Classical and quantum exact solutions for a FRW multi-scalar field cosmology with an exponential potential driven inflation

A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $\rm V(\phi,\sigma)=V_0 e^{-\lambda_1 \phi-\lambda_2 \sigma}$, which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields $\rm(\phi,\sigma)$ with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter $\rm\lambda^2=\lambda_1^2+\lambda_2^2$, as well as the e-folding function $\rm N_{e}$ which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables.Comment: Latex file, accepted in Advances and Mathematical physics, Hindawi. arXiv admin note: text overlap with arXiv:1806.0119

Las habilidad científicas en los libros de texto

El trabajo trata de analizar si los libros de texto contribuyen al desarrollo de habilidades científicas en los estudiantes de Educación Secundaria Obligatoria. La investigación se ha centrado en tres aspectos: los tipos de actividades que predominan, las habilidades científicas que se ponen en práctica y los criterios que siguen para secuenciarlas a lo largo de la etapa. Los resultados muestran que las actividades de los libros de texto están orientadas fundamentalmente al aprendizaje conceptual y que los trabajos prácticos que incluyen no permiten desarrollar la mayoría de las habilidades científicas que deberían alcanzar los estudiantes de la ESO; así mismo se comprueba que no siguen criterios coherentes para secuenciar las actividades en los diferentes cursos de la etapa

Strong enhancement of superconductivity at high pressures within the charge-density-wave states of 2H-TaS 2 and 2H-TaSe 2

We present measurements of the superconducting and charge density wave critical temperatures (Tc and TCDW) as a function of pressure in the transition metal dichalchogenides 2H-TaSe2 and 2H-TaS2. Resistance and susceptibility measurements show that Tc increases from temperatures below 1 K up to 8.5 K at 9.5 GPa in 2H-TaS2 and 8.2 K at 23 GPa in 2H-TaSe2. We observe a kink in the pressure dependence of TCDW at about 4 GPa that we attribute to the lock-in transition from incommensurate CDW to commensurate CDW. Above this pressure, the commensurate TCDW slowly decreases coexisting with superconductivity within our full pressure range.Comment: Published in Phys. Rev B 93, 184512 (2016

Bernstein-Sato functional equations, VV-filtrations, and multiplier ideals of direct summands

This paper investigates the existence and properties of a Bernstein-Sato functional equation in nonregular settings. In particular, we construct $D$-modules in which such formal equations can be studied. The existence of the Bernstein-Sato polynomial for a direct summand of a polynomial over a field is proved in this context. It is observed that this polynomial can have zero as a root, or even positive roots. Moreover, a theory of $V$-filtrations is introduced for nonregular rings, and the existence of these objects is established for what we call differentially extensible summands. This family of rings includes toric, determinantal, and other invariant rings. This new theory is applied to the study of multiplier ideals and Hodge ideals of singular varieties. Finally, we extend known relations among the objects of interest in the smooth case to the setting of singular direct summands of polynomial rings.Comment: 42 pages. A new section on Hodge ideals is included. Comments welcom