the use of the fourier bessel series in calculating error probabilities for digital communication systems using the theory of spherical symmetric random vectors one can find an expression for the error probability of a wide variety of digital communications systems these expressions however are in the form of bessel integrals which are usually difficult to solve in this paper we show how the fourier bessel series can be used to solve the integrals numerically the calculation error is found to depend on two series parameters which can be manipulated to make the error arbitrarily small two examples are used to show the utility of the technique in the first the probability of error for a cpsk communications system operating in gaussian noise and cochannel interference is found in the second the error performance for a multilevel ask communications system operating in the same corrupting environment is determined the fourier bessel series technique is a valuable practical tool for solving these and other signal detection problems

symbol to symbol performance evaluation of densely populated asynchronous ds cdma in gaussian and impulsive noise environments a fourier bessel series approach this letter considers the well established poisson impulse noise model with a random amplitude area distributed according to the spl epsiv mixture gaussian probability density function this model is used to develop fast converging truncated fourier bessel fb series expressions required to evaluate accurately the performance of a binary phase shift keying bpsk modulation scheme as part of a densely populated asynchronous direct sequence code division multiple access a ds cdma configuration the average error probability of the correlation receiver is easily and quickly obtained here even for the case of a large number of users k 100 unlike earlier attempts in this area in which the use of other analysis approaches e g closed form approach or taylor series expansion approach could not exceed the limit of k 2 and k 24 in an spl epsiv mixture impulsive and or gaussian noise environment respectively

on s shaped bifurcation curves where sz c r n 2 1 is bounded with smooth boundary aq readers interested in the derivation of the problem are referred to the work by bebernen l particularly section 2 relevant work on the analysis of this problem has been done by brown et al 2 shivaji 3 61 hastings and mcleod 7 sattinger 8 parks 9 and tam lo clearly u 0 is a solution of 1 l when 2 0 it follows from the contraction mapping theorem that l l always has a solution for a sufficiently small moreover let

second order estimate on transition layers abstract in this paper we establish a uniform c 2 estimate for level sets of stable solutions to the singularly perturbed allen cahn equation in dimensions n 10 which is optimal the proof combines two ingredients one is a reverse application of the infinite dimensional lyapunov schmidt reduction method which enables us to reduce the c 2 estimate for these level sets to a corresponding one on solutions of toda system the other one uses a small regularity theorem on stable solutions of toda system to establish various decay estimates which gives a lower bound on distances between different sheets of solutions to toda system or level sets of solutions to allen cahn equation

multiplicity of solutions to a degenerate diffusion problem abstract in this paper it is shown that the dirichlet problem p u f u u b 0 in a ball b r n loses the property of uniqueness of positive solutions u under the sole condition max b u u 0 as with u 0 0 certain prefixed zero of f provided p k 1 k being the order of u 0 what is in contrast with the so called nondegenerate case p k 1 where such hypothesis implies uniqueness this also proves that a slightly stronger convergence condition for uniqueness introduced by the authors in a previous work cannot be relaxed

exact multiplicity for degenerate two point boundary value problems with p convex nonlinearity the exact number of positive solutions of a degenerate quasilinear two point boundary value problem is investigated for the generalization of earlier results concerning the nondegenerate case with convex nonlinearity suitably defined p convex nonlinearities are considered strictly p convex c2 functions having a non negative root are classified according to the shape of the bifurcation diagram of positive solutions versus the length of the interval we have uniqueness when f 0 0 and 0 1 or 2 solutions when f 0 0 similarly to the non degenerate case provided that the number of solutions is finite however now there may also occur a continuum of solutions connected to a dead core type phenomenon the proof of our results relies on the shooting method for the characterization of the shape of the time map in contrast to the non degenerate case the shooting method does not determine directly the number of solutions owing to the lack of uniqueness of the corresponding ivp exact conditions on the uniqueness of the ivp and in the case of non uniqueness the number and types of its local solutions are given based on this all the positive solutions of the bvp can be compiled

rigorous analysis and estimates of s shaped bifurcation curves in a combustion problem with general arrhenius reaction rate laws we study the bifurcation of solutions of the combustion problem with general arrhenius reaction rate laws d 2 u d x 2 1 e u m e u 1 e u 0 1 x 1 u 1 u 1 0 for this two point boundary value problem we give a bifurcation analysis in the physically important ranges 0 m 1 and m 0 it is proved that the bifurcation curve is s shaped in certain parameter ranges and a lower bound is given for the frank kamenetskii transition value

isogeometric overlapping schwarz preconditioners for the bidomain reaction diffusion system abstract we present and study an overlapping additive schwarz preconditioner for the isogeometric discretization of a reaction diffusion system modeling the heart bioelectrical activity known as the bidomain model consisting of a degenerate system of parabolic and elliptic pde this model includes intramural fiber rotation anisotropic conductivity coefficients and is coupled through the reaction term with a system of odes which models the ionic currents of the cellular membrane the overlapping schwarz preconditioner is applied with a pcg accelerator to solve the linear system arising at each time step from the isogeometric discretization in space and a semi implicit adaptive method in time a theoretical convergence rate analysis shows that the resulting solver is scalable optimal in the ratio of subdomain element size and the convergence rate improves with increasing overlap size numerical tests in three dimensional ellipsoidal domains confirm the theoretical estimates and additionally show the robustness with respect to jump discontinuities of the orthotropic conductivity coefficients

quenching for solutions of a plasma type equation here 0 l the so called slow diffusion case the analysis will be carried out in the manner of 5 in which levine gave a complete qualitative study of problem i with m 1 the plan of our paper is as follows in the next section we present the comparison theorem and local existence of solutions for i in the third section we characterize the set of stationary solutions of i finally in the last section we establish stability and quenching results for problem i

exact multiplicity of positive solutions for a class of semilinear problem ii we consider the positive solutions to the semilinear problem u f u 0 in b n u 0 on b n where bn is the unit ball in rn n 1 and is a positive parameter it is well known that if is a smooth function then any positive solution to the equation is radially symmetric and all solutions can be parameterized by their maximum values we develop a unified approach to obtain the exact multiplicity of the positive solutions for a wide class of nonlinear functions u and the precise shape of the global bifurcation diagrams are rigorously proved our technique combines the bifurcation analysis stability analysis and topological methods we show that the shape of the bifurcation curve depends on the shape of the graph of function u u as well as the growth rale of

multiple positive solutions for nonlinear eigenvalue problems with the p laplacian abstract in this paper we consider a nonlinear eigenvalue problem driven by the p laplacian differential operator and with a nonsmooth potential using degree theoretic arguments based on the degree map for certain operators of monotone type we show that the problem has at least two nontrivial positive solutions as the parameter 0 varies in a half line

a multilevel hybrid newton krylov schwarz method for the bidomain model of electrocardiology abstract a multilevel hybrid newton krylov schwarz nks method is constructed and studied numerically for implicit time discretizations of the bidomain reaction diffusion system in three dimensions this model describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with a stiff system of ordinary differential equations the nks bidomain solver employs an outer inexact newton iteration to solve the nonlinear finite element system originating at each time step of the implicit discretization the jacobian update during the newton iteration is solved by a krylov method employing a multilevel hybrid overlapping schwarz preconditioner additive within the levels and multiplicative among the levels several parallel tests on linux clusters are performed showing that the convergence of the method is independent of the number of subdomains scalability the discretization parameters and the number of levels optimality

the set of positive solutions of semilinear equations in large balls the exact number of positive solutions of u f u 0 on finite balls in n is determined the assumptions about f u are similar to those imposed by serrin and the second author in a previous study of uniqueness of the positive solution when the spatial domain is all of n see 7 8 for finite balls of sufficiently large radius it is shown here that there are exactly two positive and hence radial solutions to this end we first prove the linear nondegeneracy of the positive solution of n this is obtained by applying the technique of monotone separation of graphs 7 to the linearised equations somewhat sharper estimates are required here see part i section 2

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

multilevel schwarz methods for elliptic partial differential equations we investigate multilevel schwarz domain decomposition preconditioners to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method in our analysis we deal with unstructured mesh partitions and with subdomain boundaries resulting from using the mesh partitioner we start from two level preconditioners with either aggregative or interpolative coarse level components then we focus on a strategy to increase the number of levels for all preconditioners we consider the additive residual update and its multiplicative variants within and between levels moreover we compare the preconditioners behaviour regarding scalability and rate of convergence numerical results are provided for elliptic boundary value problems including a convection diffusion problem when suitable stabilization becomes necessary c 2011 elsevier b v all rights reserved

symmetry for boundary blow up solutions of elliptic equations in a half space abstract in this paper we consider positive solutions of the following boundary blow up problem in half space p u f u x t u on t where t x x 1 x 2 x n x 1 0 n 2 and the nonlinear function f s satisfies for some a 0 f s 0 in 0 a f s in a under suitable conditions we show that this problem has only one positive solution and it must be a function of x1 only

diffusive logistic equation with constant yield harvesting and negative density dependent emigration on the boundary abstract the structure of positive steady state solutions of a diffusive logistic population model with constant yield harvesting and negative density dependent emigration on the boundary is examined in particular a class of nonlinear boundary conditions that depends both on the population density and the diffusion coefficient is used to model the effects of negative density dependent emigration on the boundary our existence results are established via the well known sub super solution method

multilevel additive schwarz preconditioners for the bidomain reaction diffusion system multilevel additive schwarz methods are analyzed and studied numerically for the anisotropic cardiac bidomain model in three dimensions this is the most complete model to date of the bioelectrical activity of the heart tissue consisting of a degenerate parabolic system of nonlinear reaction diffusion equations coupled with a stiff system of several ordinary differential equations describing the ionic currents through the cellular membrane due to the presence of very different scales in both space and time the numerical discretization of this system by finite elements in space and semi implicit methods in time produces very ill conditioned linear systems that must be solved at each time step the proposed multilevel algorithm employs a hierarchy of nested meshes with overlapping schwarz preconditioners on each level and is fully additive hence parallel within and among levels convergence estimates are proved for the resulting multilevel algorithm showing that its convergence rate is independent of the number of subdomains scalability of the mesh sizes of each level and of the number of levels optimality several parallel tests on a linux cluster confirm the scalability and optimality of the method as well as its parallel efficiency on both cartesian and deformed domains in three dimensions

blowup in a partial differential equation with conserved first integral a reaction diffusion equation with a nonlocal term is studied the nonlocal term acts to conserve the spatial integral of the unknown function as time evolves such equations give insight into biological and chemical problems where conservation properties predominate the aim of the paper is to understand how the conservation property affects the nature of blowup the equation studied has a trivial steady solution that is proved to be stable existence of nontrivial steady solutions is proved and their instability established numerically blowup is proved for sufficiently large initial data by using a comparison principle in fourier space the nature of the blowup is investigated by a combination of asymptotic and numerical calculations

properties of the period function for some hamiltonian systems and homogeneous solutions of a semilinear elliptic equation abstract in this work we study the period function t of solutions to the conservative equation x t f x t 0 we present conditions on f that imply the monotonicity and convexity of t as a consequence we obtain the criterium established by c chicone and find conditions easier to apply we also get a condition obtained by cima gasull and manosas about monotonicity and following some of their calculations present results on the period function of hamiltonian systems where h x y f x n 1 y n using the monotonicity of t we count the homogeneous solutions to the semilinear elliptic equation u u 1 in two dimensions

analysis of non coherent correlation in ds bpsk spread spectrum acquisition non coherent detectors for initial code synchronization acquisition of bpsk direct sequence spread spectrum signals on an awgn channel are analyzed in addition to the thermal noise in many applications such detectors are faced with the self noise due to the partial period correlations under the random code sequences assumption in this paper an exact analysis of the non coherent correlator s detection performance is carried out by using the theory of circularly symmetric random variables the exact analysis shows that the familiar gaussian approximation to the distribution function of the code self noise is justified for all cases of practical interest furthermore the overall detection performance was found to be determined asymptotically by the sum of the thermal and correlator s self noise in most cases of practical interest this asymptotic result provides a very good approximation to the actual detection performance of a non coherent correlator improving the approximations devised previously

branches of positive and free boundary solutions for some singular quasilinear elliptic problems we study the existence and multiplicity of solutions strictly positive or nonnegative having a free boundary the boundary of the set where the solution vanishes of some one dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms

a model based block triangular preconditioner for the bidomain system in electrocardiology we introduce a preconditioner for the solution of the bidomain system governing the propagation of action potentials in the myocardial tissue the bidomain model is a degenerate parabolic set of nonlinear reaction diffusion equations the nonlinear term describes the ion flux at the cellular level the degenerate nature of the problem results in a severe ill conditioning of its discretization our preconditioning strategy is based on a suitable adaptation of the monodomain model a simplified version of the bidomain one which is by far simpler to solve nevertheless is unable to capture significant features of the action potential propagation the monodomain preconditioner application to a non symmetric formulation of the bidomain system results at the algebraic level in a lower block triangular preconditioner we prove optimality of the preconditioner with respect to the mesh size and corroborate our theoretical results with 3d numerical simulations both on idealized and real ventricle geometries

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

structure of boundary blow up solutions for quasi linear elliptic problems ii small and intermediate solutions the structure of positive boundary blow up solutions to quasi linear elliptic problems of the form pu f u u on 1 0 in z1 z2 large small and intermediate solutions are obtained for sufficiently large it is known from part i see structure of boundary blow up solutions for quasilinear elliptic problems part i large and small solutions preprint that the large solution is the unique large solution to the problem we will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions our results are new even for the case p 2

on the bifurcation curve for an elliptic system of fitzhugh nagumo type abstract we study a system of partial differential equations derived from the fitzhugh nagumo model in one dimension solutions are required to satisfy zero dirichlet boundary conditions on the interval 1 1 estimates are given to describe bounds on the range of parameters over which solutions exist numerical computations provide the global bifurcation diagram for families of symmetric and asymmetric solutions in the two dimensional case we use numerical methods for zero dirichlet boundary conditions on the square domain 1 1 1 1 numerical computations are given both for symmetric and asymmetric and for stable and unstable solutions

uniqueness of the solution of a semilinear boundary value problem on considere le probleme aux valeurs limites suivant 2 u f x u 0 x u x 0 x sur pour e 0 il y a un e 0 tel que pour 0 e e ce probleme ait une solution positive unique u dans c 2 c

preconditioning the bidomain model with almost linear complexity the bidomain model is widely used in electro cardiology to simulate spreading of excitation in the myocardium and electrocardiograms it consists of a system of two parabolic reaction diffusion equations coupled with an ode system its discretisation displays an ill conditioned system matrix to be inverted at each time step simulations based on the bidomain model therefore are associated with high computational costs in this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues the torso the preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi definite a block lu decomposition of the system together with a heuristic approximation referred to as the monodomain approximation are the key ingredients for the preconditioning definition numerical results are provided for two test cases a 2d test case on a realistic slice of the thorax based on a segmented heart medical image geometry a 3d test case involving a small cubic slab of tissue with orthotropic anisotropy the analysis of the resulting computational cost both in terms of cpu time and of iteration number shows an almost linear complexity with the problem size i e of type nlog a n for some constant a which is optimal complexity for such problems

existence and uniqueness for a class of quasilinear elliptic boundary value problems abstract we prove existence and uniqueness of positive solutions for the boundary value problem r n 1 u r n 1 f u u 0 u 1 0 where x x p 2x f x xp 1 may not be decreasing on 0 and is a large parameter

newton krylov bddc solvers for nonlinear cardiac mechanics abstract the aim of this work is to design and study a balancing domain decomposition by constraints bddc solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue the contraction relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro mechanical models consisting of systems of partial and ordinary differential equations in this study the discretization of the electro mechanical models is performed by q1 finite elements in space and semi implicit finite difference schemes in time leading to the solution of a large scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation the parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a newton krylov bddc method based on the parallel solution of local mechanical problems and a coarse problem for the so called primal unknowns three dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains quasi optimal in the ratio of subdomain to mesh sizes and robust with respect to tissue anisotropy

boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions abstract we show that for large 0 the generalized boundary value problem u u u a x 1 u in u where 1 x behaves like the special case 1 in particular we show the existence of solutions with sharp boundary layers and interior spikes and determine the location of the spikes

uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large existence and uniqueness results are proved for positive solutions of a class of quasilinear elliptic equations in a domain n via a generalisation of serrin s sweeping principle in the case when is an annulus it is shown that the solution is radially symmetric

uniqueness of positive solutions for a class of quasilinear problems abstract we prove uniqueness of positive solutions for the quasilinear problems p u f u in u 0 on where p u div u p 2 u p 1 is a bounded domain in r n with smooth boundary f is p sublinear at f u u p 1 is decreasing for large u and is a large positive parameter we also obtain the asymptotic behavior of the solution obtained as

exact multiplicity of positive solutions for a class of semilinear problems we establish an exact multiplicity result of positive solutions of u f u 0inbn u 0on bn wherebnis the unit ball fsatisfiesf changes sign only once and asymptotically sublinear or linear the nonlinearities which we are concerned with here includef u u u b c u for 0 2b candf u up uqfor 1 p q precise global bifurcation diagrams are obtained

representation and asymptotic formulas for 1 dimensional linearized eigenvalue problems with dirichlet boundary condition abstract in this article nontrivial solutions to a nonlinear dirichlet boundary value problem with a small parameter and the corresponding linearized eigenvalue problems are investigated in a typical case of nonlinearity asymptotic formulas of all eigenvalues and asymptotic profiles of all eigenfunctions are proved proofs are based on the method of representation equation and asymptotic results in the corresponding neumann problem obtained in the recent papers by the author and s yotsutani

boundary blow up solutions with a spike layer abstract we prove that for large 0 the boundary blow up problem u u u a 1 u in u has a solution with a spike located near the most centered part of our proof is based on the reduction method and uses a cut off technique to avoid the difficulties for the estimates near the boundary of

singularly perturbed nonlinear dirichlet problems with a general nonlinearity let be a bounded domain in r n n 3 with a boundary c 2 we consider the following singularly perturbed nonlinear elliptic problem on e 2 u u f u 0 u 0 on u 0 on where the nonlinearity f is of subcritical growth under rather strong conditions on f it has been known that for small e 0 there exists a mountain pass solution u e of above problem which exhibits a spike layer near a maximum point of the distance function d from as e 0 in this paper we construct a solution u e of above problem which exhibits a spike layer near a maximum point of the distance function under certain conditions on f which we believe to be almost optimal

uniqueness of non negative solutions of semilinear equations in rn on etudie l unicite des solutions positives classiques u x du probleme u f u 0 dans r n u x 0 quand x avec n 1 et x x 1 x n

a uniqueness result for a singular nonlinear eigenvalue problem alfonso castrodepartment of mathematics harvey mudd college claremont ca 91711 usa castro math hmc edu eunkyung kodepartment of mathematics and statistics mississippi state university mississippi state ms 39762 usa ekko1115 gmail com r shivajidepartment of mathematics and statistics university of north carolinaat greensboro greensboro nc 27412 usa shivaji uncg edu

multipeak solutions for an elliptic system of fitzhugh nagumo type we consider the dirichlet problem for an elliptic system of fitzhugh nagumo type we prove that the problem has solutions with arbitrary many sharp peaks near the boundary but not on the boundary

the dirichlet problem for δφ e φ in an infinite sector application to plasma equilibria abstract we consider here a nonlinear elliptic equation in an unbounded sectorial domain of the plane we prove the existence of a minimal solution to this equation and study its properties we infer from this analysis some asymptotics for the stationary solution of an equation arising in plasma physics

exact multiplicity results for boundary value problems with nonlinearities generalizing cubic using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type the first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u the second one deals with a class of nonlinearities with explicit x dependence

bifurcation from a degenerate simple eigenvalue it is proved that a symmetry breaking bifurcation occurs at a simple eigenvalue despite the usual transversality condition fails and this bifurcation from a degenerate simple eigenvalue result complements the classical one with the transversality condition the new result is applied to an imperfect pitchfork bifurcation in which a forward transcritical bifurcation changes to a backward one when the perturbation parameter changes several applications in ecological and genetics models are shown

asymptotic behavior of solutions of semilinear elliptic equations in unbounded domains two approaches abstract in this paper we study the asymptotic behavior as x 1 of solutions of semilinear elliptic equations in quarter or half spaces for which the value at x 1 0 is given we prove the uniqueness and characterize the one dimensional or constant profile of the solutions at infinity to do so we use two different approaches the first one is a pure pde approach and it is based on the maximum principle the sliding method and some new liouville type results for elliptic equations in the half space or in the whole space r n the second one is based on the theory of dynamical systems

balancing neumann neumann methods for the cardiac bidomain model balancing neumann neumann preconditioners are constructed analyzed and numerically studied for the cardiac bidomain model in three dimensions this reaction diffusion system is discretized by low order finite elements in space and implicit explicit methods in time yielding very ill conditioned linear systems that must be solved at each time step the proposed algorithm is based on decomposing the domain into nonoverlapping subdomains and on solving iteratively the bidomain schur complement obtained by implicitly eliminating the degrees of freedom interior to each subdomain the iteration is preconditioned by a balancing neumann neumann method employing local neumann solves on each subdomain and a coarse bidomain solve a novel approach for the estimation of the average operator of the nonoverlapping decomposition provides a framework for designing coarse spaces for balancing neumann neumann methods the theoretical estimates obtained show that the proposed method is scalable quasi optimal and robust with respect to possible coefficient discontinuities of the bidomain operator the results of extensive parallel numerical tests in three dimensions confirm the convergence rates predicted by the theory

bpx preconditioners for the bidomain model of electrocardiology the aim of this work is to develop a bpx preconditioner for the bidomain model of electrocardiology this model describes the bioelectrical activity of the cardiac tissue and consists of a system of a non linear parabolic reaction diffusion partial differential equation pde and an elliptic linear pde modeling at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue the evolution equation is coupled through the non linear reaction term with a stiff system of ordinary differential equations the so called membrane model describing the ionic currents through the cellular membrane the discretization of the coupled system by finite elements in space and semi implicit finite differences in time yields at each time step the solution of an ill conditioned linear system the goal of the present study is to construct analyze and numerically test a bpx preconditioner for the linear system arising from the discretization of the bidomain model optimal convergence rate estimates are established and verified by two and three dimensional numerical tests on both structured and unstructured meshes moreover in a full heartbeat simulation on a three dimensional wedge of ventricular tissue the bpx preconditioner is about 35 faster in terms of cpu times than ilu 0 and an algebraic multigrid preconditioner

error performance of binary ncfsk in the presence of multiple tone interference and system noise this paper presents a general solution to the problem of calculating the error performance of binary ncfsk systems in the presence of multiple tone interference and system noise the development uses the concepts of circularly symmetric signals and expresses the results in terms of a bessel integral this integral is then evaluated using a rapidly converging fourier bessel series the error in this approximation to the integral is controlled by two parameters which may be adjusted so that the desired accuracy is attained it is determined that in the useful probability of error range and when the total tone power is constrained the error rate increases for an increase in the number of interfering tones in addition for equal amplitude tones the performance is independent of the distribution of the tones within the channel the technique used is also applicable to other detection problems where the threshold is a random variable

low dimensional qualitative and numerical approximation of bifurcation in a semilinear elliptic problem abstract a nonlinear boundary value problem exhibiting a nonlocal bifurcation in its solution set is considered it is shown that for some values of the problem parameters there is only the zero solution while for other values of these parameters two nontrivial solutions also appear these nontrivial solutions do not lie in small neighborhoods of the zero function so that the bifurcation analysis is not local to the origin the method of reduction to alternative finite dimensional problems is applied to give a numerical description of the bifurcation and in particular to describe a surface of bifurcating solutions in addition the solution set of the 1 dimensional galerkin approximation is also shown to have the same qualitative nature as the solution set of the full problem

a splitting preconditioner for a block two by two linear system with applications to the bidomain equations we construct an alternating splitting iteration scheme for solving and preconditioning a block two by two linear system arising from numerical discretizations of the bidomain equations the convergence theory of this class of splitting iteration methods is established and some useful properties of the preconditioned matrix are analyzed the potential of this approach is illustrated by numerical experiments

diffusion mediated permanence problem for a heterogeneous lotka volterra competition model we analyse the dynamics of a prototype model for competing species with diffusion coefficients d 1 d 2 in a heterogeneous environment when diffusion is switched off at each point x we have a pair of ode s the kinetic if for some x kinetic has a unique stable coexistence state we show that there exist such that for every the rd model is persistent in the sense that it has a compact global attractor within the interior of the positive cone and has a stable coexistence state the same result is true if there exist x u x v such that the semitrivial coexistence states u 0 and 0 v of the kinetic are globally asymptotically stable at x x u and x x v respectively more generally our main result shows that for most kinetic patterns stable coexistence of xspopulations can be found for some range of the diffusion coefficients singular perturbation techniques monotone schemes fixed point index global analysis of persistence curves global continuation and singularity theory are some of the technical tools employed to get the previous results among others these techniques give us necessary and or sufficient conditions for the existence and uniqueness of coexistence states conditions which can be explicitly evaluated by estimating some principal eigenvalues of certain elliptic operators whose coefficients are solutions of semilinear boundary value problems we also discuss counterexamples to the necessity of the sufficient conditions through the analysis of the local bifurcations from the semitrivial coexistence states at the principal eigenvalues an easy consequence of our analysis is the existence of models having exactly two coexistence states one of them stable and the other one unstable we find that there are also cases for which the model has three or more coexistence states

one dimensional symmetry of bounded entire solutions of some elliptic equations this paper is about one dimensional symmetry properties for some entire and bounded solutions of u f u 0 in ir we consider solutions u such that 1 u 1 and u x1 xn 1 as xn uniformly with respect to x1 xn 1 under some conditions on f we prove that the solutions only depend on the variable xn we also discuss more general elliptic operators the qualitative properties then strongly depend on the coefficients of the operator these results extend to higher dimensions and to more general operators a result of ghoussoub and gui 21 proved for n 3 ams classification 35b05 35b40 35b50 35j60