well posedness for the schrodinger korteweg de vries system we study well posedness of the cauchy problem associated to the schrodinger korteweg de vries system we obtain local well posedness for weak initial data where the best result obtained is for data in the sobolev space l 2 r x h 3 4 this result implies in particular the global well posedness in the energy space h 1 r x h 1 r both results considerably improve the previous ones by bekiranov ogawa and ponce 1997 guo and miao 1999 and tsutsumi 1993

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

a note on the arithmetic geometric mean inequality for matrices abstract we give a simple proof of the inequality aa x xbb 2 a ab where a b and x are arbitrary n n matrices and is any unitarily invariant norm for the schatten p norms p with 1 p aa x xbb p 2 a xb p if and only if aa x xbb

hilbert s fifth problem for local groups we solve hilbert s fifth problem for local groups every locally euclidean local group is locally isomorphic to a lie group jacoby claimed a proof of this in 1957 but this proof is seriously flawed we use methods from nonstandard analysis and model our solution after a treatment of hilbert s fifth problem for global groups by hirschfeld

singular value inequalities for commutators of hilbert space operators abstract we prove several singular value inequalities for commutators of hilbert space operators it is shown among other inequalities that if a b and x are operators on a complex separable hilbert space such that a and b are positive and x is compact then the singular values of ax xb are dominated by those of max a b x x where is the usual operator norm

singular values norms and commutators abstract let a i b i and x i i 1 n be bounded linear operators on a separable hilbert space such that x i is compact for i 1 n it is shown that the singular values of i 1 n a i x i b i are dominated by those of i 1 n a i b i i 1 n x i where is the usual operator norm among other applications of this inequality we prove that if a and b are self adjoint operators such that a 1 a a 2 and b 1 b b 2 for some real numbers a 1 a 2 b 1 and b 2 and if x is compact then the singular values of the generalized commutator ax xb are dominated by those of max b 2 a 1 a 2 b 1 x x this inequality proves a recent conjecture concerning the singular values of commutators several inequalities for norms of commutators are also given

well posedness and existence of bound states for a coupled schrodinger gkdv system abstract we derive some new results concerning the cauchy problem and the existence of bound states for a class of coupled nonlinear schrodinger gkdv systems in particular we obtain the existence of strong global solutions for initial data in the energy space h 1 r h 1 r generalizing previous results obtained in tsutsumi 1993 11 corcho and linares 2007 13 and dias et al submitted for publication 14 for the nonlinear schrodinger kdv system

norm inequalities for commutators of positive operators and applications let x y and z be operators on a hilbert space such that x and z are positive it is shown that left xy yz right leqslant rm max left left x right left z right right left y right applications of this commutator inequality are given

solitary waves and a stability analysis of an equation of short and long dispersive waves abstract a universal model for the interaction of long nonlinear waves and packets of short waves with long linear carrier waves is given by a system in which an equation of korteweg de vries kdv type is coupled to an equation of nonlinear schrodinger nls type the system has solutions of steady form in which one component is like a solitary wave solution of the kdv equation and the other component is like a ground state solution of the nls equation we study the stability of solitary wave solutions to an equation of short and long waves by using variational methods based on the use of energy momentum functionals and the techniques of convexity type we use the concentration compactness method to prove the existence of solitary waves we prove that the stability of solitary waves is determined by the convexity or concavity of a function of the wave speed

commutators and accretive operators abstract in this paper singular values of commutators of hilbert space operators are estimated to this aim the accretivity of a transform of the operators is applied some recent results of kittaneh f kittaneh singular value inequalities for commutators of hilbert space operators linear algebra appl 430 2009 2362 2367 are extended

unitarily invariant norm inequalities for elementary operators involving g1 operators abstract in this paper motivated by perturbation theory of operators we present some upper bounds for f a x g b x in terms of a x b x and f a x g b x in terms of a x x b where a b are g 1 operators is a unitarily invariant norm and f g are certain analytic functions further we find some new upper bounds for the schatten 2 norm of f a x x g b several special cases are discussed as well

commutator inequalities for hilbert space operators we prove singular value inequalities for positive operators some of these inequalities generalize recent results for commutators due to bhatia kitttaneh kittaneh and wang du applications of our results are given

inequalities for commutators of positive operators abstract it is shown that if a b and x are operators on a complex separable hilbert space such that a and b are compact and positive then the singular values of the generalized commutator a x x b are dominated by those of x a b where is the usual operator norm consequently for every unitarily invariant norm we have a x x b x a b it is also shown that if a and b are positive and x is compact then a x x b max a b x for every unitarily invariant norm moreover if x is positive then the singular values of the commutator a x x a are dominated by those of 1 2 a x x consequently a x x a 1 2 a x x for every unitarily invariant norm for the usual operator norm these norm inequalities hold without the compactness conditions and in this case the first two norm inequalities are the same our inequalities include and improve upon earlier inequalities proved in this context and they seem natural enough and applicable to be widely useful

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications