efficient estimation of class a noise parameters via the em algorithm the class a middleton noise model is a commonly used statistical physical parametric model for non gaussian interference superimposed on a gaussian background in this study the problem of efficient estimation of the class a parameters for small sample sizes is considered the proposed estimator is based on the em algorithm a two step iterative estimation technique that is ideally suited for the class a estimation problem since the observations can be readily treated as incomplete data for the single parameter estimation problem a closed form expression for the estimator is obtained furthermore for the single parameter estimation problem it is shown that the sequence of estimates obtained via the em algorithm converges and a characterization of the point to which the sequence converges is given in particular it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest then it must be a stationary point of the traditional likelihood function in addition for both the single parameter and two parameter estimation problems the small sample size performance of the proposed em algorithm is examined via an extensive simulation study

recursive algorithms for identification of impulse noise channels the class a middleton model is a widely accepted statistical physical parameteric model for impulsive interference superimposed on a gaussian background in the present work a recursive decision directed estimator for online identification of the parameters of the class a model is proposed this estimator is based on an adaptive bayesian classification of each of a sequence of class a envelope samples as an impulsive sample or as a background sample as each sample is so classified recursive updates of the estimates of the second moment of the background component of the interference envelope density the second moment of the impulsive component of the interference envelope density and the probability with which the impulsive component occurs are readily obtained from these estimates estimates of the parameters of the class a model follow straightforwardly since closed form expressions for the parameters exist in terms of these quantities the performance characteristics of this algorithm are investigated and an appropriately modified version is found to yield a recursive algorithm with excellent global performance

nonparametric density estimation and detection in impulsive interference channels i estimators for pt i see ibid vol 42 no 2 4 p 1684 1697 1994 nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in part i the likelihood ratio test and the small signal locally optimum nonlinearity provide the basis for the formulation of these nonparametric detection schemes several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates in particular for the problem of detecting a known signal in impulsive noise two modifications to the standard likelihood ratio test are considered the first is adapted from robust statistics whereas the second the l sub 1 error based detector is specifically formulated for use with density estimates both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities from the merits of these two tests a new detection scheme that approximates the locally optimum nonlinearity is then developed this detector which uses the nonparametric density estimators developed in part i is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study this nonparametric density estimate based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise

instability of standing waves for klein gordon zakharov equations with different propagation speeds in three space dimensions abstract this paper is concerned with the standing wave for klein gordon zakharov equations with different propagation speeds in three space dimensions the existence of standing wave with the ground state is established by applying an intricate variational argument and the instability of the standing wave is shown by applying pagne and sattinger s potential well argument and levine s concavity method

analysis of the linearization around a critical point of an infinite dimensional hamiltonian system partial differential equations that conserve energy can often be written as infinite dimensional hamiltonian systems of the following general form du dt je u where j x x is a symplectic matrix i e jj 1 and e x r is a c 2 functional defined on some hilbert space x

domain walls in the coupled gross pitaevskii equations a thorough study of domain wall solutions in coupled gross pitaevskii equations on the real line is carried out including existence of these solutions their spectral and nonlinear stability their persistence and stability under a small localized potential the proof of existence is variational and is presented in a general framework we show that the domain wall solutions are energy minimizers within a class of vector valued functions with nontrivial conditions at infinity the admissible energy functionals include those corresponding to coupled gross pitaevskii equations arising in modeling of bose einstein condensates the results on spectral and nonlinear stability follow from properties of the linearized operator about the domain wall the methods apply to many systems of interest and integrability is not germane to our analysis finally sufficient conditions for persistence and stability of domain wall solutions are obtained to show that stable pinning occurs near maxima of the potential thus giving rigorous justification to earlier results in the physics literature

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

association schemes based on maximal totally isotropic subspaces in singular pseudo symplectic spaces this paper provides some new families of symmetric association schemes based on maximal totally isotropic subspaces in singular pseudo symplectic spaces all intersection numbers of these schemes are computed

linear stability of perturbed hamiltonian systems theory and a case example in this paper we present a general theory based on a lyapunov schmidt reduction for the linearized stability of a perturbed hamiltonian system with a number of symmetries the reduction leads to an eigenvalue problem in a small subspace of the original system whose eigenvalues and eigenvectors can be used to derive the ones of the perturbed original system the krein signature of the eigenvalues can also be obtained in this framework the method is applied to the case example of the coupled nonlinear schr dinger equations giving excellent agreement with the full numerical linear stability results

stability of basic steady states of networks in bounded domains in this article we study the problem of a network of curves in a planar domain with the normal velocity proportional to each curvature and fixed angle conditions at the points at which the curves intersect we introduce the evolution problem of networks identify two cases of basic steady states in bounded and smooth domains and study their stability in terms of the geometry of the boundary

on asymptotic stability of stationary solutions to nonlinear wave and klein gordon equations we consider nonlinear wave and klein gordon equations with general nonlinear terms localized in space conditions are found which provide asymptotic stability of stationary solutions in local energy norms these conditions are formulated in terms of spectral properties of the schrodinger operator corresponding to the linearized problem they are natural extensions to partial differential equations of the known lyapunov condition for the nonlinear wave equation in three dimensional space we find asymptotic expansions as t of the solutions which are close enough to a stationary asymptotically stable solution

generalized transition waves and their properties in this paper we generalize the usual notions of waves fronts and propagation speeds in a very general setting these new notions which cover all usual situations involve uniform limits with respect to the geodesic distance to a family of hypersurfaces that are parametrized by time we prove the existence of new such waves for some time dependent reaction diffusion equations as well as general intrinsic properties some monotonicity properties and some uniqueness results for almost planar fronts the classification results which are obtained under some appropriate assumptions show the robustness of our general definitions 2012 wiley periodicals inc

an instability mechanism for radially symmetric standing waves of a nonlinear schrodinger equation abstract a condition is proved for the spectrum of nonlinear schrodinger equations linearised at a standing wave to have a positive eigenvalue the standing waves considered are radially symmetric ones in higher space dimensions the instability result is applied to show that if there are multiple asymptotically positive nondegenerate waves with a fixed number of zeroes then there is an unstable one the techniques used are dynamical systems arguments and involve a shooting argument in the space of lagrangian planes

stable standing waves of nonlinear klein gordon equations in this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear klein gordon equations

suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs abstract as one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper we determine all the suborbits of a point stabilizer in the orthogonal group on the last subconstituent and calculate the length of each suborbit moreover we discuss the quasi strongly regular graphs and the association schemes based on the last subconstituent respectively

the equivalence of weak strong and complete convergence in l_1 for kernel density estimates theorem 1 let k be a nonnegative borel measurable function on rd with f k x dx 1 then the following conditions are equivalent i j 0 in probability as n oo some f ii jn o 0 in probability as n s oo all f iii jn s 0 almost surely as n oo all f iv jn 0 exponentially as n oc i e for all e 0 there exist r no 0 such that p jne no all f v lim0h 0 and limnnhd oo also v implies iv when k is merely absolutely integrable and f k x dx 1 0

a nonparametric approach to signal detection in impulsive interference impulsive interference poses a challenge to conventional detection techniques the spl alpha stable distribution while sometimes providing a good model for impulsive interference has proven to be no exception some of these difficulties have motivated the investigation and development of computationally tractable locally suboptimum correlation and rank correlation detectors for signals embedded in impulsive interference modeled as a symmetric spl alpha stable process the performance of some of these detectors is evaluated and compared with that of the locally optimum lo locally optimum rank lor matched filter and cauchy detectors simulation results show that a rank based detector is able to approach the performance of the computationally intensive lo and lor detectors across a range of values for for spl alpha

a variational approach to multiple layers of the bistable equation in long tubes multiple layer solutions of the balanced bistable equation in infinite tubes are constructed via a variational method i start with a characterization of palais smale sequences which easily gives some global minima in the desired function classes as single layers assuming these minima are isolated as critical points i paste them together to serve as an approximate multiple layer solution if there were no exact solutions near the approximate one the negative gradient flow of the energy functional would significantly lower the energy on the other hand if the minima are kept far from each other the energy of a function near the approximate solution is not much less than that of the approximate solution this contradiction proves the existence of a solution

a degenerate isoperimetric problem and traveling waves to a bistable hamiltonian system we analyze a nonstandard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points under certain assumptions on the conformal factor we establish the existence of curves of least length under a constraint associated with enclosed euclidean area as a motivation for and application of this isoperimetric problem we identify these isoperimetric curves appropriately parametrized as traveling wave solutions to a bistable hamiltonian system of pdes we also determine the existence of a maximal propagation speed for these traveling waves through an explicit upper bound depending on the conformal factor 2015 wiley periodicals inc

stability and folds it is known that when one branch of a simple fold in a bifurcation diagram represents linearly stable solutions the other branch represents unstable solutions the theory developed here can predict instability of some branches close to folds without knowledge of stability of the adjacent branch provided that the underlying problem has a variational structure first one particular bifurcation diagram is identified as playing a special role the relevant diagram being specified by the choice of functional plotted as ordinate the results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram in many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph the theory is particularly useful in applications where a solution branch has a succession of folds

on the dynamics of solitons in the nonlinear schrodinger equation we study the behavior of the soliton solutions of the equation i frac partial psi partial t frac 1 2m delta psi frac 1 2 w varepsilon prime psi v x psi where w varepsilon prime is a suitable nonlinear term which is singular for varepsilon 0 we use the strong nonlinearity to obtain results on existence shape stability and dynamics of the soliton the main result of this paper theorem 1 shows that for varepsilon rightarrow 0 the orbit of our soliton approaches the orbit of a classical particle in a potential v x

higher energy solutions in the theory of phase transitions a variational approach abstract we establish the existence of a higher energy solution to the vector ginzburg landau equation with a triple well potential on a bounded and smooth domain on the plane this solution is obtained by a linking argument in implementing this variational approach we make several considerations on the dynamics of the negative gradient flow in particular we use the conley index to contruct a suitable one dimensional invariant set this solution has morse index two in the nondegenerate case we discuss its structure in connection with the so called triple junction configurations

hamiltonian identities for elliptic partial differential equations abstract new identities for elliptic partial differential equations are obtained several applications are discussed in particular young s law for the contact angles in triple junction formation is proven rigorously structure of level curves of saddle solutions to allen cahn equation are also carefully analyzed

parameter estimation for middleton class a interference processes the problem of estimating the parameters of the middleton class a interference model is considered on the assumption of the availability of a set of independent samples from class a envelope distribution the asymptotic performances of several estimation procedures are explored from this analysis estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient whereas more efficient likelihood based estimators are seen to be computationally unwieldy however an estimator that initiates likelihood iteration with the method of moments estimates is seen to overcome these difficulties in its asymptotic performance unfortunately simulation of this third estimator for practical sample sizes reveals poor performance under these conditions to overcome this lack of small sample efficiency a similar estimator that initiates likelihood iteration with physically motivated but nonoptimal estimates is also proposed simulation of this latter estimator for practical sample sizes indicates that near optimal performance is attained by this technique

on the pdf of the sum of random vectors there are various cases in physics and engineering sciences especially communications where one requires the envelope probability density function pdf of the sum of several random sinusoidal signals according to the correspondence between a random sinusoidal signal and a random vector the sum of random vectors can be considered as an abstract mathematical model for the above sum now it is desired to obtain the pdf of the length of the resulting vector considering the common and reasonable assumption of uniform distributions for the angles of the vectors many researchers have obtained the pdf of the length of the resulting vector only for special cases however in this paper the pdf is obtained for the most general case in which the lengths of vectors are arbitrary dependent random variables this pdf is in the form of a definite integral which may be inappropriate for analytic manipulations and numerical computations so an appropriate infinite laguerre expansion is also derived finally the results are applied to solve a typical example in computing the scattering cross section of random scatterers

on the heteroclinic connection problem for multi well gradient systems abstract we revisit the existence problem of heteroclinic connections in r n associated with hamiltonian systems involving potentials w r n r having several global minima under very mild assumptions on w we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells where length is computed with respect to a degenerate metric having conformal factor w then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times it gives rise to a heteroclinic connection between the two wells this work improves upon the approach of 22 and represents a more geometric alternative to the approaches of e g 5 10 14 17 for finding such connections

relaxation of solitons in nonlinear schrodinger equations with potential abstract in this paper we study dynamics of solitons in the generalized nonlinear schrodinger equation nls with an external potential in all dimensions except for 2 for a certain class of nonlinearities such an equation has solutions which are periodic in time and exponentially decaying in space centered near different critical points of the potential we call those solutions which are centered near the minima of the potential and which minimize energy restricted to l 2 unit sphere trapped solitons or just solitons in this paper we prove under certain conditions on the potentials and initial conditions that trapped solitons are asymptotically stable moreover if an initial condition is close to a trapped soliton then the solution looks like a moving soliton relaxing to its equilibrium position the dynamical law of motion of the soliton i e effective equations of motion for the soliton s center and momentum is close to newton s equation but with a dissipative term due to radiation of the energy to infinity

on variational characterization of four end solutions of the allen cahn equation in the plane abstract in this paper a novel variational method is developed to construct four end solutions in r 2 for the allen cahn equation four end solutions have been constructed by del pino kowalczyk pacard and wei when the angle of the ends is close to 2 or 0 using the lyapunov schmid reduction method and later by kowalczyk liu and pacard using a continuation method for general 0 2 by a special mountain pass argument in a restricted space namely a set of monotone paths of monotone functions a family of solutions in bounded domain is constructed with very good control of their nodal sets which then leads to a four end solution after sending the domains to r 2 in this way not only a family of four end solutions is constructed for any angle 0 2 the morse index of such a four end solution is also shown to be one

local well posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude abstract we study the local well posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water we use an approach proposed by kato which is based on semigroup theory for quasi linear equations we also show that singularities for the model equation can occur only in the form of wave breaking in particular surging breakers

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

a multi phase mullins sekerka system matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem we propose a generalisation of the mullins sekerka problem to model phase separation in multi component systems the model includes equilibrium equations in bulk the gibbs thomson relation on the interfaces young s law at triple junctions together with a dynamic law of stefan type using formal asymptotic expansions we establish the relationship to a transition layer model known as the cahn hilliard system we introduce a notion of weak solutions for this sharp interface model based on integration by parts on manifolds together with measure theoretical tools through an implicit time discretisation we construct approximate solutions by stepwise minimisation under the assumption that there is no loss of area as the time step tends to zero we show the existence of a weak solution

bayes error estimation using parzen and k nn procedures the use of k nearest neighbor k nn and parzen density estimates to obtain estimates of the bayes error is investigated under limited design set conditions by drawing analogies between the k nn and parzen procedures new procedures are suggested and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k nn and parzen procedures we show that by varying the decision threshold many of the biases associated with the k nn or parzen density estimates may be compensated and successful error estimation may be performed in spite of these biases experimental results are given which demonstrate the effect of kernel size and shape parzen the size of k k nn and the number of samples in the design set

unstable ground state of nonlinear klein gordon equations on demontre l instabilite de l etat fondamental des equations de klein gordon non lineaires a n dimensions d espace n 3

orbital stability of double solitons for the benjamin ono equation in this paper we prove the orbital stability of double solitons for the benjamin ono equation in the case of the kdv equation this stability has been proved in 17 parts of the proof given there rely on the fact that the euler lagrange equations for the conserved quantities of the kdv equation are ordinary differential equations since this is not the case for the benjamin ono equation new methods are required our approach consists in using a new invariant for multi solitons and certain new identities motivated by the sylvester law of inertia

stability and instability of the kdv solitary wave under the kp i flow we consider the kp i and gkp i equations in mathbb r times mathbb r 2 pi mathbb z we prove that the kdv soliton with subcritical speed 0 c in the spirit of the work by duyckaerts and merle gafa 18 1787 1840 2009 we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity this last result also holds for the gkp i equation

efficient identification of non gaussian mixtures non gaussian mixtures are commonly used as parametric models for impulsive interference superimposed on a gaussian background in this study the problem of efficient batch and recursive estimation of the parameters of such mixtures via minimization of the kullback leibler distance is considered the maximum likelihood estimator mle provides the starting point for the development of these estimators first it is shown that the mle yields consistent estimates of the parameters despite the existence of multiple roots in the kullback leibler distance function since direct implementation of the mle is difficult an alternative estimator designed with the objective of maximizing the likelihood function is proposed a simulation study of the proposed estimator reveals that it performs very well in terms of attaining the cramer rao lower bound stochastic approximation is also considered in this study a complete data modification to the standard recursion is presented which greatly facilitates its implementation three initiating estimators are developed for these recursions an iterative likelihood based scheme a batch estimator that uses a histogram of the data and an iterative scheme that integrates the concept of complete data into the method of moments estimator upon initiating the modified stochastic approximation recursion with these estimators it is seen that excellent estimates of the parameters can be obtained

suborbits of a point stabilizer in the unitary group on the last subconstituent of hermitean dual polar graphs let be a dual polar graph in a unitary space it is well known that a point stabilizer in the unitary group is transitive on the last subconstituent of in this paper we determine all the suborbits of this action calculate its rank and the length of each suborbit note that the induced subgraph on is quasi strongly regular as an application of our results all its parameters are computed

asymptotically robust detection and estimation for very heavy tailed noise the asymptotically robust detection of signals and the analogous problem of estimation of location are considered for noise distributions with heavier than exponential tails the solution to both problems is identical and is obtained when using efficacy or asymptotic variance as the performance measure the density of the noise is assumed to belong to a e contamination class where the contaminant is either 1 from the class of unimodal densities 2 from the class of densities limited in support to an interval about the mode of the nominal density or 3 a mixture of a member of 1 with a member of 2 the robust detector or estimator is similar to a censored version of the nonlinearity used for maximum likelihood estimation or locally optimal detection in the presence of noise with the nominal distribution

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

heteroclinic connections for multiple well potentials the anisotropic case we investigate the existence of solutions to systems of n differential equations representing connections between minima of potentials with several equal depths in r using variational techniques and in particular a method introduced in af we first prove such existence for n 2 and two minima dealing next with symmetric potentials corresponding to free bulk energies in crystals we establish existence for n 2 in various cases of more than two minima finally we obtain a sufficient condition establishing existence of connections to not necessarily symmetric potentials for arbitrary n and three minima

adaptive nonparametric locally optimum bayes detection in additive non gaussian noise a nonparametric generalization of the locally optimum bayes lob parametric theory of signal detection in additive non gaussian noise with independent sampling is presented from a locally asymptotically normal lan expansion of the log likelihood ratio the nonparametric detector structure in both coherent and incoherent modes is determined moreover its statistics under both hypotheses are obtained the nonparametric lan log likelihood ratio is then reduced to a least informative i e having minimum variance under the null hypothesis h sub 0 local parametric submodel which is referred to as adaptive in the adaptive submodel certain nonlinearities are replaced by their efficient estimates this is accomplished such that no information is lost when the noise first order density is no longer parametrically defined adaptive nonparametric lob detectors are thus shown to be asymptotically optimum ao canonical in signal waveform distribution free in noise statistics and identical in form in the symmetric cases to their parametric counterparts a numerical example is provided when the underlying density is middleton s see ibid vol 45 p 1129 49 may 1999 class a noise which demonstrates that even with a relatively small sample size o 10 sup 2 adaptive lob nonparametric detectors perform nearly as well as the classical lob detectors

nonparametric density estimation for classes of positive random variables a kernel based density estimator for positive random variables is proposed and analyzed in particular a nonparametric estimator is developed which takes advantage of the fact that positive random variables can be represented as the norms of random vectors by appropriately choosing the dimension of the assumed vector space the estimator can be structured to exploit a priori knowledge about the density to be estimated the asymptotic properties e g pointwise and l sub 1 consistency of this density estimator are investigated and found to be similar to the desirable features of the standard kernel estimator an upper bound on the expected value of the l sub 1 error is also derived which provides insight into the behavior of the estimator upon using this upper bound the optimal form for the estimator i e the kernel function the smoothing factor etc is selected via a minimax strategy in addition this upper bound is used to compare the asymptotic performance of the proposed estimator to that of the standard kernel estimator and to boundary corrected kernel estimators numerical examples illustrate that the proposed scheme outperforms the standard and boundary corrected estimators for a variety of density types

performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha stable process impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration an empirical justification for this procedure is that it generally causes the signal to noise ratio to increase recently very accurate models of impulsive noise were presented based on the theory of symmetric spl alpha stable probability density functions we examine the performance of optimum receivers designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric spl alpha stable process and compare it against the performance of several suboptimum receivers as a measure of receiver performance we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive monte carlo simulation

a note on the l_1 consistency of variable kernel estimates 1 introduction most consistent nonparametric density estimates have a built in smoothing parameter numerous schemes have been proposed see e g references found in rudemo 1982 or devroye and penrod 1984 for selecting the smoothing parameter as a function of the data only a process called automatization and for introducing locally adaptable smoothing parameters in this note we give conditions which insure that estimators of the form

on the asymptotic stability of solitary waves in the discrete schrodinger equation coupled to a nonlinear oscillator abstract the long time asymptotics is analyzed for finite energy solutions of the 1d discrete schrodinger equation coupled to a nonlinear oscillator the coupled system is invariant with respect to the phase rotation group u 1 for initial states close to a solitary wave the solution converges to a sum of another solitary wave and a dispersive wave which is a solution to the free schrodinger equation the proofs use the strategy of buslaev perelman v s buslaev g s perelman on the stability of solitary waves for nonlinear schrodinger equations amer math soc trans 2 164 1995 75 98 the linearization of the dynamics on the solitary manifold the symplectic orthogonal projection method of majorants etc

subconstituents of dual polar graph in finite classical space iii abstract let f q be the finite field with q elements denote by the dual polar graph of 2 dimensional orthogonal space over f q where 0 1 or 2 for any vertex p of all subconstituents i p 1 i of are studied and it is proved that i p is isomorphic to i q i where i is a subgraph of the graph of i i matrices over f q moreover some properties of the graph i are also studied in particular it is shown that i is edge regular furthermore both 2 1 and 3 1 are distance regular with intersection arrays q 2 1 q 2 q 1 1 q q 2 1 and q 3 1 q 3 q q 3 q 2 1 1 q q 2 1 respectively

multiphase solutions to the vector allen cahn equation crystalline and other complex symmetric structures we present a systematic study of entire symmetric solutions u mathbb r n rightarrow mathbb r m of the vector allen cahn equation delta u w u u 0 quad text for all quad x in mathbb r n where w mathbb r m rightarrow mathbb r is smooth symmetric nonnegative with a finite number of zeros and where w u partial w partial u 1 dots partial w partial u m top we introduce a general notion of equivariance with respect to a homomorphism f g rightarrow gamma g gamma reflection groups and prove two abstract results concerning the cases of g finite and g discrete for the existence of equivariant solutions our approach is variational and based on a mapping property of the parabolic vector allen cahn equation and on a pointwise estimate for vector minimizers

an adaptive spatial diversity receiver for non gaussian interference and noise standard linear diversity combining techniques are not effective in combating fading in the presence of non gaussian noise an adaptive spatial diversity receiver is developed for wireless communication channels with slow flat fading and additive non gaussian noise the noise is modeled as a mixture of gaussian distributions and the expectation maximization em algorithm is used to derive estimates for the model parameters the transmitted signals are detected using a likelihood ratio test based on the parameter estimates the new adaptive receiver converges rapidly its bit error rate performance is very close to optimum when relatively short training sequences are used and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution simulation results are included that illustrate various aspects of the adaptive receiver performance

entire solutions to equivariant elliptic systems with variational structure we consider the system u wu u 0 where u mathbb r n to mathbb r n for a class of potentials w mathbb r n to mathbb r that possess several global minima and are invariant under a general finite reflection group g we establish existence of nontrivial g equivariant entire solutions connecting the global minima of w along certain directions at infinity

on anisotropic order parameter models for multi phase system and their sharp interface limits abstract for a general class of diffuse anisotropic multi phase order parameter or phase field models we use formally matched asymptotic expansions to determine the asymptotic limit when a small parameter related to the thickness of the interface tends to zero in the case of anisotropic allen cahn systems we obtain in the limit that the interface moves by anisotropic mean curvature flow at triple junctions a force balance holds which in the anisotropic case includes shear forces herring torque terms acting normal to the interface we further identify the singular limit of anisotropic cahn hilliard systems

lyapunov stability of ground states of nonlinear dispersive evolution equations on presente une nouvelle demonstration de la stabilite orbitale des solitons d etat fondamental de l equation de schrodinger non lineaire pour une grande classe de non linearites on demontre la stabilite de l onde solitaire pour l equation de korteweg de vries generalisee

one dimensional phase transition problem modeling striped spin orbit coupled bose einstein condensates abstract we study the behavior of a modica mortola phase transition type problem with a non homogeneous neumann boundary condition according to the parameters of the problem this leads to the existence of either one component occupying most of the domain with an outer boundary layer containing the other component or to many interfaces on a periodic pattern this is related to the striped behavior of a two component bose einstein condensate with spin orbit coupling in one dimension we prove that minimizers of the full gross pitaevskii energy in 1d behave in the thomas fermi limit of strong intra component interaction like those of the simplified modica mortola problem we have studied in the first part

a note on robust hypothesis testing we introduce a simple new hypothesis testing procedure which based on an independent sample drawn from a certain density detects which of k nominal densities is the true density closest to under the total variation l sub 1 distance we obtain a density free uniform exponential bound for the probability of false detection

a generalization of the formulas for intersection numbers of dual polar association schemes and their applications dual polar association schemes form an important family of association schemes whose intersection numbers were computed in wan et al studies in finite geometry and the construction of incomplete block designs science press beijing 1966 in chinese in this paper we generalize the formulas for the intersection numbers and introduce their applications to pooling designs cartesian authentication codes and vertex transitive graphs

sharp threshold of global existence and instability of standing wave for a davey stewartson system this paper concerns the sharp threshold of blowup and global existence of the solution as well as the strong instability of standing wave phi t x e i omega t u x for the system i phi t delta phi a phi p 1 phi b e 1 phi 2 phi 0 quad t geq 0 quad x in bf r n quad quad quad rm ds where a 0 b 0 1 0 by combining the former results

on arbitrarily slow rates of global convergence in density estimation let a density f on rd be estimated by fn x x1 xn where x rd fn is a borel measurable function of its arguments and x1 xn are independent random vectors with common density f let p 1 be a constant one of the main results of this note is that for every sequence fn and for every positive number sequence an satisfying lim an 0 there exists an f such that e left smallint f n left x right f left x right p dx right a n infinitely often

on the solitary wave dynamics under slowly varying medium for nonlinear schrodinger equations we consider the problem of a solitary wave propagation in a slowly varying medium for a variable coefficients nonlinear schrodinger equation we prove global existence and uniqueness of solitary wave solutions for a large class of slowly varying media moreover we describe for all time the behavior of these solutions which include refracted and reflected solitary waves depending on the initial energy

phase transition in a rabi coupled two component bose einstein condensate abstract this paper deals with the study of the phase transition of the wave functions of a segregated two component bose einstein condensate under rabi coupling this yields a system of two coupled ode s where the rabi coupling is linear in the other wave function and acts against segregation we prove estimates on the asymptotic behaviour of the wave functions as the strength of the interaction gets strong or weak we also derive limiting problems in both cases

linearized instability for nonlinear schrodinger and klein gordon equations in this paper i am introducing a new technique for proving instability of bound states for hamiltonian systems there are already two disparate types of instability results in the literature the approach developed by strauss shatah 20 gave an instability criterion coming from the variational structure of the problem on the other hand jones approach 11 produced a complementary criterion related to the difference between the number of negative eigenvalues of two selfadjoint operators using quite different techniques it turns out that with the methods developed in this paper these two criteria can be derived within a single framework that also leads to a generalization of the previous results finally in order to demonstrate how this method works i apply the instability criterion in some specific examples