the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

new interaction solutions for the 3 1 dimensional jimbo miwa equation abstract in this paper based on the hirota bilinear form and a rational cosh cos type test function we will study new interaction solutions among the lump waves kinky waves and periodic waves for the 3 1 dimensional jimbo miwa equation we analyze the dynamic behaviors of the constructed solutions in four special cases in detail and the dynamic characteristics of the obtained solutions are illustrated by some interesting figures with the help of maple

new estimates for solutions of lyapunov equations results for estimating the solution of differential and algebraic lyapunov matrix equations are obtained and some of the well known results are generalized

distributed control for identical dynamically coupled systems a decomposition approach we consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems if the state space matrices of these systems satisfy a certain structural property then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant this procedure is basically a multiobjective optimization under linear matrix inequality constraints with system norms as performance indices the explicit expressions for computing these controllers are given for both h infin or h 2 performance and both for static state feedback and dynamic output feedback in discrete time at the end of the paper two application examples illustrate the effectiveness of the approach

the monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity let be a bounded lebesgue measurable domain of r n with a lipschitz boundary the following initial boundary value problem is considered u t lu f u h in q bu o on u 0 where q o t o t and 0 0 l is a uniformly elliptic operator b a boundary operator defined by bu u v bu in which v denotes the outer normal derivative on and f represents a discontinuous non linearity

generalized w symmetry algebra of the conditionally integrable nonlinear evolution equation the formal series symmetry approach is applied to the conditionally integrable nonlinear evolution equation a set of infinitely many symmetries for a 3 1 dimensional model jimbo miwa equation with a conditional equation kadomtsev petviashvilli equation are obtained by an explicitly constructable formula similar to the usual kp equation these symmetries constitute a generalized w symmetry algebra

mean square convergence of consensus algorithms in random wsns distributed consensus algorithms for estimation of parameters or detection of events in wireless sensor networks have attracted considerable attention in recent years a necessary condition to achieve a consensus on the average of the initial values is that the topology of the underlying graph is balanced or symmetric at every time instant however communication impairments can make the topology vary randomly in time and instantaneous link symmetry between pairs of nodes is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented in this paper we evaluate the convergence of the consensus algorithm in the mean square sense in wireless sensor networks with random asymmetric topologies for the case of links with equal probability of connection a closed form expression for the mean square error of the state along with the dynamical range and the optimum value of the link weights that guarantee convergence are derived for the case of links with different probabilities of connection an upper bound for the mean square error of the state is derived this upper bound can be computed for any time instant and can be employed to compute a link weight that reduces the convergence time of the algorithm

monotone solutions of a class of second order nonlinear differential equations on etudie le comportement asymptotique des solutions de l equation p t f x t x t g t g x t on donne des conditions necessaires et suffisantes pour que ces solutions soient bornees

free boundary problems and the set valued mappings we have pointed out that many free boundary problems may be reduced to find the fixed points of certain set valued mappings and have solved the free boundary problem arising in the plasma physics 7 and the free boundary problem of the water cone in an oil reservoir with bottom water 111 as examples it is the purpose of this paper to develop the idea more extensively in this paper some typical free boundary problems such as the obstacle problem the seepage surface problem the stefan problem the elenbaas equation etc are all picked up into our scheme although most of them have been attacked by other methods there are still some new things in our approach especially the multiplicity of the solutions of the elenbaas equation is interesting we prove that there are l 1 and two distinct positive solutions of the equation

the solitonic features of a nonintegrable 3 1 dimensional jimbo miwa equation abstract we investigate a nonintegrable 3 1 dimensional jimbo miwa equation by truncating the painleve expansion and performing computerized symbolic computation we obtain a new auto backlund transformation and a new family of the exact solitonic solutions sample solutions of this family are presented

explicit periodic solitary wave solutions for the 2 1 dimensional boussinesq equation in this paper 2 1 dimensional boussinesq equation is investigated by using homoclinic test method with the aid of maple new explicit periodic solitary wave solutions are obtained moreover mechanical feature of wave is exhibited

the number of positive solutions of a non linear problem with discontinuous non linearity for the non linear problem where f is a discontinuous function at 1 we show that the number of non trivial positive solutions for a given real number 0 is related to the graph of a continuous function g then by studying the function g it is possible in some special cases to give for any 0 the minimal or exact number of non trivial positive solutions

on a 145 32 binary cyclic code we discovered that a 145 32 binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x sup 4 x sup 3 x sup 2 x 1 has a minimum distance of 44

new soliton like solutions to the potential kadomstev petviashvili pkp equation in this paper new soliton like solutions are obtained for 2 1 dimensional potential kadomstev petviashvili pkp equation by using the symbolic computation method developed by gao and tian solitary wave solutions obtained in appl math comput 123 2001 29 are merely a special case in this paper the method can also be extended to other types of nolionear evolution equations in mathematical physics

on the trace bound of a matrix product this paper generalizes the main result given by fang et al ibid vol 39 p 2489 90 1994 to provide tighter bounds on the trace of the product of two real matrices

construction of exact solutions to the jimbo miwa equation through backlund transformation and symbolic computation based on a simple transformation and with the aid of symbolic computation a backlund transformation relating the jimbo miwa equation and a system of linear partial differential equations is obtained which enables us to construct exact solutions of the jimbo miwa equation through the wronskian determinants of independent solutions of the linear system particularly explicit wronskian form n soliton solutions for the jimbo miwa equation are presented moreover the introduced transformation also helps to construct bi soliton like solutions of the jimbo miwa equation due to the arbitrary functions they contain the bi soliton like solutions can represent various waves such as classical cross line bi solitons curved bi solitons and bi soliton like breathers

exact solutions to kdv equations with variable coefficients and or nonuniformities abstract a class of kdv equations with variable coefficients and or nonuniformities is discussed we derive easily the constraint conditions which must apply to this class in order to obtain exact solutions by a direct method we obtain solutions in a number of generic as well as specific cases

lagrangian approach to the study of level sets application to a free boundary problem in climatology we study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation u t delta u in a mathbb h u mu quad rm in quad q it omega times 0 t where omega subset mathbb r n is a ring shaped domain a and are given positive constants mathbb h cdot is the heaviside maximal monotone graph mathbb h s 1 if s 0 mathbb h 0 0 1 mathbb h s 0 if s 0 such equations arise in climatology the so called budyko energy balance model as well as in other contexts such as combustion we show that under certain conditions on the initial data the level sets it gamma mu mathbf x t u mathbf x t mu are n dimensional hypersurfaces in the x t space and show that the dynamics of is governed by a differential equation which generalizes the classical darcy law in filtration theory this differential equation expresses the velocity of advancement of the level surface through spatial derivatives of the solution u our approach is based on the introduction of a local set of lagrangian coordinates the equation is formally considered as the mass balance law in the motion of a fluid and the passage to lagrangian coordinates allows us to watch the trajectory of each of the fluid particles

symbolic computation and observable effect for the 2 1 dimensional symmetric regularized long wave equation from strongly magnetized cold electron plasmas abstract in this paper with the aid of computerized symbolic computation we use the generalized hyperbolic function method to obtain new families of exact analytic solutions for the 2 1 dimensional symmetric regularized long wave equation this equation describes weakly nonlinear ion acoustic and space charge waves in strongly magnetized cold electron plasmas the families we obtain consist of solitary waves and trigonometric functions we outline an observable 2 1 dimensional effect that could be of interest to future experiments on space and laboratory plasma systems the usage of the wu elimination method has also been addressed

a trace bound for a general square matrix product estimates of bounds on the solutions of lyapunov and riccati equations are important for analysis and synthesis of linear systems in this paper we propose new trace bounds for the product of two general matrices the key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds the results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases

existence of the universal attractor for the 3 d viscous primitive equations of large scale moist atmosphere abstract in this paper we consider the initial boundary value problem for the three dimensional viscous primitive equations of large scale moist atmosphere which are used to describe the turbulent behavior of long term weather prediction and climate changes by obtaining the existence and uniqueness of global strong solutions for the problem and studying the long time behavior of strong solutions we prove the existence of the universal attractor for the dynamical system generated by the primitive equations of large scale moist atmosphere

are all the equations of the kadomtsev petviashvili hierarchy integrable the kadomtsev petviashvili kp hierarchy is an infinite set of nonlinear partial differential equations in which the number of independent variables increases indefinitely as one proceeds down the hierarchy since these equations were obtained as part of a group theoretical approach to soliton equations it would appear that the kp hierarchy provides integrable scalar equations with an arbitrary number of independent variables it is shown by investigating a specific equation in 3 1 dimensions that the higher equations in the kp hierarchy are only integrable in a conditional sense the equation under study taken in isolation does not pass certain well known and reliable integrability tests thus applying painleve analysis we find that solutions exist allowing movable critical points furthermore solitary wave solutions are shown to exist that do not behave like solitons in multiple collisions on the other hand if the dependence of a solution on the first 2 1 variables is restricted by the fact that it should also satisfy the kp equation itself then the integrability conditions in the other dimensions are satisfied conditional integrability thus means that linear techniques will provide only those solutions of equations in the hierarchy that simultaneously satisfy lower equations in the same hierarchy

on the singularities of a free boundary through fourier expansion in this paper we are concerned with singular points of solutions to the unstable free boundary problem delta u chi u 0 quad hbox in b 1 the problem arises in applications such as solid combustion composite membranes climatology and fluid dynamics

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

a stability result for differential inclusions in banach spaces on etablit un resultat de stabilite pour les inclusions differentielles definies sur un espace de banach separable

existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics in this paper we consider the initial boundary value problem for the primitive equations of moist atmospheric dynamics that are used to describe the turbulent behavior of long term weather prediction and climate changes by the faedo galerkin method we obtain the existence of global weak solutions to the problem in a large scale atmosphere by studying the long time behavior of solutions we obtain trajectory and global attractors for the primitive equations of moist atmosphere

a note on uniqueness for parabolic problems with discontinuous nonlinearities parabolic problems with discontinuous nonlinearities arise as a natural simplification of various problems of mathematical physics in a model of porous medium combustion e g see norbury and stuart 4 a chemical reaction and the corresponding heat supply is started by reaching a threshold temperature and on the other hand it is expected to end when the concentration drops below a critical level there are of course many other situations where the use of discontinuous nonlinearities may be fully justified and leads to a considerable simplification of the problem fleishman and mahar 3 carl l and the literature quoted therein the resulting equations are easier to handle and the solutions are very often in good agreement with observed behavior of the system see however the remarks in fleishman and mahar 3 consequently the question of uniqueness for this kind of equation seems to be of great importance both from the analytical and numerical point of view as a model problem we consider the equation

symbolic computation and new families of exact soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces in this paper new families of soliton like solutions are obtained for 2 1 dimensional integrable broer kaup equations by using the symbolic computation method developed by gao and tian sample solutions obtained from these methods are presented solitary wave solutions are merely a special case in one family the method can also be extended to other types of nonlinear evolution equations in mathematical physics

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

coordinate independent adaptive attitude tracking control design for spacecraft robust to time varying system uncertainties abstractin this paper we consider the adaptive attitude control of spacecraft with time varying inertial properties we use a coordinate independent approach for the purpose of designing the control and estimation laws in terms of the rotation matrices representing the spacecraft body frame and reference tracking signals this method helps to overcome the difficulties regarding the attitude representation on so 3 such as ambiguities associated with quaternion representation and inherent singularities inside euler parameters we model the time variations in inertial parameters in two different ways and design adaptive control schemes for each case as the first uncertain dynamic model we consider a setting of spacecraft with multiple moving appendages and based on this model design an adaptive control scheme with three different versions where frobenious norm is used in measuring the deviation of the estimated inertia tensors from their actual values the proposed adaptive control scheme is later ex

on the origin of a trace inequality numerous authors are apparently unaware that bounds on the trace of a matrix product presented in 1995 were originally published in 1990

second order elliptic equations with mixed boundary conditions we consider the mixed boundary value problem au f in b0u g0 in b1u g1in where is a bounded open subset of rn whose boundary is divided into disjoint open subsets and by an n 2 dimensional manifold in we assume a is a properly elliptic second order partial differential operator on and bj for j 0 1 is a normal jth order boundary operator satisfying the complementing condition with respect to a on the coefficients of the operators and and are all assumed arbitrarily smooth as announced in bull amer math soc 83 1977 391 393 we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in sobolev spaces in fact we construct an open subset t of the reals such that if ds u hs au 0 then for s 12 mod 1 b0 b1 ds hs 12 hs 32 is a fredholm operator if and only if s t moreover t xew tx where the sets tx are determined algebraically by the coefficients of the operators at x if n 2 tx is the set of all reals not congruent modulo 1 to some exceptional value if n 3 tx is either an open interval of length 1 or is empty and finally if n 4 tx is an open interval of length 1

the equations of the atmosphere with humidity and saturation uniqueness and physical bounds abstract in continuation of an earlier work coti zelati and temam 2012 8 devoted to the mathematical formulation and existence of solutions for the system of moist atmosphere with saturation we address here the question of the uniqueness of solutions which is essential for giving a physical justification for the analysis of the model in coti zelati and temam 2012 8 we also derive some physical bounds on the solution as well as additional results of regularity of the solutions

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

tight probabilistic sinr constrained beamforming under channel uncertainties in downlink multi user beamforming a single basestation is serving a number of users simultaneously however energy intended for one user may leak to other unintended users causing interference with signal to interference plus noise ratio sinr being one of the most crucial quality metrics to users beamforming design with sinr guarantee has always been an important research topic however when the channel state information is not accurate the sinr requirements become probabilistic constraints which unfortunately are not tractable analytically for general uncertainty distribution therefore existing probabilistic beamforming methods focus on the relatively simple gaussian and uniform channel uncertainties and mainly rely on probability inequality based approximated solutions resulting in conservative sinr outage realizations in this paper based on the local structure of the feasible set in the probabilistic beamforming problem a systematic method is proposed to realize tight sinr outage control for a large class of channel uncertainty distributions with channel estimation and quantization errors as examples simulation results show that the sinr outage can be realized tightly which results in reduced transmit power compared to the existing inequality based probabilistic beamformers

an elliptic boundary value problem with a discontinuous nonlinearity ii soit un domaine borne dans r 2 on etudie le probleme aux valeurs limites pour k h k dans r 2 0 sur h est la fonction echelon de heaviside

trace bounds on the solution of the algebraic matrix riccati and lyapunov equation lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix riccati and lyapunov equation are derived the upper trace bound obtained in this note in many cases results in a tighter bound as compared to the upper bound for the maximal eigenvalue proposed in 1 and 2

asymptotic properties of penalized spline estimators we study the class of penalized spline estimators which enjoy similarities to both regression splines without penalty and with fewer knots than data points and smoothing splines with knots equal to the data points and a penalty controlling the roughness of the fit depending on the number of knots sample size and penalty we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines with a clear breakpoint distinguishing the cases we prove that using fewer knots results in better asymptotic rates than when using a large number of knots we obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter

incremental grassmannian feedback schemes for multi user mimo systems the communication of side information forms a key component of several effective strategies for transmitter adaptation to slowly fading channels when the relevant side information is a subspace the feedback scheme can be viewed as a lossy source compression scheme on the grassmannian manifold memoryless vector quantization on each fading block is a viable compression scheme but it neglects any temporal correlation between the blocks in this paper we propose an incremental approach to grassmannian quantization that takes advantage of temporal correlation the approach leverages existing codebooks for memoryless quantization schemes and employs a quantized form of geodesic interpolation two schemes that implement the principles of the proposed approach are presented in the first scheme the choice of the step size in the incremental update is adapted to a first order gaussmarkov model for the channel which enables the use of higher resolution codebooks in the second scheme a single bit is allocated to the step size which enables adaptation of the step size to the channel realization rather than the channel statistics this provides substantial robustness against mismatches in the model for the temporal correlation a distinguishing feature of the proposed approach is that the direction of the geodesic interpolation is specified implicitly using a point in a conventional codebook as a result the approach has an inherent ability to recover autonomously from errors in the feedback path simulation results demonstrate that these features result in improved performance over some existing schemes in a variety of channel environments

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

data integration with high dimensionality we consider situations where the data consist of a number of responses for each individual which may include a mix of discrete and continuous variables the data also include a class of predictors where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured the goal is to select which predictors affect any of the responses where the number of such informative predictors tends to infinity as the sample size increases there are marginal likelihoods for each experiment we specify a pseudolikelihood combining the marginal likelihoods and propose a pseudolikelihood information criterion under regularity conditions we establish selection consistency for this criterion with unbounded true model size the proposed method includes a bayesian information criterion with appropriate penalty term as a special case simulations indicate that data integration can dramatically improve upon using only one data source

an efficient algorithm to construct multi soliton rational solutions of the 2 1 dimensional kdv equation with variable coefficients abstract herein we present an efficient algorithm to construct multi soliton rational solutions of the 2 1 dimensional korteweg de vries equation with time dependent coefficients we employ the generalized unified method which presents a wider applicability for handling many other nonlinear evolution equations in different branches of science to find these solutions the dynamical behavior of the traveling wave solutions and their structures are discussed by different choices for the arbitrary functions in the obtained solutions

nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators periodic problems where t is a given positive number a is the subdifferential of a timedependent lower semicontinuous convex function from h into 0 a with qf f co and where b t is a possibly nonmonotone multivalued nonlinear operator from d b t c h into h such that d c d b t m for all t e 0 t the case when b t is identically zero has been investigated by many authors see e g bknilan and b is 2 nagai 13 and yamada 20 as for the case when b t is not identically zero nor monotone however it seems that very little study has been devoted to this kind of problem on the other hand the cauchy problem for 1 1 has been studied by several authors i e attouch and damlamian 11 biroli 3 koi and watanabe 9 and the author 14 151 the main objective of the present paper is to pursue and develop the method employed in 151 for the periodic problem p p this paper is composed of five sections section 2 contains some preliminaries in section 3 we shall formulate main results in two distinctive types of theorems roughly speaking according to whether the external force f t can be taken arbitrarily large or not in section 4 we shall prove them by much the same method based on a schauder tychonoff type fixed point theorem as in 151 in section 5 it will be exemplified that our results give a 248 0022 0396184 3 00

lagrangian approach to the study of level sets ii a quasilinear equation in climatology we study the dynamics and regularity of the level sets in solutions of the semilinear parabolic equation u t delta p u f is an element of ah u mu in q omega x 0 t p is an element of 1 infinity where omega subset of r n is a ring shaped domain delta p u is the p laplace operator a and mu are given positive constants and h is the heaviside maximal monotone graph h s 1 if s 0 h 0 0 1 h s 0 if s 0 the mathematical models of this type arise in climatology the case p 3 was proposed and justified by p stone in 1972 we establish the conditions on the initial data which guarantee that the level sets gamma mu t x u x t mu are hypersurfaces study the regularity of gamma mu t and derive the differential equation that governs the dynamics of gamma mu t the analysis is based on the introduction of a system of lagrangian coordinates that transforms the moving surface gamma mu t into a stationary one

interfaces in multidimensional diffusion equations with absorption terms we study the properties of interfaces in solutions of the cauchy problem for the nonlinear degenerate parabolic equation ut um aup in rn 0 t n 1 2 3 with the parameters m 1 p 0 a 0 satisfying the condition m p 2 we show that the velocity of the interface t supp u x t is given by the formula v m m 1 um 1 t where is the solution of the degenerate elliptic equation div u aup 0 0 on t the first term expresses the classical darcy law while the second one models the presence of an external force that makes the interface to move in the inward direction we give explicit formulas which represent the interface t as a bijection from 0 it is proved that the solution u and its interface t are analytic functions of time t and that they preserve the initial regularity in the spatial variables we also show that the regularity of the interface velocity v with respect to the spatial variables is better than it was at the initial instant the analysis is based on a special coordinate transformation a local version of lagrangian coordinates that renders the free boundary stationary

tight bounds for the trace of a matrix product we propose a family of new upper and lower bounds for the trace of the matrix product ab when a or b is symmetric those bounds depend on a scalar parameter and both converge monotonically to tr ab when this parameter vanishes thus providing arbitrary close approximations even large values of the parameter yield very good bounds

eigenvalue inequalities for matrix product we present a family of eigenvalue inequalities for the product of a hermitian matrix and a positive semidefinite matrix our theorem contains or extends some existing results on trace and eigenvalues

a trace inequality for matrix product we extend to arbitrary hermitian matrices a well known trace inequality for positive semidefinite matrices when using this result for the product of two matrices when only one is hermitian we improve a recent trace inequality given by fanf et al 1994

generalized solutions of parabolic initial value problems with discontinuous nonlinearities we proved recently that parabolic initial value problems with discontinuous nonlinearities have no unique weak solution in general but have a unique generalized solution in the sense of colombeau in this paper we study the relationship between generalized solutions and weak solutions

on an elliptic operator with discontinuous nonlinearity abstract a family of elliptic operators with discontinuous nonlinearity affected by the presence of a positive parameter is considered a critical value c of and the zero set ec of the corresponding critical solution u c play a special role in the treatment of these operators sharp estimates for c as a functional of boundary functions are given and the structure of ec is investigated an asymptotic formula for the solution u and its free boundary is presented as

global well posedness of the three dimensional viscous primitive equations of large scale ocean and atmosphere dynamics in this paper we prove the global existence and uniqueness regularity of strong solutions to the three dimensional viscous primitive equations which model large scale ocean and atmosphere dynamics 1 introduction large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the navier stokes equations with rotation coupled to thermodynamics and salinity diffusion transport equations which account for the buoyancy forces and stratification effects under the boussinesq approximation moreover and due to the shallowness of the oceans and the atmosphere i e the depth of the fluid layer is very small in comparison to the radius of the earth the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one which in turn leads to modeling the vertical motion by the hydrostatic balance as a result

the novel solitary wave structures and interactions in the 2 1 dimensional kortweg de vries system abstract using symbolic and algebra computation the extended tanh function method etm based on mapping method is further extended the new variable separation solutions of the 2 1 dimensional korteweg de vries kdv system are derived from the periodic wave solution and by selecting appropriate functions the evolutional behaviors of dromions and compactons on the background of jacobian elliptic wave and their interaction behaviors are investigated

constructing families of soliton like solutions to a 2 1 dimensional breaking soliton equation using symbolic computation abstract the application of computer algebra to science has a bright future in this paper using computerized symbolic computation new families of soliton like solutions are obtained for 2 1 dimensional breaking soliton equations using an ansatz these solutions contain traveling wave solutions that are of important significance in explaining some physical phenomena the method can also be applied to other types of nonlinear evolution equations in mathematical physics

an inequality for the trace of matrix product new bounds for the trace of the product of an arbitrary real matrix a and a nonnegative definite symmetric matrix b are derived in each case where the symmetric part of a is an indefinite matrix these bounds are substantial improvements over the bounds known in the literature

comments on a matrix inequality associated with bounds on solutions of algebraic riccati and lyapunov equation by j m saniuk and i b rhodes improved inequalities over the ones reported by j m saniuk and i b rhodes 1987 in the above mentioned paper ibid vol 32 p 739 40 1987 are obtained following the reasoning developed thereby relations are presented that demonstrate the improvement asserted by the commenter

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

a new trace bound for a general square matrix product using the correlated properties between the diagonal element and the singular value of the matrix we propose new trace bounds for the product of two arbitrary real square matrices and improve the recent results

new solitonic solutions to a 3 1 dimensional jimbo miwa equation abstract performing computerized symbolic computation we are able to present new analytic solutions of a 3 1 dimensional jimbo miwa equation which does not pass any of the conventional integrability tests applying the generalized tanh method we have found such exact solutions as both the nontraveling solitonic and traveling solitary waves

formulation of the equations of the humid atmosphere in the context of variational inequalities abstract the equations of the humid atmosphere with saturation are considered in the case where the saturation concentration q s is not assumed to be constant and obeys the laws of thermodynamics 22 23 32 this article starts from the observation that these equations are not correct in the extreme cases where the atmosphere is totally dry or totally wet that is when the concentration q of water vapor is equal to 0 or 1 a new formulation of the equations is proposed to remedy this difficulty in the context of variational inequalities results of existence maximum principle and regularity of solutions are derived for these new variational inequalities

inequalities for the trace of matrix product to obtain estimates of solutions of lyapunov and riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other baksalary and puntanen claimed an inequality for the trace of matrix product ibid vol 37 no 2 p 239 40 1992 that they had obtained a better estimate for the trace of the product of two matrices the purpose of this note is to point out that their main result is incorrect and a counterexample is presented

diversity of interaction solutions to the 2 1 dimensional ito equation abstract we aim to show the diversity of interaction solutions to the 2 1 dimensional ito equation based on its hirota bilinear form the proof is given through maple symbolic computations an interesting characteristic in the resulting interaction solutions is the involvement of an arbitrary function special cases lead to lump solutions lump soliton solutions and lump kink solutions two illustrative examples of the resulting solutions are displayed by three dimensional plots and contour plots

the decomposition method for solving 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation we study the solitary wave solutions of the 2 1 dimensional boussinesq equation u t t u x x u y y u 2 x x u x x x x 0 and 3 1 dimensional kp equation u x t 6u x 2 6uu x x u x x x x u y y u z z 0 in this paper by considering the decomposition scheme we first obtain the exact solitary wave solutions of the 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation for the initial conditions without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation