ is known. In this paper we study the $p$ for which equality holds. We prove some new results about the form of these "sharp" polynomials. Using these new results and using two independent computational methods we give a complete classification of these polynomials up to $d=17$. The question is motivated by the problem of classification of CR maps between spheres in different dimensions.Comment: 20 pages, latex; removed section 10 and address referee suggestions; accepted to Linear Algebra and its Application

Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

The Path of Internet Law: An Annotated Guide to Legal Landmarks

The evolution of the Internet has forever changed the legal landscape. The Internet is the world’s largest marketplace, copy machine, and instrumentality for committing crimes, torts, and infringing intellectual property. Justice Holmes’s classic essay on the path of the law drew upon six centuries of case reports and statutes. In less than twenty-five years, Internet law has created new legal dilemmas and challenges in accommodating new information technologies. Part I is a brief timeline of Internet case law and statutory developments for Internet-related intellectual property (IP) law. Part II describes some of the ways in which the Internet is redirecting the path of IP in a globalized information-based economy. Our broader point is that every branch of substantive and procedural law is adapting to the digital world. Part III is the functional equivalent of a GPS for locating the latest U.S. and foreign law resources to help lawyers, policymakers, academics and law students lost in cyberspace

Polynomials with no zeros on the bidisk

We prove a detailed sums of squares formula for two variable polynomials with no zeros on the bidisk $\mathbb{D}^2$ extending previous versions of such a formula due to Cole-Wermer and Geronimo-Woerdeman. The formula is related to the Christoffel-Darboux formula for orthogonal polynomials on the unit circle, but the extension to two variables involves issues of uniqueness in the formula and the study of ideals of two variable orthogonal polynomials with respect to a positive Borel measure on the torus which may have infinite mass. We present applications to two variable Fej\'er-Riesz factorizations, analytic extension theorems for a class of bordered curves called distinguished varieties, and Pick interpolation on the bidisk.Comment: 52 page

External managers, family ownership and the scope of SME internationalization

SMEs are important to world business and the majority of SMEs are family firms. Yet some family SMEs are inert, local firms while others are dynamic and international. Do certain governance structures encourage the scale and scope of their internationalization? We jointly apply social capital and corporate governance theories to explain the scope of family SMEs internationalization, and find that professional managers externally recruited from outside the family are important, but only for lower levels of family ownership, suggesting synergistic combinations of ownership and management. It is the combination of external capital with external managers that really works

On the Observability of Giant Protoplanets in Circumstellar Disks

We investigate the possibility to detect giant planets that are still embedded in young circumstellar disks. Based on models with different stellar, planetary, and disk masses, and different radial positions of the planet we analyze the resulting submillimeter appearance of these systems. We find that the influence of the planet on the spectral energy distribution could not be distinguished from that of other disk parameters. However, dust reemission images of the disks show that the hot region in the proximity of a young planet, along with the gap, could indeed be detected and mapped with the Atacama Large Millimeter Array in the case of nearby circumstellar disks (d<100pc) in approximate face-on orientation.Comment: ApJ, in pres

“Traduttore-traditore”: #justnot! The intersemiosis as educational challenge of arts

Um dos clichês da teoria literária e cultural é o aforismo “traduttore-traditore”. Se bem quem traduz é sempre um traidor, é também verdade que o papel do tradutor e da tradução são operações necessárias. Nesse texto abordaremos a tradução intersemiótica como um desafio educativo das artes. A teoria da tradução, a literatura comparada e a semiótica serão os fundamentos de um axioma que consideramos ontológico: traduzo, então existo.One of the clichés of literary and cultural theory is the aphorism “traduttore-traditore”. Although who translates is always a traitor, it is also true that the role of the translator and translation are necessary operations. In this text we will discuss intersemiotic translation as an educational challenge of the arts. Translation theory, comparative literature and semiotics are the foundations of an axiom we consider ontological: I translate, therefore I am

Polyphenols and Athletic Performance: A Review on Human Data

Exercise-induced aerobic bioenergetic reactions in mitochondria and cytosol increase production of reactive oxygen species. Many efforts have been carried out to identify dietary strategies or micronutrients able to prevent or at least attenuate the exercise-induced muscle damage and stress. A lot of studies are about how effective dietary intervention and oral antioxidant supplementation may be in reducing oxidative stress in athletes who exercise intensively. Commonly used nonenzymatic supplements have been proposed as ways to prevent exercise-induced oxidative stress and hence improve adaptation responses to endurance training. Plant-derived bioactive compounds can repress inflammation by inhibiting oxidative damage and interacting with the immune system. This review focuses on polyphenols and phytochemicals present in the plant kingdom that have been recently suggested to exert some positive effects on exercise-induced muscle damage and oxidative stress. This review will summarize some of the actual knowledge on polyphenolic compounds that have been demonstrated both to exert a significant effect in exercise-induced muscle damage and to play a biological/physiological role in improving physical performance. Overall, the pooled results show that polyphenols are viable supplements to improve performance in athletes

Conceito de cura da luxação recidivante do ombro

ResumoO presente trabalho analisa as principais técnicas cirúrgicas empregadas no tratamento da luxação recidivante do ombro (LRO), com o objetivo de obter a normalidade da amplitude dos movimentos articulares e associar diferentes tempos cirúrgicos num único procedimento para obter uma capacidade funcional completa, sem comprometer a normalidade dos movimentos, por causa das suturas tensas usadas nas cirurgias de Putti‐Platt, Bankart, Latarjet, Dickson‐O’Dell e outras.Após cuidadosa revisão desses métodos em uso, chegamos à conclusão de que a LRO pode ser considerada resolvida quanto à porcentagem de cura (97%). Permanecem, no entanto, limitações dos movimentos na grande maioria dos casos, aceitas até como necessárias para evitar recidivas.O nosso objetivo cirúrgico visa à obtenção de uma recuperação funcional completa, atuar simultaneamente sobre as várias lesões anatomopatológicas e abandonar a ideia das chamadas “lesões essenciais”.A imobilização do ombro operado será feita somente durante a cicatrização das partes moles em rotação neutra. Com o uso de um enxerto ósseo pediculado dispensa‐se qualquer tipo de imobilização prolongada, por causa da estabilidade obtida pela osteossíntese da coracoide no rebordo da glenoide, como na técnica de Latarjet.Essa nossa conduta, empregada desde 1959, consiste, portanto, na associação das várias técnicas com as quais se obtêm a cura sem limitação dos movimentos, por causa da redução da tensão nas suturas da cápsula e dos músculos subescapular e coracobraquial empregadas nas técnicas acima.AbstractThis paper presents the main surgical techniques applied in the treatment of anterior recurrent shoulder dislocation, aiming the achievement of the normality of articulate movements. This was obtained by combining distinct surgical procedures, which allowed the recovery of a complete functional capacity of the shoulder, without jeopardizing the normality of movement, something that has not been recorded in the case of the tense sutures of the surgical procedures of Putti‐Platt, Bankart, Latarjet, Dickson‐O’Dell and others.The careful review of the methods applied supports the conclusion that recurrent shoulder dislocation can be cured, since cure has been obtained in 97% of the treated cases. However, some degree of limitation in the shoulder movement has been observed in most of the treated cases.Our main goal was to achieve a complete shoulder functional recovery, by treating simultaneously all of the anatomical‐pathological lesions, without considering the so‐called essential lesions.The period of post‐operatory immobilization only last for the healing of soft parts; this takes place in a position of neutral shoulder rotation, since the use of vascular bone graft eliminates the need for long time immobilization, due to the shoulder stabilization provided by rigid fixation of the coracoid at the glenoid edge, as in the Latarjet's technique.Our procedure, used since 1959, comprises the association of several techniques, which has permitted shoulder healing without movement limitation. That was because of the tension reduction in the sutures of the subescapularis, capsule, and coracobraquialis muscles