instanton floer homology for lens spaces floer constructed instanton homology for integral homology three spheres in this paper we extend instanton floer homology to lens spaces l p q moreover we show a gluing formula for a variant of donaldson invariant along lens spaces as an application we prove that x mathbb cp 2 mathbb cp 2 does not admit a decomposition x x 1 cup x 2 here x 1 and x 2 are oriented simply connected non spin four manifolds with b 1 and with boundary l p 2 and p is a prime number of the form 16n 1

on certain classes of meromorphically multivalent functions associated with the generalized hypergeometric function making use of a linear operator which is defined here by means of the hadamard product or convolution involving the generalized hypergeometric function we introduce two novel subclasses w p q s a 1 a b l and w p q s a 1 a b l of meromorphically multivalent functions of order l email protected email protected

α continuity properties of one dimensional quasicrystals we apply the jitomirskaya last extension of the gilbert pearson theory to discrete one dimensional schrodinger operators with potentials arising from generalized fibonacci sequences we prove for certain rotation numbers that for every value of the coupling constant there exists an 0 such that the corresponding operator has purely continuous spectrum this result follows from uniform upper and lower bounds for the l norm of the solutions corresponding to energies from the spectrum of the operator

upper bounds on wavepacket spreading for random jacobi matrices a method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random possibly correlated jacobi matrix as an application one obtains sharp upper bounds on the diffusion exponents for random polymer models coinciding with the lower bounds obtained in a prior work the second application is an elementary argument not using multiscale analysis or the aizenman molchanov method showing that under the condition of uniformly positive lyapunov exponents the moments of the position operator grow at most logarithmically in time

stability of spectral types for jacobi matrices under decaying random perturbations abstract we study stability of spectral types for semi infinite self adjoint tridiagonal matrices under random decaying perturbations we show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under hilbert schmidt random perturbations we also obtain some results for singular spectral types

inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for the generalized hypergeometric function and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

eigenfunctions transfer matrices and absolutely continuous spectrum of one dimensional schrodinger operators on l r and its half line problem h on l2 0 with u 0 0 boundary conditions we will focus on a new approach to the absolutely continuous spectrum ac h and more generally ac h the essential support of the a c part of the spectral measures what is new in our approach is that it relies on estimates on the transfer matrix that is the 2 2 matrix te n m which takes u m 1 u m to u n 1 u n for solutions u of hu eu in the continuum case use u x u x instead of u x 1 u x we let te n te n 0 for example we will prove the following

the spectrum of differential operators with almost constant coefficients ii the absolutely continuous spectrum of differential operators of the form ly w 1 k 0n 1 k pky k k on l2 0 w is determined with pn x w x 0 the coefficients pk are assumed to satisfy pk x pk 2kw 1 x ck w pn 1 1 2n if the coefficients satisfy some additional smoothness and decay conditions the absolutely continuous part hac of any self adjoint extension of l is unitarily equivalent to the operator of multiplication by p x 0n ckx2k on l2 0 several extensions of this result as well as examples are shown

phase averaged transport for quasi periodic hamiltonians for a class of discrete quasi periodic schrodinger operators defined by covariant representations of the rotation algebra a lower bound on phase averaged transport in terms of the multifractal dimensions of the density of states is proven this result is established under a diophantine condition on the incommensuration parameter the relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra it includes the critical harper almost mathieu operator as a by product a new solution of the frame problem associated with weyl heisenberg gabor lattices of coherent states is given

a stable cohomotopy refinement of seiberg witten invariants ii the monopole map defines an element in an equivariant stable cohomotopy group refining the seiberg witten invariant part i discusses the definition of this stable homotopy invariant and its relation to the integer valued seiberg witten invariants

fourier asymptotics of fractal measures abstract a measure on r n will be called locally uniformly dimensional if br x cr for all r 1 and all x where br x denotes the ball of radius r about x for l 2 d the measure d is in i so d is well defined we show it is locally in l2 and sup r 1 r n b r y f d 2 d c f 2 under additional hypotheses we show that lim r r n b r y f d 2 2 d is comparable in size to 2 2 a number of other related results are established the special case when is an integer and is the surface measure on a c1 manifold was treated by s agmon and l hormander j analyse math 30 1976 1 38

pin 2 equivariant seiberg witten floer homology and the triangulation conjecture we define pin 2 equivariant seiberg witten floer homology for rational homology 3 spheres equipped with a spin structure the analogue of froyshov s correction term in this setting is an integer valued invariant of homology cobordism whose mod 2 reduction is the rokhlin invariant as an application we show that there are no homology 3 spheres y of rokhlin invariant one such that y y bounds an acyclic smooth 4 manifold by previous work of galewski stern and matumoto this implies the existence of non triangulable high dimensional manifolds

some applications of hadamard convolution to multivalently analytic and multivalently meromorphic functions the aim of the present study is to give several applications of hadamard product or convolution to multivalently analytic and multivalently meromorphic functions

power law subordinacy and singular spectra i half line operators we study hausdorff dimensional spectral properties of certain whole line quasiperiodic discrete schrodinger operators by using the extension of the gilbert pearson subordinacy theory that we previously developed in 19

inclusion properties for certain classes of meromorphic functions associated with the choi saigo srivastava operator abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for analytic functions and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

a characterization of the anderson metal insulator transport transition we investigate the anderson metal insulator transition for random schrodinger operators we define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the hilbert schmidt norm we introduce a local transport exponent e and set the weak metallic transport region to be the part of the spectrum with nontrivial transport i e e 0 we prove that these insulator and metallic regions are complementary sets in the spectrum of the random operator and that the local transport exponent e provides a characterization of the metal insulator transport transition moreover we show that if there is such a transition then e has to be discontinuous at a transport mobility edge more precisely we show that if the transport is nontrivial then e 1 2d where d is the space dimension these results follow from a proof that slow transport of quantum waves in random media implies the starting hypothesis for the authors bootstrap multiscale analysis we also conclude that the strong insulator region coincides with the part of the spectrum where we can perform a bootstrap multiscale analysis proving that the multiscale analysis is valid all the way up to a transport mobility edge

eigenvalue spacings and dynamical upper bounds for discrete one dimensional schrodinger operators we prove dynamical upper bounds for discrete one dimensional schrodinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations we demonstrate the applicability of our approach by a study of the fibonacci hamiltonian

the absolutely continuous spectrum of one dimensional schrodinger operators with decaying potentials we investigate one dimensional schrodinger operators with asymptotically small potentials it will follow from our results that if with then is an essential support of the absolutely continuous part of the spectral measure we also prove that if then the spectrum is purely absolutely continuous on these results are optimal

on subordinacy and analysis of the spectrum of schrodinger operators with two singular endpoints the theory of subordinacy is extended to all one dimensional schrodinger operatorsfor which the corresponding differential expression l d 2 dr 2 v r is in the limit point case at both ends of an interval a b with v r locally integrable this enables a detailed classification of the absolutely continuous and singular spectra to be established in terms of the relative asymptotic behaviour of solutions of lu xu x e as r a and r b the result provides a rigorous but straightforward method of direct spectral analysis which has very general application and somefurther properties of the spectrum are deduced from the underlying theory

some subclasses of meromorphically multivalent functions associated with a linear operator abstract let p denote the class of functions normalized by f z z p n 1 a n z n p p n 1 2 3 which are analytic and p valent in 0 z 1 making use of a linear operator which is defined here by means of the hadamard product or convolution we introduce some new subclasses of the meromorphically p valent function class p and investigate their inclusion relationships and convolution properties some integral preserving properties are also considered

solutions spectrum and dynamics for schrodinger operators on infinite domains 1 introduction and main results in this paper we investigate the relations between the rate of decay of solutions of schrodinger equations continuity properties of spectral measures of the corresponding operators and dynamical properties of the corresponding quantum systems the first main result of this paper shows that in great generality certain upper bounds on the rate of growth of l 2 norms of generalized eigenfunctions over expanding balls imply certain minimal singularity of the spectral measures consider an operator h v defined by the differential expression h v v x

text pin 2 monopole equations and intersection forms with local coefficients of four manifolds we introduce a variant of the seiberg witten equations text pin 2 monopole equations and give its applications to intersection forms with local coefficients of four manifolds the first application is an analogue of froyshov s results on four manifolds with definite intersection forms with local coefficients the second is a local coefficient version of furuta s 10 8 inequality as a corollary we construct nonsmoothable spin four manifolds satisfying rohlin s theorem and the 10 8 inequality

some criteria for meromorphic multivalent starlike functions abstract the main purpose of the present paper is to derive some new criteria for meromorphic multivalent starlike functions

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

a linear operator and associated families of meromorphically multivalent functions making use of a linear operator which is defined here by means of the hadamard product or convolution the authors introduce and investigate the various properties and characteristics of two novel families of meromorphically multivalent functions they also extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

some properties of certain meromorphically multivalent functions the main object of the present paper is to investigate some interesting properties of certain meromorphically multivalent functions associated with a linear operator l p a c

finite gap potentials and wkb asymptotics for one dimensional schrodinger operators consider the schrodinger operator h d2 dx2 v x with power decaying potential v x o x we prove that a previously obtained dimensional bound on exceptional sets of the wkb method is sharp in its whole range of validity the construction relies on pointwise bounds on finite gap potentials these bounds are obtained by an analysis of the jacobi inversion problem on hyperelliptic riemann surfaces

some properties of certain subclasses of meromorphically multivalent functions in this paper the author investigates interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of certain linear operator

a certain family of meromorphically multivalent functions abstract by making use of a familiar analogue of the ruscheweyh derivative as well as of the principle of subordination between two analytic functions the authors introduce and study rather systematically a certain family of meromorphically multivalent functions in the open unit disk u z z c and 0 several inclusion properties of this family are associated with an integral operator of the bernardi libera livingston type

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

subclasses of meromorphic functions associated with the cho kwon srivastava operator abstract we consider a multiplier transformation and some subclasses of the class of meromorphic functions which was defined by means of the hadamard product by n e cho o s kwon and h m srivastava in n e cho o s kwon h m srivastava inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations j math anal appl 300 2004 505 520

mixed lower bounds for quantum transport let h be a self adjoint operator on a separable hilbert space h h 1 given an orthonormal basis b en of h we consider the time averaged moments x p t of the position operator associated to b we derive lower bounds for the moments in terms of both spectral measure and generalized eigenfunctions u n x of the state as a particular corollary we generalize the recently obtained lower bound in terms of multifractal dimensions of and give some equivalent forms of it which can be useful in applications we establish in particular the relations between the lq norms q 1 2 of the imaginary part of borel transform of probability measures and the corresponding multifractal dimensions

on subordinacy and analysis of the spectrum of one dimensional schrodinger operators abstract by considering the behaviour as n of the ratio of l2 0 n norms of solutions of d 2 dr 2 v r u xu 0 r x r a characterisation of the absolutely continuous and singular spectra of one dimensional schrodinger operators is deduced the analysis is applicable to all operators for which l d 2 dr 2 v r is regular at 0 and in the limit point case at infinity with v r locally integrable

a class of integral operators preserving subordination and superordination for meromorphic functions the purpose of the present paper is to investigate several subordination and superordination preserving properties of a certain class of integral operators which are defined on the space of meromorphic functions in the punctured open unit disk the sandwich type theorem for these integral operators is also presented moreover we consider an application of the subordination and superordination theorem to the gauss hypergeometric function

first kdv integrals and absolutely continuous spectrum for 1 d schrodinger operator we consider 1 d schrodinger operators on l 2 r with slowly decaying potentials under some conditions on the potential related to the first integrals of the kdv equation we prove that the a c spectrum of the operator coincides with the positive semiaxis and the singular spectrum is unstable examples show that for special classes of sparse potentials these results can not be improved

almost complex 4 manifolds with vanishing first chern class an odd seiberg witten invariant imposes bounds on the signature of a closed almost complex 4 manifold with vanishing first chern class this applies in particular to symplectic 4 manifolds of kodaira dimension zero

hadamard product of certain meromorphic starlike and convex functions in this paper the authors establish certain results concerning the hadamard product for two classes related to starlike and convex univalent meromorphic functions of order a and type b with positive coefficients

a gluing theorem for the relative bauer furuta invariants in a previous paper we have constructed an invariant of fourdimensional manifolds with boundary in the form of an element in the stable homotopy group of the seiberg witten floer spectrum of the boundary here we prove that when one glues two fourmanifolds along their boundaries the bauer furuta invariant of the resulting manifold is obtained by applying a natural pairing to the invariants of the pieces as an application we show that the connected sum of three copies of the k3 surface contains no exotic nuclei in the process we also compute the floer spectrum for several seifert fibrations

spectral and dynamical properties of certain random jacobi matrices with growing parameters in this paper a family of random jacobi matrices with off diagonal terms that exhibit power law growth is studied since the growth of the randomness is slower than that of these terms it is possible to use methods applied in the study of schr odinger operators with random decaying potentials a particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional the results are applied to the infinite dumitriu edelman model 2002 and its spectral properties are analyzed

symplectic 4 manifolds with kodaira dimension zero we discuss the notion of the kodaira dimension for symplectic manifolds in dimension 4 in particular we propose and partially verify betti number bounds for symplectic 4 manifolds with kodaira dimension zero

a unified presentation of some classes of meromorphically multivalent functions the authors introduce and investigate various properties of a general class uk p a a b p k n 1 2 3 0 p 0 1 a b 1 0 b 1 which unifies and extends several known or new subclasses of meromorphically multivalent functions the properties and characteristics of this general class which are presented here include growth and distortion theorems they also involve hadamard products or convolution of functions belonging to the class uk p a b

sum rules for jacobi matrices and their applications to spectral theory we discuss the proof of and systematic application of case s sum rules for jacobi matrices of special interest is a linear combination of two of his sum rules which has strictly positive terms among our results are a complete classification of the spectral measures of all jacobi matrices j for which j j 0 is hilbert schmidt and a proof of nevai s conjecture that the szego condition holds if j j 0 is trace class

inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations making use of a multiplier transformation which is defined here by means of the hadamard product or convolution the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties some integral preserving properties in a given sector are also considered

bauer furuta invariants under mathbb z _2 actions s bauer and m furuta defined a stable cohomotopy refinement of the seiberg witten invariants in this paper we prove a vanishing theorem of bauer furuta invariants for 4 manifolds with smooth mathbb z 2 actions as an application we give a constraint on smooth mathbb z 2 actions on homotopy k3 k3 and construct a nonsmoothable locally linear mathbb z 2 action on k3 k3 we also construct a nonsmoothable locally linear mathbb z 2 action on k3

certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function in this paper we introduce and study two subclasses s p q s a 1 a b l and s p q s a 1 a b l of meromorphic p valent functions of order l email protected email protected

certain classes of meromorphic multivalent functions in this paper we introduce and investigate two new classes of meromorphic multivalent functions such results as subordination properties coefficient inequalities convolution properties and integral representations are proved several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

one dimensional schrodinger operators with random decaying potentials we investigate the spectrum of the following random schrodinger operators h omega frac d 2 dt 2 a t f x t omega wheref xt is a markovian potential studied by the russian school 8 we completely describe the transition of the spectrum from pure point type to absolutely continuous type as the decreasing order ofa t grows this is an extension to a continuous case of the result due to delyon simon souillard 6 who deal with the lattice case

bounded solutions and absolute continuity of sturm liouville operators this work is a contribution to the theory of the absolutely continuous spectrum of one dimensional schriidinger operators i e sturm liouville operators generated by differential expressions of the form ru u qu in proofs of absolute continuity for such operators and also for the closely related dirac systems always asymptotic properties of solutions of zu lu for real or complex values of 1 have played an important role see for example 18 19 8 4 9 lo in these works and a number of others particular classes of potentials q were treated using properties of solutions in the course of the proof of absolute continuity somewhat more recently the connection between asymptotic properties of solutions and absolute continuity was given a theory i e results of the following form were proved let the solutions of zu lu satisfy some specific asymptotic property for a varying in some subset of r no or almost no a priori assumptions on q then operators generated by z are absolutely continuous in this set a first result of this type was given by carmona 3 who proved that local uniform boundedness of solutions together with their derivatives in some open a set implies pure absolute continuity in this set here we will mostly rely on the concept of non or racy of solutions which was shown by gilbert and pearson 7 12 61 to be a powerful tool in the investigation of the continuous spectrum of sturm liouville operators in section 2 we give some consequences of their results whi ch are useful in proofs of absolute continuity these consequences range from non existence of imbedded eigenvalues and the existence of absolutely continuous parts to pure absolute continuity and the existence of transient 210 0022 247x 92 5 00

argument estimates of certain meromorphically multivalent functions associated with generalized hypergeometric function the object of this paper is to obtain some argument properties of meromorphically multivalent functions associated with generalized hypergeometric function we also derive the integral preserving properties in a sector

wkb asymptotic behavior of almost all generalized eigenfunctions for one dimensional schrodinger operators with slowly decaying potentials we prove the wkb asymptotic behavior of solutions of the differential equation d2u dx2 v x u eu for a e e a where v v1 v2 v1 lp r and v2 is bounded from above with a lim supx v x while v 2 x lp r 1 p 2 these results imply that schrodinger operators with such potentials have absolutely continuous spectrum on a we also establish wkb asymptotic behavior of solutions for some energy dependent potentials

on certain subclasses of meromorphically multivalent convex functions abstract making use of certain differential operators defined by hadamard product the author studies among other things the subclasses j n p 0 p p n 1 2 of meromorphically multivalent convex functions in the open unit disk u where n is any integer greater than p the author shows in particular that j n 1 p j n p and considers the integrals of functions in j n p

positive scalar curvature and 10 8 type inequalities on 4 manifolds with periodic ends we show 10 8 type inequalities for some end periodic 4 manifolds which have positive scalar curvature metrics on the ends as an application we construct a new family of closed 4 manifolds which do not admit positive scalar curvature metrics

on certain subclass of meromorphic close to convex functions in the present paper we introduce and investigate a certain new subclass mk s l a b of meromorphic close to convex functions such results as inclusion relationships coefficient inequalities and convolution property are derived relevant connections of the results presented here with those obtained in earlier works are also pointed out

modified prufer and efgp transforms and the spectral analysis of one dimensional schrodinger operators using control of the growth of the transfer matrices wediscuss the spectral analysis of continuum and discrete half line schrodinger operators with slowly decaying potentials among our results we show if where w has compact support and then h has purely a c resp purely s c spectrum on 0 if for n 1 2 a n potentials where a n are independent identically distributed random variables with e a n 0 e a 2 n 1 and 2 we find singular continuous spectrum with explicitly computable fractional hausdorff dimension

a class of meromorphically multivalent functions defined by means of a linear operator abstract let p denote the class of functions of the form f z z p n 1 a n z n p n n 1 2 3 which are analytic in the punctured open unit disk u 0 z 0 z 1 making use of a linear operator which is defined here by means of the hadamard product or convolution we introduce a new subclass m p a c h of p and investigate some properties for the class m p a c h

absolutely continuous spectrum of one dimensional schrodinger operators and jacobi matrices with slowly decreasing potentials we prove that for any one dimensional schrodinger operator with potentialv x satisfying decay condition v x cx 3 4 e the absolutely continuous spectrum fills the whole positive semi axis the description of the set in on which the singular part of the spectral measure might be supported is also given analogous results hold for jacobi matrices

some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function in the present paper we introduce and investigate each of the following new subclasses f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f as well as f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f of meromorphically p valent functions which is defined by means of a certain meromorphically p modified version of the familiar dziok srivastava linear operator involving the generalized hypergeometric function such results as inclusion relationships integral representations and convolution properties for these function classes are proved the results presented here provide extensions of those given in some earlier works several other new results are also obtained

transient and recurrent spectrum abstract we deal primarily with spectral analysis of an abstract self adjoint operator h on a hilbert space h we propose a further refinement of the absolutely continuous subspace h ac into the transient absolutely continuous subspace h tac which is the closure of those with e ith o t n for all n and the recurrent absolutely continuous subspace h rac h ac h tac we discuss general features of this breakup in a subsequent paper we construct analytic almost periodic functions v on so that h d 2 dx 2 v x on l 2 has only recurrent absolutely continuous spectrum in the sense that h rac h

fractal dimensions and the phenomenon of intermittency in quantum dynamics we exhibit an intermittency phenomenon in quantum dynamics more precisely we derive new lower bounds for the moments of order p associated to the state t e it h and averaged in time between zero and t these lower bounds are expressed in terms of generalized fractal dimensions d 1 1 p d of the measure where d is the space dimension this improves previous results obtained in terms of hausdorff and packing dimension

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2