the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

a feynman kac ito formula for magnetic schrodinger operators on graphs in this paper we prove a feynman kac ito formula for magnetic schrodinger operators on arbitrary weighted graphs to do so we have to provide a natural and general framework both on the operator theoretic and the probabilistic side of the equation on the operator side we identify a very general class of potentials that allows the definition of magnetic schrodinger operators on the probabilistic side we introduce an appropriate notion of stochastic line integrals with respect to magnetic potentials apart from linking the world of discrete magnetic operators with the probabilistic world through the feynman kac ito formula the insights from this paper gained on both sides should be of an independent interest as applications of the feynman kac ito formula we prove a kato inequality a golden thompson inequality and an explicit representation of the quadratic form domains corresponding to a large class of potentials

configurational invariants of hamiltonian systems in this paper we explore the general conditions in order that a two dimensional natural hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore liouville integrable we examine the possibility that the invariant is preserved by the hamiltonian flow on a given energy hypersurface only weak integrability and derive the additional requirement necessary to have conservation at arbitrary energy strong integrability using null complex coordinates we show that the leading order coefficient of the polynomial is an arbitrary holomorphic function in the case of weak integrability and a polynomial in the coordinates in the strongly integrable one we review the results obtained so far with strong invariants up to degree four and provide some new examples of weakly integrable systems with linear and quadratic invariants

random magnetic fields on line graphs we study the spectral and transport properties of schrodinger operators on line graphs with random magnetic fields we show that it has a pure point spectrum with exponentially decaying eigenfunctions on spectral edges whereas there appears an eigenvalue with infinite multiplicity due to the structure of line graphs we compute the electrical conductivity which is zero on spectral edges but is nonzero and finite on the isolated eigenvalue mentioned above some related problems are also discussed

an equivalence classes model of fuzzy relational databases abstract the technique of employing sets of values for tuple components to express imprecision in relational databases was proposed by buckles and petry in their classic works on fuzzy relational databases in addition to providing an intuitively appealing scheme for representing fuzzy information the model of buckles and petry possesses several key properties of the classical relational model by employing finite scalar domains with similarity relations and special fuzzy number domains buckles and petry have demonstrated that the classical properties of uniqueness of tuple interpretations and well definedness of the relational algebra can be retained in the fuzzy relational database model the key to the preservation of these properties is the fact that scalar domains with similarity relations and the fuzzy number domains can be partitioned into equivalence classes however since equivalence classes can be constructed without assuming the existence of similarity relations or special fuzzy number domains it is desirable to generalize the fuzzy relational database model to one based only on equivalence classes in this work we show that the important properties of classical relational databases and of fuzzy relational databases are preserved in a generalized model built on equivalence relations on finite database domains further we generalize the notion of a functional dependency to the fuzzy relational model

ferromagnetic ground states for the hubbard model on line graphs the author discusses some of the properties of the hubbard model on a line graph with n vertices it is shown that the model has ferromagnetic ground states if the interaction is repulsive u 0 and if the number of electrons n satisfies 2n or n or m m is a natural number that depends on the line graph for example the kagome lattice is a line graph it has m 5n 3 1

a lower bound for nodal count on discrete and metric graphs we study the number of nodal domains maximal connected regions on which a function has constant sign of the eigenfunctions of schrodinger operators on graphs under a certain genericity condition we show that the number of nodal domains of the nth eigenfunction is bounded below by n l where l is the number of links that distinguish the graph from a tree

rigorous results for the minimal speed of kolmogorov petrovskii piscounov monotonic fronts with a cutoffa we study the effect of a cutoff on the speed of pulled fronts of the one dimensional reaction diffusion equation to accomplish this we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles this existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut off parameter from these bounds we estimate the range of validity of the brunet derrida formula for a general class of reaction terms

integrable hamiltonian systems with vector potentials we investigate integrable two dimensional hamiltonian systems with scalar and vector potentials admitting second invariants which are linear or quadratic in the momenta in the case of a linear second invariant we provide some examples of weakly integrable systems in the case of a quadratic second invariant we recover the classical strongly integrable systems in cartesian and polar coordinates and provide some new examples of integrable systems in parabolic and elliptical coordinates

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

linear stability of steady states for thin film and cahn hilliard type equations we study the linear stability of smooth steady states of the evolution equation h t f h xxx x g h h x x ah under both periodic and neumann boundary conditions if a 0 we assume f 1 in particular we consider positive periodic steady states of thin film equations where a 0 and f g might have degeneracies such as f 0 0 as well as singularities like g 0

shift in the speed of reaction diffusion equation with a cut off pushed and bistable fronts abstract we study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut off we give explicit formulas for the shift in the speed for arbitrary reaction terms f u the dependence of the speed shift on the cut off parameter is a function of the front speed and profile in the absence of the cut off in order to determine the speed shift we solve the leading order approximation to the front profile u z in the neighborhood of the leading edge and use a variational principle for the speed we apply the general formula to the nagumo equation and recover the results which have been obtained recently by geometric analysis the formulas given are of general validity and we also apply them to a class of reaction terms which have not been considered elsewhere

the spectrum of infinite regular line graphs let g be an infinite d regular graph and l g its line graph we consider discrete laplacians on g and l g and show the exact relation between the spectrum of ag and that of al g our method is also applicable to di d2 semiregular graphs subdivision graphs and para line graphs

fluxes laplacians and kasteleyn s theorem the genesis of this paper was an attempt to understand a problem in condensed matter physics related to questions about electron correlations superconductivity and electron magnetic field interactions the basic idea which was proposed a few years ago is that a magnetic field can lower the energy of electrons when the electron density is not small certain very specific and very interesting mathematical conjectures about eigenvalues of the laplacian were made and the present paper contains a proof of some of them furthermore those conjectures lead to additional natural conjectures about determinants of laplacians which we both present and prove here it is not clear whether these determinantal theorems have physical applications but they might conceivably in the context of quantum field theory some but not all of the results given here were announced earlier in le

pattern selection in long wavelength convection abstract the long wavelength of the first instability in rayleigh benard convection between nearly thermally insulating horizontal plates is typical of a variety of physical systems the evolution of such an instability is described by the equation t 2 4 2 2 2 2 where is the planform function is the scaled rayleigh number and 1 the quantities represent the effects of finite biot number asymmetry in the boundary conditions at top and bottom and departures from the boussinesq approximation respectively the quantity when the original problem is self adjoint but otherwise planform selection is studied for 1 using equivariant bifurcation theory on the square lattice both rolls and squares can be stable depending on the parameters and the possible secondary bifurcations located near various codimension two singularities are analyzed on the hexagonal lattice the primary bifurcation is always degenerate when 0 of the six primary solution branches possible in this case the hexagon branch is stable when 0 both rolls and hexagons bifurcate supercritically but rolls are stable finally when and or 0 a hysteretic transition to h or h occurs depending on sgn k 2 c if stable h h coexist at larger amplitudes but if k 2 c 0 1 a further hysteretic transition takes place with increasing amplitude in which the hexagons are replaced by stable rolls

the number of nodal domains on quantum graphs as a stability index of graph partitions the courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of laplacian type operators in particular it holds for generic eigenfunctions of a quantum graph the theorem stipulates that after ordering the eigenvalues as a non decreasing sequence the number of nodal domains n of the n th eigenfunction satisfies n n here we provide a new interpretation for the courant nodal deficiency d n n n in the case of quantum graphs it equals the morse index at a critical point of an energy functional on a suitably defined space of graph partitions thus the nodal deficiency assumes a previously unknown and profound meaning it is the number of unstable directions in the vicinity of the critical point corresponding to the n th eigenfunction to demonstrate this connection the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail

on the flux phase conjecture at half filling an improved proof we present a simplification of lieb s proof of the flux phase conjecture for interacting fermion systems such as the hubbard model at half filling on a general class of graphs the main ingredient is a procedure which transforms a class of fermionic hamiltonians into reflection positive form the method can also be applied to other problems which we briefly illustrate with two examples concerning the t v model and an extended falicov kimball model

order parameter equations for long wavelength instabilities abstract we consider order parameter equations describing the nonlinear evolution of finite amplitude disturbances near the threshold of a large scale instability it is shown that the ginzburg landau equation is not valid in many cases the structure of typical order parameter equations is discussed

magnetic schrodinger operators on periodic discrete graphs abstract we consider magnetic schrodinger operators with periodic magnetic and electric potentials on periodic discrete graphs the spectrum of the operators consists of an absolutely continuous part a union of a finite number of non degenerate bands plus a finite number of flat bands i e eigenvalues of infinite multiplicity we estimate the lebesgue measure of the spectrum in terms of the betti numbers and show that these estimates become identities for specific graphs we estimate a variation of the spectrum of the schrodinger operators under a perturbation by a magnetic field in terms of magnetic fluxes the proof is based on floquet theory and a precise representation of fiber magnetic schrodinger operators constructed in the paper

nonlinear aspects of the cahn hilliard equation abstract this paper treats phase separation within the context of the phenomenological cahn hilliard equation c t m c f c k 2 c where c is the concentration m c is the mobility and f c is homogeneou s free energy which is assumed here to be a fourth degree polynomial natural boundary conditions are introduced the full set of equilibrium solutions is specified a comparison theorem for stability criteria which was postulated by langer is proved here within the framework of the natural boundary conditions energy methods are used to define and estimate the limit of monotonic global stability it is pointed out that within the parameter region where the uniform homogeneous state is the only equilibrium solution there may still exist some internal excitable region in which the homogeneous solution possesses growing fluctuations furthermore a periodic instability is shown to exist in the metastable region in addition to the well known nucleation instability

slowly oscillating wave solutions of a single species reaction diffusion equation with delay we study positive bounded wave solutions u t x x ct 0 of equation ut t x u t x u t x g u t h x x rm this equation is assumed to have two non negative equilibria u1 0 and u2 0 the birth function g c r r is unimodal and differentiable at 0 and some results also require the feedback condition g s s c our results are based on a detailed geometric description of the wave profile in particular the monotonicity of its leading edge is established we also discuss the uniqueness problem indicating a subclass g of asymmetric tent maps such that given g g there exists exactly one positive travelling front for each fixed admissible speed

anomalous nodal count and singularities in the dispersion relation of honeycomb graphs we study the nodal count of the so called bi dendral graphs and show that it exhibits an anomaly the nodal surplus is never equal to 0 or the first betti number of the graph according to the nodal magnetic theorem this means that bands of the magnetic spectrum dispersion relation of such graphs do not have maxima or minima at the usual symmetry points of the fundamental domain of the reciprocal space of magnetic parameters in search of the missing extrema we prove a necessary condition for a smooth critical point to happen inside the reciprocal fundamental domain using this condition we identify the extrema as the singularities in the dispersion relation of the maximal abelian cover of the graph the honeycomb graph being an important example in particular our results show that the anomalous nodal count is an indication of the presence of conical points in the dispersion relation of the maximal universal cover we also discover that the conical points are present in the dispersion relatio

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

back in the saddle again a computer assisted study of the kuramoto sivashinsky equation a numerical and analytical study of the kuramoto sivashinsky partial differential equation pde in one spatial dimension with periodic boundary conditions is presented the structure stability and bifurcation characteristics of steady state and time dependent solutions of the pde for values of the parameter alpha less than 40 are examined the numerically observed primary and secondary bifurcations of steady states as well as bifurcations to constant speed traveling waves limit cycles are analytically verified persistent homoclinic and heteroclinic saddle connections are observed and explained via the system symmetries and fixed point subspaces of appropriate isotropy subgroups of o 2 their effect on the system dynamics is discussed and several tertiary bifurcations observed numerically are presented

extending the fuzzy database with fuzzy numbers abstract the fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete finite universe the model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra where equivalence is required in an ordinary relational database similarity is employed in a fuzzy relational database for discrete finite universes similarity between atomic elements is described via a fuzzy similarity relation with max min transitivity two or more fuzzy numbers are defined to be similar if their union forms a continuous level set over the real line this convention effects the partitioning of fuzzy number domains that is necessary to assure the well definedness of the fuzzy relational algebra

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

fuzzy loss less decompositions in databases in this paper we deal with the problem of defining projection and join operators in the framework of a fuzzy relational database we study the properties of such operators relating to the concept of fuzzy functional dependency there are two main properties to achieve on the one hand if a relation r satisfies a dependency between two sets of attributes x and y then we want to preserve this dependency in the fuzzy projection over xy of r on the other hand we want to test a fuzzy dependency just by looking at this projection therefore such a projection operator must allow us to store the information conveyed in r into a separate relation with fewer tuples in order to define the criterion for fuzzy dependency we shall need to extend a resemblance relation defined for crisp data to the fuzzy case finally we shall introduce a fuzzy join operator which will allow us to recover the information given in a relation from its projections

prediction of traveling front behavior in a lattice gas cellular automaton model for tumor invasion cancer invasion is the process of cells detaching from a primary tumor and infiltrating the healthy tissue cancer invasion has been recognized as a complex system since a tumor s invasive behavior emerges from the combined effect of tumor cell proliferation tumor cell migration and cell microenvironment interactions cellular automata ca provide simple models of self organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting simple components here we introduce a lattice gas cellular automaton lgca model of tumor cell proliferation necrosis and tumor cell migration the impact of the tumor environment on tumor cells has been investigated in a previous study our analysis aims at predicting the velocity of the traveling invasion front which depends upon fluctuations that arise from the motion of the discrete cells at the front we find an excellent agreement between the velocities measured in simulations of the lgca and an analytical estimate derived in the cut off mean field approximation via the discrete lattice boltzmann equation and its linearization in particular we predict the front velocity to scale with the square root of the product of probabilities for mitosis and the migration coefficient finally we calculate the width of the traveling front which is found to be proportional to the front velocity

variational approach to a class of nonlinear oscillators with several limit cycles we study limit cycles of nonlinear oscillators described by the equation x nuf x x 0 with f an odd function depending on the nonlinearity this equation may exhibit one or more limit cycles we show that limit cycles correspond to relative extrema of a certain functional analytical results in the limits nu 0 and nu infinity are in agreement with previously known criteria for intermediate nu numerical determination of the limit cycles can be obtained

zariski closure of subgroups of the symplectic group and lyapunov exponents of the schrodinger operator on the strip we consider the schrodinger equation with a random potential y n 1 q n ei y n y n 1 0 whereqn is a sequence of independent identically distributed random symmetricm m matrices with real valued elements yn m n e is the real parameter andi is the identity matrix we show that if the smallest jordan algebra of matrices containing the support of the distribution of matricesqn coincides with jordan algebra of all real valued symmetric matrices then for all but maybe a finite number of values ofe all the lyapunov exponents of our schrodinger equation are different and thus the spectrum of the corresponding schrodinger operator is pure point

variational principles and the shift in the front speed due to a cutoff we apply variational principles to reaction diffusion equations in order to predict for a general reaction term the sign of the shift in the front speed due to a cutoff we develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms and the theoretical results so obtained are in excellent agreement with numerical solutions this work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff

exact fronts for the nonlinear diffusion equation with quintic nonlinearities we consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities u t u xx mu u 1 u 1 alpha u beta u 2 gamma u 3 if the parameters alpha beta and gamma obey a special relation then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters if an additional restriction is imposed explicit front solutions can be obtained the approach used can be extended to polynomials whose highest degree is odd

global feedback control for pattern forming systems global feedback control of pattern formation in a wide class of systems described by the swift hohenberg sh equation is investigated theoretically by means of stability analysis and numerical simulations two cases are considered i feedback control of the competition between hexagon and roll patterns described by a supercritical sh equation and ii the use of feedback control to suppress the blowup in a system described by a subcritical sh equation in case i it is shown that feedback control can change the hexagon and roll stability regions in the parameter space as well as cause a transition from up to down hexagons and stabilize a skewed mixed mode hexagonal pattern in case ii it is demonstrated that feedback control can suppress blowup and lead to the formation of spatially localized patterns in the weakly nonlinear regime the effects of a delayed feedback are also investigated for both cases and it is shown that delay can induce temporal oscillations as well as blowup

on the transition from pulled to pushed monotonic fronts of the extended fisher kolmogorov equation abstract the extended fisher kolmogorov equation u t u xx u xxxx f u with arbitrary positive f u satisfying f 0 f 1 0 has monotonic traveling fronts for 1 12 we find a simple lower bound on the speed of the fronts which allows to determine for a given reaction term when will the front of minimal speed be pushed

blowup for nonlinear equations using a comparison principle in fourier space on decrit une nouvelle methode pour demontrer l eclatement en temps fini pour une classe d equations paraboliques semi lineaires

hierarchy of bifurcations of space periodic structures in a nonlinear model of active dissipative media abstract this work is a detailed research of spatial periodic structures and their bifurcations in a nonlinear model of media with an active dissipation presented here is an obvious bifurcation diagram of stationary solutions attractors on a wide scale of wave numbers are studied and classified significant progress in understanding of behavior of nonstationary solutions is attained

singularities in a modified kuramoto sivashinsky equation describing interface motion for phase transition abstract phase transitions can be modeled by the motion of an interface between two locally stable phases a modified kuramoto sivashinsky equation h t 2 h 4 h 1 h 2 2 h 2 h xx h yy h xy 2 describes near planar interfaces which are marginally long wave unstable we study the question of finite time singularity formation in this equation in one and two space dimensions on a periodic domain such singularity formation does not occur in the kuramoto sivashinsky equation 0 for all 1 0 we provide sufficient conditions on the initial data and size of the domain to guarantee a finite time blow up in which a second derivative of h becomes unbounded using a bifurcation theory analysis we show a parallel between the stability of steady periodic solutions and the question of finite time blow up in one dimension finally we consider the local structure of the blow up in the one dimensional case via similarity solutions and numerical simulations that employ a dynamically adaptive self similar grid the simulations resolve the singularity to over 25 decades in h xx l and indicate that the singularities are all locally described by a unique self similar profile in h xx we discuss the relevance of these observations to the full intrinsic equations of motion and the associated physics

an extended version of the fuzzy relational database model abstract the fuzzy relational database model proposed by buckles and petry is a formal method for organizing and using fuzzy information in relational databases the model possesses two key properties that hold for classical relational databases no two tuples have identical interpretations and each relational algebra operation has a unique result the original fuzzy relational database model was based on similarity relations which were defined on finite scalar domains buckles and petry later extended the model to incorporate fuzzy number domains this extension was done without loss of consistency with the representation or the relational algebra in a recent paper we have extended the original model to proximity relations which generalize similarity relations the key properties of buckles and petry s model are preserved in the extension in this work we demonstrate that the existence of partitions on finite scalar domains in the fuzzy relational model is the key to preserving the important properties of the classical relational model we explain how proximity relations defined on finite scalar domains are used to partition the domains further we show that normal fuzzy sets can be employed as domain values these fuzzy sets become members of fi nite scalar domains and their characteristic functions are employed in generating the proximity relations of the fuzzy relational database model

a pfaffian formula for monomer dimer partition functions we consider the monomer dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights with the restriction that the only non zero monomer weights are those on the boundary we prove a pfaffian formula for the corresponding partition function as a consequence of this result multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics our proof is based on the celebrated kasteleyn theorem combined with a theorem on pfaffians proved by one of the authors and a careful labeling and directing procedure of the vertices and edges of the graph

large amplitude solutions to the sivashinsky and riley davis equations for directional solidification abstract directional solidification of a dilute binary alloy is often characterized by the appearance of deep root finger type interfaces as a model of this phenomenon we investigate the large amplitude behavior of long wave evolution equations previously derived for directional solidification in this paper we conduct a detailed asymptotic and numerical study of the periodic solutions of the sivashinsky and riley davis equations the sivashinsky equation which describes the limit of small segregation coefficient is shown to form deep root solutions which can be described in terms of elliptic functions however this equation is known to be ill posed in the sense that the solution branches are unstable and large classes of initial conditions lead to finite time blow up by considering asymptotically large surface energy riley and davis derived an evolution equation which may be considered a regularizing perturbation of the sivashinsky equation this equation has steady large amplitude solutions which are linearly stable in the absence of solutal segregation we may describe these solutions asymptotically in this limit amplitudes and wavelengths may become arbitrarily large a stability analysis suggests that with periodic boundary conditions the solution may coarsen until a single finger fills the domain if segregation effects are included both the amplitude and wavelength are bounded independent of domain size this wavelength bound gives the system a finger width selection mechanism associated with a tip splitting bifurcation that has also been observed in experiments

bifurcation analysis of cellular interfaces in unidirectional solidification of a dilute binary mixture analytical bifurcation theory is used to study interface patterns in the unidirectional solidification of a dilute binary mixture armbruster and dangelmayr s classification of bifurcation equations equivariant under the diagonal action in mathbb c 2 of the symmetry group o 2 is used to show that the local bifurcation structure of the model long wave evolution equation derived by riley and davis is equivalent to that of a codimension one normal form xamination of the bifurcation structure of the normal form then leads to a description of the development of three dimensional interface patterns during unidirectional solidification the general methodology underlying this study is also discussed and conditions under which the method can be applied to other evolution equations are derived and clearly stated

speed of pulled fronts with a cutoff we study the effect of a small cutoff epsilon on the velocity of a pulled front in one dimension by means of a variational principle we obtain a lower bound on the speed dependent on the cutoff for which the two leading order terms correspond to the brunet derrida expression to do so we cast a known variational principle for the speed of propagation of fronts in different variables which makes it more suitable for applications

surgery principles for the spectral analysis of quantum graphs we present a systematic collection of spectral surgery principles for the laplacian on a compact metric graph with any of the usual vertex conditions natural dirichlet or delta type which show

fuzzy information in extended fuzzy relational databases abstract the queries on type 2 fuzzy relational databases may get non reasonable answers and as pointed out by buckles a tuple s membership value is not static but is a measure of the appropriateness of that tuple to a given query here we use two supplementary attributes r and i e to model the concepts of fuzziness and uncertainty respectively we also use these two attribute values to compute the appropriateness of a tuple to a given query in this paper the proposed fuzzy relational model is defined by first order logical in our proposed model the classical properties of the database which are 1 database interpretation being redundant free being uniquely determined and 2 the well definedness of relational algebra are preserved for the fuzzy relational algebra therefore the proposed fuzzy relational model can capture more meaning than the conventional approaches and is more suitable to handle the real life application

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

proximity relations in the fuzzy relational database model abstract the fuzzy relational model of buckles and petry is a rigorous scheme for incorporating non ideal or fuzzy information in a relational database in addition to providing a consistent scheme for representing fuzzy information in the relational structure the model possesses two critical properties that hold for classical relational databases these properties are that no two tuples have identical interpretations and each relational operation has a unique result the fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database these relations are reflexive symmetric and max min transitive in addition to introducing fuzziness into the relational model each similarity relation induces equivalence classes in its domain it is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases in this paper we extend the fuzzy relational database model of buckles and petry to deal with proximity relations for scalar domains since reflexivity and symmetry are the only constraints placed on proximity relations they generalize the notion of similarity relations we show that it is possible to induce equivalence classes from proximity relations thus the nice properties of the fuzzy relational model of buckles and petry are preserved furthermore the removal of the max min transitivity restriction also provides database users with more freedom to express their value structures

on the principal bifurcation branch of a third order nonlinear long wave equation we study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long wavelength instability we show that the main bifurcation branch can be derived from a variational principle this allows us to obtain a close estimate of the complete branch in particular when the bifurcation is subcritical the large amplitude stable branch can be found in a simple manner

gefred a generalized model of fuzzy relational databases abstract in this paper we present a fuzzy relational databases model whose main characteristics are the integration of previous models in the same framework representation capabilities for a wide series of fuzzy information and a coherent and flexible handling of it this model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query besides it permits the user to specify the precision with which the conditions involved in a query are satisfied

order and complexity in the kuramoto sivashinsky model of weakly turbulent interfaces abstract we present a large number of new geometric ergodic and statistical properties of the kuramoto sivashinsky equation modeling interfacial turbulence in various physical contexts in addition this equation has the remarkable property of inertial manifolds where some finite dimensional dynamical system is rigorously equivalent to this infinite dimensional partial differential equation in moderate size domains up to ten periods in length a low dimensional vector field skeleton underpins even strongly chaotic regimes and controls the bifurcations of the inertial manifold the extreme numerical sensitivity of chaos in this dissipative pde requires very high precision methods despite the geometrical complexities of the bifurcation structure some statistical properties remain remarkably simple there is overwhelming evidence that for some parameter values a permanent unsteady state exists an unexpectedly simple diffusive relaxation of the large scale fluctuations is extracted from extensive numerical simulations in these calculations we observe long time tails for the correlation functions of relevant quantities we propose an explanation in terms of an effective viscosity and compare the transport in the weakly turbulent interface with related theories for random interfaces and developed turbulence

an exactly solvable travelling wave equation in the fisher kpp class for a simple one dimensional lattice version of a travelling wave equation we obtain an exact relation between the initial condition and the position of the front at any later time this exact relation takes the form of an inverse problem given the times t n at which the travelling wave reaches the positions n one can deduce the initial profile we show by means of complex analysis that a number of known properties of travelling wave equations in the fisher kpp class can be recovered in particular bramson s shifts of the positions we also recover and generalize ebert van saarloos corrections depending on the initial condition

long wave morphological instabilities in the directional solidification of a dilute binary mixture long wave instabilities in a directionally solidified binary mixture may occur in several limits sivashinsky identified a small segregation coefficient limit and obtained a weakly nonlinear evolution equation governing subcritical two dimensional bifurcation brattkus and davis identified a near absolute stability limit and obtained a strongly nonlinear evolution equation governing supercritical two dimensional bifurcation the present investigation identifies a third strongly nonlinear evolution equation arising in the small segregation coefficient large surface energy limit this equation links both of the former and describes the change from the sub to super critical bifurcations this study sets the previous long wave analyses into a logical framework

planar solitary and spiral waves of the burgers cgl equations for flames governed by a sequential reaction this paper studied the planar solitary and spiral waves of the coupled burgers complex ginzburg landau burgers cgl equations which were derived from the nonlinear evolution of the coupled long scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction having two flame fronts corresponding to two reaction zones with a finite separation distance between them first some exact solutions including the planar and solitary waves for the one dimensional burgers cgl equations that are obtained by subtle transforms and the hyperbolic tangent function expansion method second some spiral waves for the two dimensional burgers cgl equations are investigated the existence of the spiral waves is proved rigorously by schauder s fixed point theorem applied to a class of functions and the approximate solutions are also obtained by the power series expansion method furthermore some numerical simulations are carried out near 0 r 1 since the

laminarizing effects of dispersion in an active dissipative nonlinear medium abstract the kuramoto sivashinsky equation has become a popular prototype for systems which exhibit spatial temporal chaos we show here that a linear dispersion term h xxx tends to arrest such irregular behavior in favor of spatially periodic cellular structures as is consistent with prior numerical and experimental observations the study includes a normal form analysis and a numerical investigation of periodic and solitary stationary wave solutions of the equation it is shown that by 1 1 the infinite families of stationary periodic waves of the kuramoto sivashinsky equation each ending in a solitary wave have been annihilated successively such that only a lone family of periodic waves consisting of one hump kdv pulses for 3 7 remains as the only periodic stationary wave attractors of the system these periodic waves have much larger domains of attraction than the strange attractors and hence tend to dominate spatial temporal chaos in an extended domain with significant dispersion

on occurrence of spectral edges for periodic operators inside the brillouin zone the paper discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics e g schrodinger maxwell waveguide operators etc is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the reduced brillouin zone only rather than the whole zone or do the edges of the spectrum occur necessarily at the set of corner high symmetry points this is known to be true in 1d while no apparent reasons exist for this to be happening in higher dimensions in many practical cases though this appears to be correct which sometimes leads to the claims that this is always true there seems to be no definite answer in the literature and one encounters different opinions about this problem in the community in this paper starting with simple discrete graph operators we construct a variety of convincing multiply periodic examples showing that the spectral edges might occur deeply inside the brillouin zone on the other hand it is also shown that in a generic case the situation of spectral edges appearing at high symmetry points is stable under small perturbations this explains to some degree why in many maybe even most practical cases the statement still holds

minimal speed of fronts of reaction convection diffusion equations we study the minimal speed of propagating fronts of convection reaction diffusion equations of the form u t microphi u u x u xx f u for positive reaction terms with f 0 0 the function phi u is continuous and vanishes at u 0 a variational principle for the minimal speed of the waves is constructed from which upper and lower bounds are obtained this permits the a priori assessment of the effect of the convective term on the minimal speed of the traveling fronts if the convective term is not strong enough it produces no effect on the minimal speed of the fronts we show that if f u sqrt f 0 microphi u 0 then the minimal speed is given by the linear value 2sqrt f 0 and the convective term has no effect on the minimal speed the results are illustrated by applying them to the exactly solvable case u t microuu x u xx u 1 u results are also given for the density dependent diffusion case u t microphi u u x d u u x x f u

variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation we give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationut uxx f u withf 0 f 1 0 andf 0 in 0 1 which permits in principle the calculation of the exact speed for arbitraryf