method of speech recognition using time dependent interpolation and hidden dynamic value classes a speech signal is decoded by determining a production related value for a current state based on an optimal production related value at the end of a preceding state the optimal production related value being selected from a set of continuous values the production related value is used to determine a likelihood of a phone being represented by a set of observation vectors that are aligned with a path between the preceding state and the current state the likelihood of the phone is combined with a score from the preceding state to determine a score for the current state the score from the preceding state being associated with a discrete class of production related values wherein the class matches the class of the optimal production related value

on a liouville type equation with sign changing weight in this paper we study the existence nonexistence and multiplicity of non negative solutions for the family of problems u a x e f x u u h 0 where is a bounded domain in r2 and 0 is a parameter the coefficient a x is allowed to change sign the techniques used in the proofs are a combination of upper and lower solutions the trudingermoser inequality and variational methods note that when f x u 0 the equation is of liouville type

mass concentration phenomena for the l 2 critical nonlinear schrodinger equation in this paper we show that any solution of the nonlinear schr o dinger equation iu t delta u pm u frac 4 n u 0 which blows up in finite time satisfies a mass concentration phenomena near the blow up time our proof is essentially based on the bourgain s one cite mr99f 35184 which has established this result in the bidimensional spatial case and on a generalization of strichartz s inequality where the bidimensional spatial case was proved by moyua vargas and vega cite mr1671214 we also generalize to higher dimensions the results in keraani cite mr2216444 and merle and vega cite mr1628235

on the defect of compactness for the strichartz estimates of the schrodinger equations abstract in this paper we prove that every sequence of solutions to the linear schrodinger equation with bounded data in h1 r d d 3 can be written up to a subsequence as an almost orthogonal sum of sequences of the type h d 2 2nv t tn h2n x xn hn where v is a solution of the linear schrodinger equation with a small remainder term in strichartz norms using this decomposition we prove a similar one for the defocusing h1 critical nonlinear schrodinger equation assuming that the initial data belong to a ball in the energy space where the equation is solvable this implies in particular the existence of an a priori estimate of the strichartz norms in terms of the energy

on the blow up phenomenon of the critical nonlinear schrodinger equation abstract in this paper we consider the blow up phenomenon of critical nonlinear schrodinger equations in dimension 1d and 2d we define the minimal mass as the l 2 norm necessary to ignite a wave collapse and we stress its role in the blow up mechanism asymptotic compactness properties and l 2 concentration are proved the proof relies on linear and nonlinear profile decompositions

the focusing energy critical nonlinear schrodinger equation in dimensions five and higher we consider the focusing energy critical nonlinear schr odinger equation iu t delta u u 4 over d 2 u in dimensions d geq 5 we prove that if a maximal lifespan solution u colon i times bbb r d to bbb c obeys sup t in i nabla u t 2 nabla w 2 then it is global and scatters both forward and backward in time here w denotes the ground state which is a stationary solution of the equation in particular if a solution has both energy and kinetic energy less than those of the ground state w at some point in time then the solution is global and scatters we also show that any solution that blows up with bounded kinetic energy must concentrate at least the kinetic energy of the ground state similar results were obtained by kenig and merle for spherically symmetric initial data and dimensions d 3 4 5

method and apparatus for determining articulatory parameters from speech data a system and method for determining from continuous speech the instantaneous values of a set of articulatory parameters the continuous speech data is a sequence of spectral profiles obtained by spectrally sampling continuous speech the spectral samples are presented in sequence to a plurality of class transforms each establishing a respective speech phoneme class which includes plurality of speech phoneme having similar spectral and articulatory characteristics each class transform converts a speech segment included in its class and contained in a spectral sample into a predetermined set of articulatory parameter values a class discriminating transform operates in parallel with the class transforms to produce a set of probability values each indicating the probability that the spectral sample being transformed represents a phoneme in a respective speech phoneme class an array of multipliers adjusts the predetermined values of the sets produced by the class transforms by multiplying the values of each set by the probability value produced for that set by the class discriminating transform the adjusted articulatory parameter value sets are combined by adding corresponding elements to produce a set of adjusted articulatory parameter values indicative of an articulatory tract configuration appropriate for producing the sampled speech

on the cauchy problem of 3 d energy critical schrodinger equations with subcritical perturbations abstract we investigate the global well posedness scattering and blow up phenomena when the 3 d quintic nonlinear schrodinger equation which is energy critical is perturbed by a subcritical nonlinearity 1 u p u we find when the quintic term is defocussing then the solution is always global no matter what the sign of 1 is scattering will occur either when the perturbation is defocussing and 4 3 p 4 or when the mass of the solution is small enough and 4 3 p 4 when the quintic term is focusing we show the blow up for certain solutions

global wellposedness of defocusing critical nonlinear schrodinger equation in the radial case is globally wellposed in time more precisely we obtain a unique solution u u ch1 0 such that for all time u t depends continuously on the data in fact the dependence is even real analytic here moreover there is scattering for t the same statement holds for radial data h s 1 and proves in particular global existence of classical solutions in the radially symmetric case also this issue was open thus this is the analogue for nls of the result for the wave equation with quintic nonlinearity obtained by m struwe str in the radial case and by m grillakis gr s s in general in the case of the wave equation the proof is based on the following two different facts

global well posedness and scattering for the energy critical nonlinear schrodinger equation in r 3 we obtain global well posedness scattering and global l 10 spacetime bounds for energy class solutions to the quintic defocusing schrodinger equa tion in r 1 3 which is energy critical in particular this establishes global existence of classical solutions our work extends the results of bourgain 4 and grillakis 20 which handled the radial case the method is similar in spirit to the induction on energy strategy of bourgain 4 but we perform the induction analysis in both frequency space and physical space simultaneously and replace the morawetz inequality by an interaction variant first used in 12 13 the principal advantage of the interaction morawetz estimate is that it is not localized to the spatial origin and so is better able to handle nonradial solutions in particular this interaction estimate together with an almost conservation argument controlling the movement of l 2 mass in fre quency space rules out the possibility of energy concentration

blow up of the critical norm for some radial l2 super critical nonlinear schrodinger equations we consider the nonlinear schr odinger equation iu t delta u u p 1 u in dimension n geq 3 in the l 2 super critical range 1 frac 4 n p frac n 2 n 2 the corresponding scaling invariant space is dot h s c with 0 s c 1 and this covers the physically relevant case n p 3 the existence of finite time blow up solutions is known let p c frac n 2 p 1 so that dot h s c subset l p c let u t in dot h s c cap dot h 1 be a radially symmetric blow up solution which blows up at 0 t infty we prove that the scaling invariant l p c norm also blows up with a lower bound u t l p c geq log t t c n p rm as t to t

existence of solutions for perturbed fractional p laplacian equations abstract the purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p laplacian operator as follows p s u v x u p 2 u a x u r 2 u b x u q 2 u in r n where is a real parameter p s is the fractional p laplacian operator with 0 s 1 p p r min q p s and v a b r n 0 are three positive weights using variational methods we obtain nonexistence and multiplicity results for the above mentioned equations depending on and according to the integrability properties of the ratio a q p b r p our results extend the previous work of autuori and pucci 2013 5 to the fractional p laplacian setting furthermore we weaken one of the conditions used in their paper hence the results of this paper are new even in the fractional laplacian case

critical point theory on partially ordered hilbert spaces we develop some abstract critical point theory in order to prove that boundary value problems like the model problem formula on a bounded domain rn 2 p 2n n 2 have infinitely many sign changing solutions uk k n which are not comparable that is uk ul and uk ul change sign for k l we also show that there are no subsolutions u such that u uk for some k and u is positive somewhere a corresponding nonexistence result applies to supersolutions related results on the existence of sign changing solutions hold for other classes of nonlinearities

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

solitons and scattering for the cubic quintic nonlinear schrodinger equation on mathbb r 3 r 3 we consider the cubic quintic nonlinear schrodinger equation i partial t u delta u u 2u u 4u in the first part of the paper we analyze the one parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass energy curve additionally we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one parameter family of inequalities of gagliardo nirenberg type building on this work in the latter part of the paper we prove that scattering holds for solutions belonging to the region mathcal r of the mass energy plane where the virial is positive we show that this region is partially bounded by solitons also by rescalings of solitons which are not soliton solutions in their own right the discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial based methodology

stationary holomorphic discs and finite jet determination problems we construct a family of small analytic discs attached to levi non degenerate hypersurfaces in mathbb c n 1 which is globally biholomorphically invariant we then apply this technique to study unique determination problems along levi non degenerate hypersurfaces that are merely of class mathcal c 4 this method gives 2 jet determination results for germs of biholomorphisms cr diffeomorphisms as well as in the almost complex setting

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

extremal discs and the regularity of cr mappings in higher codimension we develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space we then apply the results to prove the regularity of cr homeomorphisms of such manifolds introduction in his celebrated paper lempert li introduced extremal analytic discs as geodesies of the kobayashi metric on a convex domain d c cn let a be the unit disc in the complex plane an analytic disc a d is called extremal if 0 attains its maximum among all analytic discs in d with the same values and directions at 0 g a extremal discs are important holomorphic invariants of d their boundaries lie in the boundary bd of the domain and form an invariant family of curves for the cr structure of bd lempert li l2 applies the extremal discs to the regularity of biholomorphic mappings monge amp re equations and normal forms of convex domains other applications include deformations and embeddibility of cr structures bl bd and polynomial hulls s

self focusing on bounded domains the critical nonlinear schrodinger equation nls on bounded domains models the propagation of cw laser beams in hollow core fibers unlike the nls on unbounded domains which models propagation in bulk media the ground state waveguide solutions are stable and the condition of critical power for singularity formation is generically sharp

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

a natural constraint approach to normalized solutions of nonlinear schrodinger equations and systems abstract the paper deals with the existence of normalized solutions to the system u 1 u 1 u 3 u v 2 in r 3 v 2 v 2 v 3 u 2 v in r 3 r 3 u 2 a 1 2 and r 3 v 2 a 2 2 for any 1 2 a 1 a 2 0 and 0 prescribed we present a new approach that is based on the introduction of a natural constraint associated to the problem we also show that as phase separation occurs for the solutions that we find our method can be adapted to scalar nonlinear schrodinger equations with normalization constraint and leads to alternative and simplified proofs to some results already available in the literature

jet determination of smooth cr automorphisms and generalized stationary discs we prove finite jet determination for finitely smooth cr diffeomorphisms of finitely smooth levi degenerate hypersurfaces in mathbb c n 1 by constructing generalized stationary discs glued to such hypersurfaces

the dynamics of the 3d radial nls with the combined terms in this paper we show the scattering and blow up result of the radial solution with the energy below the threshold for the nonlinear schrodinger equation nls with the combined terms iu t delta u u 4 u u 2 u qquad qquad qquad qquad rm cnls in the energy space h 1 mathbb r 3 the threshold is given by the ground state w for the energy critical nls iu t u u 4 u this problem was proposed by tao visan and zhang in comm pdes 32 1281 1343 2007 the main difficulty is lack of the scaling invariance illuminated by ibrahim et al in analysis pde 4 3 405 460 2011 we need to give the new radial profile decomposition with the scaling parameter then apply it to the scattering theory our result shows that the defocusing dot h 1 subcritical perturbation u 2 u does not affect the determination of the threshold of the scattering solution of cnls in the energy space

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

interaction between duration context and speaking style in english stressed vowels acoustic observations are reported for english front vowels embedded in a w l frame and carrying constant main stress the vowels were produced by five speakers in clear and citation form styles at varying durations but at a constant speaking rate the acoustic analyses revealed i that formant patterns were systematically displaced in the direction of the frequencies of the consonants of the adjacent pseudosymmetrical context ii that those displacements depended in a lawful manner on vowel duration iii that this context and duration dependence was more limited for clear than for citation form speech and that the smaller formant shifts of clear speech tended to be achieved by increases in the rate of formant frequency change the findings are compatible with a revised and biomechanically motivated version of the vowel undershoot model lindblom j acoust soc am 35 1773 1781 1963 that derives formant patterns from numerical information on three variables the locus target distance vowel duration and rate of formant frequency change the results further indicate that the clear samples were not merely louder but involved a systematic undershoot compensating reorganization of the acoustic patterns

quintic nls in the exterior of a strictly convex obstacle we consider the defocusing energy critical nonlinear schr odinger equation in the exterior of a smooth compact strictly convex obstacle in three dimensions for the initial value problem with dirichlet boundary condition we prove global well posedness and scattering for all initial data in the energy space

global well posedness and scattering for nonlinear schrodinger equations with combined nonlinearities in the radial case we consider the cauchy problem for the nonlinear schrodinger equation with combined nonlinearities one of which is defocusing mass critical and the other is focusing energy critical or energy subcritical the threshold is given by means of variational argument we establish the profile decomposition in h1 rd and then utilize the concentration compactness method to show the global wellposedness and scattering versus blowup in h1 rd below the threshold for radial data when d 4

existence and orbital stability of standing waves for nonlinear schrodinger systems abstract in this paper we investigate the existence of solutions in h 1 r n h 1 r n for nonlinear schrodinger systems of the form u 1 1 u 1 1 u 1 p 1 2 u 1 r 1 u 1 r 1 2 u 1 u 2 r 2 u 2 2 u 2 2 u 2 p 2 2 u 2 r 2 u 1 r 1 u 2 r 2 2 u 2 under the constraints r n u 1 2 d x a 1 0 r n u 2 2 d x a 2 0 here n 1 0 i 0 r i 1 2 p i 2 4 n for i 1 2 and r 1 r 2 2 4 n this problem is motivated by the search of standing waves for an evolution problem appearing in several physical models our solutions are obtained as constrained global minimizers of an associated functional note that in the system 1 and 2 are unknown and will correspond to the lagrange multipliers our main result is the precompactness of the minimizing sequences up to translation assuming the local well posedness of the associated evolution problem we then obtain the orbital stability of the standing waves associated to the set of minimizers

method of pattern recognition using noise reduction uncertainty a method and apparatus are provided for using the uncertainty of a noise removal process during pattern recognition in particular noise is removed from a representation of a portion of a noisy signal to produce a representation of a cleaned signal in the meantime an uncertainty associated with the noise removal is computed and is used with the representation of the cleaned signal to modify a probability for a phonetic state in the recognition system in particular embodiments the uncertainty is used to modify a probability distribution by increasing the variance in each gaussian distribution by the amount equal to the estimated variance of the cleaned signal which is used in decoding the phonetic state sequence in a pattern recognition task

on the role of quadratic oscillations in nonlinear schrodinger equations ii the l 2 critical case we consider a nonlinear semi classical schrodinger equation for which quadratic oscillations lead to focusing at one point described by a nonlinear scattering operator the relevance of the nonlinearity was discussed by r carles c fermanian kammerer and i gallagher for l 2 supercritical power like nonlinearities and more general initial data the present results concern the l 2 critical case in space dimensions 1 and 2 we describe the set of non linearizable data which is larger due to the conformal invariance as an application we precise a result by f merle and l vega concerning finite time blow up for the critical schrodinger equation the proof relies on linear and nonlinear profile decompositions

focusing and multi focusing solutions of the nonlinear schro dinger equation abstract a method of dynamic rescaling of variables is used to investigate numerically the nature of the focusing singularities of the cubic and quintic schrodinger equations in two and three dimensions and describe their universal properties the same method is applied to simulate the multi focusing phenomena produced by simple models of saturating nonlinearities

smoothing properties and retarded estimates for some dispersive evolution equations smoothing properties in the form of space time integrability properties play an important role in the study of dispersive evolution equations a number of them follow from a combination of general arguments and specific estimates we present a general formulation which makes the separation between the two types of ingredients as clear as possible and we illustrate it with the examples of the schrodinger equation of the wave equation and of a class of 1 1 dimensional equations related to the benjamin ono equation of special interest for the cauchy problem are retarded estimates expressed in terms of those properties we derive a number of such estimates associated with the last example and we mention briefly an application of those estimates to the cauchy problem for the generalized benjamin ono equation

travelling waves for the gross pitaevskii equation ii the purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the gross pitaevskii equation in dimensions two and three our arguments based on minimization under constraints yield a full branch of solutions and extend earlier results see 3 4 8 where only a part of the branch was built in dimension three we also show that there are no travelling wave solutions of small energy

normalized ground states for the nls equation with combined nonlinearities abstract we study existence and properties of ground states for the nonlinear schrodinger equation with combined power nonlinearities u u u q 2 u u p 2 u in r n n 1 having prescribed mass r n u 2 a 2 under different assumptions on q p a 0 and r we prove several existence and stability instability results in particular we consider cases when 2 q 2 4 n p 2 q p i e the two nonlinearities have different character with respect to the l 2 critical exponent these cases present substantial differences with respect to purely subcritical or supercritical situations which were already studied in the literature we also give new criteria for global existence and finite time blow up in the associated dispersive equation

chern moser operators and polynomial models in cr geometry we consider the fundamental invariant of a real hypersurface in c n its holomorphic symmetry group and analyze its structure at a point of degenerate levi form generalizing the chern moser operator to hypersurfaces of finite multitype we compute the lie algebra of infinitesimal symmetries of the model and provide explicit description for each graded component compared with a hyperquadric it may contain additional components consisting of nonlinear vector fields defined in terms of complex tangential variables as a consequence we obtain exact results on jet determination for hypersurfaces with such models the results generalize directly the fundamental result of chern and moser from quadratic models to polynomials of higher degree c 2014 elsevier inc all rights reserved

high frequency approximation of solutions to critical nonlinear wave equations this work is devoted to the description of bounded energy sequences of solutions to the equation 1 u u 4 0 in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i up to remainder terms small in energy norm and in every strichartz norm the proof relies on scattering theory for 1 and on a structure theorem for bounded energy sequences of solutions to the linear wave equation in particular we infer the existence of an a priori estimate of strichartz norms of solutions to 1 in terms of their energy

multiple normalized solutions for quasi linear schrodinger equations abstract in this paper we prove the existence of two solutions having a prescribed l 2 norm for a quasi linear schrodinger equation one of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global to overcome the lack of differentiability of the associated functional we rely on a perturbation method developed in 25

symmetric decreasing rearrangement can be discontinuous suppose f xl x2 0 is a continuously differentiable function supported in the unit disk in the plane its symmetric decreasing rearrangement is the rotationally invariant function f xl x2 whose level sets are circles enclosing the same area as the level sets of f such rearrangement preserves lp norms but decreases convex gradient integrals e g p p 1 p 0 j 1 2 3 is a sequence of infinitely differentiable functions also supported in the unit disk which converge uniformly together with first derivatives to f the symmetzed functions also converge uniformly the real question is about convergence of the derivatives of the symmetrized functions we announce that the derivatives of the symmetrized functions need not converge strongly e g it can happen that fj f p 0 for every p we further characterize exactly those f s for which convergence is assured and for which it can fail

a new rearrangement inequality and its application for l 2 constraint minimizing problems in this paper we introduce a new type rearrangement inequality based on the steiner rearrangement to show orbital stability of standing wave solutions with respect to a nonlinear schrodinger equation h 1 precompactness of minimizing sequence of l 2 constraint minimizing problem is very important usually by using the concentration compactness principle and some scaling argument h 1 precompactness is obtained to prove h 1 precompactness without scaling arguments we introduce the rearrangement the steiner rearrangement is defined as a map from h 1 to h 1 whereas our rearrangement cdot star cdot is defined as a map from h 1 times h 1 to h 1 by using the rearrangement we show a strict inequality vert nabla u star v vert l 2 2 vert nabla u vert l 2 2 vert nabla v vert l 2 2 under simple assumptions

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

finite difference approximate solutions for a mixed sub superlinear equation in ben mabrouk and ben mohamed 2006 a ben mabrouk m l ben mohamed on some critical and slightly super critical sub superlinear equations far east j appl math 23 1 2006 73 90 special volume of pdes a ben mabrouk m l ben mohamed nodal solutions for some nonlinear elliptic equations appl math comp in press doi 10 1016 j amc 2006 08 003 it has proved some theoretical results dealing with some boundary value problem du f u 0 in b and u 0 on b where b is a domain in r d with smooth boundary in the present paper we perform a difference scheme method to approximate the solution of a nonlinear evolutionary problem associated to the elliptic problem studied in ben mabrouk and ben mohamed 2006 we give at the end some numerical implementations based on a mixed sublinear superlinear term of the form f u u p email protected u q 1u

stationary discs glued to a levi non degenerate hypersurface we obtain an explicit parametrization of stationary discs glued to some levi non degenerate hypersurfaces these discs form a family which is invariant under the action of biholomorphisms we use this parametrization to construct a local circular representation of these hypersurfaces as a corollary we get the uniqueness of biholomorphisms with given 1 jet at some convenient point

method of determining uncertainty associated with acoustic distortion based noise reduction a method and apparatus are provided for determining uncertainty in noise reduction based on a parametric model of speech distortion the method is first used to reduce noise in a noisy signal in particular noise is reduced from a representation of a portion of a noisy signal to produce a representation of a cleaned signal by utilizing an acoustic environment model the uncertainty associated with the noise reduction process is then computed in one embodiment the uncertainty of the noise reduction process is used in conjunction with the noise reduced signal to decode a pattern state

existence and instability of standing waves with prescribed norm for a class of schrodinger poisson equations in this paper we study the existence and the instability of standing waves with prescribed l norm for a class of schrodinger poisson slater equations in r 0 1 i t x 1 p 2 0 when p 10 3 6 to obtain such solutions we look to critical points of the energy functional f u 1 2 ou 2l2 r3 1 4

symmetric ground state solutions of m coupled nonlinear schrodinger equations abstract we prove the existence of radial and radially decreasing ground states of an m coupled nonlinear schrodinger equation with a general nonlinearity

traveling waves for nonlinear schrodinger equations with nonzero conditions at infinity for a large class of nonlinear schrodinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity we prove the existence of nontrivial finite energy traveling waves moving with speed c in any space dimension n 3 our results are valid as well for the gross pitaevskii equation and for nls with cubic quintic nonlinearity

long time oscillation of solutions of nonlinear schrodinger equations near minimal mass ground state abstract in this paper we consider the long time dynamics of radially symmetric solutions of nonlinear schrodinger equations nls having a minimal mass ground state in particular we show that there exist solutions with initial data near the minimal mass ground state that oscillate for long time more precisely we introduce a coordinate defined near the minimal mass ground state which consists of finite and infinite dimensional part associated to the discrete and continuous part of the linearized operator then we show that the finite dimensional 2 d part approximately obeys newton s equation of motion for a particle in an anharmonic potential well showing that the infinite dimensional part is well separated from the finite dimensional part we will have long time oscillation

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

learning statistically characterized resonance targets in a hidden trajectory model a statistical trajectory speech model is constructed where the targets for vocal tract resonances are represented as random vectors and where the mean vectors of the target distributions are estimated using a likelihood function for joint acoustic observation vectors the target mean vectors can be estimated without formant data to form the model time dependent filter parameter vectors based on time dependent coarticulation parameters are constructed that are a function of the ordering and identity of the phones in the phone sequence in each speech utterance the filter parameter vectors are also a function of the temporal extent of coarticulation and of the speaker s speaking effort

compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity we study the branch of semistable and unstable solutions i e those whose morse index is at most 1 of the dirichlet boundary value problem u f x 1 u 2 on a bounded domain n which models among other things a simple electrostatic microelectromechanical system mems device we extend the results of 11 relating to the minimal branch by obtaining compactness along unstable branches for 1 n 7 on any domain and for a large class of permittivity profiles f we also show the remarkable fact that powerlike profiles f x x can push back the critical dimension n 7 of this problem by establishing compactness for the semistable branch on the unit ball also for n 8 and as long as as a byproduct we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for in a natural range in all these results the conditions on the space dimension and on the power of the profile are essentially sharp 2007 wiley periodicals inc

determination of formal cr mappings by a finite jet abstract we prove that if m is a connected real analytic holomorphically nondegenerate hypersurface in c n 1 then for any point p m there exists an integer k such that any two germs at p of local biholomorphic mappings h 1 h 2 c n 1 p c n 1 p that send m into itself and whose k jets agree at p are identical the above is a special case of a more general theorem stated for formal hypersurfaces that gives a finite jet determination result for the class of formal mappings whose jacobian determinant does not vanish identically