analytic approximation onc0 the banach spacec0is shown to possess the analytic approximation property more precisely given any uniformly continuous function on an open setg c0 an analytic map is constructed which uniformly approximates the given function

keeping track of limit cycles this article uses analytic geometry methods to bound the number of limit cycles of bounded period for a planar polynomial vector fields it introduces the notion of limit periodic sets and shows that the hilbert s 16th problem can be reduced to the existence of a uniform bound on its cyclicity it also shows the existence of a universal bound on the number of limit cycles in the perturbation of a linear focus as a consequence of the noetherian property of the bautin ideal

oscillation results for a second order damped differential equation with nonmonotonous nonlinearity abstract we present new oscillation criteria for a nonlinear second order differential equation with a damping term an essential feature of our results is that we do not require the nonlinearity to be nondecreasing furthermore as opposed to the recent results by s r grace 1989 math nachr 141 117 127 1992 j math anal appl 171 220 241 and s r grace and b s lalli 1990 j math anal appl 149 277 311 we do not impose any additional condition on the damping term p t consequently our theorems apply to new classes of equations which are not covered by the known criteria the relevance of the results obtained is illustrated with a number of carefully selected examples

twisted orlicz algebras and complete isomorphism to operator algebras abstract let g be a locally compact group let g g c be a 2 cocycle and let denote the twisted convolution associated to given a complementary pair of young functions we prove that if is continuous and strictly increasing l g l 2 g and 0 1 s t u s v t s t g for some u v s g then l g with the maximal operator space structure is completely isomorphic to an operator algebra we also present various classes of 2 cocycles for which one could obtain such algebras generalizing in part the results of 15 we apply our methods to compactly generated groups of polynomial growth and demonstrate that our results could be applied to variety of cases

oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities abstract we present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities p t x q t x i 1 n q i t x i sgn x e t where p t q t q i t e t c 0 p t is positive and differentiable 1 m 1 m 1 n no restriction is imposed on the forcing term e t to be the second derivative of an oscillatory function when n 1 our results reduce to those of el sayed m a el sayed an oscillation criterion for a forced second order linear differential equation proc amer math soc 118 1993 813 817 wong j s w wong oscillation criteria for a forced second linear differential equations j math anal appl 231 1999 235 240 sun ou and wong y g sun c h ou j s w wong interval oscillation theorems for a linear second order differential equation comput math appl 48 2004 1693 1699 for the linear equation nazr a h nazr sufficient conditions for the oscillation of forced super linear second order differential equations with oscillatory potential proc amer math soc 126 1998 123 125 for the superlinear equation and sun and wong y g sun j s w wong note on forced oscillation of nth order sublinear differential equations j math anal appl 298 2004 114 119 for the sublinear equation

existence of limit cycles and homoclinic bifurcation in a plant herbivore model with toxin determined functional response abstract in this paper we study a two dimensional toxin determined functional response model tdfrm the toxin determined functional response explicitly takes into consideration the reduction in the consumption of plants by herbivore due to chemical defense which generates more complex dynamics of the plant herbivore interactions the purpose of the present paper is to analyze the existence of limit cycles and bifurcations of the model by applying the theories of rotated vector fields and the extended planar termination principle we establish the conditions for the existence of limit cycles and homoclinic loop it is shown that a limit cycle is generated in a supercritical hopf bifurcation and terminated in a homoclinic bifurcation as the parameters vary analytic proofs are provided for all results which generalize the results presented in 11

some theorems on the existence uniqueness and nonexistence of limit cycles for quadratic systems abstract given a quadratic system qs with a focus or a center at the origin we write it in the form y p 2 x y x dy q 2 x y where p 2 and q 2 are homogeneous polynomials of degree 2 if we define f x y x dy p 2 x y yq 2 x y and g x y xq 2 x y yp 2 x y we give results of existence nonexistence and uniqueness of limit cycles if f x y g x y does not change of sign then by using these results plus the properties on the evolution of the limit cycles of the semicomplete families of rotated vector fields we can study some particular families of qs i e the qs with a unique finite singularity and the bounded qs with either one or two finite singularities

inconsistent signal feasibility problems least squares solutions in a product space presents parallel projection methods to find least squares solutions to inconsistent convex set theoretic signal synthesis problems the problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the cartesian product of the original sets a solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space the convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated

oscillation criteria for second order nonlinear differential equations involving general means consider the second order nonlinear differential equation e y a t f y 0 where a t c 0 f y c1 f y 0 and yf y 0 for y 0 furthermore f y also satisfies either a superlinear or a sublinear condition which covers the nonlinear function f y y y 1 with 1 and 0 1 respectively commonly known as the emden fowler case here the coefficient function a t is allowed to be negative for arbitrarily large values of t kamenev type oscillation criteria involving integral averages for the linear equations l y a t y 0 are extended to the nonlinear equation e by using more general means the results extend similar results on general means by philos for the linear equation l and also results based upon kamenev s integral averaging method concerning the nonlinear equation e

an oscillation criterion for second order sublinear differential equations abstract an oscillation criterion is given for the second order sublinear differential equation y a t f y 0 where a t is not assumed to be non negative and f y is non decreasing in y and yf y 0 for y 0 f y also satisfies a sublinear condition which includes the special case f y y y sgn y 0 this result extends earlier oscillation theorems of philos and the first author

global families of limit cycles of planar analytic systems the global behavior of any one parameter family of limit cycles of a planar analytic system x f x a depending on a parameter a e r is determined it is shown that any one parameter family of limit cycles belongs to a maximal one parameter family which is either open or cyclic if the family is open then it terminates as the parameter or the orbits become unbounded or it terminates at a critical point or on a compound separatrix cycle of the system this implies that the periods in a one parameter family of limit cycles can become unbounded only if the orbits become unbounded or if they approach a degenerate critical point or compound separatrix cycle of the system this is a more specific result for planar analytic systems than wintner s principle of natural termination for n dimensional systems where the periods can become unbounded in strange ways this work generalizes duff s results for one parameter families of limit cycles generated by a one parameter family of rotated vector fields in particular it is shown that the behavior at a nonsingular multiple limit cycle of any one parameter family of limit cycles is exactly the same as the behavior at a multiple limit cycle of a one parameter family of liniit cycles generated by a one parameter family of rotated vector fields

example of a weighted algebra lpw g on an uncountable discrete group abstract we construct examples of weighted algebras l p w g with 1 p 2 on uncountable free groups for p 2 no weighted algebras exist on these groups on the other hand we prove that for any amenable locally compact group g if l p w g is an algebra for some weight w and p 1 then g is compact

a norm convergence result on random products of relaxed projections in hilbert space suppose x is a hilbert space and c 1 ldots c n are closed convex intersecting subsets with projections p 1 ldots p n suppose further r is a mapping from bbb n onto 1 ldots n that assumes every value infinitely often we prove a more general version of the following result begin quote if the n tuple c 1 ldots c n is innately boundedly regular then the sequence x n defined by x 0 in x mbox arbitrary x n 1 p r n x n mbox for all n geq 0 converges in norm to some point in bigcap i 1 n c i end quote examples without the usual assumptions on compactness are given methods of this type have been used in areas like computerized tomography and signal processing

bifurcation analysis of a plant herbivore model with toxin determined functional response a system of ordinary differential equations is considered which models the plant herbivore interactions mediated by a toxin determined functional response the new functional response is a modification of the traditional holling type ii functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses a detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through hopf bifurcations and homoclinic bifurcation the results are obtained not only analytically but also confirmed and extended numerically 2007 published by elsevier inc

oscillation of second order functional differential equations with mixed nonlinearities and oscillatory potentials in this paper we study oscillation of second order functional differential equations with mixed nonlinearities p t x t q t x t t i 1nq i t x t t a isgnx t t e t where t 0 p t c 1 0 q t q i t e t c 0 p t 0 a 1 a m 1 a m 1 a n 0 n m 1 without assuming that q t q i t and e t are nonnegative the results given in y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 198 2008 375 381 have been extended to the aforementioned functional differential equation

decompositions of the free additive convolution we introduce and study a new type of convolution of probability measures denoted and called the s free additive convolution which is defined by the subordination functions associated with the free additive convolution we derive an alternating decomposition of for compactly supported and using another convolution called orthogonal additive convolution this decomposition leads to two types of complete alternating decompositions of the free additive convolution more importantly we develop an operatorial approach to the subordination property and introduce the associated notion of s free independence moreover we establish relations between convolutions associated with the main notions of noncommutative independence free monotone and boolean finally our result leads to natural decompositions of the free product of rooted graphs

all schatten spaces endowed with the schur product are q algebras we prove that the banach algebra formed by the space of compact operators on a hilbert space endowed with the schur product is a quotient of a uniform algebra also known as a q algebra together with a similar result of perez garcia for the trace class this completes the answer to a long standing question of varopoulos

oscillation theorems for nonlinear differential equations of second order abstract in this paper we present some new criteria for the oscillation of the differential equation a t x t x t p t x t q t f x t 0 the obtained results extend improve and correlate a number of existing criteria

a sublinear oscillation theorem abstract an oscillation criterion is given for the second order nonlinear differential equation y a t y 0 where a t is continuous but is not assumed to be non negative for all large values of t and y is non decreasing in y and satisfies y y 0 for y 0 this result generalizes a recent extension of belohorec s theorem due to kwong and wong and also incorporates an earlier result of coles

oscillation of sublinear second order differential equations with integrable coefficients abstract an oscillation criterion is given for the second order sublinear differential equation y a t f y 0 where a t c 0 and f y c is nondecreasing with yf y 0 for y 0 and also satisfies a sublinear condition which covers the special case f y y sgn y 0 the coefficient a t is allowed to be negative for large values of t and its integral over the nonnegative reals is finite this result extends an earlier oscillation theorem of kwong and wong for the special case

oscillation theorems for nonlinear second order differential equations in this paper some new oscillation criteria are given for the second order nonlinear differential equation r t x t x t c t x t 0 t t0 where r c t0 0 c c t0 r c r r and r r is defined by s s p 2s with p 1 a fixed real number these criteria involve the use of averaging functions

lp harmonic analysis and radon transforms on the heisenberg group in this paper harmonic analysis in the heisenberg group heisn cn r with group law z t z t z z t t 12im z z is taken to mean the joint spectral theory of the operators l heisenberg laplacian and t t the spectral decomposition of e l2 is given explicitly as e 0 e d where e 1 k 0 1 2 and e z t n 2 n 1 n 2k n 1 exp ie tn 2k exp z 24 n 2k lkn 1 z 22 n 2k where lkn 1 denotes the laguerre polynomial the eigenvalues are it e e n 2k e and l k e k e this decomposition is essentially well known but has not previously been described in this light it is also the decomposition into irreducibles of the representation of the heisenberg motion group semi direct product of heisn and u n on l2 heisn the main result is a summability in lp of the decomposition for e lp 1 p limr 1 rk 0 ed for p 1 only a weaker substitute is available and for p the decomposition is false there is also a plancherel formula for l2 2 2 k e n 2k 0 k e z 0 2dzd a number of explicit examples of the decomposition are computed including part of the schrodinger propagator eisl the heisenberg radon transform is defined by r z t n z t w 0 dw this operator was studied by geller and stein it is shown to be bounded from lp to lq if and only if p 2n 2 2n 1 and q 2n 2 some generalizations of these results to the free step two nilpotent lie groups are given but the results are not as complete

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

beurling fourier algebras on compact groups spectral theory for a compact group g we define the beurling fourier algebra a omega g on g for weights omega defined on the dual what g and taking positive values the classical fourier algebra corresponds to the case omega is the constant weight 1 we study the gelfand spectrum of the algebra realizing it as a subset of the complexification g mathbb c defined by mckennon and cartwright and mcmullen in many cases such as for polynomial weights the spectrum is simply g we discuss the questions when the algebra a omega g is symmetric and regular we also obtain various results concerning spectral synthesis for a omega g

interval criteria for oscillation of second order differential equations with mixed nonlinearities abstract in this paper we establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities p t x q t x i 1 n q i t x i sgn x e t where p t q t qi t e t are continuous functions defined on 0 p t is positive and differentiable 1 m 1 m 1 n 0 n m 1 no restriction is imposed on the potentials q t qi t and e t to be nonnegative

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are sharper than some previous results and handle the cases which are not covered by known criteria in particular several examples that dwell upon the sharp conditions of our results are also included

oscillations in superlinear differential equations of second order abstract a new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x t a t f x t 0 where a c t 0 f c r with yf y 0 for y 0 and 1 1 f y dy and f is continuously differentiable on r 0 with f y 0 for all y 0 the coefficient a is not assumed to be eventually nonnegative and the oscillation cirterion obtained involves the average behavior of the integral of a in the special case of the differential equation x t a t x t sgn x t 0 1 this criterion improves a recent oscillation result due to wong oscillation theorems for second order nonlinear differential equations proc amer math soc 106 1989 1069 1077

a note on the range of the derivatives of analytic approximations of uniformly continuous functions on c0 this paper is a contribution to the body of results concerning the size of the set of derivatives of differentiable functions on a banach space the results so far have consisted of examples of highly differentiable bump functions or functions approximating a given continuous function whose set of derivatives either is surprisingly small or has a given shape the paper under review treats the case of analytic smoothness the main result states that every uniformly continuous function on c0 more generally on a space with property k can be approximated by a real analytic function whose set of derivatives is contained in t p 0 lp this is a significant step forward as analytic functions are substantially harder to deal with than c1 smooth ones indeed a local perturbation of an analytic function necessarily changes the values of the function everywhere also of particular value is the quite precise and elegant description of the set of derivatives of the approximating function

oscillation criteria for second order nonlinear perturbed differential equations abstract some criteria are obtained which guarantee that all solutions of the second order nonlinear perturbed differential equations r t y t p t y t q t y t h t y t y t are oscillatory

integral averages and oscillation criteria of second order nonlinear differential equations the purpose of this paper is to present some new sufficient criteria for the oscillation of all solutions of the second order nonlinear differential equation a t j x x q t f x 0 t t 0 0 where a c 1 t 0 is a positive function qc t 0 has no restriction on its sign j c r c 1 r are such that 0 and j 0 email protected 0 for 0 these criteria are obtained by using a general class of the parameter functions in the averaging techniques and represent extension as well as improvement of known oscillation criteria of several authors for the generalized emden fowler equation

an alternating projection that does not converge in norm this paper proves that the method of alternating projections between two closed convex intersecting sets does not always converge in norm weak convergence was established by bregman soviet math dokl 6 1965 688 but the status of norm convergence was undetermined an explicit counterexample is provided

multi variable subordination distributions for free additive convolution abstract let k be a positive integer and let d c k denote the space of joint distributions for k tuples of selfadjoint elements in c probability space the paper studies the concept of subordination distribution of with respect to for d c k where is the operation of free additive convolution on d c k the main tools used in this study are combinatorial properties of r transforms for joint distributions and a related operator model with operators acting on the full fock space multi variable subordination turns out to have nice relations to a process of evolution towards infinite divisibility on d c k that was recently found by belinschi and nica arxiv 0711 3787 most notably one gets better insight into a connection which this process was known to have with free brownian motion

analytic approximations of uniformly continuous functions in real banach spaces abstract it is shown that if a separable real banach space x admits a separating analytic function with an additional condition property k concerning uniform behaviour of radii of convergence then every uniformly continuous mapping on x into any real banach space y can be approximated by analytic operators in particular the result applies to c0

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

generalizations of the busemann petty problem for sections of convex bodies abstract we present generalizations of the busemann petty problem for dual volumes of intermediate central sections of symmetric convex bodies it is proved that the answer is negative when the dimension of the sections is greater than or equal to 4 for two three dimensional sections both negative and positive answers are given depending on the orders of dual volumes involved and certain cases remain open for bodies of revolution a complete solution is obtained in all dimensions

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

polynomials in operator space theory the aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces for this purpose we take advantage of the basic fact that the space pm e of all m homogeneous polynomials on a vector space e can be identified with the algebraic dual of the m th symmetric tensor product m se given an operator space v we study several different types of completely bounded polynomials on v which form the operator space duals of m sv endowed with related operator structures of special interest are what we call haagerup kronecker and schur polynomials polynomials associated with different types of matrix products

families of periodic orbits virtual periods and global continuability abstract for a differential equation depending on a parameter there have been numerous investigations of the continuation of periodic orbits as the parameter is varied mallet paret and yorke investigated in generic situations how connected components of orbits must terminate here we extend the theory to the general case dropping genericity assumptions

integral averages and oscillation of second order nonlinear differential equations new oscillation criteria are given for the second order sublinear differential equation left a left t right psi left x left t right right x left t right right q left t right f left x left t right right 0 t geqslant t 0 0 where a c 1 t 0 is a nonnegative function f c with x 0 xf x x 0 for x 0 f have continuous derivative on 0 with f x x03c8 x 0 for x 0 and q c t 0 has no restriction on its sign this oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x t q t x t 0

weak amenability and 2 weak amenability of beurling algebras abstract let l 1 g be a beurling algebra on a locally compact abelian group g we look for general conditions on the weight which allows the vanishing of continuous derivations of l 1 g this leads us to introducing vector valued beurling algebras and considering the translation of operators on them this is then used to connect the augmentation ideal to the behavior of the derivation space we apply these results to give examples of various classes of beurling algebras which are weakly amenable 2 weakly amenable or fail to be even 2 weakly amenable

convolution weights on l2 spaces abstract it is known that the weighted l p space on a locally compact group is stable with respect to convolution if the weight function satisfies a certain type of convolution inequality there are several counterexamples showing that this sufficient condition is not necessary however for one class of groups namely discrete abelian groups no such counterexample is known thus there remains the possibility that the convolution inequality truly characterizes stability of convolution for weighted l p spaces on these groups in this paper we investigate this inequality and in the case p 2 reinterpret it in the light of operator theory and in the context of the theory of reproducing kernel hilbert spaces

oscillation of sublinear differential equations of second order on etudie les solutions d equations differentielles qui existent sur des intervalles de la forme t