decay of solutions of nonlinear wave equations in three space dimensions abstract given a solution of the cauchy problem for nonlinear wave equations of the type 2 u t 2 u f u 0 in three space dimensions the asymptotic behaviour in time is considered it is shown that for nonlinearities which behave like powers u 1 u uniform decay holds with a certain rate depending on if 5 1 2 1 2 13 and moreover scattering states exist if is not too small this improves former results of w a strauss j funct anal 2 1968 409 457

nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

high energy blow up for two dimensional generalized exponential type boussinesq equation abstract a finite time blow up result for the cauchy problem of two dimensional generalized boussinesq type equation with exponential type source term is considered in this paper based on an adapted concave method we derive a sufficient condition on initial data leading to the arbitrarily positive initial energy finite time blow up

the effect of bias variance estimation skewness and kurtosis of the empirical logit on weighted least squares analyses summary the bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation the covariance of the empirical logit and its estimated variance is derived neither the 2 correction of haldane 1955 and anscombe 1956 nor the 2 suggested by cox 1970 for weighted logit regression is universally effective in reducing bias other corrections are considered the distribution of the empirical logit is shown to be considerably more skewed and to have a much larger kurtosis than the comparable binomial distribution methods based directly on sufficient statistics are preferred to those based on the empirical logit

global regularity for the 2d mhd equations with mixed partial dissipation and magnetic diffusion abstract whether or not classical solutions of the 2d incompressible mhd equations without full dissipation and magnetic diffusion can develop finite time singularities is a difficult issue a major result of this paper establishes the global regularity of classical solutions for the mhd equations with mixed partial dissipation and magnetic diffusion in addition the global existence conditional regularity and uniqueness of a weak solution is obtained for the 2d mhd equations with only magnetic diffusion

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

sharp threshold of global existence and blow up of the combined nonlinear klein gordon equation abstract in this paper we show the global well posedness and blow up result of the solutions with the energy below the threshold for the combined nonlinear klein gordon equation u t t u u u p 1 u u q 1 u d 3 in the energy space h 1 r d l 2 r d where 1 4 d q p 1 4 d 2 we give a threshold of blow up and global well posedness using a modified variational approach in the spirit of ibrahim et al 2011 7

a deficiency of the odds ratio as a measure of effect size the odds ratio is probably the most widely used measure of association for binary variables it has many well recognized advantages and disadvantages vis a vis the risk ratio we demonstrate that for chained or conditional probabilities odds ratios can behave paradoxically by failing to show a reinforcement effect that is expressed very clearly when risk ratios are used

well posedness and dynamics of the stochastic fractional magneto hydrodynamic equations abstract the current paper is devoted to the well posedness and dynamics of the stochastic 2d incompressible fractional magneto hydrodynamic mhd equations driven by gaussian multiplicative noise the nonlocal fractional diffusion leads to a new difficulty in the convergence since higher order estimates cannot be obtained the commutator estimates are introduced to overcome these difficulties using the stopping time technique and monotonicity arguments the global existence and uniqueness of the weak solution are obtained in a fixed probability space finally the existence of a random attractor for the random dynamical systems generated by the solution of stochastic mhd equation is presented

introduction to scattering for radial 3d nlkg below energy norm abstract we prove scattering for some radial 3d semilinear klein gordon equations with rough data first we prove strichartz type estimates in mixed norm spaces then by using these decays we establish some local bounds by combining these results to a morawetz type estimate and a radial sobolev inequality we control the variation of an almost conserved quantity on arbitrary large intervals once we have showed that this quantity is controlled we prove that some of these local bounds can be upgraded to global bounds this is enough to establish scattering all the estimates involved require a delicate analysis due to the nature of the nonlinearity and the lack of scaling

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

analyticity of the scattering operator for the nonlinear klein gordon equation with cubic nonlinearity the wave and scattering operators for the equation left square m 2 right varphi lambda varphi 2 0 withm 0 and 0 on four dimensional minkowski space are analytic on the space of finite energy cauchy data i e l21 r3 l2 r3

a comparison of maximum likelihood and jewell s estimator of the odds ratio and relative risk in single 2 2 tables this paper compares the maximum likelihood estimators of the odds ratio and relative risk in 2 2 tables with less biased estimators recently proposed by jewell for small samples in addition to bias location in the confidence interval and relative likelihood are calculated for ranges of sample sizes probabilities of exposure or disease and true values of the odds ratio and relative risk jewell s estimators perform poorly from the perspectives of confidence intervals and likelihood given these and other problems continued use of the maximum likelihood estimators is recommended

ergodicity of stochastic magneto hydrodynamic equations driven by α stable noise abstract the current paper is devoted to the ergodicity of stochastic magneto hydrodynamic equations driven by stable noise with 3 2 2 by the maximal inequality for the stochastic stable convolution and vorticity transformation the well posedness of the mild solution for stochastic magneto hydrodynamic equation is established due to the discontinuous trajectories the existence and uniqueness of the invariant measure for stochastic magneto hydrodynamic equation are obtained by the strong feller property and the accessibility to zero instead of the irreducibility

vanishing viscosity limit of the navier stokes equations to the euler equations for compressible fluid flow we establish the vanishing viscosity limit of the navier stokes equations to the isentropic euler equations for one dimensional compressible fluid flow for the navier stokes equations there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup norm of solutions with respect to the physical viscosity coefficient may not be directly controllable furthermore convex entropy entropy flux pairs may not produce signed entropy dissipation measures to overcome these difficulties we first develop uniform energy type estimates with respect to the viscosity coefficient for solutions of the navier stokes equations and establish the existence of measure valued solutions of the isentropic euler equations generated by the navier stokes equations based on the uniform energy type estimates and the features of the isentropic euler equations we establish that the entropy dissipation measures of the solutions of the navier stokes equations for weak entropy entropy flux pairs generated by compactly supported c2 test functions are confined in a compact set in h 1 which leads to the existence of measure valued solutions that are confined by the tartar murat commutator relation a careful characterization of the unbounded support of the measure valued solution confined by the commutator relation yields the reduction of the measurevalued solution to a dirac mass which leads to the convergence of solutions of the navier stokes equations to a finite energy entropy solution of the isentropic euler equations with finite energy initial data relative to the different end states at infinity 2010 wiley periodicals inc

on the bias of commonly used measures of association for 2 x 2 tables summary the odds ratio and the relative risk are commonly used as measures of association in a fourfold table the bias of the standard point estimators of these parameters is investigated for small samples simple alternative estimators that possess superior performance in terms of bias and mean squared error are suggested

inviscid limit for damped and driven incompressible navier stokes equations in mathbb r 2 we consider the zero viscosity limit of long time averages of solutions of damped and driven navier stokes equations in mathbb r 2 we prove that the rate of dissipation of enstrophy vanishes stationary statistical solutions of the damped and driven navier stokes equations converge to renormalized stationary statistical solutions of the damped and driven euler equations these solutions obey the enstrophy balance

longtime robustness of pullback random attractors for stochastic magneto hydrodynamics equations abstract we establish backward compactness of a pullback random attractor pra from a backward limit set compact cocycle we prove that backward compactness of a pra is a necessary and sufficient condition such that its time fibers are upper semi continuous at negative infinity and obtain the minimal compact limit set also we obtain the maximal limit set in the lower semi continuity sense these results greatly reinforce the upper semi continuity result at the finite time given by cui et al 2018 in the application part we show existence backward compactness and longtime robustness of a pra for the non autonomous stochastic magneto hydrodynamics equations perturbed by a backward tempered force moreover we prove that the pra does not change on different attracted universes this fact allows us to establish the finite time robustness of the pra if the force is tempered only

on space time means and everywhere defined scattering operators for nonlinear klein gordon equations on demontre l existence d operateurs de diffusion definis partout pour certaines equations de klein gordon non lineaires

a note on point estimation of the hazard ratio in exponential distributions the maximum likelihood estimator mle of the ratio of the hazard rates in two exponential distributions is biased this bias can be important when sample sizes are small or the ratio of these two hazard rates is large when there is either no censoring or type ii censoring we propose using the uniformly minimum variance unbiased estimator umvue we show that using the umvue instead of the mle reduces the mean squared error mse we have found that the umvue always has mses smaller than the mle we have also found that the umvue leads to important reductions in the mse when the sample size used to calculate the hazard rate in the numerator of the hazard ratio is small say less than or equal to 20 regardless of the sample size in the denominator in the presence of type i censoring the proposed estimator and the mle are both biased on the basis of a monte carlo study however we obtain similar reductions in the mse using the umvue as for no censoring or type ii censoring

a comparison of several point estimators of the odds ratio in a single 2 x 2 contingency table the relative performance of the unconditioned maximum likelihood estimators umles conditional mles cmles and jewell type estimators of the odds ratio or and its logarithm were investigated in sets of single 2 x 2 contingency tables the tables were generated by complete enumeration of all possible cell frequencies consistent with a single fixed margin the bias mean squared error mse and average absolute error aae were computed for all estimators using the individual table probabilities as weights the results showed that for the or jewell s estimator usually had smaller bias mse and aae than either of the mles while the differences were often slight for mse and aae for bias it was sometimes substantial for the log or the umle usually had the lowest bias and its mse and aae were only slightly greater than those for the other estimators overall we recommend estimation on the log scale using the umle if or is to be estimated jewell s method had strong merit although it is nonsymmetric with respect to the table orientation in view of this the umle may again be favoured in some situations

space time fractional schrodinger equation with time independent potentials abstract we develop a space time fractional schrodinger equation containing caputo fractional derivative and the quantum riesz fractional operator from a space fractional schrodinger equation in this paper by use of the new equation we study the time evolution behaviors of the space time fractional quantum system in the time independent potential fields and two cases that the order of the time fractional derivative is between zero and one and between one and two are discussed respectively the space time fractional schrodinger equation with time independent potentials is divided into a space equation and a time one a general solution which is composed of oscillatory terms and decay ones is obtained we investigate the time limits of the total probability and the energy levels of particles when time goes to infinity and find that the limit values not only depend on the order of the time derivative but also on the sign positive or negative of the eigenvalues of the space equation we also find that the limit value of the total probability can be greater or less than one which means the space time fractional schrodinger equation describes the quantum system where the probability is not conservative and particles may be extracted from or absorbed by the potentials additionally the non markovian time evolution laws of the space time fractional quantum system are discussed the formula of the time evolution of the mechanical quantities is derived and we prove that there is no conservative quantities in the space time fractional quantum system we also get a mittag leffler type of time evolution operator of wave functions and then establish a heisenberg equation containing fractional operators

inviscid limit for the damped boussinesq equation abstract in this paper we consider the limit behavior of solutions to the cauchy problem for damped boussinesq equation in the regime of small viscosity in r n it is shown that the strong solutions of damped boussinesq equation converge to a strong solution of boussinesq equation in any time interval 0 t the key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped boussinesq equation which is a kind of new view we analyze the dispersion by the techniques of high low frequency decomposition and littlewood paley dyadic decomposition stationary phase estimate and some properties of bessel function

dispersion of small amplitude solutions of the generalized korteweg de vries equation abstract we study the long time behavior of small solutions of the initial value problem for the generalized korteweg de vries equation t u x 3 u x f u 0 gkdv u x 0 g x for the case where f w w s with s 1 4 23 57 3 8625 our results imply that if g l11 g l22 is sufficiently small then sup r 1 t 1 3 u t l in particular the solution tends to zero in the supremum norm the proofs make use of duhamel s formula and dispersion estimates for the linear propagator as well as chain and leibniz rules for fractional derivatives of compositions d f u lp and products d fg lp 0

decay estimates for a class of wave equations abstract in this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by e i t where r r is smooth away from the origin especially the decay estimates for the solutions of the klein gordon equation and the beam equation are simplified and slightly improved

nonlinear scattering theory for a class of wave equations in hs abstract for the semi linear higher order wave equation and the nonlinear higher order schrodinger equation we show that the scattering operators map a band in h s into h s if the nonlinearities have sub critical powers in h s the smoothness of the scattering operators and the uniform boundedness of strong solutions for the defocusing nls equation are also shown provided that the nonlinearities have subcritical growth in h 1 moreover the spatial decaying behavior of solutions in energy space for the defocusing nls equation are obtained

on scattering and everywhere defined scattering operators for nonlinear klein gordon equations asymptotic properties of solutions of the nonlinear klein gordon equation t2u u m2u f u 0 nlkg u 0 tu 0 are investigated which are inherited from the corresponding solutions v of the linear klein gordon equation t2v v m2v 0v 0 tv 0 kg in particular the finiteness of time integrals in lq over r of certain sobolevnorms in space of the solution is proved to be such a hereditary property together with a device by w a strauss and a weak decay result for the kg due to r s strichartz this is used to prove that under suitable restrictions on the nonlinearity the scattering operator for the nlkg is defined on all of l21 l2 for n 3

small sample bias of point estimators of the odds ratio from matched sets the bias of several point estimators of the odds ratio arising from matched pair data is investigated for small samples simple alternatives to the traditional maximum likelihood estimator are suggested on both the original scale and the logarithm scale in each case the suggested estimators possess a superior performance in terms of mean square error generalizations are given for 1 r matched data sets

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

remarks about the inviscid limit of the navier stokes system in this paper we prove two results about the inviscid limit of the navier stokes system the first one concerns the convergence in hs of a sequence of solutions to the navier stokes system when the viscosity goes to zero and the initial data is in hs the second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions we present here a simple proof which also works in the 3d case the 3d case is new

solutions for the fractional landau lifshitz equation abstract this article considers the dynamic equation of a reduced model for thin film micromagnetics deduced by a desimone r v kohn and f otto in a desimone r v kohn f otto a reduced theory for thin film micromagnetics comm pure appl math 55 2002 1 53 to derive the existence of weak solutions under periodical boundary condition the authors first prove the existence of smooth solutions for the approximating equation then prove the convergence of the viscosity solution when the viscosity term vanishes which implies the existence of solutions for the original equation

bias of estimates of the number needed to treat there are several commonly used measures of association between treatment and control event rates in the population pit and pic respectively one such measure the number needed to treat nnt indicates the number of patients on average who must be treated in order to prevent one additional adverse event and is equal to 1 pic pit because the population values pic and pit are unknown the sample proportions rates pc and pt are used as estimates the precision of a sample based estimator is usually exhibited in terms of confidence intervals however the accuracy of the estimator i e its bias is often ignored the purpose of the present study is to examine the degree of bias using exact calculations based on the binomial theorem we determined the bias of an estimate of nnt conditional on pc not equal pt and the bias of an adjusted estimator of the nnt for various sample sizes n 10 20 30 40 50 100 and population parameters 0 01 or pic or 0 9 0 01 or pic pit or 0 8 the magnitude and non monotonic nature of the bias are due to the nnt scale the bias of the adjusted estimator can be approximated for some studies using the tabular results in this analysis

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

the 2d mhd equations with horizontal dissipation and horizontal magnetic diffusion this paper studies the global regularity of classical solutions to the 2d incompressible magnetohydrodynamic mhd equations with horizontal dissipation and horizontal magnetic diffusion it is shown here that the horizontal component of any solution admits a global in time bound in any lebesgue space l2r with 1 r and the bound grows no faster than the order of rlogr as r increases in addition we establish a conditional global regularity in terms of the lt2lx norm of the horizontal component and the global regularity of a slightly regularized version of the aforementioned mhd equations

decay estimates for a dissipative dispersive linear semigroup and application to the viscous boussinesq equation abstract at the core of this article is the new estimate for a class of dissipative dispersive linear semigroup e t i p t arising in the study of the viscous boussinesq equation we combine the decay estimate with introducing a set of time weighted sobolev spaces where the time weights and the regularity of the sobolev spaces are determined by our decay estimate to show the global existence and asymptotic behavior of solutions to the viscous boussinesq equation in r n

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

stochastic generalized magnetohydrodynamics equations with not regular multiplicative noise well posedness and invariant measure abstract in this paper we study a stochastic magnetohydrodynamics mhd system with fractional diffusion and resistivity 0 in r d d 2 3 our main goal is to identify the conditions on under which we can prove the existence of a martingale solution the pathwise uniqueness of solution and the existence of invariant measure when the noises are multiplicative and take values in functional space bigger than the space of square integrable functions roughly speaking we prove that if 1 0 and the driving noises take values in h then the stochastic system has at least a weak martingale solution we also establish the pathwise uniqueness of solution whenever d 2 finally under the latter condition and under the addition of linear damping to the equations we are able to establish the existence of an invariant measure

existence and scattering theory for boussinesq type equations with singular data we study the initial value problem for the generalized boussinesq equation and prove existence of local and global solutions with singular initial data in weak lp spaces our class of initial data for global existence is larger than that of cho and ozawa 2007 7 long time behavior results are obtained and a scattering theory is proved in that framework with more structure we show sobolev h1 and lorentz type l p q regularity properties for the obtained solutions the approach employed is unified for all dimensions n 1

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz

hs global well posedness for semilinear wave equations abstract we consider the cauchy problem for semilinear wave equations in r n with n 3 making use of bourgain s method in conjunction with the endpoint strichartz estimates of keel and tao we establish the hs global well posedness with s