Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

Free Resolutions from Involutive Bases

We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the computation of dG certain patterns appear at several positions. In particular, it is possible to compute the constants independent of the remainder of the differential. This allows us, starting from G, to determine the Betti numbers of M without computing a minimal free resolution: Thus we obtain a new algorithm to compute Betti numbers. This algorithm has been implemented in CoCoALib by Mario Albert. This way, in comparison to some other computer algebra system, Betti numbers can be computed faster in most of the examples we have considered. For Veronese subrings S(d), we have found a Pommaret basis, which yields new proofs for some known properties of these rings. Via the theoretical statements found for G, we can identify some generators of modules in G where no constants appear. As a direct consequence, some non-vanishing Betti numbers of S(d) can be given. Finally, we give a proof of the Hyperplane Restriction Theorem with the help of Pommaret bases. This part is largely independent of the other parts of this work.

A Comparati ve Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

A Comparative Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

A Comparati ve Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

A Comparative Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

Francisco Rico y su Quijote

Este artículo-reseña valora positivamente el Quijote publicado por Francisco Rico con motivo del IV Centenario de la Segunda Parte del clásico (1615). Lo que se echa en falta no es de la exclusiva incumbencia del editor o su equipo: estudiar los libros de caballerías, la tratadística militar o la literatura hagiográfica, que se revelan fundamentales para entender el Quijote, son tareas que competen a todos los cervantistas. Detalles al margen, las herramientas a disposición del lector configuran un status quaestionis fresco y preciso; del mismo modo, las fichas lexicográficas cumplen bien su función, aunque las relativas a la botánica esperan una revisión en profundidad.

La selva confusa y Cómo se comunican dos estrellas contrarias: comedias gemelas

Cómo se comunican ha sido atribuida recientemente, por primera vez en más de tres siglos, a don Pedro Calderón de la Barca. La comparación entre esta comedia y La selva confusa, del mismo autor, avala esta atribución, ya que los paralelismos en la estructuración dramática de ambas comedias son numerosos y llamativos. Se aducen motivos para suponer que Cómo se comunican es anterior a La selva confusa, lo cual significaría una fecha tempranísima de composición dentro de la producción dramática de Calderón.

High-precision force sensing using a single trapped ion

We introduce quantum sensing schemes for measuring very weak forces with a single trapped ion. They use the spin-motional coupling induced by the laser-ion interaction to transfer the relevant force information to the spin-degree of freedom. Therefore, the force estimation is carried out simply by observing the Ramsey-type oscillations of the ion spin states. Three quantum probes are considered, which are represented by systems obeying the Jaynes-Cummings, quantum Rabi (in 1D) and Jahn-Teller (in 2D) models. By using dynamical decoupling schemes in the Jaynes-Cummings and Jahn-Teller models, our force sensing protocols can be made robust to the spin dephasing caused by the thermal and magnetic field fluctuations. In the quantum-Rabi probe, the residual spin-phonon coupling vanishes, which makes this sensing protocol naturally robust to thermally-induced spin dephasing. We show that the proposed techniques can be used to sense the axial and transverse components of the force with a sensitivity beyond the yN/\wurzel{Hz}range, i.e. in the xN/\wurzel{Hz}(xennonewton, 10^−27). The Jahn-Teller protocol, in particular, can be used to implement a two-channel vector spectrum analyzer for measuring ultra-low voltages.

Emprendimiento, instituciones y construcción de paz – Análisis de Influencia de Stakeholders en los departamentos de Nariño y Cauca

Nariño y Cauca son dos de los departamentos de Colombia más afectados por la violencia. La reciente firma de un acuerdo de un cese bilateral de hostilidades con las Fuerzas Armadas Revolucionarias de Colombia (FARC) y los diálogos de La Habana son apenas el comienzo de la Construcción de Paz (CP) que implica el esfuerzo continuo de diferentes actores (gubernamentales, sector privado, sociedad civil y organismos multilaterales) para lograr no solo una paz negativa sino una paz positiva. El apoyo al emprendimiento es una estrategia implementada por el Gobierno y por los stakeholders que participan en el proceso del posconflicto, que tiene como finalidad respaldar el proceso de integración económica de las víctimas y desmovilizados. El presente documento es un estudio exploratorio elaborado por medio de una investigación cualitativa en la temática de emprendimiento, instituciones y CP en los departamentos de Nariño y Cauca. Se utilizó una estrategia metodológica denominada Matrices de Stakeholders para representar gráficamente la influencia institucional sobre la toma decisiones e implementación de los stakeholders sobre las reformas o políticas de emprendimiento y CP en estos dos departamentos. En esta investigación se encontró que i) en general, las instituciones del gobierno de los de Nariño y Cauca son extractivas y limitan la participación de la sociedad; ii) los stakeholders de la sociedad civil a pesar de tener cierta organización y voz no están en capacidad de generar influencia más que a nivel local o comunitario; iii) los vacíos dejados por las instituciones extractivas del gobierno tienden a ser llenados por instituciones inclusivas de stakeholders del sector privado y de organismos multilaterales.