on nilpotency of matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper we study the nilpotency of matrices over commutative antirings we first provide some properties and characterizations of the nilpotent matrices in terms of principal permanental minors main diagonals and permanental adjoint matrices when a family of matrices are simultaneously considered we establish some characterizations of the simultaneous nilpotence for a family of matrices

the characterizations of h hemiregular hemirings and h intra hemiregular hemirings in this paper the concepts of fuzzy h bi ideals and fuzzy h quasi ideals of a hemiring are introduced and related properties are investigated the notion of h intra hemiregularity of a hemiring which is a generalization of the notion of intra regularity of a ring is provided some characterizations of h hemiregular hemirings h intra hemiregular hemirings and hemirings that are both h hemiregular and h intra hemiregular are derived in terms of fuzzy left fuzzy right h ideals fuzzy h bi ideals and fuzzy h quasi ideals

reaction diffusion processes described by three state quantum chains and integrability the master equation of one dimensional three species reaction diffusion processes is mapped onto an imaginary time schrodinger equation in many cases the hamiltonian obtained is that of an integrable quantum chain with known properties within this approach we search for three state integrable quantum chains with known spectra and which are related to diffusive reactive systems two integrable models are found to appear naturally in this context the uqsu 2 invariant model with external fields and the three state uqsu p m invariant perk schultz models with external fields a non local similarity transformation which brings the hamiltonian governing the chemical processes to the known standard forms is described leading in the case of periodic boundary conditions to a generalization of the dzialoshinsky moriya interaction for n state hamiltonians n 2

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

fuzzy rank preserving operators abstract analogues of characterizations of rank preserving operators on field valued matrices are determined for fuzzy matrices and for matrices over related semirings for example if m is the set of mxn fuzzy matrices and min m n 1 then a linear operator on m preserves the rank of each matrix in m if and only if it preserves the rank of those matrices in m of ranks 1 and 2 other characterizations of rank preserving operators are also given

on the benney lin and kawahara equations abstract we establish global well posedness for the initial value problem ivp associated to the so called benney lin equation this model is a korteweg de vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics we also study the limiting behaviour of solutions to this ivp when the parameters of the perturbed terms approach 0

linear operators preserving idempotent matrices over fields abstract suppose f is a field we show that if the characteristic of the field is not 2 then the semigroup of linear operators on the n n matrices over f that preserve idempotence is the group g f generated by transposition and similarity chan lim and tan have previously established that theorem for the real and complex fields by other methods we also show that the semigroup l f of linear operators on the n n matrices over f that preserve both idempotence and nonidempotence is g f when the characteristic of f is not 2 we determine the structure of l f when the characteristic of f is 2 and present some open problems

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

well posedness and blow up phenomena for a higher order shallow water equation this paper deals with the cauchy problem for a higher order shallow water equation yt auxy buyx 0 where y 2ku i x2 ku and k 2 the local well posedness of solutions for the cauchy problem in sobolev space hs r with s 7 2 is obtained under some assumptions the existence and uniqueness of the global solutions to the equation are shown and conditions that lead to the development of singularities in finite time for the solutions are also acquired finally the weak solution for the equation is considered

nonnegative rank preserving operators abstract analogues of characterizations of rank preserving operators on field valued matrices are determined for matrices witheentries in certain structures s contained in the nonnegative reals for example if s is the set of nonnegative members of a real unique factorization domain e g the nonnegative reals or the nonnegative integers m is the set of m n matrices with entries in s and min m n 4 then a linear operator on m preserves the rank of each matrix in m if and only if it preserves the ranks of those matrices in m of ranks 1 2 and 4 notions of rank and linearity are defined analogously to the field valued concepts other characterizations of rank preserving operators for matrices over these and other structures s are also given

linear preservers of zeros of matrix polynomials abstract we classify linear operators on matrices with semiring entries that preserve the zeros of multivariable matrix polynomials these matrix polynomials are defined via the adjoint operator x y xy yx as if the matrices were being considered as if over a field also we compare the results over fields with the results over semirings

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

term rank permanent and rook polynomial preservers characterizations are obtained of those linear operators on the m n matrices over an arbitrary semiring that preserve term rank we also present characterizations of permanent and rook polynomial preserving operators on matrices over certain types of semirings our results apply to many combinatorially interesting algebraic systems including nonnegative integer matrices matrices over boolean algebras and fuzzy matrices

comparison of model equations for small amplitude long waves abstract consider a body of water of finite depth under the influence of gravity bounded below by a flat impermeable surface if viscous and surface tension effects are ignored and assuming that the flow is incompressible and irrotational the fluid motion is governed by the euler equations together with suitable boundary conditions on the rigid surfaces and on the air water interface in special regimes the euler equations admit of simpler approximate models that describe pretty well the fluid response to a disturbance in situations where the wavelength is long and the amplitude is small relative to the undisturbed depth and if the stokes number is of order one then various model equations have been derived two of the most standard are the kdv equation 0 1 u t u x uu x u xxx 0 and the rlw equation 0 2 u t u x uu x u xxt 0 bona pritchard and scott showed that solutions of these two evolution equations agree to the neglected order of approximation over a long time scale if the initial disturbance in question is genuinely of small amplitude and long wavelength the same formal argument that allows one to infer 0 2 from 0 1 in small amplitude long wavelength regimes also produces a third equation namely u t u x uu x u xtt 0 kruskal in a wide ranging discussion of modelling considerations pointed to this equation as an example that might not accurately describe water waves its status has remained unresolved it is our purpose here to show that the initial value problem for the latter equation is indeed well posed moreover we show that for small amplitude long waves solutions of this model also agree to the neglected order with solutions of either 0 1 or 0 2 provided the initial data is properly imposed 1

boolean rank preserving operators and boolean rank 1 spaces abstract we study the extent to which certain theorems on linear operators on field valued matrices carry over to linear operators on boolean matrices we obtain analogues and near analogues of several such theorems one of these leads us to consider linear spaces of m n boolean matrices whose nonzero members all have boolean rank 1 we obtain a structure theorem for such spaces that enables us to determine the maximum boolean dimension of such spaces and their maximum cardinality

existence of blow up solutions in the energy space for the critical generalized kdv equation from these conservation laws h appears as an energy space so that it is a natural space in which to study the solutions note that p 2 is a special case for equation 2 indeed from the integrability theory see lax 14 we have for suitable u0 u0 and its derivatives with fast decay at infinity an infinite number of conservation laws the general question is to understand the dynamics induced by such equations local existence in time of solutions of 2 in the energy space is now well understood see kato 10 ginibre and tsutsumi 8 for the h theory s 32 kenig ponce and vega 11 for the l theory in the case of equation 1 and sharp h theory for 2 and bourgain 3 and 4 for the periodic case

linear preservers on matrices abstract let u denote either the vector space of n n matrices or the vector space of n n symmetric matrices over an infinite field f in this paper we characterize linear mappings l on u that satisfy one of the following properties i l adja adjl a for all a in u ii l preserves idempotent matrices and l in in where f is the real field r or the complex field c iii l ea el a for all a in u where f r or c

comparison between model equations for long waves and blow up phenomena abstract recently to describe the unidirectional propagation of water waves bona et al 7 introduced a fifth order kdv bbm type model 0 1 t x 1 6 x x t 1 x x x x t 2 x x x x x 3 4 2 x 2 x x x 1 12 x 2 x 1 4 3 x 0 where x t is a real valued function and 1 0 2 r in this work we plan to compare solution of the initial value problem ivp associated to the fifth order kdv bbm type model 0 1 to that of the ivp associated to the fifth order kdv model 0 2 u t 3 u x x x x x c 1 u x u x x c 2 u u x x x c 3 u 2 u x 0 where u u x t is a real valued function and 3 c 1 c 2 and c 3 are real constants with 3 0 this later model 0 2 was proposed by benney in 4 to describe the interaction of long and short waves also we will study the possibility of blow up phenomenon of the fifth order kdv bbm type model under certain restrictions on the coefficients

on invertible matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper the complete description of the invertible matrices over a commutative antiring is given and some necessary and sufficient conditions for a matrix over a commutative antiring to be invertible are obtained also cramer s rule over commutative antirings is presented the main results in this paper generalize and develop the corresponding results for the boolean matrices the fuzzy matrices the lattice matrices and the incline matrices

hamiltonian long wave expansions for free surfaces and interfaces the theory of internal waves between two bodies of immiscible fluid is important both for its interest to ocean engineering and as a source of numerous interesting mathematical model equations which exhibit nonlinearity and dispersion in this paper we derive a hamiltonian formulation of the problem of a dynamic free interface with rigid lid upper boundary conditions and of a free surface and a free interface this latter situation occurring more commonly in experiment and in nature from the formulation we develop a hamiltonian perturbation theory for the long wave limits and we carry out a systematic analysis of the principal long wave scaling regimes this analysis provides a uniform treatment of the classical works of peters and stoker 28 benjamin 3 4 ono 26 and many others our considerations include the boussinesq and kdv regimes over finite depth fluids the benjamin ono regimes in the situation in which one fluid layer is infinitely deep and the intermediate long wave regimes in addition we describe a novel class of scaling regimes of the problem in which the amplitude of the interface disturbance is of the same order as the mean fluid depth and the characteristic small parameter corresponds to the slope of the interface our principal results are that we highlight the discrepancies between the case of rigid lid and of free surface upper boundary conditions which in some circumstances can be significant motivated by the recent results of choi and camassa 6 7 we also derive novel systems of nonlinear dispersive long wave equations in the large amplitude small slope regime our formulation of the dynamical free surface free interface problem is shown to be very effective for perturbation calculations and as well it holds promise as a basis for numerical simulations c 2000 wiley periodicals inc

elliptic solutions and solitary waves of a higher order kdv bbm long wave equation abstract we provide conditions for the existence of hyperbolic unbounded periodic and elliptic solutions in terms of weierstrass functions of both third and fifth order kdv bbm korteweg de vries benjamin bona mahony regularized long wave equation an analysis for the initial value problem is developed together with a local and global well posedness theory for the third order kdv bbm equation traveling wave reduction is used together with zero boundary conditions to yield solitons and periodic unbounded solutions while for nonzero boundary conditions we find solutions in terms of weierstrass elliptic functions for the fifth order kdv bbm equation we show that the parameter 1 12 which leads to a hamiltonian represents a restriction in where there are constraint curves that never intersect a region of unbounded solitary waves this in turn shows that only dark or bright solitons and no unbounded solutions exist motivated by the lack of a hamiltonian structure for 1 12 we develop h k bounds and we show for the non hamiltonian system that dark and bright solitons coexist together with unbounded periodic solutions for nonzero boundary conditions due to the complexity of the nonlinear algebraic system of coefficients of the elliptic equation we construct weierstrass solutions for a particular set of parameters only

on nilpotent matrices over antirings in this paper the nilpotent matrices over commutative antirings are characterized in terms of principal permanental minors main diagonals and permanental adjoint matrices and a necessary and sufficient condition for a nilpotent matrix over a commutative antiring which has a given nilpotent index is obtained also a method for calculating the nilpotent index of any nilpotent matrix over a commutative entire antiring is given