A MATLAB program for the computation of the confluent hypergeometric function Φ2

We here present a sample MATLAB program for the numerical evaluation of the confluent hypergeometric function Φ2. This program is based on the calculation of the inverse Laplace transform using the algorithm suggested by Simon and Alouini in their reference textbook [1].

Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

An RNS based transform Architecture for H.264/AVC

This paper presents the architecture and the VHDL design of an integer 2-D DCT used in the H.264/AVC. The 2-D DCT computation is performed by exploiting it’s orthogonality and separability property. The symmetry of the forward and inverse transform is used in this implementation. To reduce the computation overhead for the addition, subtraction and multiplication operations, we analyze the suitability of carry-free position independent residue number system (RNS) for the implementation of 2-D DCT. The implementation has been carried out in VHDL for Altera FPGA. We used the negative number representation in RNS, bit width analysis of the transforms and dedicated registers present in the Logic element of the FPGA to optimize the area. The complexity and efficiency analysis show that the proposed architecture could provide higher through-put.

Development of a New Transform:MRT

Fourier transform methods are employed heavily in digital signal processing. Discrete Fourier Transform (DFT) is among the most commonly used digital signal transforms. The exponential kernel of the DFT has the properties of symmetry and periodicity. Fast Fourier Transform (FFT) methods for fast DFT computation exploit these kernel properties in different ways. In this thesis, an approach of grouping data on the basis of the corresponding phase of the exponential kernel of the DFT is exploited to introduce a new digital signal transform, named the M-dimensional Real Transform (MRT), for l-D and 2-D signals. The new transform is developed using number theoretic principles as regards its specific features. A few properties of the transform are explored, and an inverse transform presented. A fundamental assumption is that the size of the input signal be even. The transform computation involves only real additions. The MRT is an integer-to-integer transform. There are two kinds of redundancy, complete redundancy & derived redundancy, in MRT. Redundancy is analyzed and removed to arrive at a more compact version called the Unique MRT (UMRT). l-D UMRT is a non-expansive transform for all signal sizes, while the 2-D UMRT is non-expansive for signal sizes that are powers of 2. The 2-D UMRT is applied in image processing applications like image compression and orientation analysis. The MRT & UMRT, being general transforms, will find potential applications in various fields of signal and image processing.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

Performance analysis of a fluid queue with random service rate in discrete time

We consider a fluid queue in discrete time with random service rate. Such a queue has been used in several recent studies on wireless networks where the packets can be arbitrarily fragmented. We provide conditions on finiteness of moments of stationary delay, its Laplace-Stieltjes transform and various approximations under heavy traffic. Results are extended to the case where the wireless link can transmit in only a few slots during a frame.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Investigation of the M2/G2/1/ ∞, N Queue with Restricted Admission of Priority Customers and its Application to HSDPA Mobile Systems

This paper investigates a queuing system for QoS optimization of multimedia traffic consisting of aggregated streams with diverse QoS requirements transmitted to a mobile terminal over a common downlink shared channel. The queuing system, proposed for buffer management of aggregated single-user traffic in the base station of High-Speed Downlink Packet Access (HSDPA), allows for optimum loss/delay/jitter performance for end-user multimedia traffic with delay-tolerant non-real-time streams and partially loss tolerant real-time streams. In the queuing system, the real-time stream has non-preemptive priority in service but the number of the packets in the system is restricted by a constant. The non-real-time stream has no service priority but is allowed unlimited access to the system. Both types of packets arrive in the stationary Poisson flow. Service times follow general distribution depending on the packet type. Stability condition for the model is derived. Queue length distribution for both types of customers is calculated at arbitrary epochs and service completion epochs. Loss probability for priority packets is computed. Waiting time distribution in terms of Laplace-Stieltjes transform is obtained for both types of packets. Mean waiting time and jitter are computed. Numerical examples presented demonstrate the effectiveness of the queuing system for QoS optimization of buffered end-user multimedia traffic with aggregated real-time and non-real-time streams.

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

Efeitos do strike das estruturas geológicas de duas dimensões nas pseudos-seções de IP resistividade

Os levantamentos de IP-resistividade efetuados na Serra dos Carajás não foram executados ortogonalmente às estruturas geológicas, pois utilizaram linhas anteriormente abertas pelas equipes de geoquímica. Este fato motivou este estudo teórico da influência da direção das linhas de medidas de IP-resistividade em relação ao "strike" da estrutura. Foi usado o programa de elementos finitos de Rijo (1977), desenvolvido para levantamentos perpendiculares às estruturas com as adaptações necessárias. A modificação principal foi na rotina de transformação inversa de Fourier. Para o caso simples dos levantamentos perpendiculares, a transformada inversa é uma integral discreta com apenas sete pontos. No entanto, para as medidas obliquas, o integrando é oscilatório, e portanto, a integral a ser calculada é mais complexa. Foi adaptado um método apresentado por Ting e Luke (1981), usando dezoito pontos em cada integração. Foi constatado que o efeito da direção da linha em relação ao "strike" é desprezível para ângulos maiores que 60 graus. Para ângulos menores, o efeito consiste no alongamento da anomalia, com pequenas alterações em seu centro. Não há uma maneira simples de compensar este efeito com mudanças nos parâmetros do modelo.

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

A regularized iterative algorithm for limited-angle inverse Radon transform

The tomography problem is investigated when the available projections are restricted to a limited angular domain. It is shown that a previous algorithm proposed for extrapolating the data to the missing cone in Fourier space is unstable in the presence of noise because of the ill-posedness of the problem. A regularized algorithm is proposed, which converges to stable solutions. The efficiency of both algorithms is tested by means of numerical simulations. © 1983 Taylor and Francis Group, LLC.