existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media we prove the existence of multidimensional traveling wave solutions to the scalar equation for the transport of solutes contaminants with nonlinear adsorption and spatially periodic convection diffusion adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the lax and oleinik entropy conditions in the nondegenerate case we also prove the uniqueness of the traveling waves these traveling waves are analogues of viscous shock profiles they propagate with effective speeds that depend on the periodic porous media only up to their mean states and are given by an averaged rankine hugoniot relation this is a direct consequence of the fact that the transport equation is in conservation form we use the sliding domain method the continuation method spectral theory maximum principles and a priori estimates in the degenerate case the traveling waves are weak solutions of a degenerate parabolic equation and are only holder continuous we obtain them by taking suitable limits on the non degenerate traveling waves the uniqueness of the degenerate traveling waves is open

improving the speed of parallel decimal multiplication hardware support for decimal computer arithmetic is regaining popularity one reason is the recent growth of decimal computations in commercial scientific financial and internet based computer applications newly commercialized decimal arithmetic hardware units use radix 10 sequential multipliers that are rather slow for multiplication intensive applications therefore the future relevant processors are likely to host fast parallel decimal multiplication circuits the corresponding hardware algorithms are normally composed of three steps partial product generation ppg partial product reduction ppr and final carry propagating addition the state of the art is represented by two recent full solutions with alternative designs for all the three aforementioned steps in addition ppr by itself has been the focus of other recent studies in this paper we examine both of the full solutions and the impact of a ppr only design on the appropriate one in order to improve the speed of parallel decimal multiplication we present a new ppg method fine tune the ppr method of one of the full solutions and the final addition scheme of the other thus assembling a new full solution logical effort analysis and 0 13 mum synthesis show at least 13 percent speed advantage but at a cost of at most 36 percent additional area consumption

high speed multioperand decimal adders there is increasing interest in hardware support for decimal arithmetic as a result of recent growth in commercial financial and internet based applications consequently new specifications for decimal floating point arithmetic have been added to the draft revision of the ieee 754 standard for floating point arithmetic this paper introduces and analyzes three techniques for performing fast decimal addition on multiple binary coded decimal bcd operands two of the techniques speculate bcd correction values and correct intermediate results while adding the input operands the first speculates over one addition the second speculates over two additions the third technique uses a binary carry save adder tree and produces a binary sum combinational logic is then used to correct the sum and determine the carry into the next more significant digit multioperand adder designs are constructed and synthesized for four to 16 input operands analyses are performed on the synthesis results and the merits of each technique are discussed finally these techniques are compared to several previous techniques for high speed decimal addition

pulsating type entire solutions of monostable reaction advection diffusion equations in periodic excitable media abstract we establish the existence of pulsating type entire solutions of reaction advection diffusion equations with monostable nonlinearities in a periodic framework here the nonlinearities include the classic kpp case the pulsating type entire solutions are defined in the whole space and for all time t r by studying a pulsating traveling front connecting a constant unstable stationary state to a stable stationary state which is allowed to be a positive function we proved that there exist pulsating type entire solutions behaving as two pulsating traveling fronts coming from both directions and approaching each other the key techniques are to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions

a stability analysis of a eulerian solution method for moving boundary problems in electrochemical machining we investigate the front tracking method using marker points for the numerical solution of a class of moving boundary problems which arise in connection with certain two dimensional electrochemical machining problems the numerical method is expressed as a system of n nonlinear autonomous ordinary differential equations odes for describing the movement of n marker points on the moving boundary the system has been analysed in some cases with respect to the local stability of equilibrium solutions and to the global stability of nonequilibrium solutions the linearised local stability of the equilibrium solution is investigated in terms of the jacobi matrix for the system of odes closed form expressions for the eigenvalues and the eigenvectors of the jacobi matrix have been derived part of the method comprises the solution of a dirichlet boundary value problem this is carried out using various boundary collocation methods which are investigated the mathematical numerical model has features which are in accordance with those of the physical problem this has also been demonstrated by actual computation of some examples

reaction diffusion fronts in periodically layered media we compute the effective wavefront speeds of reaction diffusion equations in periodically layered media with coefficients that have small amplitude oscillations around a uniform mean state we compare them with the corresponding wavefront speeds in the uniform state we analyze a one dimensional model where wave propagation is along the layering direction of the medium and a two dimensional shear flow model where wave propagation is othogonal to the layering direction we find that the effective wave speed is smaller in the one dimensional model and is larger in the two dimensional model for both bistable cubic and quadratic nonlinearities of the kolmogorov petrovskii piskunov form we derive approximate expressions for the wave speeds in the bistable case

continuity of the temperature in the two phase stefan problem the classical two phase stefan problem a model for ice water melting gives rise to a singular nonlinear partial differential equation which admits a unique weak solution here we prove that this solution and therefore the temperature in the stefan problem are continuous

multioperand parallel decimal adder a mixed binary and bcd approach decimal arithmetic has been revived in recent years due to the large amount of data in commercial applications we consider the problem of multioperand parallel decimal addition with an approach that uses binary arithmetic suggested by the adoption of binary coded decimal bcd numbers this involves corrections in order to obtain the bcd result or a binary to decimal bd conversion we adopt the latter approach which is particularly efficient for a large number of addends conversion requires a relatively small area and can afford fast operation the bd conversion moreover allows an easy alignment of the sums of adjacent columns we treat the design of bcd digit adders using fast carry free adders and the conversion problem through a known parallel scheme using elementary conversion cells spreadsheets have been developed for adding several bcd digits and for simulating the bd conversion as a design tool

high speed parallel decimal multiplication with redundant internal encodings the decimal multiplication is one of the most important decimal arithmetic operations which have a growing demand in the area of commercial financial and scientific computing in this paper we propose a parallel decimal multiplication algorithm with three components which are a partial product generation a partial product reduction and a final digit set conversion first a redundant number system is applied to recode not only the multiplier but also multiples of the multiplicand in signed digit sd numbers furthermore we present a multioperand sd addition algorithm to reduce the partial product array finally a digit set conversion algorithm with a hybrid prefix network to decrease the number of the logic gates on the critical path is discussed an analysis of the timing delay and an hdl model synthesized under 90 nm technology show that by considering the tradeoff of designs among three components the overall delay of the proposed 16 16 digit multiplier takes about 11 percent less timing delay with 2 percent less area compared to the current fastest design

existence of planar flame fronts in convective diffusive periodic media we prove the existence of planar travelling wave solutions in a reaction diffusion convection equation with combustion nonlinearity and self adjoint linear part in rn n 1 the linear part involves diffusion convection terms and periodic coefficients these travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media we use the method of continuation spectral theory and the maximum principle uniqueness and monotonicity properties of solutions follow from a previous paper these properties are essential to overcoming the lack of compactness and the degeneracy in the problem

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

solute transport in porous media with equilibrium and non equilibrium multiple site adsorption travelling waves we study travelling wave solutions of a model describing solute transport through porous media where the chemical species undergoes absorption i e a retention release reaction with the surface of the porous sceleton processes of this type are of fundamental importance in different fields we do not consider the process at the microscopic scale of single grains and pores but at the microscopic scale appropriate for the measurement of the phenomena described above

fast radix 10 multiplication using redundant bcd codes we present the algorithm and architecture of a bcd parallel multiplier that exploits some properties of two different redundant bcd codes to speedup its computation the redundant bcd excess 3 code xs 3 and the overloaded bcd representation odds in addition new techniques are developed to reduce significantly the latency and area of previous representative high performance implementations partial products are generated in parallel using a signed digit radix 10 recoding of the bcd multiplier with the digit set 5 5 and a set of positive multiplicand multiples 0x 1x 2x 3x 4x 5x coded in xs 3 this encoding has several advantages first it is a self complementing code so that a negative multiplicand multiple can be obtained by just inverting the bits of the corresponding positive one also the available redundancy allows a fast and simple generation of multiplicand multiples in a carry free way finally the partial products can be recoded to the odds representation by just adding a constant factor into the partial product reduction tree since the odds uses a similar 4 bit binary encoding as non redundant bcd conventional binary vlsi circuit techniques such as binary carry save adders and compressor trees can be adapted efficiently to perform decimal operations to show the advantages of our architecture we have synthesized a rtl model for 16 times 16 digit and 34 times 34 digit multiplications and performed a comparative survey of the previous most representative designs we show that the proposed decimal multiplier has an area improvement roughly in the range 20 35 percent for similar target delays with respect to the fastest implementation

stability of traveling waves of a solute transport equation abstract we prove the large time asymptotic stability of traveling wave solutions to the scalar solute transport equation contaminant transport equation with spatially periodic diffusion adsorption coefficients in one space dimension the time dependent solutions converge in proper norms to a translate of traveling wave solutions as time approaches infinity in case of classical traveling waves the convergence rate is exponential in time for a class of small initial perturbations and for general order one perturbations the convergence holds in supremum norm in case of degenerate holder continuous traveling waves the convergence holds in l 1 norm as a byproduct uniqueness up to translation of degenerate traveling waves follows we use maximum principle l 1 contraction spectral theory and a space time invariance property of solutions

a radix 10 digit recurrence division unit algorithm and architecture in this work we present a radix 10 division unit that is based on the digit recurrence algorithm the previous decimal division designs do not include recent developments in the theory and practice of this type of algorithm which were developed for radix 2k dividers in addition to the adaptation of these features the radix 10 quotient digit is decomposed into a radix 2 digit and a radix 5 digit in such a way that only five and two times the divisor are required in the recurrence moreover the most significant slice of the recurrence which includes the selection function is implemented in radix 2 avoiding the additional delay introduced by the radix 10 carry save additions and allowing the balancing of the paths to reduce the cycle delay the results of the implementation of the proposed radix 10 division unit show that its latency is close to that of radix 16 division units comparable dynamic range of significant and it has a shorter latency than a radix 10 unit based on the newton raphson approximation

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

a fast method for solving certain integral equations of the first kind with application to conforma mapping abstract we describe a fast iterative method for solving fredholm integral equations of the first kind whose kernels have a logarithmic principal part the method is a fourier galerkin method and due to the singularity of the kernel the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative method we present examples of the computation of conformal mappings of simply and multiply connected domains

on polynomial approximation in the complex plane with application to conformal mapping we consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane while a monomial basis may be very ill conditioned we show that a basis of lagrange polynomials with fejer points as nodes is well conditioned numerical examples where we compute polynomial approximations of conformal mappings conclude the paper

on the determination of boundary collocation points for solving some problems for the laplace operator abstract boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations for which complete families of particular solutions are explicitly known the method contains various decisions which are important for its performance such as choice of solution subspace choice of basis for the subspace and choice of collocation points using a model problem some particular strategies for the determination of collocation points are investigated