characterizing completable fuzzy metric spaces recently we showed the existence of a fuzzy metric space in the sense of george and veeramani which is not completable fuzzy sets and systems 130 2002 399 here we present an internal characterization of those fuzzy metric spaces that are completable some applications are derived and some illustrative examples are given

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

pointwise estimates and stability for dispersive diffusive shock waves we study the stability and pointwise behavior of perturbed viscous shock waves for a general scalar conservation law with constant diffusion and dispersion along with the usual lax shocks such equations are known to admit undercompressive shocks we unify the treatment of these two cases by introducing a new wave tracking method based on instantaneous projection giving improved estimates even in the lax case another important feature connected with the introduction of dispersion is the treatment of a non sectorial operator an immediate consequence of our pointwise estimates is a simple spectral criterion for stability in all l p norms p 1 for the lax case and p 1 for the undercompressive case our approach extends immediately to the case of certain scalar equations of higher order and would also appear suitable for extension to systems

on some results of analysis for fuzzy metric spaces abstract a necessary and sufficient condition for a fuzzy metric space to be complete is given we prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable uniform limit theorem is generalized to fuzzy metric spaces

the gap lemma and geometric criteria for instability of viscous shock profiles an obstacle in the use of evans function theory for stability analysis of traveling waves occurs when the spectrum of the linearized operator about the wave accumulates at the imaginary axis since the evans function has in general been constructed only away from the essential spectrum a notable case in which this difficulty occurs is in the stability analysis of viscous shock profiles here we prove a general theorem the gap lemma concerning the analytic continuation of the evans function associated with the point spectrum of a traveling wave into the essential spectrum of the wave this allows geometric stability theory to be applied in many cases where it could not be applied previously we demonstrate the power of this method by analyzing the stability of certain undercompressive viscous shock waves a necessary geometric condition for stability is determined in terms of the sign of a certain melnikov integral of the associated viscous profile this sign can easily be evaluated numerically we also compute it analytically for solutions of several important classes of systems in particular we show for a wide class of systems that homoclinic solitary waves are linearly unstable confirming these as the first known examples of unstable viscous shock waves we also show that strong heteroclinic undercompressive waves are sometimes unstable similar stability conditions are also derived for lax and overcompressive shocks and for nn

number of limit cycles of the lienard equation in this paper we study a lienard system of the form x 5y2f x y52x where f x is an odd polyno mial we introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system this sequence seems to converge to the exact equation of each limit cycle we obtain also a sequence of polynomials rn x whose roots of odd multiplicity are related to the number and location of the limit cycles of the system s1063 651x 97 02809 2

extension of a class of decomposable measures using fuzzy pseudometrics in this paper we consider a topological approach to extension of t conorm based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets we prove that every non strict continuous archimedean t conorm based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma algebra generated by this algebra the existence of such an extension follows very simply from the well known caratheodory result however our topological proof offers an intuitive interpretation of the extension of decomposable measures

on the resonance structure in a forced excitable system the dynamics of forced excitable systems are studied analytically and numerically with a view toward understanding the resonance or phase locking structure in a singular limit the system studied reduces to a discontinuous flow on a two torus which in turn gives rise to a set valued circle map it is shown how to define rotation numbers for such systems and derive properties analogous to those known for smooth flows the structure of the phase locking regions for a fitzhugh nagumo system in the singular limit is also analyzed a singular perturbation argument shows that some of the general results persist for the nonsingularly perturbed system and some numerical results on phase locking in the forced fitzhugh nagumo equations illustrate this fact the results explain much of the phase locking behavior seen experimentally and numerically in forced excitable systems including the existence of threshold stimuli for phase locking the results are compared with known results for forced oscillatory systems

scaling law for the transient behavior of type ii neuron models we study the transient regime of type ii biophysical neuron models and determine the scaling behavior of relaxation times ensuremath tau near but below the repetitive firing critical current ensuremath tau ensuremath simeq c i c ensuremath i ensuremath ensuremath delta for both the hodgkin huxley and morris lecar models we find that the critical exponent is independent of the numerical integration time step and that both systems belong to the same universality class with ensuremath delta 1 2 for appropriately chosen parameters the fitzhugh nagumo model presents the same generic transient behavior but the critical region is significantly smaller we propose an experiment that may reveal nontrivial critical exponents in the squid axon

algebraically computable piecewise linear nodal oscillators a family of piecewise linear oscillators whose oscillation can be completely characterized by algebraic methods is studied it represents up to the best of authors s knowledge the first planar example where all the oscillation properties can be determined for all the values of the bifurcation parameter in fact algebraic expressions for coordinates of representative points period and characteristic multiplier of the corresponding periodic orbit are provided thus the studied family of oscillators deserves to be considered a good benchmark for testing approximate methods of analysis in nonlinear oscillation theory the piecewise linear oscillators studied are called nodal oscillators since their relevant linear parts are of node type and they are not perturbations of the harmonic oscillator they represent real models in practice as it is shown for an electronic circuit modeling a piecewise linear version of the classical van der pol oscillator

a simple fuzzy method to remove mixed gaussian impulsive noise from color images mixed impulsive and gaussian noise reduction from digital color images is a challenging task because it is necessary to appropriately process both types of noise that in turn need to be distinguished from the original image structures such as edges and details fuzzy theory is useful to build simple efficient and effective solutions for this problem in this paper we propose a fuzzy method to reduce gaussian and impulsive noise from color images our method uses one only filtering operation a weighted averaging a fuzzy rule system is used to assign the weights in the averaging so that both noise types are reduced and image structures are preserved we provide experimental results to show that the performance of the method is competitive with respect to state of the art filters

high frequency asymptotics and one dimensional stability of zel dovich von neumann doring detonations in the small heat release and high overdrive limits we establish one dimensional spectral or normal modes stability of zel dovich von neumann doring detonations in the small heat release limit and the related high overdrive limit with heat release and activation energy held fixed verifying numerical observations made by erpenbeck in the 1960s the key technical points are a strategic rescaling of parameters converting the infinite overdrive limit to a finite regular perturbation problem and a careful high frequency analysis depending uniformly on model parameters the latter recovers and extends to arbitrary amplitudes the important result of high frequency stability established by erpenbeck by somewhat different techniques notably the techniques used here yield quantitative estimates well suited for numerical stability investigation

pulse coupled resonate and fire models we analyze two pulse coupled resonate and fire neurons numerical simulation reveals that an antiphase state is an attractor of this model we can analytically explain the stability of antiphase states by means of a return map of firing times which we propose in this paper the resultant stability condition turns out to be quite simple the phase diagram based on our theory shows that there are two types of antiphase states one of these cannot be seen in coupled integrate and fire models and is peculiar to resonate and fire models the results of our theory coincide with those of numerical simulations

existence of piecewise linear differential systems with exactly n limit cycles for all n n abstract in this paper we prove that the piecewise linear differential system x y e x y x with e 0 and an odd piecewise linear periodic function of period 4 has exactly n limit cycles in the strip x 2 n 1 consequently there are piecewise linear differential systems having infinitely many limit cycles in the real plane we also provide examples of piecewise linear differential systems having exactly n limit cycles for all n n

on completion of fuzzy metric spaces completions of fuzzy metric spaces in the sense of george and veeramani are discussed a complete fuzzy metric space y is said to be a fuzzy metric completion of a given fuzzy metric space x if x is isometric to a dense subspace of y we present an example of a fuzzy metric space that does not admit any fuzzy metric completion however we prove that every standard fuzzy metric space has an up to isometry unique fuzzy metric completion we also show that for each fuzzy metric space there is an up to uniform isomorphism unique complete fuzzy metric space that contains a dense subspace uniformly isomorphic to it

multiple impulse solutions to mckean s caricature of the nerve equation i existence mckean s caricature of the nerve equation is considered the h in 1 is the heaviside function we prove the existence of multiple impulse solutions consisting of any finite number of pulses these solutions are referred to as n ple impulse solutions where n is an arbitrary positive integer

fuzzy quasi metrics for the sorgenfrey line we endow the set of real numbers with a family of fuzzy quasi metrics in the sense of george and veeramani which are compatible with the sorgenfrey topology although these fuzzy quasi metrics are not deduced explicitly from a quasi metric they possess interesting properties related to completeness for instance we prove that they are balanced and complete in the sense of doitchinov and that only one of them is right k sequentially complete we also observe that compatible fuzzy quasi metrics for the sorgenfrey line cannot be left weakly right k sequentially complete

l1 asymptotic behavior of compressible isentropic viscous 1 d flow we study the large time behavior in l1 of the compressible isentropic viscous 1 d flow under the assumption that the initial data are smooth and small we show that the solutions are approximated by the solutions of a parabolic system and in turn by diffusion waves which are solutions of burgers equations decay rates in l1 are obtained our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system 1994 john wiley sons inc

on the topological structure of km fuzzy metric spaces and normed spaces in this paper some relations among the axioms of km fuzzy metric spaces and km fuzzy normed spaces are discussed and some characterizations concerning the additional axiom are given also a quasi metric family and a quasi norm family corresponding respectively to the km fuzzy metric spaces and the km fuzzy normed spaces are introduced and studied using their properties the different topological structures of km fuzzy metric spaces and km fuzzy normed spaces with variable t norm are described and some new properties on these spaces are obtained as their special cases the topological structures and properties concerning gv fuzzy metric spaces and gv fuzzy normed spaces are presented

nonsmooth dynamics in spiking neuron models large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue one approach in computational neuroscience has been to consider the detailed electrophysiological properties of neurons and build vast computational compartmental models an alternative has been to develop minimal models of spiking neurons with a reduction in the dimensionality of both parameter and variable space that facilitates more effective simulation studies in this latter case the single neuron model of choice is often a variant of the classic integrate and fire model which is described by a nonsmooth dynamical system in this paper we review some of the more popular spiking models of this class and describe the types of spiking pattern that they can generate ranging from tonic to burst firing we show that a number of techniques originally developed for the study of impact oscillators are directly relevant to their analysis particularly those for treating grazing bifurcations importantly we highlight one particular single neuron model capable of generating realistic spike trains that is both computationally cheap and analytically tractable this is a planar nonlinear integrate and fire model with a piecewise linear vector field and a state dependent reset upon spiking we call this the pwl if model and analyse it at both the single neuron and network level the techniques and terminology of nonsmooth dynamical systems are used to flesh out the bifurcation structure of the single neuron model as well as to develop the notion of liapunov exponents we also show how to construct the phase response curve for this system emphasising that techniques in mathematical neuroscience may also translate back to the field of nonsmooth dynamical systems the stability of periodic spiking orbits is assessed using a linear stability analysis of spiking times at the network level we consider linear coupling between voltage variables as would occur in neurobiological networks with gap junction coupling and show how to analyse the properties existence and stability of both the asynchronous and synchronous states in the former case we use a phase density technique that is valid for any large system of globally coupled limit cycle oscillators whilst in the latter we develop a novel technique that can handle the nonsmooth reset of the model upon spiking finally we discuss other aspects of neuroscience modelling that may benefit from further translation of ideas from the growing body of knowledge on nonsmooth dynamics

fuzzy prokhorov metric on the set of probability measures we introduce a fuzzy metric on the set of probability measures on a fuzzy metric space the construction is an analogue in the realm of fuzzy metric spaces of the prokhorov metric on the set of probability measures on compact metric spaces

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

pointwise green function bounds for shock profiles of systems with real viscosity following the pointwise semigroup approach of zh mz 1 we establish sharp pointwise green function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic parabolic systems of conservation laws of dissipative type under the necessary assumptions z 1 z 3 z 4 of spectral stability i e stable point spectrum of the linearized operator about the wave transversality of the connecting profile and hyperbolic stability of the corresponding ideal shock of the associated inviscid system with no additional assumptions on the structure or strength of the shock these bounds are used in a companion paper mz 2 to establish nonlinear stability of small amplitude lax shocks of symmetrizable hyperbolic parabolic systems

stability of detonation profiles in the znd limit confirming a conjecture of lyng raoofi texier zumbrun we show that stability of strong detonation waves in the znd or small viscosity limit is equivalent to stability of the limiting znd detonation together with stability of the viscous profile associated with the component neumann shock moreover on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those of the limiting znd detonation while on frequencies of order one over viscosity they converge to one over viscosity times those of the associated viscous neumann shock this yields immediately a number of examples of instability and hopf bifurcation of reacting navier stokes detonations through the extensive numerical studies of znd stability in the detonation literature

spectral stability of ideal gas shock layers extending recent results in the isentropic case we use a combination of asymptotic ode estimates and numerical evans function computations to examine the spectral stability of shock wave solutions of the compressible navier stokes equations with ideal gas equation of state our main results are that in appropriately rescaled coordinates the evans function associated with the linearized operator about the wave i converges in the large amplitude limit to the evans function for a limiting shock profile of the same equations for which internal energy vanishes at one end state and ii has no unstable positive real part zeros outside a uniform ball thus the rescaled eigenvalue ode for the set of all shock waves augmented with the nonphysical limiting case form a compact family of boundary value problems that can be conveniently investigated numerically an extensive numerical evans function study yields one dimensional spectral stability independent of amplitude for gas constant in 1 2 3 and ratio of heat conduction to viscosity coefficient within 0 2 5 1 4 1 47 for air other values may be treated similarly but were not considered the method of analysis extends also to the multi dimensional case a direction that we shall pursue in a future work

iterated function systems and attractors in the km fuzzy metric spaces fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the km fuzzy metric spaces using the properties of hausdorff fuzzy metrics several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions in particular unbounded invariant sets are also examined for the iterated function systems in km fuzzy metric spaces our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces

limit cycles of continuous and discontinuous piecewise linear differential systems in r3 abstract we study the limit cycles of two families of piecewise linear differential systems in r 3 with two pieces separated by a plane in one family the differential systems are continuous on the plane and in the other family they are discontinuous on the plane the usual tool for studying these limit cycles is the poincare map but here we shall use recent results which extend the averaging theory to continuous and discontinuous differential systems all the computations have been done with the algebraic manipulator mathematica

multiple impulse solutions to mckean s caricature of the nerve equation ii stability we study mckean s caricature of a nerve conduction equation where h is the heaviside function it is proved that an n ple impulse solution resembling the superposition of n unstable solitary impulses has at most 2n 1 and at least n unstable modes exactly n unstable modes corresponding to the amplitudes and the rest of them corresponding to the spacings the n amplitude modes always exist we prove also that for an n ple impulse solution resembling the superposition of n stable solitary impulses there are at most n 1 unstable modes and all of them are of spacing type

the hausdorff fuzzy metric on compact sets we propose a method for constructing a hausdorff fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space in the sense of george and veeramani we discuss several important properties as completeness completion and precompactness some illustrative examples are given

piecewise linear differential equations and integrate and fire neurons insights from two dimensional membrane models we derive and study two dimensional generalizations of integrate and fire models which can be found from a piecewise linear idealization of the fitzhugh nagumo or morris lecar model these models give rise to new properties not present in one dimensional integrate and fire models a detailed analytical study of the models is presented in particular i for the piecewise linear fitzhugh nagumo model we determine analytically the bistability regime between stationary solutions and oscillations that is typical for class ii models ii in the piecewise morris lecar model we find a noncanonical class i transition from a stationary state to oscillations with logarithmic dependence similar to that found for leaky integrate and fire models iii furthermore we establish a relation to the recently proposed resonate and fire model and show that a short input current pulse can trigger several spikes

some questions in fuzzy metric spaces the george and veeramani s fuzzy metric defined by m x y t min x y t max x y t on 0 the set of non negative real numbers has shown some advantages in front of classical metrics in the process of filtering images in this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it as a consequence of this study we introduce throughout the paper some questions relative to fuzzy metrics also as another practical application we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples

stability of bright solitary wave solutions to perturbed nonlinear schrodinger equations abstract the propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear schrodinger equation nls when considering realistic fibers one must examine perturbed nls equations with the particular perturbation depending on the physical situation that is being modeled a common example is the complex ginzburg landau equation cgl which is a dissipative perturbation it is known that some of the stable bright solitons of the nls survive a dissipative perturbation such as the cgl given that a wave persists it is then important to determine its stability with respect to the perturbed nls a major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum since the essential spectrum of the nls is located on the imaginary axis such eigenvalues may lead to an unstable wave in fact eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum here we present a technique which can be used to track these bifurcating eigenvalues as a consequence we are able to locate the spectrum for bright solitary wave solutions to various perturbed nonlinear schrodinger equations and determine precise conditions on parameters for which the waves are stable in addition we show that a particular perturbation the parametrically forced nls equation supports stable multi bump solitary waves the technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here

fuzzy contractive mappings and fixed points in fuzzy metric spaces in the paper we introduce a new concept of fuzzy contraction which is a generalization of a fuzzy contractive mapping initiated in the article v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252 for this type of contraction the conditions guaranteeing the existence of fixed point in fuzzy m complete metric spaces in the sense of george and veeramani are established the result is supported by examples

stability of isentropic navier stokes shocks in the high mach number limit by a combination of asymptotic ode estimates and numerical evans function calculations we establish stability of viscous shock solutions of the isentropic compressible navier stokes equations with law pressure i in the limit as mach number m goes to infinity for any 1 proved analytically and ii for m 2 500 gamma in 1 2 5 or m 13 000 gamma in 2 5 3 demonstrated numerically this builds on and completes earlier studies by matsumura nishihara and barker humpherys rudd zumbrun establishing stability for low and intermediate mach numbers respectively indicating unconditional stability independent of shock amplitude of viscous shock waves for law gas dynamics in the range gamma in 1 3 other values may be treated similarly but have not been checked numerically the main idea is to establish convergence of the evans function in the high mach number limit to that of a pressureless or infinitely compressible gas with additional upstream boundary condition determined by a boundary layer analysis recall that low mach number behavior is formally incompressible

the mckean s caricature of the fitzhugh nagumo model i the space clamped system within the context of lienard equations we present the fitzhugh nagumo model with an idealized nonlinearity we give an analytical expression i for the transient regime corresponding to the emission of a finite number of action potentials or spikes and ii for the asymptotic regime corresponding to the existence of a limit cycle we carry out a global analysis to study periodic solutions the existence of which is linked to the solutions of a system of transcendental equations the periodic solutions are obtained with the help of the harmonic balance method or as limit behavior of the transient regime we show how the appearance of periodic solutions corresponds either to a fold limit cycle bifurcation or to a hopf bifurcation at infinity the resultsobtained are in agreement with local analysis methods i e the melnikov method and the averaging method the generalization of the model leads us to formulate two conjectures concerning the number of limit cycles for the piecewise linear lienard equ

common fixed point theorems in fuzzy metric spaces using the clrg property the main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces in the sense of kramosil and michalek satisfying new contractive conditions employing the common limit in the range property our results generalize and extend some recent results contained in jain et al 2012 12 to generalized contractive conditions under some control functions in the process some results about multidimensional common fixed points as coupled tripled quadrupled common fixed point results are derived from our main results

boundary layer stability in real vanishing viscosity limit in the previous paper 20 an evans function machinery for the study of boundary layer stability was developed there the analysis was restricted to strongly parabolic perturbations that is to an approximation of the form ut f u x b u ux x 1 with an elliptic matrix b however real models like the navier stokes approximation of the euler equations for a gas flow involve incompletely parabolic perturbations b is not invertible in general

stable viscosities and shock profiles for systems of conservation laws abstract many equations of mathematical physics take the form of nonlinear hyperbolic systems of conservation laws with small dissipative effects neglected typically smooth solutions must develop discontinuities shocks in finite time re incorporating dissipation helps select those discontinuities which are physically relevant for this purpose many different sorts of dissipation will do in particular the physical viscosity is typically degenerate and not convenient in this paper the author provide an understanding of what high order viscosity terms smooth the physical discontinuities a natural class of admissible viscosity terms is determined based on a simple linearized stability criterion in addition they determine a class of degenerate second order viscosity terms of physical type which are admissible these results are applied to the equations of compressible fluid dynamics to determine what conditions ensure the existence of the shock layer with viscosity and heat conduction this should be of interest to others interested in general equations of state for compressible fluids such as those investigating phase transitions

an efficient shooting algorithm for evans function calculations in large systems abstract in evans function computations of the spectra of asymptotically constant coefficient linear operators a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ode for small systems a fast shooting algorithm may be obtained by representing subspaces as single exterior products j c alexander r sachs linear instability of solitary waves of a boussinesq type equation a computer assisted computation nonlinear world 2 4 1995 471 507 l q brin numerical testing of the stability of viscous shock waves ph d thesis indiana university bloomington 1998 l q brin numerical testing of the stability of viscous shock waves math comp 70 235 2001 1071 1088 l q brin k zumbrun analytically varying eigenvectors and the stability of viscous shock waves in seventh workshop on partial differential equations part i 2001 rio de janeiro mat contemp 22 2002 19 32 t j bridges g derks g gottwald stability and instability of solitary waves of the fifth order kdv equation a numerical framework physica d 172 1 4 2002 190 216 for large systems however the dimension of the exterior product space quickly becomes prohibitive growing as n k where n is the dimension of the system written as a first order ode and k typically n 2 is the dimension of the subspace we resolve this difficulty by the introduction of a simple polar coordinate algorithm representing pure monomial products as scalar multiples of orthonormal bases for which the angular equation is a numerically optimized version of the continuous orthogonalization method of drury davey a davey an automatic orthonormalization method for solving stiff boundary value problems j comput phys 51 2 1983 343 356 l o drury numerical solution of orr sommerfeld type equations j comput phys 37 1 1980 133 139 and the radial equation is evaluable by quadrature notably the polar coordinate method preserves the important property of analyticity with respect to parameters

on fuzzy contractive mappings in fuzzy metric spaces some results on fuzzy contractive mappings in v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 253 are extended to edelstein fuzzy contractive mappings some new results are obtained by modifying the notion of convergence in fuzzy metric spaces due to specific axiom gv 2 in fuzzy metric spaces in the sense of george and veeramani this convergence is frechet

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

examples of fuzzy metrics and applications in this paper we present new examples of fuzzy metrics in the sense of george and veeramani the examples have been classified attending to their construction and most of the well known fuzzy metrics are particular cases of those given here in particular novel fuzzy metrics by means of fuzzy and classical metrics and certain special types of functions are introduced we also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection finally we give an application of this type of fuzzy metrics to color image processing we propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images obtaining promising results this application is also illustrative of how fuzzy metrics can be used in other engineering problems

a hardware friendly arithmetic method and efficient implementations for designing digital fuzzy adders a new hardware friendly mathematical method for realizing low complexity universal adder cells as well as its efficient hardware implementations is proposed in this paper this method can be used in binary logic multiple valued logic mvl and specifically digital fuzzy systems the proposed mathematical method can be implemented in both voltage and current modes the voltage mode hardware implementation is very simple and is based on input capacitors and mvl or analog inverters and buffers in addition the current mode hardware implementation leads to simple and efficient structures for digital fuzzy systems simulations are carried out for ternary logic as well as for digital fuzzy logic with high precision by using 180nm standard cmos technology and at 1 8v supply voltage simulation results demonstrate that the proposed designs have excellent functionality and are very suitable for implementing mvl and fuzzy arithmetic circuits

wavy front dynamics in a three component reaction diffusion system with one activator and two inhibitors an analytic description for traveling waves in a one dimensional reaction diffusion system with one activator and two inhibitors and with equal diffusion constants is developed using a piecewise linear approximation for the nonlinear activator reaction term the case of front waves is examined in more detail the monotonic and oscillating fronts being separately considered the corresponding wave profiles are constructed and the speed equation is obtained and discussed it is found that the fronts in the three component model propagate faster than the fronts in the two component system the front interaction is studied using numerical calculations the results show that at head on collisions two oscillating fronts produce a wavy domain which spreads in space with time

stability of viscous detonations for majda s model abstract using analytical and numerical evans function techniques we examine the spectral stability of strong detonation wave solutions of a version of majda s scalar model for a reacting gas mixture with an arrhenius type ignition function we introduce an energy estimate to limit possible unstable eigenvalues to a compact region in the unstable complex half plane and we use a numerical approximation of the evans function to search for possible unstable eigenvalues in this region our results show for the parameter values tested that these waves are spectrally stable combining these numerical results with the pointwise green function analysis of lyng raoofi texier zumbrun g lyng m raoofi b texier k zumbrun pointwise green function bounds and stability of combustion waves j differential equations 233 2 2007 654 698 we conclude that these waves are nonlinearly stable this represents the first demonstration of nonlinear stability for detonation wave solutions of a majda type model without a smallness assumption notably our results indicate that for this simplified scalar model there does not occur either in a normal parameter range or in the limit of high activation energy hopf bifurcation to galloping or pulsating solutions as is observed in the full reactive navier stokes equations this answers in the negative for this model a question posed by majda as to whether such scalar detonation models capture this aspect of detonation behavior

topological stability for fuzzy expansive maps abstract we introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces we show some basic properties of fuzzy expansive homeomorphisms moreover we prove walters s theorem in the context of fuzzy metric spaces i e a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable

stability of large amplitude viscous shock profiles of hyperbolic parabolic systems we establish nonlinear l1 h3 lp orbital stability 2 p with sharp rates of decay of large amplitude lax type shock profiles for a class of symmetric hyperbolic parabolic systems including compressible gas dynamics and magnetohydrodynamics mhd under the necessary conditions of strong spectral stability i e a stable point spectrum of the linearized operator about the wave transversality of the profile and hyperbolic stability of the associated ideal shock this yields in particular together with the spectral stability results of 50 the nonlinear stability of arbitrarily large amplitude shock profiles of isentropic navier stokes equations for a gamma law gas as 1 the first complete large amplitude stability result for a shock profile of a system with real i e partial viscosity a corresponding small amplitude result was established in 53 54 for general systems of kawashima class by a combination of kawashima type energy estimates and pointwise green function bounds where the small amplitude assumption was used only to close the energy estimates here under the mild additional assumption that hyperbolic characteristic speeds relative to the shock are not only nonzero but of a common sign we close the estimates instead by use of a goodman type weighted norm 25 26 designed to control estimates in the crucial hyperbolic modes