adaptive minimum bit error rate equalization for binary signaling we consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol interference channel with gaussian noise and a memoryless decision device if the number of equalizer coefficients is sufficient the popular minimum mean squared error mmse linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit error rate ber however when the number of equalizer coefficients is insufficient to approximate the channel inverse the minimum ber equalizer can outperform the mmse equalizer by as much as 16 db in certain cases we propose a simple stochastic adaptive algorithm for realizing the minimum ber equalizer compared to the least mean square algorithm the proposed algorithm can provide a substantial reduction in ber with no increase in complexity

adaptive minimum symbol error rate equalization for quadrature amplitude modulation we propose the adaptive minimum symbol error rate algorithm which is a low complexity technique for adapting the coefficients of a linear equalizer in systems using pulse amplitude or quadrature amplitude modulation the proposed algorithm very nearly minimizes error probability in white gaussian noise and can significantly outperform the minimum mean squared error equalizer by as much as 16 db when the number of equalizer coefficients is small relative to the severity of the intersymbol interference

classical solutions for a generalized euler equation in two dimensions abstract it is well known that the euler equations in two spatial dimensions have global classical solutions we provide a new proof which is analytic rather than geometric it is set in an abstract framework that applies to the so called lake and the great lake equations describing weakly non hydrostatic effects of bottom topography on the motion of shallow water the key ingredient is a new lpestimate on the nonlinear term the estimate is used to develop a global hmtheory for bounded domains in r 2which is similar in spirit to a 1975 paper by r temam it also provides explicit bounds on the hmnorm which grow like exp exp t

design of group sequential clinical trials with multiple endpoints abstract group sequential testing for randomized clinical trials designed with multiple endpoints is considered previously computed tables for single endpoints are still useful with a change in interpretation of certain parameters the advantage in setting sample size based on multiple endpoints is that the sample size required when a trial is designed using more than one endpoint is smaller than the sample size based on any single endpoint if the two calculations are undertaken using matching significance levels and powers an example is provided and possible extensions of the work are discussed

adaptive minimum ber linear multiuser detection for ds cdma signals in multipath channels the problem of constructing adaptive minimum bit error rate mber linear multiuser detectors is considered for direct sequence code division multiple access ds cdma signals transmitted through multipath channels based on the approach of kernel density estimation for approximating the bit error rate ber from training data a least mean squares lms style stochastic gradient adaptive algorithm is developed for training linear multiuser detectors computer simulation is used to study the convergence speed and steady state ber misadjustment of this adaptive mber linear multiuser detector and the results show that it outperforms an existing lms style adaptive mber algorithm presented by yeh et al see proc globecom sydney australia p 3590 95 1998

on the solutions of the 3d steady and unsteady primitive equations of the ocean abstract in this article the existence and uniqueness of the solution for the 3d steady viscous primitive equations pes for brevity of the ocean under the uniqueness condition are analyzed also the h 2 regularity results of the solution for the 3d steady viscous pes of the ocean under the stability condition is provided finally the convergence of the solution for the 3d unsteady viscous pes of the ocean to the solution for the 3d steady viscous pes of the ocean when t towards to infinity under the uniqueness condition is studied

inertial manifolds for nonlinear evolutionary equations abstract in this paper we introduce the concept of an inertial manifold for nonlinear evolutionary equations in particular for ordinary and partial differential equations these manifolds which are finite dimensional invariant lipschitz manifolds seem to be an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations the inertial manifolds contain the global attractor they attract exponentially all solutions and they are stable with respect to perturbations furthermore in the infinite dimensional case they allow for the reduction of the dynamics to a finite dimensional ordinary differential equation

global well posedness of the 3d primitive equations with partial vertical turbulence mixing heat diffusion the three dimensional incompressible viscous boussinesq equations under the assumption of hydrostatic balance govern the large scale dynamics of atmospheric and oceanic motion and are commonly called the primitive equations to overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection or density stratification equation in this paper we prove the global regularity of strong solutions to this model in a three dimensional infinite horizontal channel subject to periodic boundary conditions in the horizontal directions and with no penetration and stress free boundary conditions on the solid top and bottom boundaries specifically we show that short time strong solutions to the above problem exist globally in time and that they depend continuously on the initial data

constrained minimum ber multiuser detection a new linear multiuser detector that directly minimizes the bit error rate ber subject to a set of reasonable constraints is proposed it is shown that the constrained ber cost function has a unique global minimum this allows us to develop an efficient newton barrier method for finding the coefficients of the proposed detector using information about timing amplitudes channels and the signature signals of all users although the new detector cannot be shown to be optimal among linear multiuser detectors without the constraints imposed extensive simulations demonstrate that it achieves the lowest ber furthermore in some cases the ber of the proposed detector can be significantly lower than that of the decorrelating and mmse detectors

global strong solutions of navier stokes equations with interface boundary in three dimensional thin domains abstract in this article we study the spectrum of the stokes operator in a 3d two layer domain with interface obtain the asymptotic estimates on the spectrum of the stokes operator as thickness e goes to zero based on the spectral decomposition of the stokes operator a new average like operator is introduced and applied to the study of navier stokes equation in the two layer thin domains under interface boundary condition we prove the global existence of strong solutions to the 3d navier stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small this article is a continuation of our study on the stokes operator under navier friction boundary condition due to the viscosity distinction between the two layers the stokes operator displays radically different spectral structure from that under navier friction boundary condition then causes great difficulty to the analysis

existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics in this paper we consider the initial boundary value problem for the primitive equations of moist atmospheric dynamics that are used to describe the turbulent behavior of long term weather prediction and climate changes by the faedo galerkin method we obtain the existence of global weak solutions to the problem in a large scale atmosphere by studying the long time behavior of solutions we obtain trajectory and global attractors for the primitive equations of moist atmosphere

global well posedness of strong solutions to the 3d primitive equations with horizontal eddy diffusivity in this paper we consider the initial boundary value problem of the 3d primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation global well posedness of strong solutions are established with h2 initial data 2014 elsevier inc all rights reserved

on the long time stability of a temporal discretization scheme for the three dimensional viscous primitive equations in this article a semi discretized euler scheme to solve the three dimensional viscous primitive equations is studied based on suitable assumptions on the initial data and forcing terms the long time stability of the proposed scheme is proven by showing that the h 1 norm in space variables of the solutions is bounded at each time step when the time step satisfies certain smallness condition

large deviation principles for 3d stochastic primitive equations abstract in this paper we establish the freidlin wentzell s large deviations for 3d stochastic primitive equations with small noise perturbation the weak convergence approach plays an important role

the existence of a pullback attractor for the three dimensional non autonomous planetary geostrophic viscous equations of large scale ocean circulation abstract in this paper we prove the existence of a pullback attractor in h 2 for the process u t t associated with the three dimensional non autonomous planetary geostrophic viscous equations of large scale ocean circulation by asymptotic a priori estimates

optimal control of the primitive equations of the ocean with state constraints abstract we investigate in this article pontryagin s maximum principle for a class of control problems associated with the primitive equations pes of the ocean these optimal problems involve a state constraint similar to that considered in wang 2002 7 for the three dimensional navier stokes ns equations the main difference between this work and wang 2002 7 is that the nonlinearity in the pes is stronger than in the three dimensional ns systems

the exponential behavior of a stochastic globally modified cahn hilliard navier stokes model with multiplicative noise abstract in this article we study the stability of weak solutions to a stochastic version of a globally modified coupled cahn hilliard navier stokes model with multiplicative noise the model consists of the globally modified navier stokes equations for the velocity coupled with an cahn hilliard model for the order phase parameter we prove that under some conditions on the forcing terms the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions we also prove a result related to the stabilization of these equations

a non autonomous two phase flow model with oscillating external force and its global attractor abstract in this article we consider a non autonomous diffuse interface model for an isothermal incompressible two phase flow in a two dimensional bounded domain assuming that the external force is singularly oscillating and depends on a small parameter we prove the existence of the uniform global attractor a furthermore using the method similar to that of chepyzhov and vishik 2007 22 in the case of the two dimensional navier stokes systems we study the convergence of a as goes to zero let us mention that the nonlinearity involved in the model considered in this article is slightly stronger than the one in the two dimensional navier stokes system studied in chepyzhov and vishik 2007 22

asymptotic analysis of the navier stokes equations abstract new bounds are established on the number of modes which determine the solutions of the navier stokes equations in two dimensions the best bound available at present is nearly proportional to the generalized grashof number defined in the paper and less than logarithmically dependent on the spatial structure or the shape of the force driving the flow to the extent than for the case of 2 dimensional rayleigh benard convection the generalized grashof number may be identified with the usual grashof number the resulting bound on the number of modes is found to differ only slightly from a bound obtained earlier on heuristic grounds

stochastic unbiased minimum mean error rate algorithm for decision feedback equalizers capitalizing on a well known minimum mean square error mmse property for decision feedback equalization dfe along with the use of stochastic gradient approach we formulate an adaptive minimum error rate mer algorithm for dfe over m ary pam channels to be named as stochastic unbiased minimum mean error rate summer comparisons are made between our algorithm and existing mer algorithms in the literature also by invoking the central limit theorem we present an analytical proof that an unbiased mmse equalizer will approach an mer equalizer when the equalizer length approaches infinity thereby we obtain a lower bound expression for mer

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

on adaptive minimum probability of error linear filter receivers for ds cdma channels receiver architectures in the form of a linear filter front end followed by a hard limiting decision maker are considered for ds cdma communication systems based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front end in the minimum ber sense the recursive form is decision driven and distribution free for additive white gaussian noise awgn channels theoretical analysis of the ber surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two user case to the extent that the output of a linear ds cdma filter can be approximated by a gaussian random variable a minimum mean square error optimized linear filter approximates the minimum ber solution numerical and simulation results indicate that for realistic awgn ds cdma systems with reasonably low signature cross correlations the linear minimum ber filter and the mmse filter exhibit approximately the same performance the linear minimum ber receiver is superior however when either the signature cross correlation is high or the background noise is non gaussian

first order decoupled finite element method of the three dimensional primitive equations of the ocean this paper is concerned with a first order fully discrete decoupled method for solving the three dimensional 3d primitive equations of the ocean with the dirichlet boundary conditions on the side where a decoupled semi implicit scheme is used for the time discretization and the p 1 p 1 p 1 p 1 p 1 finite element for velocity pressure and density is used for the spatial discretization of these equations the h 1 l 2 h 1 optimal error estimates for the numerical solution u h n p h n theta h n and the l 2 optimal error estimate for u n h theta h n are established under the restriction of 0 h le beta 1 and 0 tau le beta 2 for some positive constants beta 1 and beta 2 moreover numerical investigations are provided to show that the first order decoupled method is of almost unconditional convergence with accuracy mathcal o h tau in the h 1 norm and mathcal o h 2 tau in the l 2 norm for solving the 3d primitive equations of the ocean numerical results are gi

global well posedness and finite dimensional global attractor for a 3 d planetary geostrophic viscous model in this paper we consider a three dimensional planetary geostrophic viscous model of the gyre scale mid latitude ocean we show the global existence and uniqueness of the weak and strong solutions to this model moreover we establish the existence of a nite dimensional global attractor to this dissipative evolution system c 2003 wiley periodicals inc

global well posedness for the lake equations abstract we prove global well posedness for the lake equations these equations arise to leading order in a low aspect ratio low froude number i e low wave speed and very small wave amplitude expansion of the three dimensional incompressible euler equations in a basin with a free upper surface and a spatially varying bottom topography well posedness means that there exists a solution that it is unique and that it depends continuously on the data i e the initial condition and the bottom topography our approach follows the works of yudovitch and bardos in constructing the solutions as the inviscid limit of solutions to a system with artificial viscosity which is the analog of the navier stokes with respect to the euler equations one of the main assumptions in the present work is a nondegenerate bottom topography

first order decoupled method of the primitive equations of the ocean i time discretization abstract in this article we study the time discretization of the first order decoupled semi implicit scheme of the 3d primitive equations of the ocean in the case of the non slip and non heat flux boundary conditions on the side the almost unconditional stability of the scheme and the optimal error estimates of the time discrete velocity pressure and density are provided

a second order decoupled implicit explicit method of the 3d primitive equations of ocean ii finite element spatial discretization summary a fully discrete second order decoupled implicit explicit method is proposed for solving 3d primitive equations of ocean in the case of dirichlet boundary conditions on the side where a second order decoupled implicit explicit scheme is used for time discretization and a finite element method based on the p1 p1 p1 p1 p1 elements for velocity pressure and density is used for spatial discretization of these primitive equations optimal h1 l2 h1 error estimates for numerical solution uhn phn hn and an optimal l2 error estimate for uhn hn are established under the convergence condition of 0 h 1 0 2 and 3h for some positive constants 1 2 and 3 furthermore numerical computations show that the h1 l2 h1 convergence rate for numerical solution uhn phn hn is of o h 2 and an l2 convergence rate for uhn hn is o h2 2 with the assumed convergence condition where h is a mesh size and is a time step size more practical calculations are performed as a further validation of the numerical method copyright 2016 john wiley sons ltd

a fourth order numerical method for the planetary geostrophic equations with inviscid geostrophic balance the planetary geostrophic equations with inviscid balance equation are reformulated in an alternate form and a fourth order finite difference numerical method of solution is proposed and analyzed in this article in the reformulation there is only one prognostic equation for the temperature field and the velocity field is statically determined by the planetary geostrophic balance combined with the incompressibility condition the key observation is that all the velocity profiles can be explicitly determined by the temperature gradient by utilizing the special form of the coriolis parameter this brings convenience and efficiency in the numerical study in the fourth order scheme the temperature is dynamically updated at the regular numerical grid by long stencil approximation along with a one sided extrapolation near the boundary the velocity variables are recovered by special solvers on the 3 d staggered grid furthermore it is shown that the numerical velocity field is divergence free at the discrete level in a suitable sense fourth order convergence is proven under mild regularity requirements

minimum bayes risk adaptive linear equalizers this paper introduces bayes risk expected loss as a criterion for linear equalization since the probability of error is equal to the bayes risk br for a particular binary loss function this work is a natural generalization of previous works on minimum probability of error pe equalizers adaptive equalization algorithms are developed that minimize the br like the minimum pe equalizers the br algorithms have low computational complexity which is comparable to that of the lms algorithm the advantage of the br criterion is that the loss function can be specified in a manner that accelerates adaptive equalizer convergence relative to the minimum pe adaptive algorithm as illustrated in simulation examples besides introducing a new criterion this paper provides another independent contribution to the field of pe minimizing equalization while most prior works focus on m ary qam type modulations with rectangular decision regions this paper uses upper bounds on the probabilities of certain events to yield tractable mathematics that apply to two dimensional constellations with arbitrarily shaped decision regions the resulting adaptive algorithm use the full information available in the phase of the error signal whereas previous algorithms use a quantized version of this error phase

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

global well posedness of the three dimensional viscous primitive equations of large scale ocean and atmosphere dynamics in this paper we prove the global existence and uniqueness regularity of strong solutions to the three dimensional viscous primitive equations which model large scale ocean and atmosphere dynamics 1 introduction large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the navier stokes equations with rotation coupled to thermodynamics and salinity diffusion transport equations which account for the buoyancy forces and stratification effects under the boussinesq approximation moreover and due to the shallowness of the oceans and the atmosphere i e the depth of the fluid layer is very small in comparison to the radius of the earth the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one which in turn leads to modeling the vertical motion by the hydrostatic balance as a result

adaptive minimum symbol error rate decision feedback equalization for multilevel pulse amplitude modulation the design of decision feedback equalizers dfes is typically based on the minimum mean square error mmse principle as this leads to effective adaptive implementation in the form of the least mean square algorithm it is well known however that in certain situations the mmse solution can be distinctly inferior to the optimal minimum symbol error rate mser solution we consider the mser design for multilevel pulse amplitude modulation block data adaptive implementation of the theoretical mser dfe solution is developed based on the parzen window estimate of a probability density function furthermore a sample by sample adaptive mser algorithm called the least symbol error rate lser is derived for adaptive equalization applications the proposed lser algorithm has a complexity that increases linearly with the equalizer length computer simulation is employed to evaluate the proposed alternative mser design for equalization application with multilevel signaling schemes

pullback attractors for a non autonomous homogeneous two phase flow model abstract this article studies the pullback asymptotic behavior of solutions for a non autonomous homogeneous two phase flow model in a two dimensional domain we prove the existence of pullback attractors a v in v the velocity has the h 1 regularity and a y in y the velocity has the l 2 regularity then we verify the regularity of the pullback attractors by proving that a v a y which implies the pullback asymptotic smoothing effect of the model in the sense that the solutions eventually become more regular than the initial data the method used in this article is similar to the one used in zhao and zhou 2007 42 in the case of the non autonomous incompressible non newtonian fluid in a two dimensional domain let us mention that the nonlinearity involved in the model considered in this article is stronger than the one in the two dimensional non newtonian flow studied in zhao and zhou 2007 42

estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems we show that the long time behavior of the projection of the exact solutions to the navier stokes equations and other dissipative evolution equations on the finite dimensional space of interpolant polynomials determines the long time behavior of the solution itself provided that the spatial mesh is fine enough we also provide an explicit estimate on the size of the mesh moreover we show that if the evolution equation has an inertial manifold then the dynamics of the evolution equation is equivalent to the dynamics of the projection of the solutions on the finite dimensional space spanned by the approximating polynomials our results suggest that certain numerical schemes may capture the essential dynamics of the underlying evolution equation