new characterizations of morrey spaces and their preduals with applications to fractional laplace equations abstract in this article the authors characterize the morrey spaces as well as their preduals via quadratic functions related to the taylor remainder of the kernel of the riesz potential as applications the authors obtain some strong capacitary inequalities which are then used to study the regularity of the duality weak solution to the fractional laplace equation with measure data

radial solutions of superlinear equations on ℝn part ii the forced case we study the effect of a forcing term in the context of the search of multiple nodal solutions u h 1 n to a class of elliptic equations of type u x f x u x h x x n where f x 0 and f is superlinear but subcritical at infinity

on the moment determinance and random mixture of nakagami m variates we study complex valued nakagami m variates establishing the moment determinance of the envelope phase and joint envelope phase nakagami m probability density functions pdf s inspired by that result we then show that nakagami m variates with arbitrary fading figure m can be accurately decomposed onto a mixture of nakagami m variates with integer or half integer m i e 2m the latter has the immediate theoretical implication that results currently known to hold for nakagami m channels under the constraint 2m can accurately be extended to arbitrary m via simple linear decomposition with weights given by the random mixture probabilities for which formulas are provided the latter is illustrated with an example of the application of the random mixture decomposition to the simplification and generalization of bit error rate ber expressions for psk modulation in the nakagami m relay channel for completeness implications on possible extensions and improvements of existing methods to generate nakagami m variates is also briefly discussed in the form of further examples

sign changing multi bump solutions for nonlinear schrodinger equations with steep potential wells we study the nonlinear schrodinger equations p u 2 a x 1 u u p 1 u u h 1 r n where p 1 is a subcritical exponent a x is a continuous function satisfying a x 0 0 lim inf x a x lim sup x a x and a 1 0 consists of 2 connected bounded smooth components 1 and 2 we study the existence of solutions u of p which converge to 0 in r n 1 u 2 and to a prescribed pair v 1 x v 2 x of solutions of the limit problem v i v i v i p 1 v i in i i 1 2 as oo

the asymptotic distribution of maxima of independent and identically distributed sums of correlated or non identical gamma random variables and its applications in this paper we show that the asymptotic probability density function pdf of the maxima of n independent and identically distributed i i d sums of independent non identically i n i d distributed gamma random variables rvs is a gumbel pdf using extreme value theory evt we will also show that the asymptotic pdf of the maxima of n i i d sums of correlated gamma rvs is a gumbel pdf some applications in wireless communication are discussed where the maxima of n i i d sums of correlated gamma rvs and maxima of n i i d sums of i n i d gamma rvs arise we discuss the utility of our results in the context of these applications

uniform bounds for strongly competing systems the optimal lipschitz case for a class of systems of semi linear elliptic equations including delta u i f i x u i beta u i sum j neq i a ij u j p quad i 1 dots k for p 2 variational type interaction or p 1 symmetric type interaction we prove that uniform l infty boundedness of the solutions implies uniform boundedness of their lipschitz norm as beta to infty that is in the limit of strong competition this extends known quasi optimal regularity results and covers the optimal case for this class of problems the proofs rest on monotonicity formulae of alt caffarelli friedman and almgren type in the variational setting and on the caffarelli jerison kenig almost monotonicity formula in the symmetric one

outage probability in η μ η μ and κ μ η μ interference limited scenarios in this paper exact closed form expressions are derived for the outage probability op in scenarios where the signal of interest soi experiences or fading the interfering signals are subject to fading and the background noise can be neglected with the only assumption that the parameter is a positive integer number for the interfering signals the derived expressions when the soi is either or distributed are given in elementary terms for maximal ratio combining mrc with independent branches if the pre combining soi power signals are distributed with their corresponding parameters being positive integer or half integer numbers the previous analysis is extended for spatially correlated mrc at the receiver

a fast and effective multidimensional scaling approach for node localization in wireless sensor networks given a set of pairwise distance estimates between nodes it is often of interest to generate a map of node locations this is an old nonlinear estimation problem that has recently drawn interest in the signal processing community due to the emergence of wireless sensor networks sensor maps are useful for estimating the spatial distribution of measured phenomena and for routing purposes we propose a two stage algorithm that combines algebraic initialization and gradient descent in particular we borrow an algebraic solution known as fastmap from the database literature adapt it to the sensor network context and motivate the placement of anchor pivot nodes on the edges of the network when all nodes can estimate their distance from the anchors the overall algorithm offers very competitive performance at low complexity quadratic in the number of nodes

decomposition of hardy morrey spaces abstract in this paper we establish the decompositions of hardy morrey spaces in terms of atoms concentrated on dyadic cubes which have the same cancellation properties of the classical hardy spaces

morse index of some min max critical points i application to multiplicity results on donne un resultat general sur des bornes inferieures pour des indices de morse de points critiques obtenus par des principes de min max en combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d equations elliptiques semi lineaires d ordre 2

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

sign changing solutions of lane emden problems with interior nodal line and semilinear heat equations abstract we consider the semilinear lane emden problem u u p 1 u in u 0 on where is a smooth bounded simply connected domain in r 2 invariant by the action of a finite symmetry group g we show that if the orbit of each point in under the action of the group g has cardinality greater than or equal to 4 then for p sufficiently large there exists a sign changing solution of e p with two nodal regions whose nodal line does not touch this result is proved as a consequence of an analogous result for the associated parabolic problem

on a critical schrodinger system in r4 with steep potential wells abstract in this paper we study the following two component elliptic system u a x a 0 u u 3 v 2 u 0 in r 4 v b x b 0 v v 3 u 2 v 0 in r 4 u v h 1 r 4 h 1 r 4 where a 0 b 0 r are constants 0 and r are parameters a x b x 0 are potentials by using variational methods we prove the existence and nonexistence of general ground state solutions maybe semi trivial and ground state solutions of the above system under some further conditions on the potentials a x b x and the parameters it is worth pointing out that the cubic nonlinearities and the coupled terms of the above system are all of critical growth owing to the sobolev embedding theorem furthermore by introducing some ideas which are different from that in the literature the phenomenon of phase separation of ground state solutions of the above system is also obtained without any symmetry conditions

reduced feedback schemes using random beamforming in mimo broadcast channels a random beamforming scheme for the gaussian mimo broadcast channel with channel quality feedback is investigated and extended considering the case where the n receivers each have n receive antennas the effects of feeding back various amounts of signal to interference plus noise ratio sinr information are analyzed using the results from order statistics of the ratio of a linear combination of exponential random variables the distribution function of the maximum order statistic of the sinr observed at the receiver is found the analysis from viewing each antenna as an individual user is extended to allow combining at the receivers where it is known that the linear mmse combiner is the optimal linear receiver and the cdf for the sinr after optimal combining is derived analytically using the delta method the asymptotic distribution of the maximum order statistic of the sinr with and without combining is shown to be in the nomenclature of extreme order statistics of type 3 the throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users finally to further reduce the amount of feedback a hard threshold is applied to the sinr feedback the amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded

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

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

a trace law for the hardy morrey sobolev space abstract this article shows that if h l p and h l q are p hardy morrey space based on the standard lebesgue measure and q hardy morrey space induced by the non negative radon measure respectively then one has the following trace law for the hardy morrey sobolev space i h l p of riesz potentials of order of h l p functions sup 0 f h l p i f h l q f h l p 1 sup x r r n 0 r b x r under 0 n 0 n 0 p n p n 0 q p n p

mean holder lipschitz potentials in curved campanato radon spaces and equations delta frac alpha 2 u mu f_k u δ α 2 u μ f k u this paper shows that under begin aligned left begin array ll 0 s 1 0 alpha n 0 beta le n 1 le min p q le max p q beta p n alpha p 1 infty lambda q np 1 s alpha n beta end array right end aligned if mu is a nonnegative radon measure on mathbb r n with the beta dimensional upper curvature mu beta infty then i alpha dot varlambda s p infty the mean holder lipschitz potential space on mathbb r n embeds continuously into mathcal l q lambda mu the curved campanato radon space on mathbb r n and yet its converse is still valid with mu being admissible doubling cf theorem 1 1 thereby discovering the gamma holder lipschitz continuity of any duality solution to the alpha th laplace equation vardelta frac alpha 2 u mu or the 1 frac n 2 cap 1 2 ldots n ni k th hessian equation f k u mu under a suitable curvature condition mu beta infty cf theorems 1 3 and 1 5

snr of generalized diversity selection combining with nonidentical rayleigh fading statistics a closed form expression for the average signal to noise ratio snr of generalized diversity selection combining using the m largest in instantaneous snr diversity signals for arbitrary m assuming that the rayleigh fading statistics on each diversity branch are identically independently distributed i i d already exists in the literature in this paper a similar closed form expression but for nonidentically distributed statistics is derived this expression specializes to known results such as the average snrs of maximal ratio combining with either i i d or non i i d diversity statistics and that of conventional selection combining csc with i i d diversity statistics in addition it provides for the first time a simple closed form solution to the combined snr of csc with non i i d diversity statistics further the closed form solution for the snr of selecting the m largest diversity signals has negligible computational complexity

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

asymptotic throughput analysis for channel aware scheduling in this paper we provide an asymptotic performance analysis of channel aware packet scheduling based on the extreme value theory we first address the average throughput of systems with a homogeneous average signal to noise ratio snr and obtain its asymptotic expression compared with the exact throughput expression the asymptotic one which is applicable to a broader range of fading channels is more concise and easier from which to get insights furthermore we confirm the accuracy of the asymptotic results by theoretical analysis and numerical simulation for a system with heterogeneous snrs normalized snr based scheduling needs to be used for fairness we also investigate the asymptotic average throughput of the normalized snr based scheduling and prove that the average throughput in this case is less than that in the homogeneous case with a power constraint

hardy sobolev spaces on strongly lipschitz domains of rn let be a strongly lipschitz domain of rn the hardy spaces hr1 and hz1 have been introduced by miyachi studia math 95 3 1990 205 jonsson et al studia math 80 2 1984 141 and chang et al j funct anal 114 1993 286 we first investigate spaces of functions in l1 whose gradients belong to hr1 or hz1 which we call hardy sobolev spaces following strichartz coll math 60 61 1 1990 129 secondly if l a is a uniformly elliptic second order divergence operator on with measurable complex coefficients subject to the dirichlet or the neumann boundary condition we compare the norms of l1 2f and f in suitable hardy spaces on depending on the boundary condition under the assumption that the heat kernel of l satisfies suitable estimates

performance analysis of joint opportunistic scheduling and receiver design for mimo sdma downlink systems in this work the sum rate performance of joint opportunistic scheduling and receiver design josrd is analyzed for multiuser multiple input multiple output mimo space division multiple access sdma downlink systems in particular we study linear rake receivers with selective combining maximum ratio combining and optimal combining in which signals received from all antennas of each mobile terminal mt are linearly combined to improve the effective signal to interference plus noise ratios sinrs by exploiting limited feedback on the effective sinrs the base station bs schedules simultaneous data transmission on multiple beams to the mts with the largest effective sinrs using extreme value theory the average sum rates and their scaling laws for josrd are derived in particular it is shown that the limiting distribution of the effective signal to interference sir is of the frechet type whereas that of the effective sinr converges to the gumbel type furthermore the sir based sum rate scaling laws are found to follow e log k with 0 e 1 which stands in contrast to the sinr based scaling laws governed by the conventional log log k form both analytical and simulation results confirm that significant performance improvement can be achieved by incorporating low complexity linear combining techniques into the design of scheduling schemes in mimo sdma downlink systems

on the bolza problem abstract we consider the following boundary value problem x v x 0 x 0 x 0 x t x 1 where t 0 x 0 x 1 r n are given we prove that this problem has infinitely many solutions provided v is even and superquadratic

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

special set and solutions of coupled nonlinear schrodinger equations a special set of n coupled nonlinear schrodinger equations which consists of 2n interaction types each of which is characterized by a specific array of interaction parameters is presented it is shown that every lame function of order n n is a solution for one or more components for one or more interaction types of this special set simple rules that relate interaction and solution types and interesting features of these relationships are presented

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

error vector magnitude analysis in generalized fading with co channel interference in this paper we derive the data aided error vector magnitude evm in an interference limited system when both the desired channel and interferers experience independent and nonidentically distributed kappa mu shadowed fading then it is analytically shown that the evm is equal to the square root of number of interferers when the desired channel and interferers do not experience fading furthermore the evm is derived in the presence of interference and noise when the desired channel experiences kappa mu shadowed fading and the interferers experience independent and identical nakagami fading moreover using the properties of the special functions the derived evm expressions are also simplified for various special cases

multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent abstract this paper deals with the following system linearly coupled by nonlinear elliptic equations u 1 u u 2 2 u v x v 2 v v 2 2 v u x u v 0 on here is a smooth bounded domain in r n n 3 1 2 1 are constants 1 is the first eigenvalue of h 0 1 2 2 n n 2 is the sobolev critical exponent and r is a coupling parameter by variational method we prove that this system has a positive ground state solution for some 0 via a perturbation argument we show that this system also admits a positive higher energy solution when is small moreover the asymptotic behaviors of the positive ground state and higher energy solutions as 0 are analyzed

efficient linear solution of exterior orientation this paper concerns an efficient algorithm for the solution of the exterior orientation problem orthogonal decompositions are used to first isolate the unknown depths of feature points in the camera reference frame allowing the problem to be reduced to an absolute orientation with scale problem which is solved using the singular value decomposition svd the key feature of this approach is the low computational cost compared to existing approaches

existence and symmetry of positive ground states for a doubly critical schrodinger system n n 2 and 1 1 satisfying 2 this problem is related to coupled nonlinear schrodinger equations with critical exponent for bose einstein condensate for different ranges of n and 0 we obtain positive ground state solutions via some quite different methods which are all radially symmetric it turns out that the least energy level depends heavily on the relations among and 2 besides for sufficiently small 0 positive solutions are also obtained via a variational perturbation approach note that the palais smale condition can not hold for any positive energy level which makes the study via variational methods rather complicated

divergence estimation of continuous distributions based on data dependent partitions we present a universal estimator of the divergence d p spl par q for two arbitrary continuous distributions p and q satisfying certain regularity conditions this algorithm which observes independent and identically distributed i i d samples from both p and q is based on the estimation of the radon nikodym derivative dp dq via a data dependent partition of the observation space strong convergence of this estimator is proved with an empirically equivalent segmentation of the space this basic estimator is further improved by adaptive partitioning schemes and by bias correction the application of the algorithms to data with memory is also investigated in the simulations we compare our estimators with the direct plug in estimator and estimators based on other partitioning approaches experimental results show that our methods achieve the best convergence performance in most of the tested cases

asymptotic estimates for the spatial segregation of competitive systems abstract for a class of population models of competitive type we study the asymptotic behavior of the positive solutions as the competition rate tends to infinity we show that the limiting problem is a remarkable system of differential inequalities which defines the functional class s in 2 by exploiting the regularity theory recently developed in conti et al indiana univ math j to appear for the elements of functional classes of the form s we provide some qualitative and regularity property of the limiting configurations besides for the case of two competing species we obtain a full description of the limiting states and we prove some quantitative estimates for the rate of convergence finally we prove some new liouville type results which allow to have uniform regularity estimates of the solutions

the p laplacian with respect to measures abstract we introduce a definition for the p laplace operator with respect to positive and finite borel measures that satisfy an adams type embedding condition

on the histogram as a density estimator l 2 theory let f be a probability density on an interval i finite or infinite i includes its finite endpoints if any and f vanishes outside of i let x1 x k be independent random variables with common density f the empirical histogram for the x s is often used to estimate f to define this object choose a reference point xosi and a cell width h let nj be the number of x s falling in the j th class interval

restricting riesz morrey hardy potentials abstract to strengthen the weak restriction principle discovered in both 2 theorem 5 1 for and 32 lemma 2 1 for this paper shows that the riesz operator i of order maps the morrey hardy space l h p to the morrey radon space l q continuously if and only if sup x r r n 0 b x r r provided 0 n 0 n 1 p n p n 0 q p n p moreover this brand new restriction principle is optimal in the sense that if n 0 then the iff statement fails quite remarkably such an optimization confirms affirmatively the conjecture in 7 remark 3 3 if p n q p p then there is no continuity of i l p l q n for an arbitrary radon measure with

positive least energy solutions and phase separation for coupled schrodinger equations with critical exponent in this paper we study the following coupled schrodinger system which can be seen as a critically coupled perturbed brezis nirenberg problem left begin array ll delta u lambda 1 u mu 1 u 3 beta uv 2 quad x in omega delta v lambda 2 v mu 2 v 3 beta vu 2 quad x in omega u geqq 0 v geqq 0 rm in omega quad u v 0 quad rm on partial omega end array right here omega subset mathbb r 4 is a smooth bounded domain lambda 1 omega 0 and beta neq 0 where lambda 1 omega is the first eigenvalue of with the dirichlet boundary condition note that the nonlinearity and the coupling terms are both critical in dimension 4 that is frac 2n n 2 4 when n 4 we show that this critical system has a positive least energy solution for negative positive small and positive large for the case in which lambda 1 lambda 2 we obtain the uniqueness of positive least energy solutions we also study the limit behavior of the least energy solutions in the repulsive case beta to infty and phase separation is expected these seem to be the first results for this schrodinger system in the critical case

error rates for nakagami m fading multichannel reception of binary and m ary signals this paper derives new closed form formulas for the error probabilities of single and multichannel communications in rayleigh and nakagami m 1960 fading closed form solutions to three generic trigonometric integrals are presented as part of the main result providing a unified method for the derivation of exact closed form average symbol error probability expressions for binary and m ary signals with l independent channel diversity reception both selection diversity and maximal ratio combining mrc techniques are considered the results are generally applicable for arbitrary two dimensional signal constellations that have polygonal decision regions operating in a slow nakagami m fading environments with positive integer fading severity index mrc with generically correlated fading is also considered the new expressions are applicable in many cases of practical interest the closed form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and m ary signals that employ an equal gain combining diversity receiver

sum rate analysis of a reduced feedback ofdma downlink system employing joint scheduling and diversity we consider joint scheduling and diversity to enhance the benefits of multiuser diversity in an orthogonal frequency division multiple access ofdma downlink system the ofdma spectrum is assumed to consist of nrb resource blocks and the reduced feedback scheme consists of each user feeding back channel quality information cqi for only the best nfb resource blocks assuming largest normalized cqi scheduling and a general value for nfb we develop a unified framework to analyze the sum rate of the system for both the quantized and nonquantized cqi feed back schemes based on this framework we provide closed form expressions for the sum rate for three different multiantenna transmitter schemes transmit antenna selection tas orthogonal space time block codes ostbc and cyclic delay diversity cdd furthermore we approximate the sum rate expression and determine the feedback ratio nfb nrb required to achieve a sum rate comparable to the sum rate obtained by a full feedback scheme

positive ground state solutions and multiple nontrivial solutions for coupled critical elliptic systems in this study we consider the following coupled elliptic system with a sobolev critical exponent p u1 1u1 1u1p1 1 1u12 1 u12 2 1u22 2 x u2 2u2 2u2p2 1 2u22 1 u12 2u22 2 1 x u1 u2 0in u1 u2 0on where rn is a bounded smooth domain n 5 2 0 for j 1 2 and 1 is the first eigenvalue of with the dirichlet boundary condition we demonstrate the existence of a positive ground state solution for problem p when the coupling parameter 1 2 under some other conditions we show the nonexistence of positive solutions for p when n 3 we also construct multiple nontrivial solutions and sign changing solutions for the following system u1 1u1 1u13 u22u1 x u2 2u2 2u23 u12u2 x u1 u2 0on where rn is a bounded smooth domain and n 4

solitary and self similar solutions of two component system of nonlinear schrodinger equations conventionally to learn wave collapse and optical turbulence one must study finite time blow up solutions of one component self focusing nonlinear schrodinger equations nlse here we consider simultaneous blow up solutions of two component systems of self focusing nlse by studying the associated self similar solutions we prove two components of solutions blow up at the same time these self similar solutions may come from solitary wave solutions with multi bumps forming abundant geometric patterns which cannot be found in one component self focusing nlse our results may provide the first step to investigate optical turbulence in two component systems of nlse

uniform holder bounds for nonlinear schrodinger systems with strong competition for the positive solutions of the gross pitaevskii system u u 1 u 3 u v 2 v v 2 v 3 u 2 v we prove that l boundedness implies c 0 boundedness for every 0 1 uniformly as moreover we prove that the limiting profile as is lipschitz continuous the proof relies upon the blowup technique and the monotonicity formulae by almgren and alt caffarelli and friedman this system arises in the hartree fock approximation theory for binary mixtures of bose einstein condensates in different hyperfine states extensions to systems with k 2 densities are given

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

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

a supplement to multidimensional scaling framework for mobile location a unified view recently while the classical multidimensional scaling mds algorithm had been claimed to be infeasible mds based algorithms including modified mds and subspace approach have been applied to the range measurements based mobile localization in this correspondence we first prove that the classical mds algorithm is feasible for the mobile localization then we show that all mds based algorithms can be unified under the same framework and they are not optimal according to the gaussian markov theorem based on the unified framework the weighted mds analysis is applied to obtain the optimum performance the performances of both the mds algorithms and their corresponding weighted mds based algorithms in the unified framework are demonstrated through simulations

error vector magnitude analysis of fading simo channels relying on mrc reception we analytically characterize the data aided error vector magnitude evm performance of a single input multiple output simo communication system relying on maximal ratio combining mrc having either independent or correlated branches that are nonidentically distributed in particular exact closed form expressions are derived for the evm in eta text mu fading and kappa w mu shadowed fading channels and these expressions are validated by simulations the derived expressions are expressed in terms of lauricella s function of the fourth kind f d n which can be easily computed furthermore we have simplified the derived expressions for various special cases such as independent and identically distributed branches rayleigh fading nakagami m fading and kappa text mu fading additionally a parametric study of the evm performance of the wireless system is presented

segregated and synchronized vector solutions for nonlinear schrodinger systems we consider the following nonlinear schrodinger system in mathbb r 3 left begin array ll delta u p x u mu u 2 u beta v 2u quad x in mathbb r 3 delta v q x v nu v 2 v beta u 2v quad x in mathbb r 3 end array right where p r and q r are positive radial potentials mu 0 nu 0 and beta in mathbb r is a coupling constant this type of system arises in particular in models in bose einstein condensates theory

gershgorin analysis of random gramian matrices with application to mds tracking we offer a redesigned form of the multidimensional scaling mds algorithm suitable to the simultaneous tracking of a large number of targets with no a priori mobility models first we employ an extreme value and asymptotic take on the theory of gershgorin spectrum bounds to perform a detailed statistical analysis of the spectrum of random n n gramian matrices which arise from dynamic constructions of mds kernels where the diagonalizer of a previous kernel is used to construct the next one the analysis reveals that even if the subspace distance between consecutive kernels is relatively large the dominant eigenspace of dynamic mds kernels are with a high probability quantified analytically associated with its first rows this feature is exploited further to design a statistically optimized and truncated variation of the jacobi algorithm which converges to the dominant eigenspace of a dynamic mds kernel as fast as the overall optimal jacobian but without the exhaustive search for the elements to be annihilated at each rotation as required in the latter under the fact that the euclidean double centered kernels of the classic mds method are asymptotically gramian and the knowledge of nystrom inspired methods to compensate for data erasures the technique presented yields a very efficient fast mds based multitarget tracking algorithm which achieves a remarkably low complexity of order o n and which is robust to arbitrary statistics of the target s dynamics

morrey potentials and harmonic maps this paper discusses trace estimates for morrey potentials i e riesz potential integrals of morrey functions leading to a consideration of the c smoothness of a class of generalized harmonic maps

fast approximated power iteration subspace tracking this paper introduces a fast implementation of the power iteration method for subspace tracking based on an approximation that is less restrictive than the well known projection approximation this algorithm referred to as the fast approximated power iteration api method guarantees the orthonormality of the subspace weighting matrix at each iteration moreover it outperforms many subspace trackers related to the power iteration method such as past nic np3 and opast while having the same computational complexity the api method is designed for both exponential windows and sliding windows our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations

asymptotic maximum order statistic for sir in kappa mu shadowed fading using tools from extreme value theory evt it is proved that when the user signal and the interferer signals undergo independent and non identically distributed i n i d kappa mu shadowed fading the limiting distribution of the maximum of l independent and identically distributed i i d signal to interference ratio sir random variables rvs is a frechet distribution it is observed that this limiting distribution is close to the true distribution of maximum for maximum sir evaluated over moderate l furthermore moments of the maximum rv is shown to converge to the moments of the frechet rv in addition the rate of convergence of the actual distribution of the maximum to the frechet distribution is derived and analyzed for different kappa and mu parameters finally results from the stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters these results are then used to derive upper bound for the rate in full array selection fas schemes for the antenna selection and the asymptotic outage probability and the ergodic rate in maximum sum capacity msc scheduling systems

segregated vector solutions with multi scale spikes for nonlinear coupled elliptic systems abstract in this paper we consider the following nonlinear coupled elliptic system a e e 2 u p x u 1 u 3 u v 2 in r n e 2 v q x v 2 v 3 u 2 v in r n u 0 v 0 in r n u 0 v 0 as x where e 0 is a parameter 1 2 0 and 0 are constants and p x and q x are two nonnegative smooth functions with different nondegenerate critical points and separated zero sets due to the lyapunov schmidt reduction method and the maximum principle we show that when is less than a small positive number there exists an e 0 0 such that for any 0 e e 0 a e has a segregated vector solution where u e v e and u e is trapped in a neighborhood of the nondegenerate critical points of p x as well as the zero sets of p x and v e is trapped in a neighborhood of the nondegenerate critical points of q x as well as the zero sets of q x moreover the amplitudes of u e res v e around the nondegenerate critical points and the zero sets of p x res q x are of a different order compared with e to the best of our knowledge these multi scale solutions to the system have not been obtained previously

radial solutions of superlinear equations on ℝn part i global variational approach we present a global variational approach to the search for multiple nodal solutions u h 1 n to a class of elliptic equations of type u x f x u x x n where n 2 f is superlinear and subcritical and f x 0

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

on the maximum likelihood approach for source and network localization we consider the source and network localization problems seeking to strengthen the relationship between the weighted least square wls and the maximum likelihood ml solutions of these problems to this end we design an optimization algorithm for source and network localization under the principle that a the wls and the ml objectives should be the same and b the solution of the ml wls objective does not depend on any information besides the set of given distance measurements observations the proposed range global distance continuation r gdc algorithm solves the localization problems via iterative minimizations of smoothed variations of the wls objective each obtained by convolution with a gaussian kernel of progressively smaller variances since the last not smoothed wls objective derives directly from the ml formulation of the localization problem and the r gdc requires no initial estimate to minimize it final result is maximum likelihood approach to source and network localization problems the performance of the r gdc method is compared to that of state of the art techniques such as semidefinite programming sdp nonlinear newton least squares nls and the stress of a majorizing complex objective function smacof algorithms as well as to the cramer rao lower bound crlb the comparison reveals that the solutions obtained with the r gdc algorithm is insensitive to initial estimates and provides a localization error that closely approaches that of the corresponding fundamental bounds the r gdc is also found to achieve a complexity order comparable to that of the smacof which is known for its efficiency

a new method for singular value loop shaping in design of multiple channel controllers in this note simple symmetric interval bounds on the singular values of a matrix based on its gershgorin disks are proposed this allows the gershgorin theorem to be used not only to provide information about the location of the eigenvalues of a matrix but also its singular values this is utilized for the proposition of a new design technique for singular value loop shaping based on the diagonal dominance methodology for design of linear multivariable plants in return this allows multiple channel simply structured controllers to be designed with a view to robustness and to meet constraints and specifications on the behavior of its singular values a design example is given demonstrating the effectiveness of this approach