Automatic Differentiation Tools in Optimization Software

We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the gradient and Hessian matrix can be computed with guaranteed bounds in time and memory requirementsComment: 11 page

The central density of R136 in 30 Doradus

The central density rho_0 of a stellar cluster is an important physical parameter for determining its evolutionary and dynamical state. How much mass segregation there is, or whether the cluster has undergone core collapse both depends on rho_0. We reanalyze the results of a previous paper that gives the mass density profile of R136 and combine them with both a conservative upper limit for the core parameter and a more uncertain recent measurement. We thus place a lower limit on rho_0 under reasonable and defensible assumptions about the IMF, finding rho_0 >~ 1.5x10^4 Msun/pc^3 for the conservative assumption a < 0.4 pc for the cluster core parameter. If we use the lower, but more uncertain value a = 0.025 pc, the central density estimate becomes greater than 10^7 Msun/pc^3. A mechanism based on the destruction of a large number of circumstellar disks is posited to explain the hitherto unexplained increase in reddening presented in that same work.Comment: 6 pages, 2 figure

Thermal Decomposition of Diphenyl Tetroxane in Chlorobenzene Solution

The thermal decomposition of Cyclic Diperoxide of Benzaldehyde 3,6-diphenyl-1,2,4,5-tetroxane, (DFT) in chlorobenzene solution in the studied temperature range (130°C - 166°C) satisfactorily satisfies a first order law up to 60% conversions of diperoxide. DFT would decompose through a mechanism in stages and initiated by the homolytic breakdown of one of the peroxidic bonds of the molecule, with the formation of the corresponding intermediate biradical. The concentration studied was very low, so that the effects of secondary reactions of decomposition induced by free radicals originated in the reaction medium can be considered minimal or negligible. The activation parameters for the unimolecular thermal decomposition reaction of the DFT are ΔH# = 30.52 ± 0.3 kcal·mol-1 and ΔS# = -6.38 ± 0.6 cal·mol-1 K-1. The support for a step-by-step mechanism instead of a process concerted is made by comparison with the theoretically calculated activation energy for the thermal decomposition of 1,2,4,5-tetroxane.Fil: Bordón, Alexander Germán. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; ArgentinaFil: Pila, Andrea Natalia. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Profeta, Mariela Inés. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; ArgentinaFil: Jorge, María J.. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; ArgentinaFil: Jorge, Lilian Cristina. Universidad Nacional del Nordeste. Facultad de Ciencias Veterinarias; ArgentinaFil: Romero, Jorge Marcelo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; ArgentinaFil: Jorge, Nelly Lidia. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentin

UMD Banach spaces and the maximal regularity for the square root of several operators

In this paper we prove that the maximal $L^p$-regularity property on the interval $(0,T)$, $T>0$, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$.Comment: 23 pages. To appear in Semigroup Foru

Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

Relative cyclic homology of square zero extensions

Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler that the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra. We also give new proofs of two theorems of Goodwillie, obtaining an improvement of one of them.Comment: 24 pages. Definitive version, to appear in Crelle Journa

Orthogonal forms and orthogonality preservers on real function algebras

We initiate the study of orthogonal forms on a real C$^*$-algebra. Motivated by previous contributions, due to Ylinen, Jajte, Paszkiewicz and Goldstein, we prove that for every continuous orthogonal form $V$ on a commutative real C$^*$-algebra, $A$, there exist functionals $\varphi_1$ and $\varphi_2$ in $A^{*}$ satisfying $$V(x,y) = \varphi_1 (x y) + \varphi_2 (x y^*),$$ for every $x,y$ in $A$. We describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between unital commutative real C$^*$-algebras. As a consequence, we show that every orthogonality preserving linear bijection between unital commutative real C$^*$-algebras is continuous.Comment: To appear in Linear and Multilinear Algebr