The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs

Let ${\mathcal G}$ be a graph family defined on a common (labeled) vertex set $V$. A set $S\subseteq V$ is said to be a simultaneous metric generator for ${\cal G}$ if for every $G\in {\cal G}$ and every pair of different vertices $u,v\in V$ there exists $s\in S$ such that $d_{G}(s,u)\ne d_{G}(s,v)$, where $d_{G}$ denotes the geodesic distance. A simultaneous adjacency generator for ${\cal G}$ is a simultaneous metric generator under the metric $d_{G,2}(x,y)=\min\{d_{G}(x,y),2\}$. A minimum cardinality simultaneous metric (adjacency) generator for ${\cal G}$ is a simultaneous metric (adjacency) basis, and its cardinality the simultaneous metric (adjacency) dimension of ${\cal G}$. Based on the simultaneous adjacency dimension, we study the simultaneous metric dimension of families composed by lexicographic product graphs

Perceveid Social Support in middle school students

Research on school climate has among its purposes to contribute to improving the quality of education, one of the main challenges of the Mexican educational system, particularly at the level of basic education. Our aim was to explore the relationships between the dimensions of school climate of perceived social the support teacher-student, support student-student and opportunities for autonomy and academic performance. The study was non-experimental and correlational. The sample consisted of 325 students from a middle school in northeastern Mexico, with a mean age of 13.4 years who responded to a scale of perceived school climate. The results show that students perceive great teacher support associated with student-student support and opportunities for autonomy. In addition, we found that academic achievement related to teacher support and opportunities for autonomy. These data are consistent with the country´s educational policy, which emphasizes the teacher´s role as facilitator of student learning to improve learning outcomes and the quality of education.Fil: Rodriguez, María Concepción. Universidad Autónoma de Nuevo León; MéxicoFil: Vivas, Jorge Ricardo. Universidad Nacional de Mar del Plata. Facultad de Psicología. Centro de Investigación en Procesos Básicos, Metodologías y Educación; ArgentinaFil: Comesaña, Ana. Universidad Nacional de Mar del Plata. Facultad de Psicología. Centro de Investigación en Procesos Básicos, Metodologías y Educación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Ramirez, Laura Minerva. Universidad Autónoma de Nuevo León; MéxicoFil: Peña, José Armando. Universidad Autónoma de Nuevo León; Méxic

Degenerate four-wave mixing in triply-resonant Kerr cavities

We demonstrate theoretical conditions for highly-efficient degenerate four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency $\omega_0-\Delta \omega$ can, in the presence of pump light at $\omega_0$, be converted with quantum-limited efficiency into an output shifted signal of frequency $\omega_0 + \Delta \omega$, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes $\sim10$ cubic wavelengths and quality factors $\sim1000$. The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting "quantum" arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.Comment: 13 pages, 8 figures. To appear in Physical Review

EL CONTEXTO SOCIAL Y EL CAMBIO TIPOLÓGICO Y TECNOLÓGICO EN EL DISEÑO DE LAS VIVIENDAS IRREGULARES EN EL ÁREA NATURAL PROTEGIDA DEL PARQUE NACIONAL DEL NEVADO DE TOLUCA: CASO DE ESTUDIO, RAÍCES Y LOMA ALTA

Como una alternativa al análisis del deterioro del ambiente y la reducción de los recursos naturales, este artículo presenta un criterio metodológico para explicar, cómo el cambio tipológico y tecnológico de las viviendas irregulares, han establecido el detrimento del medio ambiente, así mismo, se muestra cómo se ha generado la pérdida del bosque

Improving rainfall nowcasting and urban runoff forecasting through dynamic radar-raingauge rainfall adjustment

The insufficient accuracy of radar rainfall estimates is a major source of uncertainty in short-term quantitative precipitation forecasts (QPFs) and associated urban flood forecasts. This study looks at the possibility of improving QPFs and urban runoff forecasts through the dynamic adjustment of radar rainfall estimates based on raingauge measurements. Two commonly used techniques (Kriging with External Drift (KED) and mean field bias correction) were used to adjust radar rainfall estimates for a large area of the UK (250,000 km2) based on raingauge data. QPFs were produced using original radar and adjusted rainfall estimates as input to a nowcasting algorithm. Runoff forecasts were generated by feeding the different QPFs into the storm water drainage model of an urban catchment in London. The performance of the adjusted precipitation estimates and the associated forecasts was tested using local rainfall and flow records. The results show that adjustments done at too large scales cannot provide tangible improvements in rainfall estimates and associated QPFs and runoff forecasts at small scales, such as those of urban catchments. Moreover, the results suggest that the KED adjusted rainfall estimates may be unsuitable for generating QPFs, as this method damages the continuity of spatial structures between consecutive rainfall fields