strong primeness of hermitian jordan systems this paper establishes the strong primeness of all jordan systemsjof hermitian type trapped between ample hermitian elements of a prime associative systemrand its martindale system of symmetric quotientsq r h0 r j h q r this completes the converse of zelmanov s classification of strongly prime jordan systems providing if as well as only if classifications of strongly prime and primitive jordan systems

the initial boundary value problems for a class of nonlinear wave equations with damping term abstract in this paper we study the existence and uniqueness of the global generalized solution and the global classical solution the blowup of the solution and the energy decay of the solutions of the initial boundary value problems for a class of nonlinear wave equations

long time behavior of a class of thermoelastic plates with nonlinear strain abstract in recent years a class of vibrating plates with nonlinear strain of p laplacian type was studied by several authors the present paper contains a first thermoelastic model of that class of problems including both fourier and non fourier heat laws our main result establishes the existence of global and exponential attractors for the strongly damped problem through a stabilizability inequality in addition for the weakly damped problem we establish the exponential stability of its galerkin semiflows

using monte carlo method for ranking efficient dmus for ranking efficient dmus some methods have been developed these methods are not able to rank non extreme efficient dmus in this paper using monte carlo method a method has been developed which is able to rank all extreme and non extreme efficient dmus

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

on global solution of an initial boundary value problem for a class of damped nonlinear equations abstract in this paper we consider the following problem u t t u t 2 u u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t u x t 0 t 0 where r n is a bounded domain with smooth boundary under some assumptions of the initial data u 0 x u 1 x and the nonlinear function f u the existence of global weak solutions and global strong solutions are obtained by means of the potential well method

a discrete model for an ill posed nonlinear parabolic pde we study a finite difference discretization of an ill posed nonlinear parabolic partial differential equation the pde is the one dimensional version of a simplified two dimensional model for the formation of shear bands via anti plane shear of a granular medium for the discretized initial value problem we derive analytically and observed numerically a two stage evolution leading to a steady state i an initial growth of grid scale instabilities and ii coarsening dynamics elaborating the second phase at any fixed time the solution has a piecewise linear profile with a finite number of shear bands in this coarsening phase one shear band after another collapses until a steady state with just one jump discontinuity is achieved the amplitude of this steady state shear band is derived analytically but due to the ill posedness of the underlying problem its position exhibits sensitive dependence analyzing data from the simulations we observe that the number of shear bands at time t decays like t 1 3 from this scaling law we show that the time scale of the coarsening phase in the evolution of this model for granular media critically depends on the discreteness of the model our analysis also has implications to related ill posed nonlinear pdes for the one dimensional perona malik equation in image processing and to models for clustering instabilities in granular materials 2001 elsevier science b v all rights reserved

using monte carlo method for ranking interval data abstract some methods have been presented for ranking efficient decision making units dmus in data envelopment analysis dea this paper addresses the ranking of interval data by using monte carlo method this method is based on a paper g r jahanshahloo f hosseinzadeh lotfi h zhiani rezai f rezai balf using monte carlo method for ranking efficient dmus applied mathematics and computation 162 2005 371 379 the worthwhile this method is its ability in ranking of extreme and non extreme efficient dmus

critical and sup critical initial energy finite time blowup phenomena for the fourth order wave equations with nonlinear strain term abstract this paper is devoted to the blowup phenomena for a class of fourth order wave equation with nonlinear strain term first for the model equation with strain structure we prove the finite time blowup of solution for the critical initial energy i e e 0 d then the finite time blowup and the upper bound of the blowup time are established for the sup critical initial energy i e e 0 0

a weakly nonlinear analysis of elasto plastic microstructure models at certain critical values of the hardening modulus the governing equations of elasto plastic flow may lose their hyperbolicity and exhibit two modes of ill posedness shear band and flutter ill posedness these modes of ill posedness are characterized by the uncontrolled growth of modes at infinitely fine scales which ultimately violates the continuum assumption in previous work l an and a peirce siam j appl math 54 1994 pp 708 730 a continuum model accounting for microscale deformations was built linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale in this paper a weakly nonlinear analysis is used to explore the immediate post critical behavior of the solutions for both one dimensional and anti plane shear models post critical deformations in the plastic regions are shown to be governed by the boussinesq equation one of the completely integrable pdes having so

discontinuous bifurcation states for associated smooth plasticity and damage with isotropic elasticity abstract for many constitutive equations the tangent tensor consists of a rank one modification to the isotropic elasticity tensor with a total of two elasticity parameters and one parameter describing the current state of inelasticity for small deformations general expressions are derived for the loss of ellipticity the corresponding normal to the bifurcation plane and the mode of discontinuous bifurcation for the velocity gradient if the principal basis of an evolution tensor is used the current stress or strain state is characterized by two additional parameters the small number of material and state parameters makes it feasible to use contour plots to iilustrate all possible combinations that can provide a discontinuous bifurcation these bifurcation maps can be used to illustrate the bifurcation properties of a particular plasticity or continuum damage constitutive model conversely the bifurcation maps can be used in conjunction with experimental data on bifurcation features to assist in the development of constitutive equations that provide the correct failure criterion for a given material under all possible stress paths

new explicit solutions of the nonlinear wave equations with damping term for the nonlinear wave equation with damping term introduced in z j yang g w chen initial value problem for a nonlinear wave equation with damping term acta math appl sin 23 2000 45 in chinese u t t 2bu x x t au x x x x b u x n x a 0 b 0 n 2 a new similarity reduction is presented by means of the direct reduction method due to clark and kruskal and the solutions for the equations with n 3 are given by using the new similarity reduction by using similarity reductions and the ingenious construction of a proper auxiliary equation some new special solutions such as one real solitary wave solution and one singular solitary wave solutions for b 0 and two complex solutions for b 0 are presented respectively

quadratic jordan systems of hermitian type abstract in this paper we extend zel manov s classification of linear jordan systems triple systems and pairs of hermitian type to quadratic jordan systems over an arbitrary ring of scalars using associative triple systems of the first kind for what we believe to be a more natural tool to describe special jordan triples we show that an i special prime quadratic jordan triple system the ideals of which remain semiprime with a nonzero hermitian part lies between an ample subspace of hermitian elements in a prime associative triple system and those in its martindale system of symmetric quotients modulo some extra definitions the structure of strongly prime jordan pairs of hermitian type follows almost immediately from the jordan triple result

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

stability regions for maintaining efficiency in data envelopment analysis abstract this paper develops a procedure for performing a sensitivity analysis of the efficient decision making units dmus within the charnes et al ccr european journal of operational research 2 1978 429 444 model of data envelopment analysis dea the procedure yields an exact input stability region and output stability region within which the efficiency of a specific efficient dmu remains unchanged such stability regions are simply characterized by optimal solutions of modified ccr models which are easily computed in contrast to existing sufficient conditions for the preservation of efficiency under changes in inputs or outputs the paper provides both necessary and sufficient conditions for an efficient dmu to remain efficient the procedure is illustrated by numerical examples somewhat surprisingly for real world data sets for most of the efficient dmus the amount of some individual input can be infinitely increased when keeping other inputs and all outputs constant this indicates that these efficient dmus are located at extreme positions

a mathematical model for localization in granular flow the phrase localization of flow refers to a phenomenon in plasticity in which deformation becomes concentrated in thin bands of intense shearing this paper proposes a two dimensional continuum model which isolates some mathematical issues relevant to such shear banding the challenge is to follow the solution after illposedness appears in the equations a particular solution in this regime is constructed in the quasi static approximation the paper also lists several open problems suggested by the model besides addressing research questions the paper is partly intended as an expository paper for mathematicians interested in shear bands

global attractors and their hausdorff dimensions for a class of kirchhoff models this paper studies the existence regularity and hausdorff dimensions of global attractors for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x it proves that under rather mild conditions the dynamical system associated with above mentioned models possesses in phase space x a global attractor which has further regularity in x 1 x and has finite hausdorff dimension for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

on the initial boundary problem for fourth order wave equations with damping strain and source terms abstract in this paper we study the global existence and blow up of solutions to the fourth order equations u t t u t 2 u u i 1 n x i i u x i f u x t 0 where 0 under appropriate assumptions on the initial data and parameters in the above equation we establish two results on blow up of solutions with arbitrary initial energy e 0 also by using a potential well we show the global existence of solutions for the fourth order wave equation with some i s and f s especially it is proved that the energy decays exponentially as t

data envelopment analysis with imprecise data abstract in original data envelopment analysis dea models inputs and outputs are measured by exact values on a ratio scale cooper et al management science 45 1999 597 607 recently addressed the problem of imprecise data in dea in its general form we develop in this paper an alternative approach for dealing with imprecise data in dea our approach is to transform a non linear dea model to a linear programming equivalent on the basis of the original data set by applying transformations only on the variables upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations it is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post dea model and the endurance indices we then proceed still further in formulating another post dea model for determining input thresholds that turn an inefficient unit to an efficient one

global attractor for a class of kirchhoff models the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x by combining the decomposition idea with the operate technique it proves that under rather mild conditions the dynamical system associated with above mentioned ibvp possesses in different phase spaces a global attractor which is connected respectively for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space

cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow abstract the paper studies the existence both locally and globally in time stability decay estimates and blowup of solutions to the cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow under the assumption that the nonlinear term of the equations is of polynomial growth order say it proves that when 1 the cauchy problem admits a unique local solution which is stable and can be continued to a global solution under rather mild conditions when 5 and the initial data is small enough the cauchy problem admits a unique global solution and its norm in l 1 p r decays at the rate 1 t p 2 2 p for 2 p 10 and if the initial energy is negative then under a suitable condition on the nonlinear term the local solutions of the cauchy problem blow up in finite time

the structure of strongly prime quadratic jordan algebras abstract we extend the structure theory for strongly prime jordan algebras of arbitrary dimension to quadratic algebras of characteristic 2 we show that such j are either 1 hermitian forms h 0 a j h q a lying between an ample subspace of hermitian elements in a prime associative algebra a and those in its martindale ring of quotients q a 2 clifford forms with a scalar extension j j which is an algebra j j q 1 of a nondegenerate quadratic from q with basepoint 1 or 3 albert forms with a scalar extension j j which is a 27 dimensional split albert algebra j h 3 k of 3 3 hermitian matrices over an 8 dimensional split octonion algebra k as a consequence the simple jordan algebras of arbitrary dimension are either hermitian h 0 a for simple a or clifford forms in j q 1 or are albert algebras in particular our methods give an idempotent free classification of all simple finite dimensional algebras which are i special the key to this characterization is the existence of zel manov polynomials in the free special jordan algebra which are both hermitian polynomials whose values always look like hermitian elements and at the same time clifford polynomials nontrivial on 3 3 hermitian matrices hence on special algebras with 3 interconnected idempotents if a zel manov polynomial does not vanish on j then j is of hermitian type and if it does vanish on j then j is of clifford type one example of such a polynomial is q48 p16 x1 y1 z1 w1 p16 x2 y2 z2 w2 p16 x3 y3 z3 w3 for p16 d2x y z 2 dx y w dx y w dx y z x y z thus the structure of jordan algebras depends very directly on polynomial identities and commutators

long time dynamics for a class of kirchhoff models with memory this paper is concerned with a class of kirchhoff models with memory effects utt 2u div u p 2 u 0 s 2u t s ds ut f u h defined in a bounded domain of rn this non autonomous equation corresponds to a viscoelastic version of kirchhoff models arising in dynamics of elastoplastic flows and plate vibrations under assumptions that the exponent p and the growth of f u are up to the critical range it turns out that the model corresponds to an autonomous dynamical system in a larger phase space by adding a component which describes the relative displacement history then the existence of a global attractor is granted furthermore in the subcritical case this global attractor has finite hausdorff and fractal dimensions

primitive jordan pairs and triple systems abstract in this paper we give a characterization of primitivity of jordan pairs and triple systems in terms of their local algebras as a consequence of that local characterization we extend to jordan pairs and triple systems most of the known results about primitive jordan algebras in particular we describe primitive jordan pairs and triple systems over an arbitrary ring of scalars in the sense of the structure of primitive quadratic jordan algebras by j a anquela t cortes and f montaner 1995 j algebra172 530 553 5 1

the structure of primitive quadratic jordan algebras in this paper we give a complete description of primitive quadratic jordan algebras following the classification of strongly prime quadratic jordan algebras k mccrimmon and e i zel manov adv math 69 no 2 1988 133 222 the proof is based in two results of independent interest we show that every p i primitive jordan algebra is simple and unital with nonzero socle and prove that associative tight tight envelopes of special primitive jordan algebras are also primitive primitive as a consequence of the latter fact we see that an associative algebra a is one sided primitive if and only if a is primitive and an associative algebra a with involution is primitive if and only if an ample subspace h 0 a is primitive

arbitrarily positive initial energy blowup and blowup time for some fourth order viscous wave equation abstract this paper is devoted to the finite time blowup phenomena for a class of fourth order wave equation with viscous damping term it is shown that the high initial energy finite time blowup associated with the upper bound of the blowup time is established by introducing a new auxiliary function and employing an adapted concavity method

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

global existence asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term abstract the paper studies the global existence asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term it proves that under rather mild conditions on nonlinear terms and initial data the above mentioned problem admits a global weak solution and the solution decays exponentially to zero as t respectively in the states of large initial data and small initial energy in particular in the case of space dimension n 1 the weak solution is regularized to be a unique generalized solution and if the conditions guaranteeing the global existence of weak solutions are not valid then under the opposite conditions the solutions of above mentioned problem blow up in finite time and an example is given

on the general decay of a nonlinear viscoelastic plate equation with a strong damping and p x t laplacian abstract in this paper we consider a nonlinear viscoelastic plate equation with a lower order perturbation of a p x t laplacian operator of the form u t t 2 u p x t u 0 t g t s u s d s u t f u 0 x t q t 0 t associated with initial and dirichlet neumann boundary conditions under suitable conditions on g f and the variable exponent of the p x t laplacian operator we prove a general decay result in the presence of a strong damping u t 0 acting in the domain this equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations

primitivity in jordan systems is ubiquitous abstract the main result of the paper asserts that if a jordan pair v v v is primitive at some 0 b v then it is primitive at any 0 b v also if a jordan triple system t is primitive at some 0 b t then it is primitive at any 0 b t as a tool similar results concerning one sided primitivity and primitivity of associative pairs and triple systems are established equivalences between our definitions of primitivity and some other appearing in the literature are also obtained as a consequence

finite dimensional attractors for the kirchhoff models with critical exponents the paper studies the existence of the finite dimensional global attractor and exponential attractor for the dynamical system associated with the kirchhoff models utt u m 1 u ut 2u h ut g u f x it proves that for the subcritical and critical cases 1 m n 2 n 2 with n 6 the above mentioned dynamical system possesses in phase spaces x1 a finite dimensional global attractor and a weak exponential attractor respectively

a class of fourth order wave equations with dissipative and nonlinear strain terms we study the initial boundary value problem for a class of fourth order wave equations with dissipative and nonlinear strain terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions

finite dimensional attractors for the kirchhoff models the paper studies the existence of the finite dimensional global attractor and exponential attractor for the dynamical system associated with the kirchhoff models arising in elasto plastic flow utt div u m 1 u ut 2u h ut g u f x by using the method of l trajectories and the operator technique it proves that under subcritical case 1 m n 2 n 2 the above mentioned dynamical system possesses in different phase spaces a finite dimensional weak global attractor and a weak exponential attractor respectively for application the fact shows that for the concerned elasto plastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the fractal dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

an extension to data envelopment analysis with preference structure for estimating overall inefficiency this paper extends data envelopment analysis dea with preference structure by fully considering the substitution effects among different inputs or outputs when the unit cost and price information on inputs and outputs are available the generalized weighted ccr gwccr models proposed in this paper can provide some scalar values for measuring the overall inefficiency it is found that the gwccr models focus on the relative aspects of overall inefficiency instead of the absolute aspects focused on by the weighted additive dea model