A note on the computation of the Frobenius number of a numerical semigroup

In this note we observe that the Frobenius number and therefore the conductor of a numerical semigroup can be obtained from the maximal socle degree of the quotient of the corresponding semigroup algebra by the ideal generated by the biggest generator of the semigroup.Comment: Some typos in the introduction have been correcte

In situ temperature measurements in microwave-heated gassolid catalytic systems. Detection of hot spots and solid-fluid temperature gradients in the ethylene epoxidation reaction

Infrared thermographic techniques have been used for the first time to determine real-time gas and solid temperatures, as well as gas- solid temperature gradients in microwave heated structured reactors. A special reactor vessel has been developed that allows direct observation of the catalyst under microwave heating, and an operating procedure is presented to obtain gas and solid apparent emissivities as a function of temperature. These values are thereafter used to calculate temperatures at any point in the gas and solid phases under reaction. The method has been used to obtain gas and solid temperatures during the ethylene epoxidation reaction carried out on a silver-copper oxide catalyst. The direct heating of the monolith walls produced a stable, large temperature gradient between the solid and the gas phase

LOS ANIMALES DOMÉSTICOS EN EL MODO DE VIDA DE LAS ETNIAS DE LA MONTAÑA DE GUERRERO, MÉXICO

Objective: The objective was to analyze the way the native families from Guerrero Montain integrated domestic animals to strategies for their own lives to satisfied food needed, income and productive goods.Design/methodology/approximation: Two hundred and twelve Mestizo, Na savi, Nahua and Me´phaa producers were randomly selected to be directly and personal interviewed. Sample size was calculated based on maximum variance (0.25) and margin error of 6.5%. information about labor, productive activities and recollection, external income, and grain production was recorded. Factor analysis and cluster analysis were multivariate technique used.Results: Six ways of living were identified, four of them integrated domestic animals, but all of them integrated agriculture. Dominating ways of living were Forest-Agriculture-Cattle raising-Migration (28.8%), Agriculture-Cattle raisin (27.4%) and Agriculture-Cattle raising-Migration (17%). The Mestizo families and Nahuas had easily access to productive resources than native Na savi and Me´phaa families. The current productive activities were originated since colonial time and through time immigration was integrated as income diversification.Findings/Conclusions: Integration of domestic animals and combination of labor land, forest depending on the age and experience years of producers. The absence of domestic animals motivated immigration as a source of income.Limitation of the study/implication: The experience years of producers, easily access to productive resources and the needs of the native families form the Guerrero Mountain were determining to living way of peasants.Objetivo: El objetivo fue analizar la manera de integrar animales domésticos a estrategias de vida por las familias de las Etnias de la Montaña de Guerrero, para satisfacer sus necesidades de alimentos, de ingresos y de bienes. Diseño/metodología/aproximación: Se entrevistó a 212 productores mestizos, Na savi, Nahua y Me´phaa elegidos aleatoriamente. El tamaño de muestra se calculó con base a máxima varianza (0.25) y un margende error de 6.5%. Por entrevista directa se obtuvo información de la familia, mano de obra, actividades agropecuarias y de recolección, ingreso externo y producción de granos. Los métodos análisis defactores y agrupación por clusters fueron empleados.Resultados: Se identificaron seis modos de vida, cuatro integraron animales domésticos y todos integraron agricultura. Los modos de vida dominantes fueron Bosque-Agricultura-Ganadería-Migración (28.8%), Agricultura-Ganadería (27.4%) y Agricultura-Ganadería-Migración (17%). Las familias mestizas y Nahuas tuvieron mayor acceso a recursos productivos que las familias de etnias Na savi y Me´phaa. Las actuales actividades productivas se originaron en la época colonial y con el tiempo se integró la migración, al modo de vida, para diversificar el ingreso.Limitaciones del estudio/implicaciones: Los años de experiencia, la facilidad de acceder a los recursos productivos y la necesidad de las familias de las etnias de la montaña de Guerrero fueron determinantespara los modos de vida campesina.Hallazgos/conclusiones: La integración de animales domésticos y la combinación de la tierra de labor, el bosque y los animales domésticos dependió de la edad y experiencia del productor. La ausencia deganado doméstico motiva la migración como fuente de ingresos

Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted automata, equations of ordinary generating functions and continued fractions. This new methodology is called Counting Automata Methodology. It is a variation of the technique proposed by Rutten, which is called Coinductive Counting

Energy-Efficient Thermal-Aware Scheduling for RT Tasks Using TCPN

This work leverages TCPNs to design an energy-efficient, thermal-aware real-time scheduler for a multiprocessor system that normally runs in a low state energy at maximum system utilization but its capable of increasing the clock frequency to serve aperiodic tasks, optimizing energy, and honoring temporal and thermal constraints. An off-line stage computes the minimum frequency required to run the periodic tasks at maximum CPU utilization, the proportion of each task''s job to be run on each CPU, the maximum clock frequency that keeps temperature under a limit, and the available cycles (slack) with respect to the system with minimum frequency. Then, a Zero-Laxity online scheduler dispatches the periodic tasks according to the offline calculation. Upon the arrival of aperiodic tasks, it increases clock frequency in such a way that all periodic and aperiodic tasks are properly executed. Thermal and temporal requirements are always guaranteed, and energy consumption is minimized

Primes in numerical semigroups

Let 0 be the numerical semigroup generated by a and b with Frobenius number g(a,b)=ab-a-b. In this note, we prove that there exists a prime number p in with p < g(a,b) when the product ab is sufficiently large. Two related conjectures are posed and discussed as well

Primes in numerical semigroups

Let $0Frobenius number$g(a,b)=ab-a-b$. In this note, we prove that there exists a prime number$p\in \langle a,b\rangle $with$

A flexible framework for real-time thermal-aware schedulers using timed continuous petri nets

This work presents TCPN-ThermalSim, a software tool for testing Real-Time Thermal-Aware Schedulers1. This framework consists of four main modules. The first one helps the user to define the problem: Task set with periods, deadlines and worst case execution times in CPU cycles, along with the CPU characteristics, temperature and energy consumption. The second module is the Kernel simulation, which builds up a global simulation model according to the configuration module. In the third module, the user selects the scheduler algorithm. Finally the last module allows the execution of the simulation and present the results. The framework encompasses two modes: Manual and automatic. In manual mode the simulator uses the task set data provided in the first section. In automatic mode the task set is generated by parameterizing the integrated UUniFast algorithm