Adaptive multivariate rational data fitting with applications in electromagnetics

On efficient computation of rational {1,2}-pseudo-inverses for multivariable rational matrix-valued functions and their applications

The use of multivariable rational functions for nonlinear data representation and classification

A cluster-based multiprocessor system that was introduced and analyzed by D. Agrawal and I. Mahgoub (1985, 1987) is considered. The analysis was based on an approximate analytical model, and the results were compared with those obtained for the crossbar and multiple-bus systems using the same model. A simulation model that relaxes two unrealistic assumptions of the approximate analytical model used by Agrawal and Mahgoub is developed here. The results obtained from the simulation model are compared with those obtained from the approximate analytical model for the cluster-based, crossbar, and multiple-bus systems. The simulation results confirm the conclusions arrived at in the previous studies.

We present a well-parallelizable algorithm which, taking a straight-line program for the evaluation of a vectorial field of rational functions of Q(X 1,...,X n ) as input, decides whether they allow a rational potential function and, in case of affirmative answer, computes it as output. We introduce a mixed model of representation of polynomials to allow the application of integration techniques and show how to perform some basic operations with it. The algorithm is presented as a family of arithmetic networks of polynomial size and poly logarithmic depth in the degree of the occurring polynomials.KeywordsRational FunctionPartial FractionGreat Common DivisorProbabilistic AlgorithmParallel TimeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A biaxial thermomechanical disk test for glassy polymers

Effective coefficient asymptotics of multivariate rational functions via semi-numerical algorithms for polynomial systems

The transfer functions G(s) for different types of heat exchangers obtained from their partial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representation is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer functions G^(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n=1,2,…,N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix G^(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix G^(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer function model G(s). The presented results show: (a) the advantage of the counter-flow regime over the parallel-flow one; (b) better approximation quality for the transfer function channels with dominating heat conduction effects, as compared to the channels characterized by the transport delay associated with the heat convection.

Computing with polynomials given byblack boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators

Reconstructing rational functions with FireFly

The purpose of this paper is to investigate the limits of multivariate rational functions with the aid of the theory of real valuations. The following is one of our main results. For two nonzero polynomials f, g ∈ ℝ[x1,…,xn] and (a1,…,an) ∈ ℝn, the (finite) limit of the rational function [Formula: see text] at (a1,…,an) does not exist if and only if (1) there exists a sequence u1(x),…,un(x) of polynomials over ℝ in one variable x such that ui(0) = ai for i = 1,…,n, g(u1(x),…,un(x)) ≠ 0, but [Formula: see text]; or (2) there exist two sequences u1(x),…,un(x) and w1(x),…,wn(x) of polynomials over ℝ in one variable x such that ui(0) = wi(0) = ai for i = 1,…,n, g(u1(x),…,un(x)) ⋅ g(w1(x),…,wn(x)) ≠ 0, but [Formula: see text].

Queueing systems to study the energy consumption of a campus WLAN

In this paper we consider dual-band GSM networks, where voice and data services are offered to users moving over an area covered with overlapping macrocells and microcells. For this wireless network context we develop simple approximate analytical models of the system dynamics, and we exploit such analytical models for the design and planning of the critical system parameters, with particular attention to the number of traffic channels to be activated within macrocells.

In this paper, approximate analytical models are devised for regular deflection networks with arbitrary node connectivity and buffered nodes. The main feature of the proposed models is the capability to handle a large class of distributed routing schemes, which includes, as particular cases, most of the previously considered routing schemes.

The ATM adaptation layer type 5 (AAL5) is a new adaptation layer protocol for the ATM layer of broadband integrated services digital networks. Among several features, it is unique in the sense that it includes an end-of-packet (EOP) indicator in the header of the ATM cell (the ATM-layer-user-to-ATM-layer-user (AUU) parameter in the payload type (PT) field). It was previously suggested that the use of this indicator may be used to provide a means by which buffer occupancy can be reduced by dropping cells from already incomplete packets (Armitage, 1993). The objective of this paper is to study the performance of this layer and the effectiveness of the EOP indicator. The performance measures of interest are the probability of packet loss and the mean packet delay. An approximate analytical model is constructed in which the blocking of a tagged source is kept track of in an exact manner. The rest of the sources are modeled approximately. The accuracy of the model is enhanced through an iterative approach. A simulation model is also constructed to assess the accuracy of the approximate model.

Hyperthermia in conjunction with radiation therapy is a promising method for the treatment of superficially or eccentrically located recurrent or advanced primary malignant tumours. The external hyperthermia applicators most commonly used are radiative electromagnetic (including microwave) or ultrasound devices. Each type of device has its own limitations. The aim was to evaluate the temperature distributions obtained as well as the acute and subacute toxicities in patients that were treated with both radiative radiative electromagnetic and ultrasound applicators to the same tumours. Thirty-nine patients treated to 41 hyperthermia fields for a total of 197 hyperthermia treatments were analysed. Thermal parameter include mean, Tmax, mean Tave, mean Tmin, T50, T90, %T > 43.5 degrees C and %T < 41 degrees C. Acute toxicities including pain in field, referred pain, blister/ulceration, positional discomfort and subacute toxicities (occurring with 24 h of treatment) were determined for each type of hyperthermia applicator. Although there were increased acute toxicities (in-field or referred pain) associated with the ultrasound treatments no significant differences between the two methods of heating were observed in temperature distributions or subacute toxicities. We conclude that there is no generally preferred method of heating superficially or eccentrically located tumours and the type of applicator should be selected on a tumour-size and site-specific basis.