El dominio de la variable: variable didáctica en el álgebra escolar

En el análisis del discurso matemático manifiesto en un texto de álgebra escolar, hemos encontrado que el dominio de la variable es un concepto presente desde la aparición de las expresiones generalizadoras de operaciones, relaciones y propiedades de los números reales, que tan sólo se explicita en el estudio del álgebra de las expresiones algebraicas. Este concepto, junto con el de conjunto de referencia de una expresión y con el de conjunto solución, juega un papel protagónico en diferentes contextos del álgebra escolar, que le permiten configurarse como una variable didáctica imprescindible en la significación de muchos otros conceptos algebraicos.

La construcción social de la noción de variable

Este documento centra su atención en la noción de variable como elemento básico de la construcción de conceptos relacionados a fenómenos de variación y cambio. Partimos de que la variable no es una idea construida como un objeto o proceso aislado, sino que surge necesariamente de la relación de al menos dos entidades cambiantes que en la mayoría de los casos una de ellas es la variable tiempo. Pretendemos realizar el estudio de la variable desde diferentes dimensiones: la epistemológica, la cognitiva, la didáctica y la sociocultural, para poder tener elementos que nos permitan determinar qué procesos favorecen la construcción de esta noción y asimismo realizar su caracterización.

Acerca de la enseñanza de inecuaciones de una variable

En el artículo se exponen dos métodos de resolución de inecuaciones. Se comparan desde varios puntos de vista y se comentan algunos aspectos del trabajo realizado a partir de 1983 en la enseñanza de dicho tópico en la facultad de ciencias de la Universidad Central de Venezuela.

Performance analysis of a register insertion ring with a variable size buffer

There has been a recent revival of interest in the register insertion (RI) protocol because of its high throughput and low delay characteristics. Several variants of the protocol have been investigated with a view to integrating voice and data applications on a single local area network (LAN). In this paper the performance of an RI ring with a variable size buffer is studied by modelling and simulation. The chief advantage of the proposed scheme is that an efficient but simple bandwidth allocation scheme is easily incorporated. Approximate formulas are derived for queue lengths, queueing times, and total end-to-end transfer delays. The results are compared with previous analyses and with simulation estimates. The effectiveness of the proposed protocol in ensuring fairness of access under conditions of heavy and unequal loading is investigated.

Variable frequency microwave curing of polymer materials in microelectronics packaging applications

The use of variable frequency microwave technology in curing of polymer materials used in microelectronics applications is discussed. A revolutionary open-ended microwave curing system is outlined and assessed using experimental and numerical approaches. Experimental and numerical results are presented, demonstrating the feasibility of the system

Numerical simulation of encapsulant curing within a variable frequency microwave processing system

Curing of encapsulant material in a simplified microelectronics package using an open oven Variable Frequency Microwave (VFM) system is numerically simulated using a coupled solver approach. A numerical framework capable of simulating electromagnetic field distribution within the oven system, plus heat transfer, cure rate, degree of cure and thermally induced stresses within the encapsulant material is presented. The discrete physical processes have been integrated into a fully coupled solution, enabling usefully accurate results to be generated. Numerical results showing the heating and curing of the encapsulant material have been obtained and are presented in this contribution. The requirement to capture inter-process coupling and the variation in dielectric and thermophysical material properties is discussed and illustrated with simulation results.

On the application of variable frequency microwave technology for processing of individual surface mount components

Dual-section variable frequency microwave systems enable rapid, controllable heating of materials within an individual surface mount component in a chip-on=board assembly. The ability to process devices individually allows components with disparate processing requirements to be mounted on the same assembly. The temperature profile induced by the microwave system can be specifically tailored to the needs of the component, allowing optimisation and degree of cure whilst minimising thermomechanical stresses. This paper presents a review of dual-section microwave technology and its application to curing of thermosetting polymer materials in microelectronics applications. Curing processes using both conventional and microwave technologies are assessed and compared. Results indicate that dual-section microwave systems are able to cure individual surface mount packages in a significantly shorter time, at the expense of an increase in thermomechanical stresses and a greater variation in degree of cure.

Shallow water model for aluminium electrolysis cells with variable top and bottom

The MHD wave instability in commercial cells for electrolytic aluminium production is often described using ‘shallow water’ models. The model [1] is extended for a variable height cathode bottom and anode top to account for realistic cell features. The variable depth of the two fluid layers affects the horizontal current density, the wave development and the stability threshold. Instructive examples for the 500 kA cell are presented.

On variable frequency microwave processing of heterogeneous chip-on-board assemblies

Variable Frequency Microwave (VFM) processing of heterogeneous chip-on-board assemblies is assessed using a multiphysics modelling approach. The Frequency Agile Microwave Oven Bonding System (FAMOBS) is capable of rapidly processing individual packages on a Chip-On-Board (COB) assembly. This enables each package to be processed in an optimal manner, with temperature ramp rate, maximum temperature and process duration tailored to the specific package, a significant benefit in assemblies containing disparate package types. Such heterogeneous assemblies may contain components such as large power modules alongside smaller modules containing low thermal budget materials with highly disparate processing requirements. The analysis of two disparate packages has been assessed numerically to determine the applicability of the dual section microwave system to curing heterogeneous devices and to determine the influence of differing processing requirements of optimal process parameters.

Effects of exercise intensity on salivary antimicrobial proteins and markers of stress in active men

In the present study, we assessed the effects of exercise intensity on salivary immunoglobulin A (s-IgA) and salivary lysozyme (s-Lys) and examined how these responses were associated with salivary markers of adrenal activation. Using a randomized design, 10 healthy active men participated in three experimental cycling trials: 50% maximal oxygen uptake (VO2max), 75%VO2max, and an incremental test to exhaustion. The durations of the trials were the same as for a preliminary incremental test to exhaustion (22.3 min, sx = 0.8). Timed, unstimulated saliva samples were collected before exercise, immediately after exercise, and 1 h after exercise. In the incremental exhaustion trial, the secretion rates of both s-IgA and s-Lys were increased. An increase in s-Lys secretion rate was also observed at 75%VO2max. No significant changes in saliva flow rate were observed in any trial. Cycling at 75%VOmax and to exhaustion increased the secretion of alpha-amylase and chromogranin A immediately after exercise; higher cortisol values at 75%VO2max and in the incremental exhaustion trial compared with 50%VO2max were observed 1 h immediately after exercise only. These findings suggest that short-duration, high-intensity exercise increases the secretion rate of s-IgA and s-Lys despite no change in the saliva flow rate. These effects appear to be associated with changes in sympathetic activity and not the hypothalamic - pituitary - adrenal axis.

Some Ecological Consequences Of The Physiological And Biochemical Effects Of Petroleum Compounds On Marine Mollusks

The problems of relating the results of experiments in the laboratory to events in nature are twofold: to equate the response to a single variable (hydrocarbons) with the natural variability in the biological material in a multivariate environment, and to consider whether the response established experimentally has any relevance to the animal's chances of survival and reproduction (i.e. its fitness) in the natural population. Recent studies of the effects of petroleum hydrocarbons on marine invertebrates are reviewed, with an emphasis on the physiological and cytochemical responses by bivalve molluscs. The dose-response relations that emerge suggest the intensity of the 'signal' that must be detected in nature if the chronic, sublethal effects of petroleum pollution are to be measured. The natural variability in these physiological and cytochemical processes are then reviewed and the main causes of variability in natural populations, both endogenous and exogenous, discussed. These results indicate the extent of the `noise' above which the signal from possible pollution effects must be detected. The results from recent field studies on the common mussel, Mytilus edulis, are discussed. The results are as complex as expected, but it proves possible to reduce the variance in the measured responses so that pollution effects, including those due to hydrocarbons, can be detected. The ecological consequences of the observed effects of petroleum hydrocarbons are then discussed in terms of reproductive effort and reproductive value. Considerable variation between populations exists here also and this can be used to help in the interpretation of the extent of the impact of the environment on the ecology of the population. The result is to place the findings of the laboratory experiments in an ecological context of natural variability and of the physiological costs of adaptation.