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Mathematical Solutions (mathematical + solution)
Selected AbstractsA simple procedure to approximate slip displacement of freestanding rigid body subjected to earthquake motionsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2007Tomoyo Taniguchi Abstract A simple calculation procedure for estimating absolute maximum slip displacement of a freestanding rigid body placed on the ground or floor of linear/nonlinear multi-storey building during an earthquake is developed. The proposed procedure uses the displacement induced by the horizontal sinusoidal acceleration to approximate the absolute maximum slip displacement, i.e. the basic slip displacement. The amplitude of this horizontal sinusoidal acceleration is identical to either the peak horizontal ground acceleration or peak horizontal floor response acceleration. Its period meets the predominant period of the horizontal acceleration employed. The effects of vertical acceleration are considered to reduce the friction force monotonously. The root mean square value of the vertical acceleration at the peak horizontal acceleration is used. A mathematical solution of the basic slip displacement is presented. Employing over one hundred accelerograms, the absolute maximum slip displacements are computed and compared with the corresponding basic slip displacements. Their discrepancies are modelled by the logarithmic normal distribution regardless of the analytical conditions. The modification factor to the basic slip displacement is quantified based on the probability of the non-exceedence of a certain threshold. Therefore, the product of the modification factor and the basic slip displacement gives the design slip displacement of the body as the maximum expected value. Since the place of the body and linear/nonlinear state of building make the modification factor slightly vary, ensuring it to suit the problem is essential to secure prediction accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [source] A simple approach for optimum channel reservation for hand-over calls in cellular systemsINTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 4 2006Mohamed Laith In cellular mobile communication systems, while an active subscriber is moving from one cell to another, the service of his call needs to be handed over to the base station of the new cell. In such a case, cutting the service, due to all channels being busy at the new base station, would be more annoying to subscribers than normal congestion at the first initiation of calls. This paper is concerned with providing a simple approach for choosing the optimum set of channels that need to be reserved for hand-over calls, while maintaining an acceptable overall system performance. The approach evaluates channel reservation at the cell level, taking into account the offered traffic, that is both the newly initiated original traffic and the hand-over traffic. The approach produces a simple mathematical solution based on Erlang-B formula. It uses the concept of ,Combined Failure Rate' to evaluate the required reservation. The approach is supported by a simulation study that verifies its validity. Applications of the approach to illustrate its use are also presented.,Copyright © 2006 John Wiley & Sons, Ltd. [source] The Development of the Observational MethodGEOMECHANICS AND TUNNELLING, Issue 5 2008Wulf Schubert o.Univ.-Prof. A continuous observation during construction always has been an important element of geotechnical engineering for minimizing risks. The reasons are the uncertainties in the geological and geotechnical models, as well as the limited capability to sufficiently accurately describe the complex ground behaviour. In the early days design of geotechnical structures thus was mainly based on experience. As usual, experience was used to develop mathematical solutions to the problem. To account for the inherent scatter of parameters and uncertainties in the models, the assumptions made during design had and have to be verified or falsified during construction by observations. For safe and economical construction, the design has to be adjusted during construction to the actual conditions. The term "observational method" was first formally introduced by Peck and Terzaghi. The original ideas behind the method have not always been understood or followed. After a brief historical review of the observational method the current status of the method is critically reviewed, and further developments discussed. Die Beobachtungsmethode einst und jetzt Die Schwierigkeit, den Baugrund ausreichend zu erkunden und dessen Interaktion mit dem Bauwerk zutreffend mathematisch zu modellieren, erfordert die laufende Beobachtung während des Baus, um die Baumaßnahmen an die tatsächlichen Verhältnisse anzupassen und das Risiko vermindern zu können. Mit vermehrter Erfahrung wurden auch Analysemodelle entwickelt. Zur Berücksichtigung der unvermeidlichen Streuung der Baugrundeigenschaften und der Unsicherheiten in den Modellen wurden und werden während des Baus Beobachtungen durchgeführt. Die Bezeichnung "Beobachtungsmethode" wurde formal von Peck und Terzaghi eingeführt. Die damals formulierten Grundsätze wurden nicht immer verstanden und befolgt. Im Beitrag wird nach einem kurzen historischen Rückblick über Entstehung und Entwicklung der Methode der derzeitige Stand kritisch beleuchtet, und weitere Entwicklungen werden diskutiert. [source] The mathematical modelling of the osmotic dehydration of shark fillets at different brine temperaturesINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 4 2006Saheeda Mujaffar Summary The effect of brine temperature (20, 30, 40 and 50 °C) on the osmotic drying behaviour of shark slabs (10 × 5 × 1 cm) in saturated (100°) brine was investigated. The parameters investigated were weight reduction, water loss, salt gain and water activity. Salt uptake and moisture data were analysed using various mathematical solutions based on Fick's Law of Diffusion and the effective diffusion coefficients were predicted after considering the process variables. The expressions presented by Azuara et al. (1992), based on the model presented by Crank (1975), were successfully used to predict the equilibrium point and to calculate diffusion coefficients at not only the initial stages of dehydration, but also at different times during the osmotic process. [source] Application of the envelope-transient method to the analysis and design of autonomous circuitsINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2005Almudena Suárez Abstract The envelope transient enables a very efficient simulation of circuits with two different time scales, such as those that contain modulated signals (for example, amplifier or mixers), where an accurate prediction of intermodulation distortion is needed. The method has also been extended to oscillator analysis, where it requires additional techniques in order to avoid convergence to degenerate mathematical solutions, for which the circuit is not actually oscillating. It allows an efficient analysis of transients in these circuits and an accurate prediction of the phase-noise spectrum. This article presents an overview of the envelope-transient method and its most recent applications to the simulation of autonomous circuits, such as free and forced oscillators, frequency dividers, and phase-locked loops. Using this method, the operation bands of these circuits (which are delimited by qualitative stability changes or bifurcations) can be determined in a straightforward manner. This technique can also be applied to predict intermodulation distortion in self-oscillating mixers and to simulate the response of synchronized oscillators containing modulated signals. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005. [source] | ||||||||||