6,713 research outputs found
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 be a polynomial of
degree with positive coefficients and no negative coefficients, such
that when . A sharp estimate is known. In this paper
we study the 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 . 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 worldâs largest marketplace, copy machine, and instrumentality for committing crimes, torts, and infringing intellectual property. Justice Holmesâs 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 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
âTraduttore-traditoreâ: #justnot! The intersemiosis as educational challenge of arts
Um dos clichĂȘs da teoria literĂĄria e cultural Ă© o aforismo âtraduttore-traditoreâ. Se bem quem traduz Ă© sempre um traidor, Ă© tambĂ©m verdade que o papel do tradutor e da tradução sĂŁo operaçÔes necessĂĄrias. Nesse texto abordaremos a tradução intersemiĂłtica como um desafio educativo das artes. A teoria da tradução, a literatura comparada e a semiĂłtica serĂŁo os fundamentos de um axioma que consideramos ontolĂłgico: traduzo, entĂŁo existo.One of the clichĂ©s of literary and cultural theory is the aphorism âtraduttore-traditoreâ. 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
Italy: the âillegality factoryâ? Theory and practice of refugeesâ reception in Sicily
The recent surge of migrants crossing the Mediterranean in search of protection has presented a major challenge for the whole European Union. What has been labelled as a ârefugee crisisâ is first and foremost a crisis of international politics and the result of inadequate response mechanisms at local level. This paper focuses on the case of Sicily, the second main area of arrival, after Greece, when migration to the Mediterranean reached its peak. With a long history of immigration, since 2015 the Italian island has seen the implementation of a new approach based on âhotspotsâ: designated areas for the separation of those deemed as economic migrants from âgenuine asylum seekersâ. In the view of some, this has made Italy into a model of migration management, as opposed to the chaotic situation of the Greek islands. The hotspot approach, however, has been also criticised for being engrained on practices that many deem unlawful, actively producing discrimination and condemning many migrants to an illegal status on the Italian soil. Informed by findings from an international research project (EVI-MED), this paper examines this complex scenario, exploring the social, legal and human implications of the refugeesâ reception system in Italy
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