some remarks on the blow up rate for the 3d magnetic zakharov system we continue our study 8 on the cauchy problem for the three dimensional magnetic zakharov system zsm iet e ne i e b e 0 nt v vt n e 2 b i e e b 0 with initial data zsm 1 e 0 x e0 x n 0 x n0 x v 0 x v0 x let e n v c 0 t h1 r3 l2 r3 l2 r3 be a blow up solution to the cauchy problem zsm zsm 1 and let t be its blow up time then e n satisfies the space time integral estimate e 1 0t r3 n t x qdx 1q r3 e t x 2qdx 1q dt where 1e e 0 14 and q 32 1 e 32 2 the estimate e 1 implies that for a 1 supt 0 t t t ae n t lq r3 e t l2q r3 2 in particular if e n v is a radially symmetric solution to zsm zsm 1 then supt 0 t t t ae n t lq d e t l2q d 2 where a 0 13 and d x r3 x 1

strong connections and chern connes pairing in the hopf galois theory we reformulate the concept of connection on a hopf galois extension b p in order to apply it in computing the chern connes pairing between the cyclic cohomology hc 2 n b and k 0 b this reformulation allows us to show that a hopf galois extension admitting a strong connection is projective and left faithfully flat it also enables us to conclude that a strong connection is a cuntz quillen type bimodule connection to exemplify the theory we construct a strong connection super dirac monopole to find out the chern connes pairing for the super line bundles associated to a super hopf fibration

blowup for fractional nls abstract we consider fractional nls with focusing power type nonlinearity i t u s u u 2 u t x r r n where 1 2 s 1 and 0 for s n 2 and 0 2 s n 2 s for s n 2 we prove a general criterion for blowup of radial solutions in r n with n 2 for l 2 supercritical and l 2 critical powers 2 s n in addition we study the case of fractional nls posed on a bounded star shaped domain r n in any dimension n 1 and subject to exterior dirichlet conditions in this setting we prove a general blowup result without imposing any symmetry assumption on u t x for the blowup proof in r n we derive a localized virial estimate for fractional nls in r n which uses balakrishnan s formula for the fractional laplacian s from semigroup theory in the setting of bounded domains we use a pohozaev type estimate for the fractional laplacian to prove blowup

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

blowup result for a type of generalized zakharov system abstract we study the blowup for a type of generalized zakharov system in this paper it is proved that the solution of such system either blows up in finite time or blows up in infinite time provided that the initial energy is negative

blow up of h1 solution for the nonlinear schrodinger equation we consider the blow up of the solution in h1 for the following nonlinear schrodinger equation i tu u u p 1u x rn t 0 u 0 x u0 x x rn t 0 where n 2 and 1 4 n p min n 2 n 2 5 we prove that if the initial data u0 in h1 are radially symmetric and have negative energy then the solution of in h1 blows up in finite time we do not assume that xu0 l2 and therefore our result is the generalization of the results of glassey 4 and m tsutsumi 18 for the radially symmetric case

blowup results for the kgs system with higher order yukawa coupling in this paper we investigate the klein gordon schrodinger kgs system with higher order yukawa coupling in spatial dimensions n 3 we establish a perturbed virial type identity and prove blowup results relied on lyapunov functionals for kgs system with a negative energy level additionally we give a result with respect to the blowup rate in finite time for the radial solution in 3 spatial dimensions

on uniqueness and continuation properties after blow up time of self similar solutions of nonlinear schrodinger equation with critical exponent and critical mass we consider the nonlinear schrodinger equation with critical power where u 0 t n c and o h1 o x o l2 with this nonlinear term the equation 1 1 has a conformal invariance thus one yields explicit self similar solutions which have the following property they have minimum l2 norm among blow up solutions in this paper we first focus on uniqueness properties of these self similar solutions in a certain class we then look at the possible continuations of these solutions after the blow up time

iteration schemes for the divide and conquer eigenvalue solver we propose globally convergent iteration schemes for updating the eigenvalues of a symmetric matrix after a rank 1 modification such calculations are the core of the divide and conquer technique for the symmetric tridiagonal eigenvalue problem we prove the superlinear convergence right from the start of our schemes which allows us to improve the complexity bounds of 3 the effectiveness of our algorithms is confirmed by numerical results which are reported and discussed

the electrostatic limit for the 3d zakharov system abstract we consider the vectorial zakharov system describing langmuir waves in a weakly magnetized plasma in its original derivation zakharov 1972 the evolution for the electric field envelope is governed by a schrodinger type equation with a singular parameter which is usually large in physical applications motivated by this we study the rigorous limit as this parameter goes to infinity by using some strichartz type estimates to control separately the fast and slow dynamics in the problem we show that the evolution of the electric field envelope is asymptotically constrained onto the space of irrotational vector fields

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

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

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

strong connections on quantum principal bundles a gauge invariant notion of a strong connection is presented and characterized it is then used to justify the way in which a global curvature form is defined strong connections are interpreted as those that are induced from the base space of a quantum bundle examples of both strong and non strong connections are provided in particular such connections are constructed on a quantum deformation of the two sphere fibrations2 rp2 a certain class of stronguq 2 connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq dependent hermitian metric a particular form of the yang mills action on a trivialuq 2 bundle is investigated it is proved to coincide with the yang mills action constructed by a connes and m rieffel furthermore it is shown that the moduli space of critical points of this action functional is independent ofq

geometry of quantum principal bundles i a theory of principal bundles possessing quantum structure groups and classical base manifolds is presented structural analysis of such quantum principal bundles is performed a differential calculus is constructed combining differential forms on the base manifold with an appropriate differential calculus on the structure quantum group relations between the calculus on the group and the calculus on the bundle are investigated a concept of pseudo tensoriality is formulated the formalism of connections is developed in particular operators of horizontal projection covariant derivative and curvature are constructed and analyzed generalizations of the first structure equation and of the bianchi identity are found illustrative examples are presented

virial type blow up solutions for the zakharov system with magnetic field in a cold plasma abstract in this paper we study blow up solutions of virial type to the zakharov system with magnetic field in a cold plasma in r n n 2 3 after obtaining some a priori estimates on those terms generated by the magnetic field we obtain a virial type blow up result to the system under consideration the result suggests that the magnetic field in a cold plasma doesn t affect the virial type blow up character of the zakharov system

advances in multidimensional integration this paper gives a personal bird s eye view of some aspects of multivariate numerical integration it will sketch what happened during the past 50 years and point the reader s attention to what did not happen

existence of self similar blow up solutions for zakhrov equation in dimension two part i we consider the zakharov equation in space dimension two left begin array 20 c iu t delta u nu frac 1 c 0 2 n tt delta n delta left u right 2 end array right we prove the existence of blow up solutions stable self similar blow up solutions for this problem and we study various properties of these solutions

the posedness of the periodic initial value problem for generalized zakharov equations abstract in this paper firstly we study the periodic initial value problem of generalized zakharov equations if 0 p 4 we obtain the existence and uniqueness of the global classical solution by means of galerkin method and integral estimates secondly we study the periodic initial boundary value problem of generalized zakharov equations if p 2 1 a 2 e 0 2 1 3 a 2 e 0 1 a 2 e 0 and initial data satisfy some conditions we prove that these have blowup of local solution

optimal lower bound estimates for the blow up rate for the zakharov system in a nonhomogeneous medium abstract in this paper we obtain lower bound estimates for the blow up rate of finite time blow up solutions to the cauchy problem for the zakharov system in a nonhomogeneous medium in two space dimensions by introducing suitable scale transformations of space and time and the use of compactness arguments we derive an optimal lower bound estimate in the energy space h 2 r 2 l 2 r 2 h 1 r 2 for the blow up rate for t near the finite blow up time t also we give an application to the virial identity for the zakharov system under study

blow up and nonlinear instability for the magnetic zakharov system abstract this study deals with the generalized zakharov system with magnetic field first of all we construct a kind of blow up solutions and establish the existence of blow up solutions to the system through considering an elliptic system next we show the nonlinear instability for a kind of periodic solutions in addition we consider the concentration properties of blow up solutions for the system under study at the end of this paper we establish the global existence of weak solutions to the cauchy problem of the system under consideration

blow up results of viriel type for zakharov equations we consider the zakharov equations in n for n 2 n 3 we first establish a viriel identity for such equations and then prove a blow up result for solutions with a negative energy

global dynamics below the ground state energy for the zakharov system in the 3d radial case abstract we consider the global dynamics below the ground state energy for the zakharov system in the 3d radial case we obtain dichotomy between the scattering and the growup

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

quantum principal bundles and corresponding gauge theories a generalization of classical gauge theory is presented in which compact quantum groups play the role of the internal symmetry groups all considerations are performed in the framework of a noncommutative geometric formalism of locally trivial quantum principal bundles over classical smooth manifolds quantum counterparts of classical gauge bundles and classical gauge transformations are introduced and investigated a natural dierential calculus on quantum gauge bundles is constructed and analyzed kinematical and dynamical properties of corresponding gauge theories are discussed a particular attention is given to the purely quantum phenomenas appearing in the formalism and their physical interpretation an example with quantum su 2 group is considered

equations of langmuir turbulence and nonlinear schrodinger equation smoothness and approximation we consider the following family of systems parametrized by e 0 which describe langmuir s turbulence in the case where initial data are sufficiently small we study the asymptotic behaviour of the solutions ee ne when e goes to zero for d 1 2 3 namely we state convergence results of ee ne to the couple e e 2 where e is the solution of the nonlinear schrodinger equation moreover in three dimensions we show that the smooth solution ee ne is defined on 0 tmax e with tmax e going to infinity as e goes to 0

numerical evaluation of reproducing kernel hilbert space inner products a new approach to numerically evaluate an inner product or a norm in an arbitrary reproducing kernel hilbert space rkhs is considered the proposed methodology enables us to approximate the rkhs inner product with the desired accuracy avoiding analytical expressions furthermore its implementation is illustrated by means of some classic examples and compared with the standard iterative method provided by weiner for this purpose finally applications in both the problem of representing approximately second order stochastic processes by means of series expansions and in the problem of signal detection are studied

concentration properties of blow up solutions and instability results for zakharov equation in dimension two part ii we consider the zakharov equation in space dimension two left begin array 20 c iu t delta u nu frac 1 c 0 2 n tt delta n delta left u right 2 end array right