existence and stability of propagating fronts for an autocatalytic reaction diffusion system we study a one dimensional reaction diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic a b 2b and a cubic a 2b 3b autocatalysis the parameters of this system are in the ratio d d b d a of the diffusion constants of the reactant a and the autocatalyst b and the relative activity ii of the cubic reaction first for all values of d 0 and k greater than or equal to 0 we prove the existence of a family of propagating fronts or travelling waves describing the advance of the reaction in particular in the quadratic case k 0 we recover the results of billingham and needham phil trans r sec london a 334 1991 1 24 then if d is close to 1 and k is sufficiently small we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted sobolev spaces this extends part of the results that are known for the scalar equation to which our system reduces when d 1 c 1998 elsevier science b v

travelling waves of auto catalytic chemical reaction of general order an elliptic approach abstract in this paper we study the existence and non existence of travelling wave to parabolic system of the form a t a x x a f b b t d b x x a f b with f a degenerate nonlinearity in the context of an auto catalytic chemical reaction a is the density of a chemical species called reactant a b that of another chemical species b called auto catalyst and d d b d a 0 is the ratio of diffusion coefficients d b of b and d a of a respectively such a system also arises from isothermal combustion the nonlinearity is called degenerate since f 0 f 0 0 one case of interest in this article is the propagating wave fronts in an isothermal auto catalytic chemical reaction of order n a n b n 1 b with 1 n 2 and d 1 due to different molecular weights and or sizes of a and b the resulting nonlinearity is f b b n explicit bounds v and v that depend on d are derived such that there is a unique travelling wave of every speed v v and there does not exist any travelling wave of speed v v new to the literature it is shown that v v d when d 1 furthermore when d 1 it is shown rigorously that there exists a v min such that there is a travelling wave of speed v if and only if v v min estimates on v min improve significantly that of early works another case in which two different orders of isothermal auto catalytic chemical reactions are involved is also studied with interesting new results proved

stability of moving fronts in the ginzburg landau equation we use renormalization group ideas to study stability of moving fronts in the ginzburg landau equation in one spatial dimension in particular we prove stability of the real fronts under complex perturbations this extends the results of aronson and weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the ginzburg landau equation

transition from pushed to pulled fronts in piecewise linear reaction diffusion systems abstract the front dynamics in reaction diffusion equations with a piecewise linear reaction term is studied a transition from pushed to pulled fronts when they propagate into the unstable state is found using a variational principle this transition occurs for a critical value of the discontinuity position in the reaction function in particular we study how the transition depends on the properties of the reaction term and on the delay time our results are in good agreement with the numerical solutions of the model

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

new answers to an old question in the theory of differential algebraic equations in the context of linear differential algebraic equations daes one finds different associated explicit ordinary differential equations odes among them essential underlying and inherent explicit regular ones abbreviated euodes and ierodes euodes have been introduced in 1991 for index 2 daes in hessenberg form by means of special transformations ierodes result within the framework of the projector based decoupling each such explicit ode is occasionally considered to rule the flow of the dae the question to which extend euodes and ierodes are related to each other has been asked promptly after 1991 for index 2 hessenberg form daes answers have been given in 2005 saying that euodes represent somehow condensed ierodes recently euodes have been indicated for general arbitrary index daes and it has been proved that they are condensed ierodes the understanding of the relation between the ierode and the euodes enables to uncover the stability behavior of the dae flow in the present paper we show that both the ierodes and euodes of a dae with arbitrary high index do not at all depend on derivatives of the right hand side we consider adjoint pairs of daes and provide generalizations of the classical lagrange identity furthermore we address lyapunov spectra and lyapunov regularity

on the turing patterns in one dimensional gradient skew gradient dissipative systems in this article fundamental properties concerning the turing patterns are considered in one dimensional dissipative systems with gradient skew gradient structure introduced in m kuwamura and e yanagida phys d 175 2003 pp 185 195 it is a natural extension of free energy which covers reaction diffusion systems of activator inhibitor type the theory based on this concept provides a new perspective on a fundamental problem of what unique turing pattern is to be selected among many

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

adjoint sensitivity analysis for differential algebraic equations the adjoint dae system and its numerical solution an adjoint sensitivity method is presented for parameter dependent differential algebraic equation systems daes the adjoint system is derived along with conditions for its consistent initialization for daes of index up to two hessenberg for stable linear daes stability of the adjoint system for semi explicit daes or of an augmented adjoint system for fully implicit daes is shown in addition it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system

holotransformations of bacterial colonies and genome cybernetics we present a study of colony transformations during growth of bacillus subtilis under adverse environmental conditions it is a continuation of our pilot study of adaptive self organization during growth of bacterial colonies physica a 187 1992 378 first we identify and describe the transformations pathway i e the excitation of the branching modes from bacillus subtilis 168 grown under diffusion limited conditions and the phase transformations between the tip splitting phase phase t and the chiral phase phase c which belong to the same mode this pathway shows the evolution of complexity as the bacteria are exposed to adverse growth conditions we present the morphology diagram of phases t and c as a function of agar concentration and pepton level as expected the growth of phase t is ramified fractal like or dla like at low pepton level about 1 g 1 and turns compact at high pepton level about 10 g 1 the growth of phase c is also ramified at low pepton level and turns denser and finally compact as the pepton level increases generally speaking the colonies develop more complex patterns and higher micro level organization for more adverse environments we use the growth velocity as a response function to describe the growth at low agar concentration and low pepton level phase c grows faster than phase t and for a high agar concentration about 2 phase t grows faster we observe colony transformations between the two phases phase transformations they are found to be consistent with the fastest growing morphology selection principle adopted from azoic systems the transformations are always from the slower phase to the faster one hence we observe t c transformations at low agar concentrations and c t transformations at high agar concentrations we have observed both localized and extended transformations usually the transformations are localized for more adverse growth conditions and extended for growth conditions close to the boundaries between morphologies we have observed also transformations between different branching modes as well as transformations via virtual states motivated by the contemporary knowledge about phages and plasmids we postulate a theoretical framework to comply with our experimental findings we explain our observations using these assumptions as well as our proposal of co mutations and auto catalytic mutations as presented in the above mentioned pilot paper this theoretical framework is a part of the new evolving picture of genome cybernetics we also discuss the concept of adaptive genome changes which are based on pre existing knowledge as well as the concept of genetic learning i e changes in response to a new problem which develop the potential for adaptive genome changes these concepts follow naturally if the picture of genome cybernetics is accepted we conclude with a discussion of the implications and with further predictions to be tested experimentally derived from our assumptions

speed shift in reaction diffusion equations with cutoff abstract front solutions in a reaction diffusion equations with cutoff are obtained analytically using piecewise linear approximations of the reaction term the piecewise emulation allows us to study analytically the effect of the cutoff for fronts propagating into metastable and unstable states a general relationship between the cutoff threshold and the parameters involved into the reaction term is derived our results are in excellent agreement with that existing in the literature and prove that the piecewise emulation is an useful procedure to deal with complex reaction diffusion equations under cutoff

on the stability of the abramov transfer for differential algebraic equations of index 1 the transfer of boundary conditions for ordinary differential equations developed by abramov zh vychisl mat mat fiz 1 1961 pp 542 545 is a stable method for representing the solution spaces of linear boundary value problems instead of boundary value problems matrix valued initial value problems are solved when integrating these differential equations the inner independence of the columns of the solution matrix and hence of the solutions of the resulting linear system of equations remains valid balla and marz have generalized abramov s transfer for homogenized index 1 differential algebraic equations siam j numer anal 33 1996 pp 2318 2332 in this article a direct version of the abramov transfer for inhomogeneous linear mbox index 1 differen linebreak 4 tial algebraic equations is developed and the numerical stability of this method is proved

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

travelling kinks in schlogl s second model for non equilibrium phase transitions using the separation technique developed by osborne and stuart 1980 travelling wave solutions are written down for the nonlinear reaction diffusion equation of schlogl s second model assuming that the necessary conditions for the static phase coexistence are satisfied

speed selection for traveling wave solutions to the diffusion reaction equation with cubic reaction term and burgers nonlinear convection the problem of traveling wave tw speed selection for solutions to a generalized murray burgers kpp fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results depending on the magnitude of a parameter inherent in the reaction term i the term is either a concave function or a function with the inflection point and ii transition from pulled to pushed tw solution occurs due to interplay of two nonlinear terms the reaction term and the burgers convection term explicit pushed tw solutions are derived it is shown that physically observable tw solutions i e solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition can be determined by seeking the tw solution characterized by the maximum decay rate at its leading edge in the appendix the developed approach is applied to a non linear diffusion reaction equation that is widely used to model premixed turbulent combustion

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

renormalization group and the ginzburg landau equation we use renormalization group methods to prove detailed long time asymptotics for the solutions of the ginzburg landau equations with initial data approaching asx different spiraling stationary solutions a universal pattern is formed depending only on this asymptotics at spatial infinity

vacillating hecke tableaux and linked partitions we introduce the structure of vacillating hecke tableaux by using the hecke insertion algorithm developed by buch kresch shimozono tamvakis and yong we establish a one to one correspondence between vacillating hecke tableaux and linked partitions which arise in free probability theory we define a hecke diagram as a young diagram possibly with a marked corner a vacillating hecke tableau is defined as a sequence of hecke diagrams subject to a certain condition on addition and deletion of rook strips the notion of a rook strip was introduced by buch in the study of the littlewood richardson rule for stable grothendieck polynomials we show that the crossing number and the nesting number of a linked partition can be determined by the maximal number of rows and the maximal number of columns of diagrams in the corresponding vacillating hecke tableau the proof relies on a theorem due to thomas and yong as consequences we confirm two conjectures on the distribution of the crossing number and the nesting number over linked partitions and ordinary partitions respectively proposed by de mier and kim

existence and nonexistence of travelling waves of a reaction diffusion system abstract in this paper we study the existence and nonexistence of travelling waves of the reaction diffusion system a t a x x e a x a b k a b q b t d b x x d e b x a b k a b q where a b are concentration densities of the two chemical species d 0 is the ratio of diffusion coefficients of the two chemical species involved e is the strength of the electric field applied k 0 is a parameter and q 1 the system arises from the study of two dimensional iodate arsenous acid iaa reaction with a constant electric field applied iaa reaction is very much studied in experiments and demonstrates the interesting phenomenon of instability driven by buoyancy of travelling waves by using a novel approach explicit bounds c d e and c d e are derived such that there is a unique travelling wave of every speed c c d e and there does not exist any travelling wave of speed c c d e with q being fixed in addition c d e bears a close resemblance of the minimum travelling wave speed of the classical case of d 1 and e 0 when 0 e 1 and d 1

pushed global modes in weakly inhomogeneous subcritical flows abstract a new type of nonlinear global mode or fully nonlinear synchronized solution arising in the dynamics of open shear flows which behave as oscillators annu rev fluid mech 22 1990 473 and in optical parametric oscillators j opt soc am b 17 2000 997 is identified in the context of the real subcritical ginzburg landau equation with slowly varying coefficients the nonlinear global modes satisfy a boundary condition accounting for the inlet of the flow we show that the spatial structure of these new nonlinear global modes consists of a localized state limited by a pushed upstream front that withstand the mean advection and a fast return to zero downstream achieved either by a second stationary front facing backward or by a saddle node bifurcation driven by the non parallelism of the flow we derive scaling laws for the slope of the nonlinear global modes at the inlet and for the position of the maximum amplitude which are in agreement with similar scaling obtained in experiments with a shear layer in a hele shaw cell phys rev lett 82 1999 1442 extension to the complex ginzburg landau equation is discussed in a large region of parameters the nonlinear global modes have the same spatial structure as in the real case and oscillate at a global frequency selected at threshold by the pushed front in parameters region where these pushed global modes are not selected new states with a non periodic in time behavior are exhibited

studies of bacterial branching growth using reaction diffusion models for colonial development abstract various bacterial strains exhibit colonial branching patterns during growth on poor substrates these patterns reflect bacterial cooperative self organization and cybernetic processes of communication regulation and control employed during colonial development one method of modeling is the continuous or coupled reaction diffusion approach in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields in the context of branching growth this idea has been pursued by a number of groups we present an additional model which includes a lubrication fluid excreted by the bacteria we also add fields of chemotactic agents to the other models we then present a critique of this whole enterprise with focus on the models potential for revealing new biological features

multilinear function series and transforms in free probability theory abstract the algebra mul b of formal multilinear function series over an algebra b and its quotient symmul b are introduced as well as corresponding operations of formal composition in the setting of mul b the unsymmetrized r and t transforms of random variables in b valued noncommutative probability spaces are introduced these satisfy properties analogous to the usual r and t transforms the latter being just the reciprocal of the s transform but describe all moments of a random variable not only the symmetric moments the partially ordered set of noncrossing linked partitions is introduced and is used to prove properties of the unsymmetrized t transform

kondo effect in single atom contacts the importance of the atomic geometry co single atom junctions on copper surfaces are studied by scanning tunneling microscopy and ab initio calculations the kondo temperature of single cobalt atoms on the cu 111 surface has been measured at various tip sample distances ranging from tunneling to the point contact regime the experiments show a constant kondo temperature for a whole range of tip substrate distances consistently with the predicted energy position of the spin polarized d levels of co this is in striking difference to experiments on co cu 100 junctions where a substantial increase of the kondo temperature has been found our calculations reveal that the different behavior of the co adatoms on the two cu surfaces originates from the interplay between the structural relaxations and the electronic properties in the near contact regime

finite size effects in random energy models and in the problem of polymers in a random medium by the use of traveling wave equations we calculate the finite size corrections to the free energy of random energy models in their low temperature phases and in the neighborhood of the transition temperature we find that although the extensive part of the free energy does not show any critical behavior when the temperature approaches its transition value the finite size corrections signal the transition by becoming singular we obtain a scaling form for these finite size corrections valid in the limitn andt t c by considering a generalized random energy model in the limit of a very large number of steps we obtain results for the finite size corrections in the problem of a polymer in a random medium

on the s transform over a banach algebra abstract the s transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a b valued banach noncommutative probability space for an arbitrary unital complex banach algebra b also a new proof of the additivity of the r transform in this setting is given

instabilities and propagation properties in a fourth order reaction diffusion equation in this paper we investigate the instability and the propagation properties of a class of reaction diffusion equations of fourth order two examples are introduced the extended fisher kolmogorov equation efk and the swift hohenberg equation sh both have been studied before by related methods see for example peletier and rottschafer 2004 19 van saarloos 2003 24 but the analysis here will support the introduced linear mechanism in front selection these two equations support a patterned front solutions and the double eigenvalue mechanism is used to provide evidence for that and to determine a minimal front speed

structural stability and selection of propagating fronts in semilinear parabolic partial differential equations an alternative viewpoint for the selection problem in propagating front systems is presented we propose that the selected solution can be identified through analysis of the structural stability of the solutions in question a solution to a given equation is considered structurally stable if it suffers only an infinitesimal change when the equation not the solution is perturbed infinitesimally applying the structural stability condition we identify selected solutions for semilinear parabolic partial differential equations single mode equations of the fisher type and multiple mode equations that assume something of a generalized fisher form the structural stability condition is confirmed for the subclass of single mode equations to which the aronson weinberger theorem applies in partial differential equations and related topics edited by j a goldstein springer heidelberg 1975 for other single mode equations and multiple mode equations the structural stability condition is confirmed numerically equations possessing multiple physically realizable solutions are also studied and several causes for such behavior are identified we describe what we believe to be the fundamental feature distinguishing physically realizable and physically unrealizable solutions

speed selection mechanism for propagating fronts in reaction diffusion systems with multiple fields we introduce a speed selection mechanism for front propagation in reaction diffusion systems with multiple fields this mechanism applies to pulled and pushed fronts alike and operates by restricting the fields to large finite intervals in the comoving frames of reference the unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field making thus the solution approximately translation invariant the fronts for the various fields may propagate at different speeds all of them being determined though through this mechanism we present analytic results for the case of piecewise parabolic potentials and numerical results for other cases

wave linked partitions and 312 avoiding permutations with primacy being 1 abstract in this paper we mainly study connected non crossing linked partitions which are vividly called wave linked partitions and their relation to 312 avoiding permutations with primacy being 1 let w n be the set of wave linked partitions of 1 2 n and let w n k be the number of wave linked partitions of 1 2 n with wave of length k we obtain that the enumeration of w n 1 is counted by the well known nth catalan number cn and we present the recurrence relation of w n k let p1 n be the set of 312 avoiding permutations of 1 2 n with primacy being 1 as a main result we construct an interesting bijection between w n and p1 n by introducing a labeling rule on wave linked partitions the labeling rule implies that the major index of such kind of permutations can be easily obtained from the labels of certain vertices in the corresponding wave linked partitions

higher dimensional localized patterns in excitable media abstract the excitable reaction diffusion equation model of the form e u t e 2 2 u u v v t 2 v u v is considered when u is assumed to be of mckean s piecewise linear type the interfacial approach can be applied to the stability of various localized patterns in higher dimensional spaces it is shown that a band shaped localized pattern is destabilized into a zig zag mode or a varicose mode and that a disk shaped localized pattern is destabilized into static modes and when is small into an oscillatory mode like a breather motion numerical simulations are performed to confirm such destabilizations for more general nonlinear functions u

emergence of approximate translation invariance in finite intervals as a speed selection mechanism for propagating fronts we introduce a velocity selection criterion for fronts propagating into unstable and metastable states we restrict these fronts to large finite intervals in the comoving frame of reference and require that their centers be insensitive to the locations of the ends of the finite intervals thus exhibiting effectively an approximate translation invariance only one monotonic front has this behavior and its velocity is the one that is physically selected we present analytic results in the case of piecewise parabolic potentials and numerical results in other cases

contest based on a directed polymer in a random medium we introduce a simple one parameter game derived from a model describing the properties of a directed polymer in a random medium at his turn each of the two players picks a move among two alternatives in order to maximize his final score and minimize opponent s return for a game of length n we find that the probability distribution of the final score s n develops a traveling wave form rm prob s n m f m v n with the wave profile f z unusually decaying as a double exponential for large positive and negative z in addition as the only parameter in the game is varied we find a transition where one player is able to get his maximum theoretical score by extending this model we suggest that the front velocity v is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially and for which standard traveling wave theory applies

hopf algebras and the logarithm of the s transform in free probability let k be a positive integer and let g k denote the set of all joint distributions of k tuples a 1 a k in a noncommutative probability space a such that a 1 a k 1 g k is a group under the operation of the free multiplicative convolution we identify g k as the group of characters of a certain hopf algebra y k then by using the log map from characters to infinitesimal characters of y k we introduce a transform ls for distributions g k ls is a power series in k noncommuting indeterminates z 1 z k its coefficients can be computed from the coefficients of the r transform of by using summations over chains in the lattices nc n of noncrossing partitions the ls transform has the linearizing property that ls ls ls g k such that in the particular case k 1 one has that y 1 is naturally isomorphic to the hopf algebra sym of symmetric functions and that the ls transform is very closely related to the logarithm of the s transform of voiculescu by the formula ls z z log s z g 1 in this case the group g 1 can be identified as the group of characters of sym in such a way that the s transform its reciprocal 1 s and its logarithm log s relate in a natural sense to the sequences of complete elementary and respectively power sum symmetric functions

addition of certain non commuting random variables soit g le groupe libre non commutatif sur deux generateurs et soit u j j 1 2 les unites dans l 2 g correspondant a la translation a gauche par les generateurs et on considere l 2 g la fonction g g e soient x j des operateurs de la forme x j j u j les operateurs x j peuvent etre consideres comme des variables aleatoires de moments ou de facon equivalente avec des distributions donnees par les fonctionnelles analytiques j ou j f avec ces conventions la distribution de x 1 x 2 depend seulement des distributions de x 1 et x 2 on explique cette relation

the parity of the number of permutation tableaux in a fixed shape permutation tableaux were introduced in the study of totally positive grassmannian cells and are connected with the steady state of asymmetric exclusion process which is an important model from statistical mechanics the notion of linked partitions was introduced by dykema in the study of the unsymmetrized t transform in free probability theory in this paper we mainly establish the parity of the number of permutation tableaux of a fixed shape to achieve the aim we utilize the linked partitions as an intermediate structure to be specific we first introduce the structures of rainbow linked partitions and non rainbow linked partitions and then we establish an involution on the set of linked partitions of 1 n according to these two special structures combining the involution with a bijection between linked partitions of 1 n and permutation tableaux of length n given by chen et al 2 we obtain the desired result that the number of permutation tableaux of a fixed shape is odd in addition we present several interesting correspondences among rainbow linked partitions compositions of integers and unimodal permutations we also have a generalized bijection between the linked partitions and permutations

travelling waves in radially symmetric parabolic systems on montre que toutes les solutions ondes planes de propagation ou stationnaire de certains systemes paraboliques a symetrie radiale peuvent etre trouvees en resolvant une equation differentielle scalaire associee

speed of wave front solutions to hyperbolic reaction diffusion equations the asymptotic speed problem of front solutions to hyperbolic reaction diffusion hrd equations is studied in detail we perform linear and variational analyses to obtain bounds for the speed in contrast to what has been done in previous work here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds for some functions it is possible to determine the speed without any uncertainty this is also achieved for some systems of hrd i e time delayed lotka volterra equations that take into account the interaction among different species an analytical analysis is performed for several systems of biological interest and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently s1063 651x 99 06211 x

selection stability and renormalization abstract we illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem this consideration leads us to a renormalization group study of the problem the study illustrates two very general conclusions 1 singular perturbations in applied mathematics are best understood as renormalized perturbation methods and 2 amplitude equations are renormalization group equations

non commutative functions and the non commutative free levy hincin formula abstract the paper is discussing infinite divisibility in the setting of operator valued boolean free and more general c free independences particularly using hilbert bimodule and non commutative function techniques we obtain analogues of the levy hincin integral representation for infinitely divisible real measures

piecewise linear emulation of propagating fronts as a method for determining their speeds we use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction diffusion equation replacing it thus with a set of simple linear inhomogeneous differential equations the resulting analytic solution constitutes an excellent approximation to the exact propagating front as is explicitly shown in the case of cubic and quintic nonlinearities yielding also the correct value for the physically selected speed of the observable front such a piecewise linear emulation can be used for any nonlinearity giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states especially pushed fronts

transfer of boundary conditions for daes of index 1 in this paper the concept of abramov s method for transferring boundary conditions posed for regular ordinary differential equations odes is applied to index 1 differential algebraic equations daes having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of abramov s method we consider boundary value problems for index 1 linear daes both with constant and varying leading matrices we describe the relations defining the subspaces of solutions satisfying the prescribed boundary conditions at one end of the interval the index 1 daes which realize the transfer are given and their properties are studied the results are reformulated for inhomogeneous index 1 daes as well

invariant painleve analysis and coherent structures of two families of reaction diffusion equations exact closed form coherent structures pulses fronts domain walls having the form of complicated traveling waves are constructed for two families of reaction diffusion equations by the use of invariant painleve analysis these analytical solutions which are derived directly from the underlying pde s are investigated in the light of restrictions imposed by the ode that any traveling wave reduction of the corresponding pde must satisfy in particular it is shown that the coherent structures a asymptotically satisfy the ode governing traveling wave reductions and b are accessible to the pde from compact support initial conditions the solutions are compared with each other and with previously known solutions of the equations

multiplicative functions on the lattice of non crossing partitions and free convolution the lattice of non crossing partitions was introduced by kreweras kre in 1972 and examined further by poupard pou and edelman edel ede2 in the last time there has been an increased interest in this lattice on one hand from the purely combinatorial point of view siu eds sire bss and on the other hand from a quantum probabilistic point of view gss spel spe2 spe3 we became interested in this lattice when we noticed that it is connected with some new form of convolution for probability measures the free convolution introduced by voiculescu voil voi2 voi3 this connection between the free convolution and the lattice of non crossing partitions is exactly analogous to the connection between the usual convolution and the lattice of all partitions we shall work out this connection in the last part of this work the intention of this article is to show that both the purely combinatorial and the probabilistic point of view can benefit from each other motivated by voiculescu s formula for the r series of free convolution we examine multiplicative functions on the lattice of non crossing partitions and prove our main theorem which is much in the spirit of voiculescu s formula we shall then use this main theorem for deriving some known results on non crossing partitions in a unified way this part of our work is purely combinatorial the free convolution serves only as a motivation for our theorem in the last section we shall switch to the probabilistie side and show how the lattice of non crossing partitions determines the structure of the free convolution voiculescu s formula will then follow as an easy corollary of our main theorem in this respect we shall get a purely combinatorial proof of this formula without any operator algebraic or functional analytic tools