a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

global regularity for a class of 2d generalized tropical climate models abstract this paper establishes the global existence and regularity of solutions to a two dimensional 2d tropical climate model tcm with fractional dissipation the inviscid counterpart of this model was derived by frierson majda and pauluis 8 as a model for tropical geophysical flows this model reflects the interaction and coupling among the barotropic mode u the first baroclinic mode v of the velocity and the temperature the systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization the aim here is the global regularity with the least dissipation we prove two main results first the global regularity of the system with v and for 1 and 3 2 and second the global regularity of the system with v for 3 2 the proofs of these results are not trivial and the requirements on the fractional indices appear to be optimal the key tools employed here include the maximal regularity for general fractional heat operators the littlewood paley decomposition and besov space techniques lower bounds involving fractional laplacian and simultaneous estimates of several coupled quantities

an extension of the beale kato majda criterion for the euler equations the beale kato majda criterion asserts that smooth solutions to the euler equations remain bounded past t as long as is finite ohgr being the vorticity we show how to replace this by a weaker statement on where j is a frequency localization around

on the well posedness of the euler equations in the triebel lizorkin spaces we prove local in time unique existence and a blowup criterion for solutions in the triebel lizorkin space for the euler equations of inviscid incompressible fluid flows in n n 2 as a corollary we obtain global persistence of the initial regularity characterized by the triebel lizorkin spaces for the solutions of two dimensional euler equations to prove the results we establish the logarithmic inequality of the beale kato majda type the moser type of inequality as well as the commutator estimate in the triebel lizorkin spaces the key methods of proof used are the littlewood paley decomposition and the paradifferential calculus by j m bony 2002 john wiley sons inc

a note on well posedness for camassa holm equation in this note we investigate the problem of well posedness for a shallow water equation with data having critical regularity our results are based on the use of besov spaces b2 rs which generalize the sobolev spaces hs with critical index s 3 2

a fractionally spaced blind equalizer based on linear programming we formulate the blind fractionally spaced equalization fse problem as one that minimizes a piecewise linear convex function subject to some linear constraints on the equalizer parameters we show that this formulation achieves both the interference removal and the carrier phase recovery when the input signal possesses a certain quadrature amplitude modulation qam type symmetry a fast linear programming implementation is presented to solve the convex minimization problem computer simulation results indicate the new linear programming based fse is able to accurately equalize channels that are known to be not equalizable by t spaced or baud rate blind equalizers and yields superior performance to other blind fse methods

global behavior of positive solutions of nonlinear three point boundary value problems we investigate the structure of the positive solution set for nonlinear three point boundary value problems of the form u h t f u 0 u 0 0 u 1 lambdau eta where eta epsilon 0 1 is given lambda epsilon 0 1 n is a parameter f epsilon c 0 infinity 0 infinity satisfies f s 0 for s 0 and h epsilon c 0 1 0 infinity is not identically zero on any subinterval of 0 1 our main results demonstrate the existence of continua of positive solutions of the above problem c 2004 elsevier ltd all rights reserved

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii fixed point theorem the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions is studied the results are a generalization and continuation of the recent results on this issue an example is provided to illustrate the theory

global well posedness issues for the inviscid boussinesq system with yudovich s type data the present paper is dedicated to the study of the global existence for the inviscid two dimensional boussinesq system we focus on finite energy data with bounded vorticity and we find out that under quite a natural additional assumption on the initial temperature there exists a global unique solution no smallness conditions are imposed on the data the global existence issues for infinite energy initial velocity and for the benard system are also discussed

precise regularity results for the euler equations abstract it has already been proved under various assumptions that no singularity can appear in an initially regular perfect fluid flow if the l norm of the velocity s curl does not blow up here that result is proved for flows in smooth bounded domains of r d d 2 when the regularity is expressed in terms of besov or triebel lizorkin spaces

the existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 α 2 this paper is mainly concerned with the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1 a 2 the results are obtained by the fixed point theorem combined with solutions operator theorems

global well posedness for the 2d inviscid benard system with fractional diffusivity and yudovichʼs type data abstract in this paper we consider the cauchy problem of the two dimensional inviscid benard system with fractional diffusivity we show that there is a global unique solution to this system with yudovich s type data

hardy spaces and the two dimensional euler equations with nonnegative vorticity we prove that certain quadratic expressions involving the gradient of a weakly superharmonic function in r belong to a local hardy space as an application we provide a new proof of j m delort s convergence theorem for solutions of the two dimensional euler equations with vorticities of one sign department of mathematics university of california berkeley california 94720 sfb 256 institut fur angewandte mathematik beringstrasse 4 d5300 bonn 1 ger many this content downloaded from 207 46 13 101 on sat 08 oct 2016 05 44 35 utc all use subject to http about jstor org terms

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

on the deformations of the incompressible euler equations we consider systems of deformed system of equations which are obtained by some transformations from the system of incompressible euler equations these have similar properties to the original euler equations including the scaling invariance for one form of deformed system we prove that finite time blow up actually occurs for generic initial data while for the other form of the deformed system we prove the global in time regularity for smooth initial data moreover using the explicit functional relations between the solutions of those deformed systems and that of the original euler system we derive the condition of finite time blow up of the euler system in terms of solutions of one of its deformed systems as another application of those relations we deduce a lower estimate of the possible blow up time of the 3d euler equations

on well posedness of two component camassa holm system in the critical besov space abstract in this paper we study the cauchy problem for a two component camassa holm system in the critical besov space b 2 1 1 2 we obtain the solution local existence and prove the solution mapping is holder continuous with respect to the initial value

existence of vortex sheets with reflection symmetry in two space dimensions the main purpose of this work is to establish the existence of a weak solution to the incompressible 2d euler equations with initial vorticity consisting of a radon measure with distinguished sign in h 1 compactly supported in the closed right half plane superimposed on its odd reflection in the left half plane we make use of a new a priori estimate to control the interaction between positive and negative vorticity at the symmetry axis we prove that a weak limit of a sequence of approximations obtained by either regularizing the initial data or by using the vanishing viscosity method is a weak solution of the incompressible 2d euler equations we also establish the equivalence at the level of weak solutions between mirror symmetric flows in the full plane and flows in the half plane finally we extend our existence result to odd l 1 perturbations without distinguished sign of our original initial vorticity

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

on the global well posedness for the axisymmetric euler equations this paper deals with the global well posedness of the 3d axisymmetric euler equations for initial data lying in critical besov spaces b p 1 1 3 p in this case the bkm criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity

reduced hausdorff dimension and concentration cancellation for two dimensional incompressible flow where v t v1 v2 is the fluid velocity p is the scalar pressure dv dt av at v v v and vo is an initial incompressible velocity field i e div vo 0 in this paper we study the detailed limiting behavior of approximate solution sequences for 2 d euler with vortex sheet initial data a sequence of smooth velocity fields v8 x t is an approximate solution sequence for 2 d euler provided that v is incompressible i e div v 0 and satisfies the following properties 1 the velocity fields v6 have uniformly bounded local kinetic energy i e

controllability of semilinear boundary problems with nonlocal initial conditions the main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions we show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary the included application to a size structured population equation provides a motivation for abstract results

the vanishing viscosity limit in the presence of a porous medium we consider the flow of a viscous incompressible newtonian fluid in a perforated domain in the plane the domain is the exterior of a regular lattice of rigid particles we study the simultaneous limit of vanishing particle size and distance and of vanishing viscosity under suitable conditions on the particle size particle distance and viscosity we prove that solutions of the navier stokes system in the perforated domain converges to solutions of the euler system modeling inviscid incompressible flow in the full plane that is the flow is not disturbed by the porous medium and becomes inviscid in the limit convergence is obtained in the energy norm with explicit rates of convergence

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

on the spectral dynamics of the deformation tensor and new a priori estimates for the 3d euler equations in this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3d incompressible euler equations using the evolution equation of the l2 norm of spectra we deduce new a priori estimates of the l2 norm of vorticity as an immediate corollary of the estimate we obtain a new sufficient condition of l2 norm control of vorticity we also obtain decay in time estimates of the ratios of the eigenvalues in the remarks we discuss what these estimates suggest in the study of searching initial data leading to possible finite time singularities we find that the dynamical behaviors of l2 norm of vorticity are controlled completely by the second largest eigenvalue of the deformation tensor

uniformly local l p estimate for 2 d vorticity equation and its application to euler equations with initial vorticity in bmo we shall prove the global existence theorem for the 2 dimensional euler equations in open image in new window with the initial vorticity in bmo containing functions which do not decay at infinity and have logarithmic singularities

a gradient search interpretation of the super exponential algorithm this article reviews the super exponential algorithm proposed by shalvi and weinstein 1993 for blind channel equalization the principle of this algorithm hadamard exponentiation projection over the set of attainable combined channel equalizer impulse responses followed by a normalization is shown to coincide with a gradient search of an extremum of a cost function the cost function belongs to the family of functions given as the ratio of the standard l sub 2p and l sub 2 sequence norms where p 1 this family is very relevant in blind channel equalization tracing back to donoho s 1981 work on minimum entropy deconvolution and also underlying the godard 1980 or constant modulus and the earlier shalvi weinstein algorithms using this gradient search interpretation which is more tractable for analytical study we give a simple proof of convergence for the super exponential algorithm finally we show that the gradient step size choice giving rise to the super exponential algorithm is optimal

weak solutions of 2 d euler equations with initial vorticity in l log l abstract in this note we prove global in time existence of weak solutions of 2 0 euler equations for incompressible fluid flows in the whole plane of r 2 when the initial vorticity is in the zygmund class l log l the solution is constructed by a vanishing viscosity limit of the sequence of solutions to the navier stokes equations with the same initial data this is a limiting case of the corresponding results of diperna and majda in which global existence of weak solutions was obtained for initial vorticity in l 1 l p 1 p

undermodeled equalization a characterization of stationary points for a family of blind criteria we attack specific problems related to equalizer performance in undermodeled cases in which assumptions of perfect equalizability are dismissed in favor of a more realistic situation in which no equalizer setting may achieve perfect channel equalization we derive a characterization of candidate convergent points for a family of blind criteria which appeal tacitly or wittingly to maximizing the ratio of different sequence norms of the combined channel equalizer impulse response this may be accomplished in a practical implementation by using equalizer output cumulants of different orders the popular godard and shalvi weinstein schemes are accommodated at one extreme of the family of criteria we also show that each maximum at the other extreme of the family involving progressively higher order output cumulants yields precisely a wiener response this suggests that blind algorithms using progressively higher order statistics may converge more closely to a wiener response than those using more modest order statistics we show moreover that the superexponential family of algorithms is also included and establish a convergence proof for undermodeled cases that appeals to no approximation finally some apparently novel bounds on attainable open eye measures in undermodeled cases are also derived

existence and regularity of solutions to nonlocal retarded differential equations in this paper the existence and uniqueness of different types of solutions to a class of semilinear retarded differential equations with nonlocal history conditions are obtained by a fixed point argument also finite dimensional approximation of these solutions in a hilbert space is established

lagrangian solutions to the 2d euler system with l1 vorticity and infinite energy we consider solutions to the two dimensional incompressible euler system with only integrable vorticity thus with possibly locally infinite energy with such regularity we use the recently developed theory of lagrangian flows associated to vector fields with gradient given by a singular integral in order to define lagrangian solutions for which the vorticity is transported by the flow we prove strong stability of these solutions via strong convergence of the flow under the only assumption of l1 weak convergence of the initial vorticity the existence of lagrangian solutions to the euler system follows for arbitrary l1 vorticity relations with previously known notions of solutions are established

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

a remark on vorticity maximal function in this note the following inequality is proved for any nonnegative measure h 1 r2 x r2 and 0 r 1 there holds 1 b x r c ln1r 12 h 1 where c is a positive constant using 1 an estimate for the vorticity maximal function similar to the estimate in majda a majda remarks on weak solutions for vortex sheets with a distinguished sign indiana univ math j 42 1993 921 939 is established without assuming the initial vorticity having compact support from this a more simple proof of the delort s celebrated theorem j m delort existence de mappes de fourbillon en dimension deux j amer math soc 4 1991 553 586 is presented

existence of solutions for neutral functional differential evolution equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii s fixed point theorem we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions the results we obtained are a generalization and continuation of the recent results on this issue in the end an example is given to show the application of our results

global regularity for some oldroyd b type models we investigate some critical models for visco elastic flows of oldroyd b type in dimension 2 we use a transformation that exploits the oldroyd b structure to prove an l bound on the vorticity which allows us to prove global regularity for our systems 2014 wiley periodicals inc

detection and parameter estimation of multiple nongaussian sources via higher order statistics simultaneous detection of signal arriving at a sensor array and estimation of their parameters is carried out using higher than second order statistics information theoretic criteria which are at least theoretically insensitive to additive gaussian noise are developed to estimate consistently the parameters as well as the number of non gaussian but unknown sources the novel cumulant based algorithms can estimate parameters of more sources with fewer sensors simulations confirm superior resolution capability of the proposed methods for both narrow band and wideband sources in the presence of low snr additive correlated gaussian noise

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

incompressible flows of an ideal fluid with unbounded vorticity in this paper we study solutions to the euler equations of an ideal incompressible fluid in rn singular at the origin with a finite symmetry group for an admissible class of finite groups we prove a local existence and uniqueness theorem in even dimensions this theorem covers some symmetric flows with essentially unbounded vorticity in arbitrary dimension including n 3 we construct local in time solutions with vorticity that behaves e g like a function of homogeneous degree zero near the origin the symmetry condition provides necessary additional cancellations and is preserved by the evolution due to uniqueness

existence uniqueness and regularity of solutions to semilinear nonlocal functional differential problems abstract in this paper we consider a semilinear nonlocal functional differential problem in a banach space we first establish the existence uniqueness and continuation of a mild solution we then prove some regularity results for this mild solution under different conditions finally we consider some applications of the abstract results

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

local ill posedness of the incompressible euler equations in c 1 and b 1_ infty 1 we show that the 2d euler equations are not locally well posed in the sense of hadamard in the c 1 space and in the besov space b 1 infty 1 our approach relies on the technique of lagrangian deformations of bourgain and li strong ill posedness of the incompressible euler equations in borderline sobolev spaces arxiv 1307 7090 we show that the assumption that the data to solution map is continuous in either c 1 or b 1 infty 1 leads to a contradiction with a result in w 1 p of kato and ponce rev mat iberoam 2 73 88 1986