tensor products of complete lattices and their application in constructing quantales abstract this paper aims to implement tensor products of complete lattices into fuzzy set theory the most convenient approach for this purpose is to view the tensor product of two complete lattices as the family of all join reversing maps between those lattices we show that some fundamental constructions in fuzzy set theory are tensor products examples of such circumstances include the following to mention only three of them the complete lattice of all lower semicontinuous maps from a topological space into a continuous lattice is the tensor product of the topology of the space and the range lattice a binary operation coming from zadeh s extension principle is the tensor product of the minkowski multiplication with the multiplication of the underlying unital quantale triangle functions on nonnegative left continuous distribution functions are tensor products of the real unit interval and the extended nonnegative half line equipped respectively with a left continuous t norm and the usual addition

some exact solutions of the ideal mhd equations through symmetry reduction method abstract we use the symmetry reduction method based on lie group theory to obtain some exact solutions the so called invariant solutions of the ideal magnetohydrodynamic equations in 3 1 dimensions in particular these equations are invariant under a galilean similitude lie algebra for which the classification by conjugacy classes of r dimensional subalgebras 1 r 4 was already known we restrict our study to the three dimensional galilean similitude subalgebras that give us systems composed of ordinary differential equations here some examples of these solutions are presented with a brief physical interpretation

on the l fuzzy brouwer fixed point theorem in this paper it is proved that in every l cube with l a completely distributive lattice has the fixed point property with respect to the hutton product l topology stratified l cubes are shown to have the fixed point property provided l has a countable base

an extension of the fuzzy unit interval to a tensor product with completely distributive first factor abstract the original hutton interval i l can algebraically be identified with the tensor product i l of the real unit interval i and a complete lattice l due to this the tensor product m l with m a completely distributive lattice is considered as a generalization of the lattice i l when appropriately endowed with an l topology the tensor product m l becomes also an l topological extension of i l if m is separable it has a countable join base free of supercompact elements many of the l topological features of i l are retained to wit urysohn lemma and tietze urysohn extension theorem for m l valued functions are then proved the relationship of m l to the l fuzzy topological modification of m in the sense of d zhang and y m liu 27 is discussed

rotational degeneracy of hyperbolic systems of conservation laws the purpose of the paper is to study wave patterns of hyperbolic systems in which rotational symmetry creates a specific kind of degeneracy in this situation hyperbolicity is necessarily non strict so that the elementary waves have interesting patterns the discussion is centered around a theorem on existence and uniqueness of solutions of the riemann problem we give a unified presentation of examples from continuum mechanics

an insertion theorem for continuous valued functions and its consequences spaces in which open sets take values in the l interval i l are investigated we prove a theorem concerning the insertion of a continuous function with values in i l with l a complete lattice we establish certain factorizations of the functors i l and i l with l a hypercontinuous lattice the latter result and the insertion theorem provide a partial answer to a recent open question related to insertion of lattice valued functions as another application of the insertion theorem we establish a relation between complete regularity in the categories of l topological and i l topological spaces with l a frame

on r l o we prove there exists a somewhat simpler description of l and its fuzzy topology than the one given by hutton 2 and a considerably simpler description of than the one given by rodabaugh 4 as a result of this simplification we are able to give a direct proof of the continuity of an open problem in 4

adaptive coordinated tracking of multi agent systems with quantized information abstract in this paper we study the adaptive coordinated tracking problem for continuous time first order integrator systems with quantized information under switching undirected and fixed directed communication graphs respectively the combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated both the logarithmic quantizers and uniform quantizers are considered it is shown that when logarithmic quantizers are used exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter simulation examples are provided to illustrate the results

average consensus with packet drop communication average consensus consists in the problem of determining the average of some quantities by means of a distributed algorithm it is a simple instance of problems arising when designing estimation algorithms operating on data produced by sensor networks simple solutions based on linear estimation algorithms have already been proposed in the literature and their performance has been analyzed in detail if the communication links which allow the data exchange between the sensors have some loss then the estimation performance will degrade in this contribution the performance degradation due to this data loss is evaluated

distributed consensus for multiagent systems with communication delays and limited data rate this paper considers the average consensus problem for multiagent networks with communication delays and limited data rate on one hand communication delays often exist in information acquisition and transmission on the other hand only limited state information of agents can be transmitted to their neighbors at each time step due to bandwidth constraints the average consensus problem becomes much more complicated when both delays and data rate constraints are to be considered in this paper a distributed consensus protocol is proposed based on dynamic encoding and decoding it is shown that for a connected network as long as the time delays are bounded the average consensus can be achieved with a finite communication data rate in particular it is shown that merely a one bit information exchange between each pair of adjacent agents at each time step suffices to guarantee the average consensus

singular vortex in magnetohydrodynamics we obtain an exact solution of the ideal magnetohydrodynamics equations in 3 1 dimensions the construction of the solution is based on the invariants of the group o 3 of rotations it is a deep generalization of the known solution which describes a radial flow with spherical waves it is shown that in the irreducible solution the velocity and magnetic field vectors of the particle are coplanar to the radius vector of the particle the solution is represented as an involutive invariant subsystem of pdes with two independent variables and finite relation which contains a functional arbitrariness

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

scaling symmetries conservation laws and action principles in one dimensional gas dynamics scaling symmetries of the planar one dimensional gas dynamic equations with adiabatic index are used to obtain lagrangian and eulerian conservation laws associated with the symmetries the known eulerian symmetry operators for the scaling symmetries are converted to the lagrangian form in which the eulerian spatial position of the fluid element is given in terms of the lagrangian fluid labels conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established the corresponding lagrangian and eulerian form of the conservation laws are determined by application of noether s theorem a nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry conserved vector an action principle incorporating known conservation laws using lagrangian constraints is developed noether s theorem for the constrained action principle gives the same formulas for the conserved vector as the classical noether theorem except that the lie symmetry vector field now includes the effects of nonlocal potentials noether s theorem for the constrained action principle is used to obtain nonlocal conservation laws the scaling symmetry conservation laws only apply for special forms of the entropy of the gas

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

coordination of passive systems under quantized measurements in this paper we investigate a passivity approach to collective coordination and synchronization problems in the presence of quantized measurements and show that coordination tasks can be achieved in a practical sense for a large class of passive systems

forty years of hutton fuzzy unit interval this note is a very short history of a specific fuzzy topological space the hutton s fuzzy unit interval 0 1 l which occupies one of the central positions in fuzzy topology on that occasion the superiority of l valued topology over 0 1 valued topology is being discussed we then show how the hutton s concept evolved after obvious identifications we can today say that 0 1 l is the tensor product 0 1 l of the lattices 0 1 and l an account of the consequences of this new view point is hoped to appear thereafter

generalized symmetries for the ideal mhd equations abstract for the nonlinear ideal mhd equations we give potential and local scaling symmetries which are two different generalizations of the classical lie point symmetries they transform given similarity solutions to new exact solutions some physical applications are discussed

distributed consensus over digital networks with limited bandwidth and time varying topologies in this paper we consider discrete time distributed average consensus with limited communication data rate and time varying communication topologies we design a distributed encoding decoding scheme based on quantization of scaled innovations and a control protocol based on a symmetric compensation method we develop an adaptive scheme to select the numbers of quantization levels according to whether the associated channel is active or not we prove that if the network is jointly connected then under the protocol designed average consensus can be asymptotically achieved and the convergence rate is quantified especially if the duration of any link failure in the network is bounded then the control gain and the scaling function can be selected properly such that 5 level quantizers suffice for asymptotic average consensus with an exponential convergence rate

sticky particles and scalar conservation laws one dimensional scalar conservation laws with nondecreasing initial conditions and general fluxes are shown to be the appropriate equations to describe large systems of free particles on the real line which stick under collision with conservation of mass and momentum

a categorical accommodation of various notions of fuzzy topology different definitions of fuzzy topology have been stated and developed in the literature but have not been satisfactorily related to each other and to ordinary topology to remedy this a new fuzzy topological category fuzz is defined it is a significant generalization of previous definitions it is the simplest setting yet constructed into which ordinary topology and these previous definitions may be placed by identifying each with a different subcategory of fuzz it therefore allows us to conveniently analyze the relative merits of previous definitions give coherence to known results and indicate appropriate directions for future development and it generates and may be viewed as both including and included in categories of fuzzy topological spaces which exhibit higher order fuzziness

distributed coordination of multi agent systems with quantized observer based encoding decoding integrative design of communication mechanism and coordinated control law is an interesting and important problem for multi agent networks in this paper we consider distributed coordination of discrete time second order multi agent systems with partially measurable state and a limited communication data rate a quantized observer based encoding decoding scheme is designed which integrates the state observation with encoding decoding a distributed coordinated control law is proposed for each agent which is given in terms of the states of its encoder and decoders it is shown that for a connected network 2 bit quantizers suffice for the exponential asymptotic synchronization of the states of the agents the selection of controller parameters and the performance limit are discussed it is shown that the algebraic connectivity and the spectral radius of the laplacian matrix of the communication graph play key roles in the closed loop performance the spectral radius of the laplacian matrix is related to the selection of control gains while the algebraic connectivity is related to the spectral radius of the closed loop state matrix furthermore it is shown that as the number of agents increases the asymptotic convergence rate can be approximated as a function of the number of agents the number of quantization levels communication data rate and the ratio of the algebraic connectivity to the spectral radius of the laplacian matrix of the communication graph

distributed averaging on digital erasure networks iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels these algorithms do not require the agents to have any knowledge about the global network structure or size almost sure convergence to state agreement is proved and the communication and computational complexities of the algorithms are analyzed both the number of transmissions and the number of computations performed by each agent of the network are shown to grow not faster than poly logarithmically in the desired precision the impact of the graph topology on the algorithms performance is analyzed as well moreover it is shown how in the presence of noiseless communication feedback one can modify the algorithms significantly improving their performance versus complexity trade off

radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions abstract radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced which allow one to capture concentration of mass the transformation to a one dimensional system with source terms is performed and physically meaningful boundary conditions at the origin are determined entropy conditions are derived and applied to single out physical nonnegative mass and dissipative entropic solutions a complete solution to the pseudo riemann problem with initial data exhibiting a single delta shock on a sphere is obtained

constrained consensus in unbalanced networks with communication delays in this note a constrained consensus problem is studied for multi agent systems in unbalanced networks in the presence of communication delays here each agent needs to lie in a closed convex constraint set while reaching a consensus the communication graphs are directed dynamically changing and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length the analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary to tackle the loss of symmetry caused by unbalanced graphs and communication delays a novel approach is proposed the idea is to estimate the distance from each agent to the intersection set of all agents constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction it is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system it is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded finally a numerical example is included to illustrate the obtained theoretical results

shadow waves entropies and interactions for delta and singular shocks this paper deals with two key problems for delta or singular shock solutions to systems of conservation laws that of their entropy admissibility conditions which is connected to the notorious uniqueness problem and that of their interaction we choose to represent systems of conservation laws by nets of functions which are piecewise constant or constant with respect only to the space variable here called shadow waves all the calculations can then be done on each element of such nets using only the usual rankine hugoniot conditions a 3 3 pressureless gas dynamics model is the main example in the paper

on the hierarchy of partially invariant submodels of differential equations it is noted that the partially invariant solution pis of differential equations in many cases can be represented as an invariant reduction of some piss of the higher rank this introduces a hierarchic structure in the set of all piss of a given system of differential equations an equivalence of the two step and the direct ways of construction of piss is proved the hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations in this framework the complete classification of regular partially invariant solutions of ideal mhd equations is given

quantized data based distributed consensus under directed time varying communication topology distributed average consensus dac is investigated for multiagent systems mass with directed time varying communication topology and quantized communication data we propose a communication feedback based distributed consensus protocol suitable for directed time varying topologies to deal with the inconsistency between the internal state of each agent s encoder and the output of its neighbors decoder and give rigorous analysis for the consensus of the mas the consensus protocols are designed based on uniform quantizers with scaling a finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure the exponential consensus by properly choosing system parameters in addition the lower bound is proved to be merely 1 bit for the directed fixed topology case no matter how large the agent number is a numerical example is presented to demonstrate the results obtained

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

similarity solutions for the two dimensional nonstationary ideal mhd equations a similarity analysis of the non linear two dimensional non stationary ideal mhd equations is presented in the case of a magnetic field perpendicular to the isentropic motion of the plasma the authors establish the complete lie algebra of infinitesimal symmetries the laws of conservation are mentioned the similarity method for partial differential equations as a procedure for reducing the number of independent variables is applied repeatedly finally they obtain systems of ordinary differential equations for similarity solutions of the mhd equations considered

generalized variational principles global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics we study systems of conservation laws arising in two models of adhesion particle dynamics the first is the system of free particles which stick under collision the second is a system of gravitationally interacting particles which also stick under collision in both cases mass and momentum are conserved at the collisions so the dynamics is described by 2 2 systems of conservations laws we show that for these systems global weak solutions can be constructed explicitly using the initial data by a procedure analogous to the lax oleinik variational principle for scalar conservation laws however this weak solution is not unique among weak solutions satisfying the standard entropy condition we also study a modified gravitational model in which instead of momentum some other weighted velocity is conserved at collisions for this model we prove both existence and uniqueness of global weak solutions we then study the qualitative behavior of the solutions with random initial data we show that for continuous but nowhere differentiable random initial velocities all masses immediately concentrate on points even though they were continuously distributed initially and the set of shock locations is dense

symmetry groups and similarity solutions of mhd equations a similarity analysis of the nonlinear nonstationary real mhd equations is presented for several cases of real mhd the complete lie algebra of infinitesimal symmetries is calculated using subalgebras of this lie algebra reduced systems for similarity solutions can be obtained some similarity solutions of the ideal mhd equations are discussed

a class of accelerated solutions of the two dimensional ideal magnetohydrodynamic equations a particular class of exact solutions of the two dimensional time dependent magnetohydrodynamic equations for an ideal isothermal plasma is presented the associated flows have non vanishing acceleration a special form of the mapping between eulerian and lagrangian coordinates is assumed and the acceleration term has to have the form of a potential force the class of potentials compatible with these assumptions is derived and the constraints imposed by the vanishing resistivity then lead to a restriction of the admissible flow fields some explicit solutions are constructed and their properties are investigated

the pulsrodon in 2 1 dimensional magneto gasdynamics hamiltonian structure and integrability an elliptic vortex type ansatz introduced into a 2 1 dimensional system governing rotating homentropic magneto gasdynamics with a parabolic gas law is shown to lead to a finite dimensional nonlinear dynamical system which admits exact analytical solution in terms of an elliptic function and integral representation the dynamical system is demonstrated to be hamiltonian and equivalent to the stationary reduction of the integrable nonlinear schrodinger equation coupled with a steen ermakov pinney equation a novel magneto gasdynamic analogue of the pulsrodon of shallow water f plane theory is isolated thereby confined and time periodic magneto gasdynamic flows are constructed explicitly

some questions in fuzzy topology the purpose of this paper is to discuss some basic questions related mainly to hutton s l fuzzy unit interval some of those questions are stated here for the first time while some of them are long standing related results are surveyed in some cases

continuous time and sampled data based average consensus with logarithmic quantizers this paper considers the average consensus problem for multi agent systems with continuous time first order dynamics logarithmic quantization is considered in the communication channels and continuous time and sampled data based protocols are proposed for the continuous time protocol we give an explicit upper bound of the consensus error in terms of the initial states the quantization density and the parameters of the network graph it is shown that in contrast with the case with uniform quantization the consensus error in the logarithmic quantization case is always uniformly bounded independent of the quantization density and the b asymptotic average consensus is ensured under the proposed protocol i e the asymptotic consensus error converges to zero as the sector bound b of the logarithmic quantizer approaches zero for the sampled data based protocol we give sufficient conditions on the sampling interval to ensure the b asymptotic average consensus numerical examples are given to demonstrate the effectiveness of the protocols

finite level quantized synchronization of discrete time linear multiagent systems with switching topologies in this paper the synchronization of discrete time linear multiagent systems is studied with finite communication data rate and switching topology flows a class of quantized observer based communication schemes and a class of certainty equivalence principle based cooperative control laws are proposed with adaptive encoders and decoders it is shown that if the pairs of agents state matrices and control matrices multiplied by laplacian eigenvalues of the weakly connected components are simultaneously stabilizable and the communication topology flow is frequently connected then there exist such protocols leading to synchronization exponentially fast furthermore only finite bits of information exchange per step are required to guarantee the synchronization if the communication channels are frequently active for first order dynamics the dwell time and the number of bits are both related to the unstable mode of agent dynamics the number of agents the frequency of connectivity and the laplacian eige

numerical approximations of pressureless and isothermal gas dynamics we study several schemes of first or second order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations the pressureless gas system is weakly hyperbolic giving rise to the formation of density concentrations known as delta shocks for the isothermal gas system the infinite speed of expansion into vacuum leads to zero timestep in the godunov method based on exact riemann solver the schemes we consider are able to bypass these difficulties they are proved to satisfy positiveness of density and discrete entropy inequalities to capture the delta shocks and to treat data with vacuum

quantized consensus over directed networks with switching topologies abstract this paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies we propose an effective distributed protocol with an adaptive finite level uniform quantized strategy under which consensus among agents is guaranteed with weaker communication conditions in particular we analytically prove that each agent sending 5 level quantized information to each of its neighbors together with 3 level quantized information to itself at each time step which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded by dropping the typical common left eigenvector requirement for the existence of common quadratic lyapunov function we conduct the convergence analysis based on the notion of input to output stability the proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability and it fits well into the digital network framework

hidden symmetries associated with the projective group of nonlinear first order ordinary differential equations hidden symmetries those not found by the classical lie group method for point symmetries are reported for nonlinear first order ordinary differential equations odes which arise frequently in physical problems these are for the special class of the eight nonabelian two parameter subgroups of the eight parameter projective group the first order odes can be transformed by non local transformations to new separable first order odes which then can be reduced to quadratures the first order odes include riccati equations and equations which in particular cases are of the form of abel s equation the procedure demonstrates the feasibility of integrating nonlinear odes that do not show any apparent lie group point symmetry applications to the vlasov characteristic equation and the reaction diffusion equation are given

lie symmetries and exact solutions of the barotropic vorticity equation lie group methods are used for the study of various issues related to symmetries and exact solutions of the barotropic vorticity equation the lie symmetries of the barotropic vorticity equations on the f and planes as well as on the sphere in rotating and rest reference frames are determined a symmetry background for reducing the rotating reference frame to the rest frame is presented the one and two dimensional inequivalent subalgebras of the lie invariance algebras of both equations are exhaustively classified and then used to compute invariant solutions of the vorticity equations this provides large classes of exact solutions which include both rossby and rossby haurwitz waves as special cases we also discuss the possibility of partial invariance for the plane equation thereby further extending the family of its exact solutions this is done in a more systematic and complete way than previously available in literature

simultaneous compensation of input and state delays for nonlinear systems abstract the problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback in this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length the key challenge in contrast to the case of only input delay is that the input delay free system on which the design and stability proof of the closed loop system under predictor feedback are based is infinite dimensional we resolve this challenge and we design the predictor feedback law that compensates the input delay we prove global asymptotic stability of the closed loop system using two different techniques one based on the construction of a lyapunov functional and one using estimates on solutions we present two examples one of a nonlinear delay system in the feedforward form with input delay and one of a scalar linear system with simultaneous input and state delays

brief paper stability analysis for multi agent systems using the incidence matrix quantized communication and formation control the spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi agent control problems in particular we consider the problem of state agreement with quantized communication and the problem of distance based formation control in both cases stabilizing control laws are provided when the communication graph is a tree it is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi agent control problems

well posedness for pressureless flow we study the uniqueness problem for pressureless gases previous results on this topic are only known for the case when the initial data is assumed to be a bounded measurable function this assumption is unnatural because the solution is in general a radon measure in this paper the uniqueness of the weak solution is proved for the case when the initial data is a radon measure we show that besides the oleinik entropy condition it is also important to require the energy to be weakly continuous initially our uniqueness result is obtained in the same functional space as the existence theorem

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

group invariant solutions and optimal systems for multidimensional hydrodynamics the group properties of the three dimensional 3 d one temperature hydrodynamic equations including nonlinear conduction and a thermal source are presented a subgroup corresponding to axisymmetric geometry is chosen and the details of the construction of the one and two dimensional optimal systems are shown the two dimensional optimal system is used to generate 23 intrinsically different reductions of the 2 d partial differential equations to ordinary differential equations these ordinary differential equations can be solved to provide analytic solutions to the original partial differential equations two example analytic solutions are presented a 2 d axisymmetric flow with a p2 asymmetry and a 3 d spiraling flow

representation theorems for l fuzzy quantities abstract in this paper representation theorems are given for l fuzzy quantities which permit a better understanding of fuzziness in particular representation theorems due to negoita and ralescu 17 and to sherwood and taylor 23 are extended to the scope of complete and brouwerian lattices

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper