Algunas demostraciones del valor de la potencia de un punto con respecto a una circunferencia

Se proponen tres demostraciones sobre el valor de la potencia de un punto con respecto a una circunferencia. La primera utiliza el método de la geometría analítica, y las propiedades de las soluciones de la ecuación de segundo grado. La segunda se basa sólo en el Teorema de Pitágoras. Y, la tercera utiliza el álgebra de vectores. Por último, se da el resultado de la potencia de un punto con respecto a una elipse. Con esto se intenta suplir el hueco en los libros de texto, de nivel de Bachillerato, que no recogen una demostración general sobre la constancia de la potencia del punto con respecto a una circunferencia.

Estrategias utilizadas en la traducción del lenguaje natural al lenguaje algebraico

En esta comunicación presentamos parte de los resultados obtenidos en las investigaciones realizadas dentro de Planes Nacionales de Investigación Educativa del C.I.D.E. durante los cursos 1987-88 y 1988-89, que trataban de averiguar las dificultades del aprendizaje del álgebra en secundaria. El objetivo inicial de este trabajo era estudiar las dificultades planteadas en la resolución de problemas de enunciado verbal en los que se utiliza una ecuación de primer grado o un sistema lineal de dos ecuaciones con dos incógnitas, ya que considerabamos, como la mayoría de los profesores lo hace, que la mayor dificultad presentada en álgebra estaba en la resolución de estos problemas.

La equivalencia de las representaciones de la solución particular por los métodos de reducción de orden y variación de parámetros

Usando el método de variación de parámetros, construimos la solución particular de una ecuación diferencial de segundo orden. Luego demostramos que es una representación diferente pero equivalente a aquella solución construida por el método de reducción de orden.

Calcium currents in interstitial cells from the guinea-pig bladder.

OBJECTIVE: To determine whether there are inward currents in interstitial cells (IC) isolated from the guinea-pig detrusor and if so, to characterise them using the patch-clamp technique and pharmacological agents. MATERIALS AND METHODS: Using the whole-cell patch-clamp technique, inward currents were studied in IC enzymatically isolated from the detrusor of the guinea-pig bladder. Currents were evoked by stepping positively from a holding potential of - 80 mV. RESULTS: Outward K+ currents were blocked by Cs+ internal solution to reveal inward currents, which activated at voltages more positive than - 50 mV, peaked at 0 mV, reversed near + 50 mV and were half-maximally activated at - 27 mV. The inward currents showed voltage-dependent inactivation and were half-maximally inactivated at - 36 mV. Fitting the activation and inactivation data with a Boltzmann function revealed a window current between - 40 mV and + 20 mV. The decay of the current evoked at 0 mV could be fitted with a single exponential with a mean time-constant of 88 ms. Replacing external Ca2+ with Ba2+ significantly increased this to 344 ms. The current amplitude was augmented by Ba2+, and by Bay K 8644. Inward currents were significantly reduced by 1 microm nifedipine, across the voltage range, but the blockade was more effective on the current evoked at 0 mV than that evoked by a step to - 20 mV, perhaps indicating voltage-dependence of the action of nifedipine or another component of inward current. Increasing the concentration of the drug to 10 microm caused no further significant reduction either at 0 mV or at -20 mV. However, in the presence of 1 microm nifedipine the latter current was significantly reduced by 100 microm Ni2+. Both currents were significantly reduced in Ca2+-free solution. CONCLUSIONS: IC from the guinea-pig detrusor possess inward currents with typical characteristics of L-type Ca2+ current. They also have a component of inward Ca2+ current, which was resistant to nifedipine, but sensitive to Ni2+. Further work is needed to characterise the latter conductance. PMID: 16686735 [PubMed - indexed for MEDLINE]

Ultralow Silicon Substrate Noise Crosstalk Using Metal Faraday Cages in an SOI Technology

In mixed signal integrated circuits noise from the digital circuitry can upset the sensitive analogue circuitry. The Faraday cage structure reported here is based on the unique ground plane SOI technology developed some of the authors. The suppression of crosstalk achieved is an order of magnitude greater than that previously published for frequencies up to 10 GHz. The significance of the technology will be even greater as the operating frequency is increased. This collaborative EPSRC project was judge as tending to outstanding.

Pulsed evaporative cooling of ion cloud in an electron beam ion trap

A technique for producing cold ensembles of trapped highly charged ions is described. The ions, trapped in an electron beam ion trap, can undergo a drastic contraction during the pulsed mode of evaporative cooling, if a truncated Boltzmann distribution is assumed. The underlying theory and the experimental results are presented.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Fully nonlinear ion-sound waves in a dense Fermi magnetoplasma

The nonlinear propagation of ion-sound waves in a collisionless dense electron-ion magnetoplasma is investigated. The inertialess electrons are assumed to follow a non-Boltzmann distribution due to the pressure for the Fermi plasma and the ions are described by the hydrodynamic (HD) equations. An energy balance-like equation involving a new Sagdeev-type pseudo-potential is derived in the presence of the quantum statistical effects. Numerical calculations reveal that the profiles of the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number. The present studies might be helpful to understand the excitation of nonlinear ion-sound waves in dense plasmas such as those in superdense white dwarfs and neutron stars as well as in intense laser-solid density plasma experiments.

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail

Electronic excitation in metals through hyperthermal atoms

A hyperthermal hydrogen/deuterium atom beam source with a defined energy distribution has been employed to investigate the kinetically induced electron emission from noble metal surfaces. A monotonous increase in the emission yield was found for energies between 15 and 200 eV. This, along with an observed isotope effect, is described in terms of a model based on Boltzmann type electron energy distributions.

Characterization of T-type calcium current and its contribution to electrical activity in rabbit urethra.

Rabbit urethral smooth muscle cells were studied at 37 degrees C by using the amphotericin B perforated-patch configuration of the patch-clamp technique, using Cs(+)-rich pipette solutions. Two components of current, with electrophysiological and pharmacological properties typical of T- and L-type Ca(2+) currents, were recorded. Fitting steady-state inactivation curves for the L current with a Boltzmann equation yielded a V(1/2) of -41 +/- 3 mV. In contrast, the T current inactivated with a V(1/2) of -76 +/- 2 mV. The L currents were reduced by nifedipine (IC(50) = 225 +/- 84 nM), Ni(2+) (IC(50) = 324 +/- 74 microM), and mibefradil (IC(50) = 2.6 +/- 1.1 microM) but were enhanced when external Ca(2+) was substituted with Ba(2+). The T current was little affected by nifedipine at concentrations

Numerical simulations of fluid-structure interactions in single-reed mouthpieces

Most single-reed woodwind instrument models rely on a quasistationary approximation to describe the relationship between the volume flow and. the pressure difference across the reed channel. Semiempirical models based on the quasistationary approximation are very useful in explaining the fundamental characteristics of this family of instruments such as self-sustained oscillations and threshold of blowing pressure. However, they fail at explaining more complex phenomena associated with the fluid-structure interaction during dynamic flow regimes, such as the transient and steady-state behavior of the system as a function. of the mouthpiece geometry. Previous studies have discussed the accuracy of the quasistationary approximation but the amount of literature on the subject is sparse, mainly due to the difficulties involved in the measurement of dynamic flows in channels with an oscillating reed. In this paper, a numerical technique based on the lattice Boltzmann method and a finite difference scheme is proposed in order to investigate the characteristics of fully coupled fluid-structure interaction in single-reed mouthpieces with different channel configurations. Results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasistationary approximation. However, simulations carried out for a dynamic regime with dn oscillating reed show that the phenomenon associated with flow detachment and reattachment diverges considerably frorn the theoretical assumptions. Furthermore, in the case of long reed channels, the results obtained for the vena contracta factor are in significant disagreement with those predicted by theory. For short channels, the assumption of constant vena contracta was found to be valid for only 40% of the duty cycle. (c) 2007 Acoustical Society of America.