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

discrete breathers in a two dimensional fermi pasta ulam lattice using asymptotic methods we investigate whether discrete breathers are supported by a two dimensional fermi pasta ulam lattice a scalar one component two dimensional fermi pasta ulam lattice is shown to model the charge stored within an electrical transmission lattice a third order multiple scale analysis in the semi discrete limit fails since at this order the lattice equations reduce to the 2 1 dimensional cubic nonlinear schrodinger nls equation which does not support stable soliton solutions for the breather envelope we therefore extend the analysis to higher order and find a generalised 2 1 dimensional nls equation which incorporates higher order dispersive and nonlinear terms as perturbations we find an ellipticity criterion for the wave numbers of the carrier wave numerical simulations suggest that both stationary and moving breathers are supported by the system calculations of the energy show the expected threshold behaviour whereby the energy of breathers does em not go to zero with the amplitude we find that the energy threshold is maximised by stationary breathers and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

exponential energy decay of solutions for an integro differential equation with strong damping abstract the initial boundary value problem for an integro differential equation with strong damping in 0 u t t m u 2 2 u 0 t g t s u s d s u t f u is considered where is a bounded domain with a smooth boundary the asymptotic behavior of solutions is discussed under some conditions on g decay estimates of the energy function of solutions are also given via an integral inequality introduced by komornik 1994 11

existence and nonexistence of global solutions of some system of semilinear wave equations abstract an initial boundary value problem for systems of semilinear wave equations in a bounded domain is considered we prove the global existence uniqueness and blow up of solutions by energy methods and give some estimates for the lifespan of solutions

lifespan of solutions to semilinear damping wave equations in de sitter spacetime abstract this paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de sitter spacetime the first problem comes from the latter problem of conjecture of strauss in de sitter spacetime and the second problem arises from the latter problem of conjecture of glassey in de sitter spacetime we give blowup and lifespan of solutions on those two problems comparing with non damping case established in yan 2018 one can see that the damping term with a positive bounded time dependent coefficient does not effect blowup of solutions meanwhile we establish a new ode blowup result concerning damping term

an example of blow up for the complex kdv equation and existence beyond the blow up the kdv equation with smooth complex initial data that blows up in a finite amount of time is studied first examples are given using the elliptic solutions of airault mckean and moser second the kdv flow of spectral coordinates is described showing that blow up occurs when eigenvalues run to infinity in finite time but eigenvalue collisions are harmless and do not cause a singularity eigenvalue collisions and blow up are studied numerically finally the solutions are continued through the singularity by continuing the coordinate flows on the appropriate riemann surface

lifespan of semilinear wave equation with scale invariant dissipation and mass and sub strauss power nonlinearity abstract in this paper we study the blow up of solutions for semilinear wave equations with scale invariant dissipation and mass in the case in which the model is somehow wave like a strauss type critical exponent is determined as the upper bound for the exponent in the nonlinearity in the main theorems two blow up results are obtained for the subcritical case and for the critical case respectively in both cases an upper bound lifespan estimate is given

discrete breathers in honeycomb fermi pasta ulam lattices we consider the two dimensional fermi pasta ulam lattice with hexagonal honeycomb symmetry which is a hamiltonian system describing the evolution of a scalar valued quantity subject to nearest neighbour interactions using multiple scale analysis we reduce the governing lattice equations to a nonlinear schrodinger nls equation coupled to a second equation for an accompanying slow mode two cases in which the latter equation can be solved and so the system decoupled are considered in more detail firstly in the case of a symmetric potential we derive the form of moving breathers we find an ellipticity criterion for the wavenumbers of the carrier wave together with asymptotic estimates for the breather energy the minimum energy threshold depends on the wavenumber of the breather we find that this threshold is locally maximised by stationary breathers secondly for an asymmetric potential we find stationary breathers which even with a quadratic nonlinearity generate no second harmonic component in the breather plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure finally we compare the properties of stationary breathers in the square triangular and honeycomb lattices

entropy based tests of uniformity abstract the power properties of an entropy based test are investigated when used for testing uniformity on 0 1 percentage points and power against seven alternatives are reported compared with other tests of uniformity the entropy based test possesses good power properties for many alternatives some asymptotic null and alternative distributions are derived for sample sizes up to 100 the table of percentage points provides a practical guide for using this test a theory of entropy based tests of distributional hypotheses other than uniformity is outlined

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

nonlinear constructive interference in electrical lattices we analyze the constructive interference of input signals in nonlinear discrete two dimensional media the media consist of inductor capacitor lattices with saturating voltage dependent capacitors we find that nonlinearity significantly boosts the ability of such media to generate large amplitude output signals from small amplitude inputs to understand this boosting we develop a general perturbative method suitable for finding the steady state solution of a damped n ifmmode times else texttimes fi n nonlinear lattice that is driven at a single frequency we verify our theory using extensive numerical simulations

steady state perturbative theory for nonlinear circuits we study the steady state behavior of a damped driven nonlinear lrc oscillator where the nonlinearity arises due to voltage dependent capacitance the driving or input signal is assumed to be a pure tone using an iterative perturbative solution technique combined with an energy conservation argument we show that the oscillator transfers energy from the fundamental to higher harmonics we determine a series expansion of the two norm of the steady state output signal and show that in a large region of parameter space the two norm depends superlinearly on the input amplitude we also use the two norm calculation to devise a performance goal that the infinity norm of the steady state output signal should satisfy in order for the nonlinear system to have a genuine boost over the corresponding linear system taken together these results are a step toward the automatic design of nonlinear systems that have an optimal boost over corresponding linear systems

global existence and blow up of solutions for higher order viscoelastic wave equation with a nonlinear source term abstract the initial boundary value problem for some nonlinear higher order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied the existence of global weak solutions for this problem is established by using the galerkin method meanwhile under suitable conditions on relaxation function g and the positive initial energy as well as non positive initial energy it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given

nonhomogeneous boundary value problems the diffusion equation is solved under stochastic nonhomogeneity using eigen function expansion and the georges method the statistical moments of the solution process are computed through the two previously mentioned techniques and proved to be the same a general solution is obtained under general initial and boundary conditions a random source composed of deterministic and stochastic parts is taken into consideration the stochastic part is then restricted to a generalized gaussian field mainly modulated white noise a special case is considered under constant noise level and constant average noise a numerical case study concerning pollution in a stream is solved and a parametric study is achieved through various figures

information indices unification and applications the unified framework of information theoretic statistics was established by kullback 1959 since then numerous information indices have been developed in various contexts this paper represents many of these indices in a unified context the unification thread is the discrimination information function information indices are all logarithmic measures of discrepancy between two probability distributions first we present a summary of informational aspects of the basic information functions a unification of various information theoretic modeling approaches and some explication in terms of traditional measures we then tabulate a unified representation of assortments of information indices developed in the literature for maximum entropy modeling covariate information and influence diagnostics the subjects of these indices include parametric model fitting nonparametric entropy estimation categorical data analysis the linear and exponential family regression and time series the coverage however is not exhaustive the tabulation includes sampling theory and bayesian indices but the focus is on interpretation as descriptive measures and inferential properties are noted tangentially finally applications of some information indices are illustrated through modeling duration data for sprint s churned customer and choice of long distance provider

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

asymptotic analysis of combined breather kink modes in a fermi pasta ulam chain we find approximations to travelling breather solutions of the one dimensional fermi pasta ulam fpu lattice both bright breather and dark breather solutions are found we find that the existence of localised bright solutions depends upon the coefficients of cubic and quartic terms of the potential energy generalising an earlier inequality derived by james cr acad sci paris 332 581 2001 we use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear schr o dinger equation at leading order and hence construct an asymptotic form for the breather we show that in the absence of a cubic potential energy term the lattice supports combined breathing kink waveforms the amplitude of breathing kinks can be arbitrarily small as opposed to traditional monotone kinks which have a nonzero minimum amplitude in such systems we also present numerical simulations of the lattice verifying the shape and velocity of the travelling waveforms and confirming the long lived nature of all such modes

discrete breathers in a two dimensional spring mass lattice we consider a two dimensional spring mass lattice with square symmetry in which each particle experiences a nonlinear onsite potential and nonlinear nearest neighbour interactions at equilibrium the particles are equally spaced in both the horizontal and vertical directions and all springs are unextended motivated by the work of marin et al 1998 phys lett a 248 225 9 2001 phys lett a 281 21 5 we seek a solution in which most of the breather s energy is focused along three chains we construct an asymptotic approximation to the breather using the method of multiple scales to describe the coherent oscillations in the three main chains that constitute the discrete breather we reduce the equation of motion to a nonlinear schrodinger equation for the leading order term and find a family of solutions which encompasses both stationary and moving bright soliton solutions we use numerical simulations of the lattice to verify the shape and velocity of breathers and find that while stationary breathers are found to persist for long times moving breathers decay by radiating energy in the direction perpendicular to their motion

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

global nonexistence results for a class of hyperbolic systems abstract our concern in this paper is to prove blow up results to the non autonomous nonlinear system of wave equations u t t u a t x v p v t t v b t x u q t 0 x r n in any space dimension we show that a curve f p q 0 depending on the space dimension on the exponents p q and on the behavior of the functions a t x and b t x exists such that all nontrivial solutions to the above system blow up in a finite time whenever f p q 0 our method of proof uses some estimates developed by galaktionov and pohozaev in 11 for a single non autonomous wave equation enabling us to obtain a system of ordinary differential inequalities from which the desired result is derived our result generalizes some important results such as the ones in del santo et al 1996 12 and galaktionov and pohozaev 2003 11 the advantage here is that our result applies to a wide variety of problems

finite time blow up to critical semilinear wave equation outside the ball in 3 d abstract in this paper we study the initial boundary value problem of critical semilinear wave equation with small initial data in 3 d blow up result will be established no matter how small the data are we find a radial and positive solution of the corresponding linear problem then our blow up result follows from the idea of zhou and han 2014 what is more we get the upper bound of the lifespan estimate

on the recovery of joint distributions from limited information the paper considers the role of entropy and other information theoretic concepts in the description and formation of joint distributions for m random variables the discussion includes a review of methods for constructing discrete and continuous joint distributions from the component marginal distributions we then propose a minimum cross entropy approach that recovers continuous joint distributions from the joint and marginal moments and the marginal densities the large sample properties of the associated estimator are outlined and a simple demonstration problem that highlights the advantages and drawbacks of the proposed method is presented

explosive solutions of stochastic nonlinear beam equations with damping abstract this study considers a class of damped stochastic nonlinear beam equations driven by multiplicative noise by an appropriate energy inequality we provide sufficient conditions such that the local solutions of the stochastic equations blow up with a positive probability or are explosive in an l 2 sense we also derive estimates of the upper bound of the blow up time

testing exponentiality based on kullback leibler information in this paper a test of fit for exponentiality based on the estimated kullback leibler information is proposed the procedure is applicable when the exponential parameter is or is not specified under the null hypothesis the test uses the vasicek entropy estimate so to compute it a window size m must first be fixed a procedure for choosing m for various sample sizes is proposed and corresponding critical values are computed by monte carlo simulations

the lifespan for 3d quasilinear wave equations with nonlinear damping terms abstract in this paper we study the initial boundary value problem for a system of nonlinear wave equations involving nonlinear damping terms in a bounded domain the nonexistence of global solutions is discussed under some conditions on the given parameters estimates on the lifespan of solutions are also given our results extend and generalize the recent results in k agre m a rammaha system of nonlinear wave equations with damping and source terms differential integral equations 19 2006 1235 1270 especially the blow up of weak solutions in the case of non negative energy

localized excitations in two dimensional hamiltonian lattices we analyze the origin and features of localized excitations in a discrete two dimensional hamiltonian lattice the lattice obeys discrete translational symmetry and the localized excitations exist because of the presence of nonlinearities we connect the presence of these excitations with the existence of local integrability of the original n degree of freedom system on the basis of this explanation we make several predictions about the existence and stability of these excitations this work is an extension of previously published results on vibrational localization in one dimensional nonlinear hamiltonian lattices phys rev e 49 1994 836 thus we confirm earlier suggestions about the generic property of hamiltonian lattices to exhibit localized excitations independent on the dimensionality of the lattice

global solutions and finite time blow up for some system of nonlinear wave equations abstract an initial boundary value problem for systems of semi linear wave equations in a bounded domain is considered the global existence uniqueness and blow up of solutions by energy methods and give some estimates for the lifespan of solutions are proved

blow up of solutions for some non linear wave equations of kirchhoff type with some dissipation abstract the initial boundary value problem for non linear wave equations of kirchhoff type with dissipation in a bounded domain is considered we prove the blow up of solutions for the strong dissipative term u t and the linear dissipative term u t by the energy method and give some estimates for the life span of solutions we also show the nonexistence of global solutions with positive initial energy for non linear dissipative term by vitillaro s argument

information distinguishability with application to analysis of failure data abstract in maximum entropy me modeling the information discrepancy between two distributions is measured in terms of their entropy difference in discrimination information statistics the information discrepancy between two distributions is measured in terms of the kullback leibler function i e relative entropy or cross entropy this article presents an equivalence between kullback leibler functions and entropy differences involving an me distribution based on this equivalence the concept of information discrimination id distinguishability is introduced as a unifying framework for the two methods of measuring information discrepancy between distributions applications of id distinguishability as diagnostics for examining robustness of parametric procedures and sensitivity of nonparametric statistics across parametric families of distributions is proposed the equivalence result facilitates estimation of kullback leibler functions in terms of entropy estimates application of the id distinguish

a characterisation of the proportional hazards model through a measure of discrimination between two residual life distributions summary a time dependent kullback leibler discrimination function is defined by comparing residual life distributions at each age t it is proved that the resulting kullback leibler discrimination function is constant in t if and only if the two survival distributions satisfy a proportional hazards model let x and y be two nonnegative random variables representing times to failure of two systems let f x pr x x and g y pr y y be the failure distributions of x and y with survival functions f x 1 f x and g y 1 g y respectively where f o g o 1 we assume that f and g are differentiable with densities f t f t and g t g t respectively and hazard rate functions af x f x f x and ag x g x g x the kullback leibler discrimination information i x y or i f g is defined as

general decay and blow up of solutions for a system of viscoelastic wave equations with nonlinear boundary source terms abstract in this work an initial boundary value problem for a system of viscoelastic wave equations with nonlinear boundary source term of the form u i t t u i u i t t 0 t g i t s u i s d s u i t 0 in 0 t u i x 0 i x u i t x 0 i x in u i x t 0 on 0 0 t u i t t u i 0 t g i t s u i s d s u i t f i u 0 on 1 0 t where i 1 l l 2 is considered in a bounded domain in r n n 1 by the faedo galerkin approximation method we obtain existence and uniqueness of weak solutions under appropriate assumptions on initial data and the relaxation functions we establish general decay and blow up results associated to solution energy estimates for lifespan of solutions are also given

discrete breathers in a two dimensional hexagonal fermi pasta ulam lattice we consider a two dimensional fermi pasta ulam fpu lattice with hexagonal symmetry using asymptotic methods based on small amplitude ansatz at third order we obtain a eduction to a cubic nonlinear schr o dinger equation nls for the breather envelope however this does not support stable soliton solutions so we pursue a higher order analysis yielding a generalised nls which includes known stabilising terms we present numerical results which suggest that long lived stationary and moving breathers are supported by the lattice we find breather solutions which move in an arbitrary direction an ellipticity criterion for the wavenumbers of the carrier wave symptotic estimates for the breather energy and a minimum threshold energy below which breathers cannot be found this energy threshold is maximised for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed several of the results obtained are similar to those obtained for the square fpu lattice butt wattis em j phys a bf 39 4955 2006 though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics and the isotropy of the generalised nls equation

capturing the intangible concept of information abstract the purpose of this article is to discuss the intricacies of quantifying information in some statistical problems the aim is to develop a general appreciation for the meanings of information functions rather than their mathematical use this theme integrates fundamental aspects of the contributions of kullback lindley and jaynes and bridges chaos to probability modeling a synopsis of information theoretic statistics is presented in the form of a pyramid with shannon at the vertex and a triangular base that signifies three distinct variants of quantifying information discrimination information kullback mutual information lindley and maximum entropy information jaynes examples of capturing information by the maximum entropy me method are discussed it is shown that the me approach produces a general class of logit models capable of capturing various forms of sample and nonsample information diagnostics for quantifying information captured by the me logit models are given and decom

global and blow up solutions for a system of nonlinear hyperbolic equations with dissipative terms abstract in this paper we study a nonlinear hyperbolic system with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of weak solution secondly via some inequalities applying the potential method and the concave method we discuss the asymptotic and blow up behavior of weak solution with different conditions

discrete breathers on symmetry determined invariant manifolds for scalar models on the plane square lattice a group theoretical approach for studying localized periodic and quasiperiodic vibrations in two and three dimensional lattice dynamical models is developed this approach is demonstrated for the scalar models on the plane square lattice the symmetry determined invariant manifolds admitting existence of localized vibrations are found and some types of discrete breathers are constructed on these manifolds a general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed this method allows one to decompose the corresponding system of linear differential equations with time dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system

global existence and blow up of solutions for a kirchhoff type plate equation with damping the initial boundary value problem for a kirchhoff type plate equation in a bounded domain is considered we show the blow up of solutions and the lifespan estimates for three different ranges of initial energy global existence of solutions is proved by the potential well theory and decay estimates of the energy function are established by using nakao s inequality

global existence uniform decay and blow up of solutions for a system of petrovsky equations abstract in this paper we investigate global existence uniform decay and blow up of solutions for the following petrovsky equations u t t 2 u u t p 1 u t f u u v x t 0 t v t t 2 v v t q 1 v t f v u v x t 0 t where is a bounded domain of r n n 1 2 3 having a smooth boundary and f is a c 1 function given by f u v u v r 1 2 u v r 1 2 r 3 1 0 for the case of p q 1 we obtain the blow up of solutions and the lifespan estimates for four different ranges of initial energy for the case of 1 p q r we show the blow up of solutions when the initial energy is negative or nonnegative at less than the mountain pass level value global existence of solutions is proved by the potential well theory and decay estimates of the energy function are established by using nakao s inequality