solving the hierarchy of the nonisospectral kdv equation with self consistent sources via the inverse scattering transform the hierarchy of the nonisospectral kdv equation with self consistent sources is derived n soliton solutions of the hierarchy are obtained through the inverse scattering transform we develop new treatment of singularities appearing in the lax pair in the process of determining time revolutions of scattering data our approach is general and can apply to other 1 1 dimensional nonisospectral soliton hierarchy with self consistent sources

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

the local to global principle for triangulated categories via dimension functions we formulate a general abstract criterion for verifying the local to global principle for a rigidly compactly generated tensor triangulated category our approach is based upon an inductive construction using dimension functions using our criterion we give a new proof of the theorem that the local to global principle holds for such categories when they have a model and the spectrum of the compacts is noetherian as further applications we give a new set of conditions on the spectrum of the compacts that guarantee the local to global principle holds and use this to classify localising subcategories in the derived category of a semi artinian absolutely flat ring

integration of the soliton hierarchy with self consistent sources in contrast with the soliton equations the evolution of the eigenfunctions in the lax representation of soliton equation with self consistent sources sescs possesses singularity we present a general method to treat the singularity to determine the evolution of scattering data the akns hierarchy with self consistent sources the mkdv hierarchy with self consistent sources the nonlinear schrodinger equation hierarchy with self consistent sources the kaup newell hierarchy with self consistent sources and the derivative nonlinear schrodinger equation hierarchy with self consistent sources are integrated directly by using the inverse scattering method the n soliton solutions for some sescs are presented it is shown that the insertion of a source may cause the variation of the velocity of soliton this approach can be applied to all other 1 1 dimensional soliton hierarchies

solving soliton equations with self consistent sources by method of variation of parameters abstract starting from the solutions of soliton equations and corresponding eigenfunctions obtained by darboux transformation we present a new method to solve soliton equations with self consistent sources sescs based on method of variation of parameters the kdv equation with self consistent sources kdvscs is used as a model to illustrate this new method in addition we apply this method to construct some new solutions of the derivative nonlinear schrodinger equation with self consistent sources dnlsscs such as phase solution dark soliton solution bright soliton solution and breather type solution

the spectrum of prime ideals in tensor triangulated categories we define the spectrum of a tensor triangulated category k as the set of so called prime ideals endowed with a suitable topology in this very generality the spectrum is the universal space in which one can define supports for objects of k this construction is functorial with respect to all tensor triangulated functors several elementary properties of schemes hold for such spaces e g the existence of generic points or some quasi compactness locally trivial morphisms are proved to be nilpotent we establish in complete generality a classification of thick ideal subcategories in terms of arbitrary unions of closed subsets with quasi compact complements thomason s theorem for schemes mutatis mutandis we also equip this spectrum with a sheaf of rings turning it into a locally ringed space we compute examples and show that our spectrum unifies the schemes of algebraic geometry and the support varieties of modular representation theory

supports and filtrations in algebraic geometry and modular representation theory working with tensor triangulated categories we prove two theorems relative to supports and then discuss their incarnations in algebraic geometry and in modular representation theory first we show that an indecomposable object has connected support then we consider the filtrations by dimension or codimension of the support and prove that the associated subquotients decompose as sums of local terms

block sor preconditioned projection methods for kronecker structured markovian representations kronecker structured representations are used to cope with the state space explosion problem in markovian modeling and analysis currently an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of markov chains mcs underlying such representations this paper proposes a block successive overrelaxation bsor preconditioner for hierarchical markovian models hmms throughout the paper the hmm acronym stands for hierarchical markovian models and should not be confused with the hmm that is sometimes used for hidden markov models that are composed of multiple low level models and a high level model that defines the interaction among low level models the kronecker structure of an hmm yields nested block partitionings in its underlying continuous time mc which may be used in the bsor preconditioner the computation of the bsor preconditioned residual in each iteration of a preconditioned projection method becomes the problem of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of the chosen partitioning the proposed bsor preconditioner solves these systems using sparse lu or real schur factors of diagonal blocks the fill in of sparse lu factorized diagonal blocks is reduced using the column approximate minimum degree colamd ordering a set of numerical experiments is presented to show the merits of the proposed bsor preconditioner

circulant preconditioners for stochastic automata networks stochastic automata networks sans are widely used in modeling communication systems manufacturing systems and computer systems the san approach gives a more compact and efficient representation of the network when compared to the stochastic petri nets approach to find the steady state distribution of sans it requires solutions of linear systems involving the generator matrices of the sans very often direct methods such as the lu decomposition are inefficient because of the huge size of the generator matrices an efficient algorithm should make use of the structure of the matrices iterative methods such as the conjugate gradient methods are possible choices however their convergence rates are slow in general and preconditioning is required we note that the milu and minv based preconditioners are not appropriate because of their expensive construction cost in this paper we consider preconditioners obtained by circulant approximations of sans they have low construction cost and can be inverted efficiently we prove that if only one of the automata is large in size compared to the others then the preconditioned system of the normal equations will converge very fast numerical results for three different sans solved by cgs are given to illustrate the fast convergence of our method

capture and confinement of solitons in nonlinear integrable systems the system describing the interaction of a long wave with a short wave packet on thex y plane is considered the solutions are found to describe a soliton that comes from infinity and then is captured into a conditionally periodical oscillatory regime the solutions are also found that describe a soliton coming from infinity and then decaying into two solitons one goes to infinity and the other is captured into a conditionally periodical oscillatory regime the obtained results are relevant to some problems of hydrodynamics plasma physics solid state physics etc

nonisospectral integrable nonlinear equations with external potentials and their gbdt solutions auxiliary systems for matrix nonisospectral equations including coupled nls with external potential and kdv with variable coefficients were introduced explicit up to the inversion of finite matrices solutions of nonisospectral equations were constructed using the gbdt version of the backlund darboux transformation

on the nonisospectral modified kadomtsev peviashvili equation abstract two types of grammian solutions to the nonisospectral modified kadomtsev peviashvili mkp equation are derived with the help of the pfaffian derivative formulae starting from the grammian solutions obtained we construct the nonisospectral mkp equation with self consistent sources by applying the source generalization procedure whose solutions can be given simultaneously

the n soliton solutions of the sine gordon equation with self consistent sources abstract the hierarchy of the sine gordon equation with self consistent sources is derived by using the eigenfunctions of recursion operator the bilinear form of the sine gordon equation with self consistent sources is given and the n soliton solutions are obtained through hirota method and wronskian technique respectively some novel determinantal identities are presented to treat the nonlinear term in the time evolution and finish the wronskian verifications

iterative aggregation disaggregation techniques for nearly uncoupled markov chains iterative aggregation disaggregation methods provide an efficient approach for computing the stationary probability vector of nearly uncoupled also known as nearly completely decomposable markov chains three such methods that have appeared in the literature recently are considered and their similarities and differences are outlined specifically it is shown that the method of takahashi corresponds to a modified block gauss seidel step and aggregation whereas that of vantilborgh corresponds to a modified block jacobi step and aggregation the third method that of koury et al is equivalent to a standard block gauss seidel step and iteration for each of these methods a lemma is established which shows that the unique fixed point of the iterative scheme is the left eigenvector corresponding to the dominant unit eigenvalue of the stochastic transition probability matrix in addition conditions are established for the convergence of the first two of these methods convergence conditions for the third having already been established by stewart et al all three methods are shown to have the same asymptotic rate of convergence

chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems abstract the present paper deals with the problem of computing a few of the eigenvalues with largest or smallest real parts of a large sparse nonsymmetric matrix we present a general acceleration technique based on chebyshev polynomials and discuss its practical application to arnoldi s method and the subspace iteration method the resulting algorithms are compared with the classical ones in a few experiments which exhibit a sharp superiority of the arnoldi chebyshev approach

technical note a markov chain partitioning algorithm for computing steady state probabilities this paper presents a partitioning algorithm for recursively computing the steady state probabilities for a finite irreducible markov chain or a markov process the algorithm contains a matrix reduction routine followed by a vector enlargement routine the matrix reduction routine repeatedly partitions the transition matrix for the markov chain creating a sequence of smaller reduced transition matrices the vector enlargement routine computes the components of the steady state probability vector by starting with the smallest reduced matrix and working sequentially toward the original transition matrix this procedure produces an exact solution for the steady state probabilities no special structure is required for the markov chain in theory the procedure imposes no limit on the size of the largest markov chain to which the partitioning algorithm can be applied in practice roundoff errors may require modifications to the method

support theory via actions of tensor triangulated categories we give a definition of the action of a tensor triangulated category t on a triangulated category k in the case that t is rigidly compactly generated and k is compactly generated we show this gives rise to a notion of supports which categorifies work of benson iyengar and krause and extends work of balmer and favi we prove that a suitable version of the local to global principle holds very generally a relative version of the telescope conjecture is formulated and we give a sufficient condition for it to hold

integration of the nonlinear schroedinger equation with a self consistent source it is shown that the nonlinear schroedinger equation with a self consistent source admits investigation by the inverse scattering method for the dirac operator the conditions are found under which the solutions of the nonlinear schroedinger equation with a self consistent source describe the creation and annihilation of solitons

regenerative analysis and steady state distributions for markov chains we apply regenerative theory to derive certain relations between steady state probabilities of a markov chain these relations are then used to develop a numerical algorithm to find these probabilities the algorithm is a modification of the gauss jordan method in which all elements used in numerical computations are nonnegative as a consequence the algorithm is numerically stable

newton s method solver for high speed viscous separated flowfields a new method for calculating the 2 d laminar navier stokes equations is presented the method uses newton s method for nonlinear systems of equations to find steady state solutions the navier stokes equations are approximated by finite differences using roe s flux difference splitting second order accuracy is attained by using spekreijse s interpolation with van albada s limiter the exact newton s method jacobian matrix is inverted by using recent sparse matrix routines the symbolic manipulation package macsyma is used to develop and write the fortran code

solving the kdv hierarchy with self consistent sources by inverse scattering method abstract the evolution of the eigenfunctions in the lax representation of the kdv hierarchy with self consistent sources possesses singularity by proposing a method to treat the singularity to determine the evolution of scattering data the kdv hierarchy with self consistent sources is integrated by the inverse scattering method the soliton solutions of these equations are obtained it is shown that the insertion of a source may cause the variation of the speed of soliton this approach can be applied to other 1 1 dimensional soliton hierarchies

generalized darboux transformations for the kp equation with self consistent sources the kp equation with self consistent sources kpescs is treated in the framework of the constrained kp equation this offers a natural way to obtain the lax representation for the kpescs based on the conjugate lax pairs we construct the generalized binary darboux transformation with arbitrary functions in time t for the kpescs which in contrast to the binary darboux transformation of the kp equation provides a non auto backlund transformation between two kpescss with different degrees the formula for n times repeated generalized binary darboux transformation is proposed and enables us to find the n soliton solution and lump solution as well as some other solutions of the kpescs

toeplitz circulant preconditioners for toeplitz systems and their applications to queueing networks with batch arrivals the preconditioned conjugate gradient method is employed to solve toeplitz systems t n bf x bf b where the generating functions of the n by n toeplitz matrices t n are functions with zeros in this case circulant preconditioners are known to give poor convergence whereas band toeplitz preconditioners offer only linear convergence and can handle only real valued functions with zeros of even orders we propose here preconditioners which are products of band toeplitz matrices and circulant matrices the band toeplitz matrices are used to cope with the zeros of the given generating function and the circulant matrices are used to speed up the convergence rate of the algorithm our preconditioner can handle complex valued functions with zeros of arbitrary orders we prove that the preconditioned toeplitz matrices have singular values clustered around 1 for large n we apply our preconditioners to solve the stationary probability distribution vectors of markovian queueing models with batch arrivals we show that if the number of servers is fixed independent of the queue size n then the preconditioners are invertible and the preconditioned matrices have singular values clustered around 1 for large n numerical results are given to illustrate the fast convergence of our methods

negaton and positon solutions of the soliton equation with self consistent sources the korteweg de vries kdv equation with self consistent sources kdves is used as a model to illustrate this method we present a generalized binary darboux transformation gbdt with an arbitrary time dependent function for the kdves as well as the formula for n times repeated gbdt this gbdt provides non auto backlund transformation between two kdv equations with different degrees of sources and enables us to construct more general solutions with n arbitrary t dependent functions by taking the special t function we obtain multisoliton multipositon multinegaton multisoliton positon multinegaton positon and multisoliton negaton solutions of the kdves

iterative methods for overflow queuing models ii preconditioned conjugate gradient methods are employed to find the steady state probability distribution of markovian queuing networks that have overflow capacity different singular preconditioners that can be handled by separation of variables are discussed the resulting preconditioned systems are nonsingular numerical results show that the number of iterations required for convergence grows very slowly with the queue sizes

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

two binary darboux transformations for the kdv hierarchy with self consistent sources two binary integral type darboux transformations for the kdv hierarchy with self consistent sources are proposed in contrast with the darboux transformation for the kdv hierarchy one of the two binary darboux transformations provides non auto backlund transformation between two nth kdv equations with self consistent sources with different degrees the formula for the m times repeated binary darboux transformations are presented this enables us to construct the n soliton solution for the kdv hierarchy with self consistent sources

soliton scattering with amplitude changes of a negative order akns equation the paper investigates a nonlinear model which provides soliton scattering with amplitude changes this is a nonlinear equation in negative order akns hierarchy we derive its n soliton solutions through hirota method for dynamics 1 soliton is characterized by an asymmetric shape and time dependent amplitude then by means of asymptotic analysis it is found that two soliton scattering provides not only phase shifts but also amplitude changes for each soliton which differs from classical soliton interactions where only phase shifts appear appendix a gives a tentative discussion on lax integrability and formal hamiltonian structures of the negative order hierarchy and appendix b lists reductions of equations and solutions

conjugate gradient like algorithms for solving nonsymmetric linear systems this paper presents a unified formulation of a class of the conjugate gradient like algorithms for solving nonsymmetric linear systems the common framework is the petrov galerkin method on krylov subspaces we discuss some practical points concerning the methods and point out some of the interrelations between them 1 introduction in the recent few years a large number of generalizations of the conjugate gradient and conjugate residual methods which are very successful in solving symmetric positive definite linear systems have been proposed for solving nonsymmetric linear systems 3 6 5 7 12 in this paper we present an abstract framework which includes most of these methods and many new ones our goal is to understand the relationships among the methods and to synthesize consider the general linear system

triangular and skew symmetric splitting method for numerical solutions of markov chains in this paper a theorem is presented to indicate that there exists a nonnegative constant e 0 such that the matrix a q email protected is a positive definite matrix where email protected r n x n is an identity matrix and q email protected r n x n is a matrix with positive diagonal and nonpositive off diagonal elements then a class of triangular and skew symmetric splitting tss iteration method is applied to solve the positive definite linear system ax b for obtaining the stationary probability vector of an irreducible markov chain theoretical analyses show that the tss iteration method converges unconditionally to the unique solution of the linear system with the upper bound of its contraction factor dependent only on the spectrum of the triangular part and independent of the eigenvectors of the matrices involved moreover the inexact triangular and skew symmetric splitting itss iteration method which employs certain krylov subspace methods as the inner iteration processes at each step of the outer tss iteration method is proposed to accelerate the convergence of the tss iteration method numerical experiments are used to illustrate the effectiveness of the tss and itss iteration methods

an iterative aggregation disaggregation algorithm for solving linear equations a general procedure is given for solving large sets of linear equations by first rewriting them in a form suitable for aggregation of both the variables and equations followed by disaggregation a computational algorithm which iteratively aggregates and disaggregates is shown to converge geometrically to the exact solution provided the original problem has a structure suitable for such aggregation the algorithm exhibits fast computation times small main memory requirements and robustness to the starting point a rigorous foundation for aggregation and disaggregation is provided by the equations employed by this algorithm

symbolic computation backlund transformation and analytic n soliton like solution for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas abstract with symbolic computation a bilinear backlund transformation is presented for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas and correspondingly the one soliton like solution is derived from the backlund transformation simultaneously the n soliton like solution in double wronskian form is also given besides the authors verify that the n 1 and n soliton like solutions satisfy the backlund transformation the results obtained in this paper might be valuable for the study of the nonuniform media

relative error bounds for the lu decomposition via the gth algorithm recently the author showed that the grassmann taksar heyman gth algorithm computes the steady state distribution of a finite state markov chain with low relative error here it is shown that the lu decomposition computed in the course of the gth algorithm also has low relative error the proof requires a refinement of the methods used in the earlier paper

the solutions of the nls equations with self consistent sources we construct the generalized darboux transformation with arbitrary functions at time t for the akns equation with self consistent sources aknsescs which in contrast with the darboux transformation for the akns equation provides a non auto backlund transformation between two aknsescss with different degrees of sources the formula for n times repeated generalized darboux transformation is proposed by reduction the generalized darboux transformation with arbitrary functions at time t for the nonlinear schrodinger equation with self consistent sources nlsescs is obtained and enables us to find the dark soliton bright soliton and positon solutions for nls escs and nls escs the properties of these solution are analysed

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

complete modules and torsion modules suppose that r is a ring and that a is a chain complex over r inside the derived category of differential graded a modules there are naturally defined subcategories of a torsion objects and of a complete objects under a finiteness condition on a we develop a morita theory for these subcat egories find conceptual interpretations for some associated algebraic functors and in appropriate commutative situations identify the associated functors as local homology or local cohomology some of the results are suprising even in the case r z and a z p 1 introduction let r be a ring and r mod the derived category of chain complexes of left modules see section 1 2 we choose a fixed complex a which is perfect in other words isomorphic in mod to a complex of finite length in which the entries are finitely generated projective modules we de clare another complex n to be a trivial if hom a a0 0 where hom denotes the chain complex of morphisms in r mod going further we say that x is a torsion if hom x at 0 for all a trivial n9 and that x is a complete if homr n9x 0 for all a trivial n we then study the category ators of a torsion complexes and the category acomp of a complete complexes both of these are triangulated full subcategories of r mod it turns out that these categories are equivalent to one another and also equivalent to the derived category of dif ferential graded modules over the endomorphism complex of a we construct approximation functors celu r mod at0rs and a r mod acomp for an object m of r mod9 the complex celu m is a kind of a cellular approxi mation to m in the sense that it is the best approximation to m which can be cobbled together from a and its suspensions the complex ma is the bousfield localization of m with respect to a homology theory on r mod derived from a we provide algebraic formulas for the functors and find that the functors are related in interesting ways one of which involves an arithmetic square we also show that if cciia r has certain finite dimensionality properties then an object m of r mod is a torsion or a complete if and only if the homology groups 77 m individually satisfy appropriate torsion or completeness conditions suppose now that r is a commutative ring that 7 c r is a finitely generated ideal that a r i9 and that k is the associated koszul complex the complex a

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

multigrid algorithm from cyclic reduction for markovian queueing networks a multigrid method based on cyclic reduction strategy is proposed to solve huge nonsymmetric singular linear systems arising from markovian queueing networks a simple way to construct the matrix dependent prolongation and restriction operators is presented in this paper numerical results for multiple queues are given to illustrate the efficiency and robustness of our methods

convergence properties of krylov subspace methods for singular linear systems with arbitrary index abstract krylov subspace methods have been recently considered to solve singular linear systems ax b in this paper we derive the necessary and sufficient conditions guaranteeing that a krylov subspace method converges to a vector adb px0 where ad is the drazin inverse of a and p is the projection p i a d a let k be the index of a we further show that a d b px 0 x 0 r a k 1 n a is a generalized least squares solution of ax b in r a k n a finally we present the convergence bounds for the quasi minimal residual algorithm qmr and transpose free quasi minimal residual algorithm tfqmr the index k of a in this paper can be arbitrary which extends to the main results of freund and hochbruck numer linear algebra appl 1 1994 403 420 that only considers the case k 1

generalized tensor idempotents and the telescope conjecture we transpose rickard s construction of idempotent representations to the general context of tensor triangulated categories we connect our construction to the telescope conjecture and prove that the latter is of local nature as an illustration we extend the affine telescope theorem of neeman to arbitrary noetherian schemes we also develop supports for non compact objects

on the toda lattice equation with self consistent sources the toda lattice hierarchy with self consistent sources and their lax representation are derived we construct a forward darboux transformation fdt with arbitrary functions of time and a generalized forward darboux transformation gfdt for toda lattice with self consistent sources tlscs which can serve as a non auto backlund transformation between tlscs with different degrees of sources with the help of such dt we can construct many types of solutions to tlscs such as rational solution solitons positons negetons and soliton positons soliton negatons positon negatons etc and study properties and interactions of these solutions

smoothed aggregation multigrid for markov chains a smoothed aggregation multigrid method is presented for the numerical calculation of the stationary probability vector of an irreducible sparse markov chain it is shown how smoothing the interpolation and restriction operators can dramatically increase the efficiency of aggregation multigrid methods for markov chains that have been proposed in the literature the proposed smoothing approach is inspired by smoothed aggregation multigrid for linear systems supplemented with a new lumping technique that assures well posedness of the coarse level problems the coarse level operators are singular m matrices on all levels resulting in strictly positive coarse level corrections on all levels numerical results show how these methods lead to nearly optimal multigrid efficiency for an extensive set of test problems both when geometric and algebraic aggregation strategies are used

integrability of the modified generalised vakhnenko equation integrability of the modified generalised vakhnenko equation is investigated systematically based on binary bell polynomials its bilinear representation n soliton solutions bilinear backlund transformation and lax pair are succinctly constructed moreover the conservation laws of the modified generalised vakhnenko equation are discussed by using corresponding lax pair furthermore the quasiperiodic solution of the modified generalised vakhnenko equation is presented by applying hirota direct method and riemann theta function the asymptotic behavior of the one periodic wave is analyzed in details it is shown that the one periodic wave solution tends to the one soliton solution under a small amplitude limit 0 finally the new n soliton solutions of the standard vakhnenko equation are presented it would be specially mentioned that all the results of modified generalised vakhnenko equation can be reduced to the generalised vakhnenko equation and standard vakhnenko equation under the special case of 1 and 1 0 respectively

negatons positons rational like solutions and conservation laws of the korteweg de vries equation with loss and non uniformity terms solitons negatons positons rational like solutions and mixed solutions of a non isospectral equation the korteweg de vries equation with loss and non uniformity terms are obtained through the wronskian technique the non isospectral characteristics of the motion behaviours of some solutions are described with some figures made by using mathematica we also derive an infinite number of conservation laws of the equation

a modified kdv equation with self consistent sources in non uniform media and soliton dynamics two non isospectral modified kdv equations with self consistent sources are derived which correspond to the time dependent spectral parameter satisfying t and t 3 respectively gauge transformation between the first non isospectral equation corresponding to t and its isospectral counterpart is given from which exact solutions and conservation laws for the non isospectral one are easily listed besides solutions to the two nonisospectral modified kdv equations with self consistent sources are derived by means of the hirota method and the wronskian technique respectively nonisospectral dynamics and source effects including one soliton characteristics in non uniform media two solitons scattering and special behaviours related to sources for example the ghost solitons in the degenerate two soliton case are investigated analytically

numerical methods in markov chain modeling this paper describes and compares several methods for computing stationary probability distributions of markov chains the main linear algebra problem consists of computing an eigenvector of a sparse nonsymmetric matrix associated with a known eigenvalue it can also be cast as a problem of solving a homogeneous singular linear system we present several methods based on combinations of krylov subspace techniques single vector power iteration relaxation procedures and acceleration techniques we compare the performance of these methods on some realistic problems

lumpable continuous time stochastic automata networks abstract the generator matrix of a continuous time stochastic automata network san is a sum of tensor products of smaller matrices which may have entries that are functions of the global state space this paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous time san in which aggregation is performed automaton by automaton when there exists a lumpable partitioning induced by the tensor representation of the generator it is shown that an efficient aggregation iterative disaggregation algorithm may be employed to compute the steady state distribution the results of experiments with two san models show that the proposed algorithm performs better than the highly competitive block gauss seidel in terms of both the number of iterations and the time to converge to the solution

the numerical solution of stochastic automata networks abstract stochastic automata networks san s have recently received attention in the literature as an efficient means of modelling parallel systems such as communicating processes concurrent processors shared memory etc the advantage that the san approach has over generalized stochastic petri nets and indeed over any markovian analysis that requires the generation of a transition matrix is that its representation remains compact even as the number of states in the underlying markov chain begins to explode our concern in this paper is with the numerical issues that are involved in solving san networks we introduce stochastic automata and consider the numerical difficulties that result from their interaction we examine how the product of a vector with a compact san descriptor may be formed for this operation is the basis of all iterative solution methods we describe possible solution methods including the power method the method of arnoldi and gmres and show that the two latter methods greatly out perform the power method the method usually used in conjunction with stochastic automata networks finally we consider one possible means of preconditioning but conclude that further research is needed

circulant preconditioners for failure prone manufacturing systems this paper studies the application of preconditioned conjugate gradient methods in solving for the steady state probability distribution of manufacturing systems we consider the optimal hedging policy for a failure prone one machine system the machine produces one type of product and its demand has finite batch arrival the machine states and the inventory levels are modeled as markovian processes we construct the generator matrix for the machine inventory system the preconditioner is constructed by taking the circulant approximation of the near toeplitz structure of the generator matrix we prove that the preconditioned linear system has singular values clustered around one when the number of inventory levels tends to infinity hence conjugate gradient methods will converge very fast when applied to solving the preconditioned linear system numerical examples are given to verify our claim the average running cost for the system can be written in terms of the steady state probability distribution the optimal hedging point can then be obtained by varying different values of the hedging point

adelic models of tensor triangulated categories abstract we show that a well behaved noetherian finite dimensional stable monoidal model category has a model built from categories of modules over completed rings in an adelic fashion special cases include abelian groups the hasse square chromatic homotopy theory a module theoretic chromatic fracture square and rational torus equivariant homotopy theory first step to the model of 30

exact algorithms for singular tridiagonal systems with applications to markov chains in this paper we propose two exact algorithms to solve the steady state probability distributions of irreducible markov chains whose generator matrices have tridiagonal structure the first exact algorithm is based on divide and conquer procedure and the second one is a parallel algorithm examples on random walks and queuing networks are given to demonstrate the usefulness of the algorithms

a direct method for deriving a multi soliton solution for the problem of interaction of waves on the x y plane explicit expressions are found for a multi soliton solution of the system of equations describing the interaction of waves on thex y plane the proof of all necessary statements follows from the theory of matrices and is not based on the inverse scattering method the obtained results are closely related to some problems of mathematical physics

the n soliton solutions for the non isospectral mkdv equation the bilinear form of the non isospectral mkdv equation is given and the exact n soliton solutions are obtained through hirota method and wronskian technique respectively c

stochastic dynamic job shops and hierarchical production planning this paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products the concept of a dynamic job shop is introduced by interpreting the system as a directed graph and the structure of the system dynamics is characterized for its use in the asymptotic analysis the optimal control problem for the system is a state constrained problem since the number of parts in any buffer between any two machines must remain nonnegative a limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities as the rate of change in machine states approaches infinity the value function of the original problem is shown to converge to that of the limiting problem and the convergence rate is obtained furthermore near optimal controls for the original problem are constructed from near optimal controls of the limiting problem and an error estimate is obtained on the near optimality of the constructed controls

boundary value methods for solving transient solutions of markovian queueing networks in this paper we consider boundary value methods bvms for finding transient solutions of markovian queueing networks algebraic multigrid amg methods with modified restriction operator are applied to solve the resulting system of linear equations numerical examples are given to demonstrate the efficiency of our proposed method

solution of an initial boundary value problem for coupled nonlinear waves the authors derive and study a hierarchy of nonlinear coupled evolution equations among which is the coupled korteveg de vries schrodinger equation for which they prove that a mixed initial boundary value problem is solvable they give the method of solution together with the backlund transformation and establish the infinite set of conserved densities they finally discuss the applicability of such equations in plasma physics and hydrodynamics

derived hall algebras the purpose of this work is to define a derived hall algebra mathcal dh t associated to any dg category t under some finiteness conditions our main theorem states that mathcal dh t is associative and unital it is shown that mathcal dh t contains the usual hall algebra mathcal h t when t is an abelian category we will also prove an explicit formula for the derived hall numbers purely in terms of invariants of the triangulated category associated to t as an example we describe the derived hall algebra of an hereditary abelian category

solitonic interactions and double wronskian type solutions for a variable coefficient variant boussinesq model in the long gravity water waves abstract under investigation in this paper is a variable coefficient variant boussinesq vcvb model for the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth connection between the vcvb model and a variable coefficient ablowitz kaup newell segur system is revealed under certain constraints with the help of the symbolic computation multi solitonic solutions in terms of the double wronskian determinant for the vcvb model are derived interactions among the vcvb solitons are discussed a novel dynamic property is observed i e the coexistence of elastic inelastic interactions