The Case of H2_2C3_3O Isomers, Revisited: Solving the Mystery of the Missing Propadienone

To date, two isomers of H$_2$C$_3$O have been detected, namely, propynal (HCCCHO) and cylclopropenone (c-H$_2$C$_3$O). A third, propadienone (CH$_2$CCO), has thus far eluded observers despite the fact that it is the lowest in energy of the three. This previously noted result is in contradiction of the minimum energy principle, which posits that the abundances of isomers in interstellar environments can be predicted based on their relative stabilities - and suggests, rather, the importance of kinetic over thermodynamic effects in explaining the role of such species. Here, we report results of \textit{ab initio} quantum chemical calculations of the reaction between H and (a) HC$_3$O, (b) H$_2$C$_3$O (both propynal and propadienone), and (c) CH$_2$CHCO. We have found that, among all possible reactions between atomic hydrogen and either propadienone or propynal, only the destruction of propadienone is barrierless and exothermic. That this destruction pathway is indeed behind the non-detection of CH$_2$CCO is further suggested by our finding that the product of this process, the radical CH$_2$CHCO, can subsequently react barrierlessly with H to form propenal (CH$_2$CHCHO) which has, in fact, been detected in regions where the other two H$_2$C$_3$O isomers are observed. Thus, these results not only shed light on a previously unresolved astrochemical mystery, but also further highlight the importance of kinetics in understanding the abundances of interstellar molecules.Comment: ApJ, accepted: 14 pages, 2 figure

Algunas soluciones exactas para una ecuación de Klein Gordon

In solving practical problems in science and engineering arises as a direct consequence differential equations that explains the dynamics of the phenomena. Finding exact solutions to this equations provides importan information about the behavior of physical systems. The Lie symmetry method allows tofind invariant solutions under certain groups of transformations for differential equations.This method not very well known and used is of great importance in the scientific community. By this approach it was possible to find several exactinvariant solutions for the Klein Gordon Equation uxx − utt = k(u). A particularcase, The Kolmogorov equation uxx − utt = k1u + k2un was considered.These equations appear in the study of relativistic and quantum physics. The general solutions found, could be used for future explorations on the study for other specific K(u) functions.Al resolver problemas prácticos en ciencia e ingeniería surge como consecuencia directa las ecuaciones diferenciales que explican la dinámica de los fenómenos. Encontrar soluciones exactas a estas ecuaciones proporciona información importante sobre el comportamiento de los sistemas físicos. El método de simetría de Lie permite encontrar soluciones invariantes bajo ciertos grupos de transformaciones para ecuaciones diferenciales. Este método, poco conocido y utilizado, es de gran importancia en la comunidad científica. Mediante este enfoque, fue posible encontrar varias soluciones exactas invariables para la ecuación de Klein Gordon uxx - utt = k (u). Un caso particular, se consideró la ecuación de Kolmogorov uxx - utt = k1u + k2un. Estas ecuaciones aparecen en el estudio de la física relativista y cuántica. Las soluciones generales encontradas podrían utilizarse para futuras exploraciones en el estudio para otras funciones específicas de K (u)

Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions in coalitions), assuming that preferences are given. However, there is little discussion on this assumption. In fact, agents receive different utilities if they belong to different partitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be computed in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational or complexity assumptions

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Desarrollo de competencias docentes en la Licenciatura en Enseñanza de las Matemáticas de la Universidad de Colima, mediante la implementación de una comunidad de práctica

Este proyecto de intervención aborda el desarrollo de competencias docentes en la Licenciatura en Enseñanza de las Matemáticas de la Universidad de Colima, mediante la implementación de una comunidad de práctica basada en los principios de gestión del conocimiento. Las fases desarrolladas fueron creación de una comunidad de práctica con los docentes de matemáticas, mapeo del conocimiento, combinación del conocimiento en la organización mediante el diseño del plan de intervención para la gestión de competencias docentes centradas en el aprendizaje, uso del conocimiento mediante la implementación de la intervención y toma de decisiones sobre la difusión, almacenamiento y acceso al conocimiento construido en la Facultad de Ciencias de la Educación de la Universidad de Colima. Los métodos de recolección de datos fueron la observación y entrevista. De manera concluyente se puede afirmar que los docentes de la Licenciatura en Enseñanza de las Matemáticas de la Universidad de Colima incorporaron estrategias centradas en el aprendizaje en su planeación de asignatura y su práctica docente

On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule

We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest non-trivial example is given by the N=2 SQM with a real $(1,2,1)$ multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian hamiltonian is encountered when solving the equation of motion of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page

Supersymmetric Nambu−-Jona-Lasinio Model on N=1/2{\cal N}=1/2 four-dimensional Non(anti)commutative Superspace

We construct the Lagrangian of the ${\cal N}=1$ four-dimensional generalized supersymmetric Nambu$-$Jona-Lasinio (SNJL) model, which has ${\cal N}=1/2$ supersymmetry (SUSY) on non(anti)commutative superspace. A special attention is paid to the examination on the nonperturbative quantum dynamics: The phenomenon of dynamical-symmetry-breaking/mass-generation on the deformed superspace is investigated. The model Lagrangian and the method of SUSY auxiliary fields of composites are examined in terms of component fields. We derive the effective action, examine it, and solve the gap equation for self-consistent mass parameters.Comment: 16 pages, TeX mistakes corrected, accepted for publication in JHEP, 25 Jan. 200