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

asymptotic properties of the algebraic constant modulus algorithm the algebraic constant modulus algorithm acma is a noniterative blind source separation algorithm it computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem we analyze its asymptotic properties and show that unlike cma it converges to the wiener beamformer when the number of samples or the signal to noise ratio snr goes to infinity we also sketch its connection to the related jade algorithm and derive a version of acma that converges to a zero forcing beamformer this gives improved performance in applications that use the estimated mixing matrix such as in direction finding

an existence result for homoclinic solutions to a nonlinear second order ode through differential inequalities abstract in this paper an existence result of homoclinic solutions to a nonlinear second order ode is presented to this end a method based on differential inequalities is used

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

mean field equation of liouville type with singular data topological degree we consider the following mean field equation gv h ev mh ev 1 4 j 1n j qj 1 on m where m is a compact riemann surface with volume 1 h is a positive c1 function on m and and j are constants satisfying j 1 in this paper we derive the topological degree counting formula for noncritical values of we also give several applications of this formula including existence of the curvature 1 metric with conic singularities doubly periodic solutions of electroweak theory and a special case of self gravitating strings 2015 wiley periodicals inc

profile of blow up solutions to the exponential neumann boundary value problem abstract arising in problems of prescribed gaussian and geodesic curvatures we consider a blow up sequence of solutions to the following exponential neumann boundary value problem u n v n x x 2 n e 2 u n in b r u n h n x x n e u n on b r r 2 where denotes the outer unit normal vector to b r r 2 and n 1 we establish a uniform estimate for this blow up sequence of solutions near an isolated singular blow up point we treat two cases n and n separately and obtain two different uniform pointwise estimates

existence and multiplicity result for the singular toda system abstract we consider the toda system on a compact surface g u 1 2 1 h 1 e u 1 h 1 e u 1 d v g 1 2 h 2 e u 2 h 2 e u 2 d v g 1 4 j 1 j 1 j p j 1 u 2 2 2 h 2 e u 2 h 2 e u 2 d v g 1 1 h 1 e u 1 h 1 e u 1 d v g 1 4 j 1 j 2 j p j 1 where h i are smooth positive functions i are positive real parameters p j are given points on and i j are numbers greater than 1 we give existence and multiplicity results using variational and morse theoretical methods it is the first existence result when some of the i j s are allowed to be negative

sufficient conditions for the stability of a class of second order systems this paper provides sufficient conditions to assess the stability and input to state stability of a class of second order systems by only looking at the structure of the dynamic equations these results are proven by using the variable gradient method to build suitable lyapunov functions the paper includes a number of relevant examples that highlight the value of the contribution

constant q curvature metrics in arbitrary dimension working in a given conformal class we prove existence of constant q curvature metrics on compact manifolds of arbitrary dimension under generic assumptions the problem is equivalent to solving a nth order non linear elliptic differential or integral equation with variational structure where n is the dimension of the manifold since the corresponding euler functional is in general unbounded from above and below we use critical point theory jointly with a compactness result for the above equation

asymptotic stability for anisotropic kirchhoff systems we study the question of asymptotic stability as time tends to infinity of solutions of dissipative anisotropic kirchhoff systems involving the p x laplacian operator governed by time dependent nonlinear damping forces and strongly nonlinear power like variable potential energies this problem had been considered earlier for potential energies which arise from restoring forces whereas here we allow also the effect of amplifying forces global asymptotic stability can then no longer be expected and should be replaced by local stability the results are further extended to the more delicate problem involving higher order damping terms

perturbations of the half linear euler weber type differential equation abstract we investigate oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 viewed as a perturbation of another half linear differential equation of the same form r t x c t x 0 the obtained oscillation and nonoscillation criteria are formulated in terms of the integral c t c t h p t d t where h is a function which is close to the principal solution of in a certain sense a typical model of in applications is the half linear euler weber differential equation with the critical coefficients x p t p p t p log 2 t x 0 p p 1 p p p 1 2 p 1 p p 1 we establish oscillation and nonoscillation criteria for perturbations of this equation some open problems and perspectives of the further research along this line are also formulated

scalar curvatures on sn soit m n g une variete de riemann compacte de dimension n 3 et r x une fonction lisse sur m n on etudie si r x peut etre la courbure scalaire d une metrique g qui est conforme point par point a la metrique originale g

growth conditions for uniform asymptotic stability of damped oscillators abstract the present paper is devoted to an investigation on the uniform asymptotic stability for the linear differential equation with a damping term x h t x 2 x 0 and its generalization p x h t p x p p x 0 where 0 and p z z p 2 z with p 1 sufficient conditions are obtained for the equilibrium x x 0 0 to be uniformly asymptotically stable under the assumption that the damping coefficient h t is integrally positive the obtained condition for the damped linear differential equation is given by the form of a certain uniform growth condition on h t another representation which is equivalent to this uniform growth condition is also given our results assert that the equilibrium can be uniformly asymptotically stable even if h t is unbounded an example is attached to show this fact in addition easy to use conditions are given to guarantee that the uniform growth condition is satisfied moreover a sufficient condition expressed by an infinite series is presented the relation between the representation of an infinite series and the uniform growth condition is also clarified finally our results are extended to be able to apply to the above mentioned nonlinear differential equation

existence and non existence results for the su 3 singular toda system on compact surfaces we consider the su 3 singular toda system on a compact surface g u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 4 m 1m 1m pm 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 4 m 1m 2m pm 1 where hi are smooth positive functions on i r pm and im 1 we give both existence and non existence results under some conditions on the parameters i and im existence results are obtained using variational methods which involve a geometric inequality of new type non existence results are obtained using blow up analysis and localized poho aev type identities

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

stability properties of solutions of linear second order differential equations with random coefficients abstract the equation x a 2 t x 0 a t a k 0 if t k 1 t t k k n is considered where a k k 1 is given and t k k 1 is a random sequence sufficient conditions are proved which guarantee either stability or instability for the zero solution stability means that all solutions almost surely tend to zero as t by instability we mean that the sequence of the expected values of the amplitudes of every solution tends to infinity as k it turns out that a k k implies stability for all absolutely continuous distributions and for the overwhelming majority of the singular distributions the instability theorem is applied to the problem of random swinging when a k k 1 is periodic with two different terms meissner s equation and t k t k 1 k 1 are independent identically distributed random variables the application gives conditions for stochastic parametric resonance

length and cost dependent local minima of unconstrained blind channel equalizers baud rate linear blind equalizers may converge to undesirable stable equilibria due to different mechanisms one such mechanism is the use of linear fir filters as equalizers it is shown that this type of local minima exist for all unconstrained blind equalizers whose cost functions satisfy two general conditions the local minima generated by this mechanism are thus called length dependent local minima another mechanism is generated by the cost function adopted by the blind algorithm itself this type of local minima are called cost dependent local minima it is shown that several well designed algorithms do not have cost dependent local minimum whereas other algorithms such as the decision directed equalizer and the stop and go algorithm sga do unlike many existing convergence analysis the convergence of the godard 1980 algorithms gas and standard cumulant algorithms scas under gaussian noise is also presented computer simulations are used to verify the analytical results

global asymptotic stability for damped half linear oscillators abstract a necessary and sufficient condition is established for the equilibrium of the oscillator of half linear type with a damping term p x h t p x p x 0 to be globally asymptotically stable the obtained criterion is given by the form of a certain growth condition of the damping coefficient h t and it can be applied to not only the cases of large damping and small damping but also the case of fluctuating damping the presented result is new even in the linear cases p 2 it is also discussed whether a solution of the half linear differential equation r t p x c t p x 0 that converges to a non zero value exists or not some suitable examples are included to illustrate the results in the present paper

the liouville equation with singular data a concentration compactness principle via a local representation formula abstract for a bounded domain r 2 we establish a concentration compactness result for the following class of singular liouville equations u e u 4 j 1 m j p j in where pj j 0 and pj denotes the dirac measure with pole at point pj j 1 m our result extends brezis merle s theorem comm partial differential equations16 1991 1223 1253 concerning solution sequences for the regular liouville equation where the dirac measures are replaced by lp data p 1 in some particular case we also derive a mass quantization principle in the same spirit of li shafrir indiana univ math j 43 1994 1255 1270 our analysis was motivated by the study of the bogomol nyi equations arising in several self dual gauge field theories of interest in theoretical physics such as the chern simons theory self dual chern simons theories lecture notes in physics vol 36 springer verlag berlin 1995 and the electroweak theory selected papers on gauge theory of weak and electromagnetic interactions world scientific singapore

relationships between the constant modulus and wiener receivers the godard 1980 or the constant modulus algorithm cma is an effective technique for blind receiver design in communications however due to the complexity of the constant modulus cm cost function the performance of the cm receivers has primarily been evaluated using simulations theoretical analysis is typically based on either the noiseless case or approximations of the cost function the following question while resolvable numerically for a specific example remains unanswered in a generic manner in the presence of channel noise where are the cm local minima and what are their mean squared errors mse in this paper a geometrical approach is presented that relates the cm to wiener or minimum mse receivers given the mse and the intersymbol user interference of a wiener receiver a sufficient condition is given for the existence of a cm local minimum in the neighborhood of the wiener receiver the mse bounds on cm receiver performance are derived and shown to be tight in simulations the analysis shows that while in some cases the cm receiver performs almost as well as the nonblind wiener receiver it is also possible that due to its blind nature the cm receiver may perform considerably worse than a nonblind wiener receiver

energy quantization for a singular super liouville boundary value problem in this paper we develop the blow up analysis and establish the energy quantization for solutions to super liouville type equations on riemann surfaces with conical singularities at the boundary in other problems in geometric analysis the blow up analysis usually strongly utilizes conformal invariance which yields a noether current from which strong estimates can be derived here however the conical singularities destroy conformal invariance therefore we develop another more general method that uses the vanishing of the pohozaev constant for such solutions to deduce the removability of boundary singularities

sufficient conditions for the local convergence of constant modulus algorithms the constant modulus cm criterion has become popular in the design of blind linear estimators of sub gaussian i i d processes transmitted through unknown linear channels in the presence of unknown additive interference the existence of multiple cm minima however makes it difficult for cm minimizing schemes to generate estimates of the desired source as opposed to an interferer in multiuser environments in this paper we present three separate sufficient conditions under which gradient descent gd minimization of cm cost will locally converge to an estimator of the desired source at a particular delay the sufficient conditions are expressed in terms of statistical properties of the initial estimates specifically cm cost kurtosis and signal to interference plus noise ratio sinr implications on cm gd initialization methods are also discussed

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

bubbling solutions for the liouville equation with a singular source non simple blow up abstract we are concerned with the existence of blowing up solutions to the following boundary value problem u e u 4 n 0 in u 0 on where is a smooth and bounded domain in r 2 such that 0 n is a positive number close to an integer n n 1 from the right side 0 defines the dirac measure with pole at 0 and 0 is a small parameter we assume that is n 1 symmetric and the regular part of the green s function satisfies a nondegeneracy condition both assumptions are verified if is the unit ball and we find a solution which exhibits a non simple blow up profile as 0

blowing up solutions to an anisotropic emden fowler equation with a singular source we consider the following anisotropic emden fowler equation with a singular source div a x v e2a x ev 4 a p pin v 0on where p r2 constant 0 n a x is a positive smooth function and p denotes the dirac measure with pole at point p if p is a local maximum point of a x we construct a family of solutions ve with arbitrary m bubbles concentrating at p and the quantity e2 a x eve 8 m 1 a p

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

stability of solutions for some classes of nonlinear damped wave equations we consider two classes of semilinear wave equations with nonnegative damping which may be of type on off or integrally positive in both cases we give a sufficient condition for the asymptotic stability of the solutions in the case of integrally positive damping we show that such a condition is also necessary

convex cost functions in blind equalization existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient isi when an fir equalizer is used the authors impose convexity on the cost function and anchoring of the equalizer away from the all zero setup they establish that there exists a globally convergent blind equalization strategy for 1d pulse amplitude modulation pam systems with bounded input data discrete or continuous even when the equalizer is truncated the resulting cost function is a constrained l sub 1 norm of the joint impulse response of the channel and the equalizer the results apply to arbitrary linear channels provided there are no unit circle zeros and apply regardless of the initial isi that is whether the eye is initially open or closed they also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l sub 1 cost function

on a class of elliptic problems in r symmetry and uniqueness results in the plane r 2 we classify all solutions for an elliptic problem of liouville type involving a radial weight function as a consequence we clarify the origin of the non radially symmetric solutions for the given problem as established by chanillo and kiessling for a more general class of liouville type problems we show that rather than radial symmetry the solutions always inherit the invariance of the problem under inversion with respect to suitable circles this symmetry result is derived with the help of a shrinking sphere method

low complexity variable forgetting factor mechanism for blind adaptive constrained constant modulus algorithms in this paper we propose a novel low complexity variable forgetting factor vff mechanism for blind adaptive constrained constant modulus ccm recursive least squares rls algorithms applied to linear interference suppression in direct sequence code division multiple access ds cdma systems the proposed variable forgetting factor mechanism employs an updated component related to the time average of the constant modulus cm cost function to automatically adjust the forgetting factor in order to ensure good tracking of the interference and the channel convergence and tracking analyses are carried out analytical expressions for predicting the mean squared error of the proposed adaptation technique are obtained simulation results are presented for nonstationary environments and show that the proposed variable forgetting factor mechanism achieves superior performance to previously reported methods at a reduced complexity

classification of radial solutions for semilinear elliptic systems with nonlinear gradient terms abstract we are concerned with the classification of positive radial solutions for the system u v p v f u where p 0 and f c 1 0 is a nondecreasing function such that f t 0 for all t 0 we show that in the case where the system is posed in the whole space r n such solutions exist if and only if 1 0 s f t d t p 2 p 1 d s this is the counterpart of the keller osserman condition for the case of single semilinear equation similar optimal conditions are derived in case where the system is posed in a ball of r n if f t t q q 1 using dynamical system techniques we are able to describe the behaviour of solutions at infinity in case where the system is posed in the whole r n or around the boundary in case of a ball

a sup inf type inequality for conformal metrics on riemann surfaces with conical singularities abstract a sup inf type inequality is proved for the regular part of conformal factors for riemannian metrics on surfaces with conical singularities of positive order 0 the proof is based on the explicit representation formula for solutions of the singular liouville equation and generalizes to the singular case an argument by i shafrir

on multivortices in the electroweak theory ii existence of bogomol nyi solutions in ℝ2 in this paper we study the bogomol nyi equations of the electroweak theory in the full plane we will show that for any distribution of the vortices there exists a two parameter family of gauge distinct solutions moreover we also establish some sharp decay rate estimates for these solutions

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

weighted barycentric sets and singular liouville equations on compact surfaces given a closed surface we prove a general existence result for some elliptic pde with exponential nonlinearities and negative dirac deltas extending a theory recently obtained for the regular case this is done by global methods since the associated euler functional might be unbounded from below we define a new model space generalizing the so called space of formal barycenters and characterizing up to homotopy equivalence its low sublevels as a result the analytic problem is reduced to a topological one concerning the contractibility of this model space to this aim we prove a new functional inequality in the spirit of chen and li 1991 11 and then employ a min max scheme based on conical construction jointly with the blow up analysis in bartolucci and montefusco 2007 4 after bartolucci and tarantello 2002 brezis and merle 1991 and this study is motivated by abelian chern simons theory in self dual regime or from the problem of prescribing the gaussian curvature with conical singularities generalizing a problem raised in kazdan and warner 1974 24

convergence of solutions of nonlinear systems with integrable forcing term and its applications to a biological model a non autonomous nonlinear system with a time variational forcing term is considered for such a system the global attraction of the origin is discussed whose result is suggestive to an ecological problem as well because the system is reduced to a lotka volterra predator prey model with prey receiving an environmental time variation by an appropriate transformation a numerical simulation is also shown to suggest a new mathematical insight beyond our intuition

half linear oscillation criteria perturbation in term involving derivative abstract we consider the nonoscillatory half linear differential equation r t x c t x 0 x x p 2 x p 1 and we study oscillatory properties of its perturbation r t r t x c t c t x 0 we use the riccati technique and relationship between and a certain associated linear equation the results are applied to the perturbed euler type equation

global attractivity for half linear differential systems with periodic coefficients abstract the system to be considered in this paper is x y a t x y b t p x p y here a t is a 2 2 diagonal matrix and b t is a 2 2 anti diagonal matrix and q z z q 2 z with q 1 the coefficients of b t are assumed to be periodic but the coefficients of a t are not necessarily periodic the system is of half linear type sufficient conditions are given for the zero solution of the half linear system to be globally asymptotically stable the zero solution of the system x y b t p x p y is stable but is not attractive our concern is to clarify a positive effect of the diagonal part a t x y on the global asymptotic stability for the half linear system some simple examples are included to illustrate the main result

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

geometrical characterizations of constant modulus receivers convergence properties of the constant modulus cm and the shalvi weinstein sw algorithms in the presence of noise remain largely unknown a new geometrical approach to the analysis of constant modulus and shalvi weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel receiver response this approach provides a unified framework within which various blind and nonblind wiener receivers can all be analyzed by circumscribing an ellipsoid by norm balls of different types a necessary and sufficient condition for the equivalence among constant modulus shalvi weinstein zero forcing and wiener receivers are obtained answers to open questions with regard to cm and sw receivers including their locations and their relationship with wiener receivers are provided for the special orthogonal channel and the general two dimensional 2 d channel receiver impulse response it is also shown that in two dimensions each cm or sw receiver is associated with one and only one wiener receiver

a necessary and sufficient condition for global asymptotic stability of time varying lotka volterra predator prey systems abstract the purpose of this paper is to present a necessary and sufficient condition which guarantees that an interior equilibrium of a certain predator prey system is globally asymptotically stable this ecological system is a model of lotka volterra type whose prey population receives time variation of the environment we assume that the time varying coefficient is weakly integrally positive and has a weaker property than uniformly continuous our necessary and sufficient condition is expressed by an improper double integral on the time varying coefficient our work is inspired by the study of the stability theory for damped linear oscillators

asymptotic stability and asymptotic solutions of second order differential equations abstract we improve simplify and extend on quasi linear case some results on asymptotical stability of ordinary second order differential equations with complex valued coefficients obtained in our previous paper g r hovhannisyan asymptotic stability for second order differential equations with complex coefficients electron j differential equations 2004 85 2004 1 20 to prove asymptotic stability of second order differential equations we establish stability estimates using integral representations of solutions via asymptotic solutions and error estimates several examples are discussed

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

entire radial solutions of elliptic systems and inequalities of the mean curvature type abstract in this paper we study first nonexistence of radial entire solutions of elliptic systems of the mean curvature type with a singular or degenerate diffusion depending on the solution u in particular we extend a previous result given in r filippucci nonexistence of radial entire solutions of elliptic systems j differential equations 188 2003 353 389 moreover in the scalar case we obtain nonexistence of all entire solutions radial or not of differential inequalities involving again operators of the mean curvature type and a diffusion term we prove that in the scalar case nonexistence of entire solutions is due to the explosion of the derivative of every nonglobal radial solution in the right extremum of the maximal interval of existence while in that point the solution is bounded this behavior is qualitatively different with respect to what happens for the m laplacian operator studied in r filippucci nonexistence of radial entire solutions of elliptic systems j differential equations 188 2003 353 389 where nonexistence of entire solutions is due even in the vectorial case to the explosion in norm of the solution at a finite point our nonexistence theorems for inequalities extend previous results given by naito and usami in y naito h usami entire solutions of the inequality div a d u d u f u math z 225 1997 167 175 and ghergu and radulescu in m ghergu v radulescu existence and nonexistence of entire solutions to the logistic differential equation abstr appl anal 17 2003 995 1003

uniform asymptotic stability for damped linear oscillators with variable parameters abstract in this paper sufficient conditions for uniform asymptotic stability of the damped linear oscillators with variable coefficients are presented the result of the present study can be applied to even the case of negative damping the conditions presented herein are shown to be essential for uniform asymptotic stability

domains of attraction of shalvi weinstein receivers domains of attraction doa of shalvi weinstein 1990 receivers are analyzed it is shown that there is a one to one correspondence between doa in the receiver parameter space and those in the global or combined channel receiver parameter space for general noiseless channels doa of sw receivers in the global response space are the minimum distance decision regions on a unit sphere in the presence of noise and for the class of orthogonal channels doa of sw receivers for independent and identically distributed i i d input signals are the minimum distance decision regions on an ellipsoid determined by the channel coefficients and the noise variance the doa in the receiver parameter space are also characterized for the general nonuniformly distributed sources the size of the doa is shown to be affected by the signal power the signal constellation the noise level and the channel condition it is also demonstrated that although the optima of the shalvi weinstein algorithm and those of the constant modulus algorithm are one to one correspondent their doa are different in general

uniform global asymptotic stability for oscillators with superlinear damping abstract the present paper deals with the damped superlinear oscillator x h t q x 2 x 0 where 0 and q z z q 2 z with q 2 the origin x x 0 0 is the only equilibrium of this oscillator we herein establish a sufficient condition for the equilibrium to be uniformly globally asymptotically stable we conclude that under the assumption that the damping coefficient h t is integrally positive if the integral from to t of a particular solution of the first order nonlinear differential equation u h t q u 1 0 diverges to negative infinity uniformly with respect to then the equilibrium is uniformly globally asymptotically stable the above mentioned result is expressed by an implicit condition we examine when the implicit condition is satisfied and when it is not satisfied we also give explicit sufficient conditions which assure that the equilibrium is uniformly globally asymptotically stable using the obtained result we present an example of which the equilibrium is uniformly globally asymptotically stable even if h t is unbounded

stability for a damped nonlinear oscillator abstract the stability of the null solution of eq 1 1 below is discussed under some unusual assumptions we obtain new stability results for this classical oscillator equation our approach allows extensions to both the vector case and the case of the whole real line

fractionally spaced equalization using cma robustness to channel noise and lack of disparity in the noise free case the fractionally spaced equalization using constant modulus fse cm criterion has been studied previously its minima were shown to achieve perfect equalization when zero forcing zf conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity however to our best knowledge the effect of additive channel noise on the fse cm cost function minima has not been studied in this paper we show that the noisy fse cm cost function is subject to a smoothing effect with respect to the noise free cost function the result of which is a tradeoff between achieving zero forcing and noise enhancement furthermore we give an analytical closed form expression for the loss of performance due to the noise in terms of input output mean square error mse under the zf conditions the fse cm mse is shown to be mostly due to output noise enhancement and not to residual intersymbol interference isi when there is lack of disparity an irreducible amount of isi appears independently of the algorithm it is the lower equalizability bound for given channel conditions and equalizer length the so called minimum mse mmse the mmse lower bound is the sum of the mmse and of additional mse mostly due to noise enhancement finally we compare the fse cm mse to this lower bound

vanishing pohozaev constant and removability of singularities conformal invariance of two dimensional variational problems is a condition known to enable a blow up analysis of solutions and to deduce the removability of singularities in this paper we identify another condition that is not only sufficient but also necessary for such a removability of singularities this is the validity of the pohozaev identity in situations where such an identity fails to hold we introduce a new quantity called the pohozaev constant which on one hand measures the extent to which the pohozaev identity fails and on the other hand provides a characterization of the singular behavior of a solution at an isolated singularity we apply this to the blow up analysis for super liouville type equations on riemann surfaces with conical singularities because in the presence of such singularities conformal invariance no longer holds and a local singularity is in general non removable unless the pohozaev constant is vanishing