uniqueness of positive solutions for semilinear elliptic systems abstract we prove uniqueness of positive solutions for the system u f v v g u in u v 0 on where is a bounded domain in r n f g r r and f x x p g x x q at for some positive numbers p q with p q 1

optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

existence and non existence of nontrivial solutions for schrodinger systems via nehari pohozaev manifold abstract this paper is concerned with existence of bound states for a coupled gradient system of nonautonomous schrodinger equations which arises from studies of nonlinear optics and bose einstein condensates by using variational methods that are constrained to a nehari pohozaev manifold we obtain existence of nonnegative and positive bound states solutions in particular we show non existence result for a minimizing problem

existence and concentration of positive solutions for a system of coupled saturable schrodinger equations abstract it is considered a saturable system of coupled schrodinger equations with asymptotically linear nonlinearities the bound states solutions with finite energy are proved to exist and have a concentration behavior under hypotheses involving the coupling and saturation parameters the proof is based on variational methods

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

suboptimum multiuser receivers for convolutionally coded asynchronous ds cdma systems motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code division multiple access cdma systems developed by giallorenzi and wilson see ibid vol 44 no 8 p 997 1996 and the potentially poor performance of the conventional receiver due to multiuser interference and the near far problem we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver the multiuser receivers discussed are of two types the first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately the second set of approaches are integrated approaches that perform both the equalization and decoding operations together we study linear decision feedback and trellis tree based approaches in each category the asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying bpsk receiver termed asymptotic multiuser coding gain or amcg is used as a performance criterion throughout also computer simulations are used whenever the computation of the amcg is not feasible it is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity

uniqueness of topological solutions and the structure of solutions for the chern simons system with two higgs particles the existence of topological solutions for the chern simons equation with two higgs particles has been proved by lin ponce and yang 16 however both the uniqueness problem and the existence of non topological solutions have been left open in this paper we consider the case of one vortex at origin among others we prove the uniqueness of topological solutions and give a complete study of the radial solutions in particular the existence of some non topological solutions

bifurcation diagrams of coupled schrodinger equations radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations a numerical solver for initial value problems for such systems is developed based on matlab and numerical bifurcation diagrams are obtained according to the behavior of the solutions various bifurcation diagrams of coupled schrodinger equations from nonlinear physics are obtained which suggests the uniqueness of the ground state solution

a family of likelihood ascent search multiuser detectors approaching optimum performance via random multicodes with linear complexity tse and verdu proved that the global maximum likelihood gml detector achieves unit asymptotic multiuser efficiency ame in the limit of large random spreading cdma in this paper we show that the wide sense sequential likelihood ascent search wslas detectors achieve unit ame with channel load 1 2 1 4 ln 2 bits s hz in simulations for random multicode equal power systems the wslas with a linear per bit complexity approaches the gml ber in all snr with channel load as high as 1 05 bits s hz

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

on hamiltonian elliptic systems with periodic or non periodic potentials abstract this paper is concerned with the following hamiltonian elliptic system u b x u v x u h v x u v v b x v v x v h u x u v for x r n existence and multiplicity of solutions are obtained for the systems with periodic or non periodic potentials v via variational methods

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

tight bounds on the capacity of binary input random cdma systems in this paper we consider code division multiple access cdma communication over a binary input additive white gaussian noise awgn channel using random spreading for a general class of symmetric distributions for spreading sequences in the limit of a large number of users we prove an upper bound to the capacity the bound matches the formula obtained by tanaka using the replica method we also show concentration of various relevant quantities including mutual information and free energy the mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios

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

classification and sharp range of flux pairs for radial solutions to a coupled system abstract in this paper we study a coupled system of two nonlinear partial differential equations in the plane which is related to liouville equations non abelian higgs bps vortex equations or two higgs electroweak model with singularities at the origin in addition to deriving the uniqueness of the so called topological solutions we also clarify the structure of all types of solutions including the blow up ones under various conditions on coefficients and parameters appearing in the system furthermore the sharp range of flux pairs associated with specific types of solutions is considered as well

on the solutions of liouville systems for some prescribed m 0 together with the dirichlet boundary condition u 0 on 0 the liouville equation finds applications in various fields of physics and mathematics to name a few it represents the newtonian potential of a cluster of self gravitating mass distribution where a 0 1 6 36 37 the electric potential induced by charge carriers in the theory of electrolytes where a 0 31 and maximal entropy solutions of the incompressible euler equation 23 9 in the field of differential geometry it stands for the problem of finding a metric corresponding to a prescribed gaussian curvature 3 10 the system analog of l takes the form

uniqueness of positive solutions for a class of semipositone elliptic systems abstract we consider the system u f v x v g u x u 0 v x where is a ball in r n n 1 and is its boundary are positive parameters and f g are smooth functions that are negative at the origin and f x x p and g x x q for large x for some p q 0 with p q 1 we establish the uniqueness of positive solutions when the parameters and are large

on a 145 32 binary cyclic code we discovered that a 145 32 binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x sup 4 x sup 3 x sup 2 x 1 has a minimum distance of 44

on optimum asymptotic multiuser efficiency of randomly spread cdma we extend the result by tse and verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access cdma with binary phase shift keying input random gaussian and random binary antipodal spreading are considered we obtain the optimum asymptotic multiuser efficiency of a k user system with spreading gain n when k and n rightarrow infty and the loading factor k n grows logarithmically with k under some conditions it is shown that the optimum detector in a gaussian randomly spread cdma system has a performance close to the single user system at high signal to noise ratio when k and n rightarrow infty and the loading factor k n is kept less than log 3 k 2 random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained furthermore we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency we obtain a condition such that for any binary input an n times k random matrix whose entries are chosen randomly from a finite set is a detecting matrix as k and n rightarrow infty

a family of likelihood ascent search multiuser detectors an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency in this paper the bit error performance of a family of likelihood ascent search las multiuser detectors is analyzed an upper bound on the ber of any las detector is obtained by bounding the fixed point region with the worst initial detector the concept of indecomposable errors developed by verdu is applied to tighten the upper bound in a special instance the upper bound is reduced to that for all the local maximum likelihood detectors the upper bound is comparable with that of the optimum detector obtained by verdu a lower bound on the asymptotic multiuser efficiency ame is then obtained it is shown that there are nontrivial cdma channels such that a las detector can achieve unit ame regardless of user number the ame lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient cdma

radial symmetry results for fractional laplacian systems abstract in this paper we generalize the direct method of moving planes for the fractional laplacian to the system case considering a coupled nonlinear system with fractional laplacian we first establish a decay at infinity principle and a narrow region principle using these principles we then obtain two radial symmetry results for the decaying solutions of the fractional laplacian systems finally we apply our method to fractional schrodinger systems and fractional henon systems

uniqueness of the positive solution for a class of semilinear elliptic systems abstract we prove the uniqueness of the positive radially symmetric solution to the following problem u v p 1 0 x b 1 v w p 2 0 x b 1 w u p 3 0 x b 1 u v w 0 x b 1 where p i 0 i 1 2 3 and b 1 is the unit ball in r n

on the capacity loss due to separation of detection and decoding the performance loss due to separation of detection and decoding on the binary input additive white gaussian noise awgn channel is quantified in terms of mutual information results are reported for both the code division multiple access cdma channel in the large system limit and the intersymbol interference isi channel the results for cdma rely on the replica method developed in statistical mechanics it is shown that a previous result of shamai and verdu found for gaussian input alphabet holds also for binary input alphabets for the isi channel the performance loss is calculated via the bahl cocke jelinek raviv bcjr algorithm comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision feedback equalizer

stationary solitons of a three wave model generated by type ii second harmonic generation in quadratic media abstract in this paper we prove the uniqueness of stationary standing wave solutions of an optical model generated by type ii second harmonic generation shg with behaviors tending to zero at infinity under certain conditions on parameters in addition we provide the same issues for the dirichlet boundary value problems on the ball centered at the origin a classification of solutions for radial case is also established

on the classification of standing wave solutions to a coupled schrodinger system in this paper we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear schrodinger equation we establish the existence and uniqueness of solutions to the dirichlet problem on the ball and entire space as the parameters within certain regions in addition a complete structure of different types of solutions for the radial case is also provided

on the uniqueness and structure of solutions to a coupled elliptic system abstract in this paper we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear schrodinger equation we establish the existence and uniqueness of solutions to the dirichlet problem on the ball in addition the nonexistence of the ground state solutions under certain conditions on the nonlinearities and the complete structure of different types of solutions to the shooting problem are proved

bounds on the sum capacity of synchronous binary cdma channels in this paper we obtain a family of lower bounds for the sum capacity of code division multiple access cdma channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution the envelope of this family gives a relatively tight lower bound in terms of the number of users spreading gain and the noise distribution the derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero the noisy channel bound approaches the noiseless case the behavior of the lower bound shows that for small noise power the number of users can be much more than the spreading gain without any significant loss of information overloaded cdma a conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution as the noise level increases and or the ratio of the number of users and the spreading gain increases the conjectured upper bound approaches the lower bound we have also derived asymptotic limits of our bounds that can be compared to a formula that tanaka obtained using techniques from statistical physics his bound is close to that of our conjectured upper bound for large scale systems

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

uniqueness of topological multi vortex solutions for a skew symmetric chern simons system in this paper we consider a skew symmetric chern simons system problem with a coupling parameter our main goal is that when the coupling parameter is small the topological type solutions to this system problem are uniquely determined by the location of their vortex points this result follows by the bubbling analysis and the non degeneracy of linearized equations

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

new existence and symmetry results for least energy positive solutions of schrodinger systems with mixed competition and cooperation terms abstract in this paper we focus on existence and symmetry properties of solutions to the cubic schrodinger system u i i u i j 1 d i j u j 2 u i in r n i 1 d where d 2 i i i 0 i j j i r for j i n 2 3 the underlying domain is either bounded or the whole space and u i h 0 1 or u i h rad 1 r n respectively we establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients as well as in the purely cooperative case

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

an existence result on positive solutions for a class of semilinear elliptic systems consider the system where is a positive parameter and is a bounded domain in r n we prove the existence of a large positive solution for large when lim x f mg x x 0 for every m 0 in particular we do not need any monotonicity assumptions on f g nor any sign conditions on f 0 g 0

suboptimum soft output detection algorithms for coded multiuser systems in this paper we consider coded asynchronous multiuser signals in an additive white gaussian noise channel since optimum joint multiuser detection mud and forward error correction fec decoding is characterized with a very high computational complexity we consider disjoint mud and fec decoding the optimum disjoint multiuser detector is the soft output maximum a posteriori detector that provides sequences of a posteriori probabilities to the corresponding fec decoders it involves backward and forward recursions resulting in high complexity and processing delay in this paper we consider several suboptimum soft output disjoint multiuser detectors that involve only forward recursions and have reduced complexity and delay

decay symmetry and existence of solutions of semilinear elliptic systems our utmost aim was originally to establish the existence of solutions of system however in this effort we got sidetracked to consider other questions in this way we come to interesting results on asymptotic behavior of solutions on symmetry properties of such solutions and the existence of ground states

large system analysis of multiuser detection with an unknown number of users a high snr approach we analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver in this environment users activity must be estimated along with any other parameters such as data power and location our main goal is to determine the performance loss caused by the need for estimating the identities of active users which are not known a priori to prevent a loss of optimality we assume that identities and data are estimated jointly rather than in two separate steps we examine the performance of multiuser detectors when the number of potential users is large statistical physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency special attention is paid to the fixed point equation whose solution yields the multiuser efficiency of the optimal maximum a posteriori detector in the large signal to noise ratio regime our analysis yields closed form approximate bounds to the minimum mean squared error in this regime these illustrate the set of solutions of the fixed point equation and their relationship with the maximum system load next we study the maximum load that the detector can support for a given quality of service specified by error probability

symmetry results for elliptic schrodinger systems on half spaces abstract in this paper we prove some symmetry and monotonicity results for classical positive solutions for elliptic schrodinger systems on half spaces with the neumann type condition our methods employ the alexandrov serrin method of moving planes combined with hopf s lemma at a corner

iterative multiuser joint decoding optimal power allocation and low complexity implementation we consider a canonical model for coded code division multiple access cdma with random spreading where the receiver makes use of iterative belief propagation bp joint decoding we provide simple density evolution analysis in the large system limit large number of users of the performance of the bp decoder and of some suboptimal approximations based on interference cancellation ic based on this analysis we optimize the received user signal to noise ratio snr distribution in order to maximize the system spectral efficiency for given user channel codes channel load users per chip and target user bit error rate ber the optimization of the received snr distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms remarkably under the optimized snr assignment the suboptimal minimum mean square error mmse ic based decoder performs almost as well as the more complex bp decoder moreover for a large class of commonly used convolutional codes we observe that the optimized snr distribution consists of a finite number of discrete snr levels based on this observation we provide a low complexity approximation of the mmse ic decoder that suffers from very small performance degradation while attaining considerable savings in complexity as by products of this work we obtain a closed form expression of the multiuser efficiency me of power mismatched mmse filters in the large system limit and we extend the analysis of the symbol by symbol maximum a posteriori probability map multiuser detector in the large system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities

on the average near far resistance for mmse detection of direct sequence cdma signals with random spreading the performance of a near far resistant finite complexity minimum mean squared error mmse linear detector for demodulating direct sequence ds code division multiple access cdma signals is studied assuming that the users are assigned random signature sequences we obtain tight upper and lower bounds on the expected near far resistance of the mmse detector averaged over signature sequences and delays as a function of the processing gain and the number of users since the mmse detector is optimally near far resistant these bounds apply to any multiuser detector that uses the same observation interval and sampling rate the lower bound on near far resistance implies that even without power control linear multiuser detection provides near far resistant performance for a number of users that grows linearly with the processing gain

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

an iterative multiuser decoder for near capacity communications the combination of forward error correction fec coding and random interleaving is shown to overcome the limitations of multiuser detectors decoders when the user cross correlations are high in particular one can asymptotically achieve single user performance in a highly correlated multiuser system in addition an optimal iterative multiuser detector is derived from iterative techniques for cross entropy minimization a practical suboptimal implementation of this algorithm is presented and simulations demonstrate that even with highly correlated users it achieves optimal asymptotic efficiency the effects of the theoretical limits on channel capacity are evident in many of the simulation results the complexity of the suboptimal algorithm is approximately o 2 sup k o 2 sup spl kappa per bit per iteration where k is the number of users and spl kappa is the code constraint length

ground states for a system of schrodinger equations with critical exponent abstract we study the following system of nonlinear schrodinger equations u u u p 1 u v x r n v v v 2 2 v u x r n where n 3 2 2 n n 2 1 p 2 1 and are positive parameters satisfying 0 we show that there is some critical value 0 0 1 such that this system has a positive ground state solution if 0 0 in the case 0 there exists 0 such that this system has no ground state solutions if while this system has a positive ground state solution if in particular if p 2 1 the system has no nontrivial solutions some further properties of the ground state solutions are also studied this seems to be the first result for such a critical schrodinger system

on global bifurcation for quasilinear elliptic systems on bounded domains general second order quasilinear elliptic systems with nonlinear boundary conditions on bounded domains are formulated into nonlinear mappings between sobolev spaces it is shown that the linearized mapping is a fredholm operator of index zero this and the abstract global bifurcation theorem of jacobo pejsachowicz patrick j rabier degree theory for c1 fredholm mappings of index 0 j anal math 76 1998 289 319 allow us to carry out bifurcation analysis directly on these elliptic systems at the abstract level we establish a unilateral global bifurcation result that is needed when studying positive solutions finally we supply two examples of cross diffusion population model and chemotaxis model to demonstrate how the theory can be applied

symmetry of minimizers for some nonlocal variational problems abstract we present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems this approach which generalizes the reflection method is based on the existence of some integral identities we study the identities that lead to symmetry results the functionals that can be considered and the function spaces that can be used then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of laplacian for the generalized choquard functional and for the standing waves of the davey stewartson equation

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

symmetry results for semilinear elliptic systems in the whole space in this paper we obtain symmetry results of gidas ni nirenberg type for cooperative nonlinear elliptic systems in the whole space

singularly perturbed elliptic systems abstract we study the existence and concentration behavior of positive solutions for a class of hamiltonian systems two coupled nonlinear stationary schrodinger equations combining the legendre fenchel transformation with mountain pass theorem we prove the existence of a family of positive solutions concentrating at a point in the limit where related functionals realize their minimum energy in some cases the location of the concentration point is given explicitly in terms of the potential functions of the stationary schrodinger equations

liouville type theorems monotonicity results and a priori bounds for positive solutions of elliptic systems this paper is a contribution to the study of boundary value problems for systems of elliptic partial differential equations

symmetry and non existence of positive solutions for fractional p laplacian systems abstract chen and li 2018 developed maximum principles for the fractional p laplacian which carry out the direct method of moving planes to the fractional p laplacian equation in this paper we generalize their method to the system case and obtain a symmetry result for the fractional p laplacian system on the whole space we also consider the system on the upper half space and obtain a non existence result

existence and uniqueness of positive radial solutions for the lane emden system in this article we consider component wise positive radial solutions of a weakly coupled system of elliptic equations in a ball with homogeneous nonlinearities the existence is well known in general we give a result for the remaining cases the uniqueness is less studied we complement the known results

multiuser ml sequence estimator for convolutionally coded asynchronous ds cdma systems the optimal multiuser sequence estimator is formulated for an asynchronous direct sequence code division multiple access ds cdma system where each user employs convolutional coding to improve its performance on a nondispersive additive white gaussian noise awgn channel it is shown that the decoder may be implemented efficiently using a viterbi algorithm which operates on a time varying trellis with a number of states which is exponential in the product of the number of users in the system and the constraint length of the codes used for the rate 1 2 code case the asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying bpsk receiver termed asymptotic multiuser coding gain or amcg is then upper and lower bounded the amcg parameter unifies the asymptotic coding gain parameter and the asymptotic multiuser efficiency parameter which are traditional figure of merit parameters for single user coded systems and multiuser uncoded systems respectively finally some simulations are presented to illustrate the performance of the maximum likelihood sequence estimator mlse at moderate and low bit error rates