A Natural Rank Problem for Homogeneous Polynomials and Connections with the Theory of Functions of Several Complex Variables

We study a natural extremal problem about the vector space consisting of all homogeneous polynomials of degree $d$ in $n+1$ variables with real coefficients, together with the zero polynomial. We define the {\it rank} of a polynomial to be the number of distinct monomials appearing in the polynomial with non-zero coefficient. We are particularly interested in those homogeneous polynomials whose quotient with the homogeneous polynomial $x_0+x_1+\cdots+x_n$ is a polynomial of degree $d-1$ with maximal rank. For each degree $d$, we seek the minimum rank for an element of this subfamily and we seek to describe those polynomials with minimum rank. We call such polynomials {\it sharp} polynomials. These problems have a simple solution for polynomials in one and two variables. The three-variable case is interesting and non-trivial, but well-understood. This research question has its roots in the study of proper polynomial mappings between balls in complex Euclidean spaces of different dimensions and the degree estimates problem. D\u27Angelo, Kos and Riehl \cite{degree} and Lebl and Peters \cite{hyperplaneq} used a graph-theoretic approach to solve this problem in the case of proper monomial mappings. Lebl and Peters give a minimum rank estimate that answers our question in the three variable case. A family of sharp polynomials was described by D\u27Angelo and has been extensively studied. Brooks and Grundmeier \cite{notes} provided a new proof of the minimum rank theorem in the three-variable case using a commutative algebra approach. They reformulate the problem as a question about homogeneous ideals and address it by studying the Hilbert function and the graded Betti number of certain ideals. Using the same method as Brooks and Grundmeier, we give a sharp estimate for the minimum rank of homogeneous polynomials of our subfamily in four variables as well as a family of sharp polynomials. Moreover, we state a general result on the minimum rank for polynomials in $n+1$ variables. Although this estimate is sharp in the three- and four- variable cases, the estimate is not sharp when the number of variables is greater than four

DISEÑO DE EDIFICIOS DE CUATRO NIVELES EMPLEANDO AISLADORES SÍSMICOS DE BASE FRICCIONAL DE TRIPLE PÉNDULO FPT PARA LA ZONA SÍSMICA #4 DE GUATEMALA

El presente trabajo de investigación realiza el análisis sísmico con criterios de diseño para la funcionalidad continua en construcciones fundamentales, con el fin de minimizar el daño que logre padecer los elementos estructurales, no estructurales y elementos de una construcción ante sismos severos, a un daño menor. Para esto se hace la comprobación si una estructura de base fija y base aislada poseen la función de conseguir los parámetros que instituye la funcionalidad continua. Comenzando con la recolección y adquisición de datos acerca de la funcionalidad continua y la conducta de los aisladores de tipo triple péndulo friccional. La modelación y estudio sísmico para las condiciones presentadas se hace en el programa ETABS con el cual desde los resultados logrados se tendrá la posibilidad de validar o negar las hipótesis propuestas en el trabajo. Llevando a cabo esta comprobación en la muestra de análisis de una construcción de 4 niveles con una configuración estructural a base de marcos dúctiles de concreto reforzado, en diferentes municipios en la cual se realiza la comprobación tomando en cuenta la estructura con base fija y para la misma implementada con el aislador FPT

The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness

Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with minimal smoothness (namely, the class $C^2$) and let $b$ be a locally integrable function on $D$. We characterize boundedness (resp., compactness) in $L^p(D), p > 1$, of the commutator $[b, P]$ of the Bergman projection $P$ in terms of an appropriate bounded (resp. vanishing) mean oscillation requirement on $b$. We also establish the equivalence of such notion of BMO (resp., VMO) with other BMO and VMO spaces given in the literature. Our proofs use a dyadic analog of the Berezin transform and holomorphic integral representations going back (for smooth domains) to N. Kerzman & E. M. Stein, and E. Ligocka.Comment: 35 pages with references; published versio

Aplicación del Índice de Seguridad en Centros Educativos (ISCE) en módulos educativos del C. E. INSA, en el municipio de Santa Ana, departamento de Santa Ana, El Salvador

El Salvador es un país muy vulnerable a diversos eventos catastróficos, ya sean de origen natural o antrópico. Y los edificios de los centros educativos no son la excepción. Una de las necesidades primordiales por la cual es importante conocer el estado actual en el que se encuentran los edificios, es debido a que albergan a estudiantes a partir de los 3 años de edad, los cuales son más vulnerables ante cualquier tipo de desastre

Host-parasite co-metabolic activation of antitrypanosomal aminomethyl-benzoxaboroles

<div><p>Recent development of benzoxaborole-based chemistry gave rise to a collection of compounds with great potential in targeting diverse infectious diseases, including human African Trypanosomiasis (HAT), a devastating neglected tropical disease. However, further medicinal development is largely restricted by a lack of insight into mechanism of action (MoA) in pathogenic kinetoplastids. We adopted a multidisciplinary approach, combining a high-throughput forward genetic screen with functional group focused chemical biological, structural biology and biochemical analyses, to tackle the complex MoAs of benzoxaboroles in <i>Trypanosoma brucei</i>. We describe an oxidative enzymatic pathway composed of host semicarbazide-sensitive amine oxidase and a trypanosomal aldehyde dehydrogenase TbALDH3. Two sequential reactions through this pathway serve as the key underlying mechanism for activating a series of 4-aminomethylphenoxy-benzoxaboroles as potent trypanocides; the methylamine parental compounds as pro-drugs are transformed first into intermediate aldehyde metabolites, and further into the carboxylate metabolites as effective forms. Moreover, comparative biochemical and crystallographic analyses elucidated the catalytic specificity of TbALDH3 towards the benzaldehyde benzoxaborole metabolites as xenogeneic substrates. Overall, this work proposes a novel drug activation mechanism dependent on both host and parasite metabolism of primary amine containing molecules, which contributes a new perspective to our understanding of the benzoxaborole MoA, and could be further exploited to improve the therapeutic index of antimicrobial compounds.</p></div

Report from Working Group 3: Beyond the standard model physics at the HL-LHC and HE-LHC

This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as $3$ ab$^{-1}$ of data taken at a centre-of-mass energy of 14 TeV, and of a possible future upgrade, the High Energy (HE) LHC, defined as $15$ ab$^{-1}$ of data at a centre-of-mass energy of 27 TeV. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by $20-50\%$ on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will, generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis