stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

new stabilization criteria for linear time varying systems with state delay and norm bounded uncertainties this note deals with the stabilization problem of a class of un certain linear time varying systems with state delay simple stabilizability criteria are proposed in terms of the global controllability of the nominal system the feature of this note is that the stabilizability conditions and stabilizing controllers do not involve the solution of any riccati differential equation and hence they are easy to verify and design index terms controllability lyapunov function riccati equation sta bilization state delay uncertain systems

disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

the characterizations of h hemiregular hemirings and h intra hemiregular hemirings in this paper the concepts of fuzzy h bi ideals and fuzzy h quasi ideals of a hemiring are introduced and related properties are investigated the notion of h intra hemiregularity of a hemiring which is a generalization of the notion of intra regularity of a ring is provided some characterizations of h hemiregular hemirings h intra hemiregular hemirings and hemirings that are both h hemiregular and h intra hemiregular are derived in terms of fuzzy left fuzzy right h ideals fuzzy h bi ideals and fuzzy h quasi ideals

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

on λ semirings abstract a semiring is an ordered semiring s equipped with a star operation such that for any a b s a b is the least fixed point of the linear mapping x ax b over s the notion of semirings is a generalization of several important concepts such as continuous semirings weak inductive semirings and the kleene algebras of conway and kozen we investigate several basic properties of semirings and obtain results on semirings in relation to preorders duality and formal power series some of these results can be seen as generalizations of relevant results on inductive semirings

a spinorial formulation of the maximum clique problem of a graph we present a new formulation of the maximum clique problem of a graph in complex space we start observing that the adjacency matrix a of a graph can always be written in the form a b2 where b is a complex symmetric matrix formed by vectors of zero length null vectors and the maximum clique problem can be transformed in a geometrical problem for these vectors this problem in turn is translated in spinorial language and we show that each graph uniquely identifies a set of pure spinors that is vectors of the endomorphism space of clifford algebras and the maximum clique problem is formalized in this setting so that this much studied problem may take advantage from recent progresses of pure spinor geometry

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

delay dependent stochastic stability criteria for markovian jumping neural networks with mode dependent time varying delays and partially known transition rates abstract in this paper the problem of stochastic stability criterion of markovian jumping neural networks with mode dependent time varying delays and partially known transition rates is considered some new delay dependent stability criteria are derived by choosing a new class of lyapunov functional the obtained criteria are less conservative because free weighting matrices method and a convex optimization approach are considered finally a numerical example is given to illustrate the effectiveness of the proposed method

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

model approximation for switched genetic regulatory networks the model approximation problem is studied in this paper for switched genetic regulatory networks grns with time varying delays we focus on constructing a reduced order model to approximate the high order grns considered under the switching signal subject to certain constraints such that the approximation error system between the original and reduced order systems is exponentially stable with a disturbance attenuation performance the stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell time method for the approximation error system then the solvability conditions for the reduced order models for the grns are also established using the projection method furthermore the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm finally several examples are provided to illustrate the effectiveness and the advantages of the proposed methods

fuzzy bi ideals in ordered semigroups given a set s a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the unit segment of the real line if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept was first introduced by zadeh fuzzy groups have been first considered by rosenfelt fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed in the present paper we endow s with the structure of an ordered semigroup and define fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups we define the fuzzy bi ideals in ordered semigroups and we give the main theorem which characterizes the bi ideals in terms of fuzzy bi ideals then we characterize the left and right simple the completely regular and the strongly regular ordered semigroups by means of fuzzy bi ideals we also study the decomposition of left and right simple ordered semigroups and of ordered semigroups having the property a a2 for all a in terms of fuzzy bi ideals this decomposition is uniquely defined

regular ordered semigroups in terms of fuzzy subsets given a set s a fuzzy subset of s or a fuzzy set in s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers if the set s bears some structure one may distinguish some fuzzy subsets of s in terms of that additional structure this important concept of a fuzzy set was first introduced by zadeh fuzzy groups have been first considered by rosenfeld fuzzy semigroups by kuroki a theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed some results on ordered groupoids semigroups have been already given by the same authors in n kehayopulu m tsingelis fuzzy sets in ordered groupoids semigroup forum 65 2002 128 132 n kehayopulu m tsingelis the embedding of an ordered groupoid into a poe groupoid in terms of fuzzy sets inform sci 152 2003 231 236 n kehayopulu m tsingelis fuzzy bi ideals in ordered semigroups inform sci 171 2004 13 28 where s has been endowed with the structure of an ordered semigroup and defined fuzzy analogous for several notions that have been proved to be useful in the theory of ordered semigroups the characterization of regular rings in terms of right and left ideals is well known the characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left right ideals and quasi ideals is well known as well the characterization of regular le semigroups that is lattice ordered semigroups having a greatest element in terms of right ideal elements and left ideal elements or right left and quasi ideal elements is also known in the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals then we characterize the regular ordered semigroups in terms of fuzzy right fuzzy left ideals and fuzzy quasi ideals the paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of fuzzy ordered semigroups some of our results are true for ordered groupoids in general

mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic hopfield neural networks abstract recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention but there has been little work on the stability analysis of the numerical solutions to delayed stochastic hopfield neural networks dshnns so far the aim in this paper is to study the mean square exponential stability of the split step theta sst method and the stochastic linear theta slt method for the underlying model it is proved that for any 0 1 2 there exists a constant 0 depending on such that the numerical schemes produced by the sst method and the slt method are mean square exponentially stable for 0 under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model for the case 1 2 1 we show the same stability conclusion for all 0 to carry out the required conclusion a novel technique for the stability analysis of discrete numerical schemes with multi time delays namely the weighted sum lyapunov functional method is proposed finally a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

lmi conditions for global robust stability of delayed neural networks with discontinuous neuron activations without assuming that the neuron activations are bounded some delay independent criteria for interval delayed neural networks with discontinuous neuron activations are derived to guarantee global robust stability by using the generalized lyapunov method and linear matrix inequality lmi technique the obtained results improve and extend those given in earlier literature and two numerical examples are also given to show the effectiveness of our results

on stability and stabilization of t s fuzzy time delayed systems in this paper the stability analysis and control design of takagi sugeno ts fuzzy systems subject to uncertain time delay are addressed the proposed approach is based on linear matrix inequalities and the lyapunov krasovskii theory where a new fuzzy weighting dependent lyapunov krasovskii functional is introduced by employing the gu discretization technique and strategies to add slack matrix variables less conservative conditions are obtained numerical experiments are performed to illustrate the effectiveness of the proposed methodology

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

regular fuzzy duo rings in this paper we shall introduce the concept of a fuzzy bi ideal a fuzzy quasi ideal in a ring and give some properties of such fuzzy ideals we also give a characterization of a regular fuzzy duo ring in terms of fuzzy ideals

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

continuous characterizations of the maximum clique problem given a graph g whose adjacency matrix is a the motzkin strauss formulation of the maximum clique problem is the quadratic program max xtax xte 1 x 0 it is well known that the global optimum value of this qp is 1 1 g where g is the clique number of g here we characterize the following properties pertaining to the above qp 1 first order optimality 2 second order optimality 3 local optimality 4 strict local optimality these characterizations reveal interesting underlying discrete structures and are polynomial time verifiable a parametrization of the motzkin strauss qp is then introduced and its properties are investigated finally an extension of the motzkin strauss formulation is provided for the weighted clique number of a graph

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

vague soft hemirings abstract xu et al introduced the concept of vague soft sets which is an extension to the soft set and the vague set in this paper we apply the concept of vague soft sets to hemiring theory the notion of q vague soft left h ideals of a hemiring is introduced and some related properties are investigated

rings with chain conditions abstract the aim of this paper is to find out some new results about fuzzy ideals to characterise artinian rings and noetherian rings by fuzzy ideals and to give alternative proofs of some well known results of artinian and noetherian rings by fuzzy ideal theoretic techniques

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

α β fuzzy ideals of hemirings we give a characterization of different types of a b fuzzy ideals of hemirings where a b q q q and a q special attention is paid to q fuzzy prime and semiprime ideals

μ semirings and μ lamda semirings we introduce and study semirings and semirings which generalize inductive semirings and weak inductive semirings respectively also we discuss the semiring of formal power series with coefficients in such a semiring and prove that the semiring of formal power series with coefficients in a weak inductive semiring semiring semiring semiring is a weak inductive semirng semiring semiring semiring respectively this gives a positive answer to one of esik and kuich s open problems

design of state dependent switching laws for stability of switched stochastic neural networks with time delays we study the stability properties of switched stochastic neural networks ssnns with time varying delays whose subsystem is not necessarily stable we introduce state dependent switching sds as a tool for stability analysis some sds laws for asymptotic stability and p th moment exponentially stable are designed by employing lyapunov krasovskii l k functional and lyapunov razumikhin l r method respectively it is shown that the stability of ssnns with time varying delays composed of unstable subsystems can be achieved by using sds law the control gains in the designed sds laws can be derived by solving the lmis in derived stability criteria two numerical examples are provided to demonstrate the effectiveness of the proposed sds laws

normal l fuzzy ideals in semirings abstract in this paper we introduce the notion of a normal l fuzzy left resp right ideal in a semiring and investigate some properties

novel stability analysis for recurrent neural networks with multiple delays via line integral type l k functional this paper studies the stability problem of a class of recurrent neural networks rnns with multiple delays by using an augmented matrix vector transformation for delays and a novel line integral type lyapunov krasovskii functional a less conservative delay dependent global asymptotical stability criterion is first proposed for rnns with multiple delays the obtained stability result is easy to check and improve upon the existing ones then two numerical examples are given to verify the effectiveness of the proposed criterion

fock space description of simple spinors cartan s simple often called pure spinors corresponding to even dimensional complex vector spaces are defined in terms of the associated maximal totally null planes their geometrical properties are derived and described using notions familiar to physicists dirac and weyl spinors gamma matrices tensors formed bilinearly from pairs of spinors and creation and annihilation operators of fermi states a new theorem characterizes a simple spinor by the properties of the vector t b where is an arbitrary spinor and b is the matrix connecting the gamma matrices with their transposes the cartan constraint equations on the components of simple spinors are given a new geometrically transparent derivation based on the action on simple spinors of a maximal abelian subgroup of the group spin

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

fuzzy k ideals of semirings the aim of this paper is to introduce the notions of fuzzy k ideals prime fuzzy k ideals and semiregularity of semirings and to characterize prime fuzzy k ideals semiregular semirings noetherian semirings and artinian semirings by fuzzy k ideals

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

global asymptotic stability of delayed cellular neural networks a new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented the obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior point algorithm a numerical example is used to show the effectiveness of the obtained result

delayed standard neural network models for control systems in order to conveniently analyze the stability of recurrent neural networks rnns and successfully synthesize the controllers for nonlinear systems similar to the nominal model in linear robust control theory the novel neural network model named delayed standard neural network model dsnnm is presented which is the interconnection of a linear dynamic system and a bounded static delayed or nondelayed nonlinear operator by combining a number of different lyapunov functionals with s procedure some useful criteria of global asymptotic stability and global exponential stability for the continuous time dsnnms cdsnnms and discrete time dsnnms ddsnnms are derived whose conditions are formulated as linear matrix inequalities lmis based on the stability analysis some state feedback control laws for the dsnnm with input and output are designed to stabilize the closed loop systems most rnns and neurocontrol nonlinear systems with or without time delays can be transformed into the dsnnms to be stability analyzed or stabilization synthesized in a unified way in this paper the dsnnms are applied to analyzing the stability of the continuous time and discrete time rnns with or without time delays and synthesizing the state feedback controllers for the chaotic neural network system and discrete time nonlinear system it turns out that the dsnnm makes the stability conditions of the rnns easily verified and provides a new idea for the synthesis of the controllers for the nonlinear systems

zeon algebra and combinatorial identities we show that the ordinary derivative of a real analytic function of one variable can be realized as a grassmann berezin type integration over the zeon algebra the z integral as a by product of this representation we give new proofs of the faa di bruno formula and spivey s identity m z spivey j integer seq 11 2008 08 2 5 and we recover the representation of the stirling numbers of the second kind and the bell numbers of staples and schott european j combin 29 2008 pp 1133 1138 the approach described here is suitable to accommodate new z integral representations including stirling numbers of the first kind central delannoy euler fibonacci and genocchi numbers and the special polynomials of bell generalized bell hermite and laguerre

characterizations of h intra and h quasi hemiregular hemirings the concepts of c email protected q d fuzzy h bi h quasi ideals of hemirings are introduced some new characterization theorems of these kinds of fuzzy h ideals are also given in particular some characterizations of the h intra hemiregular and h quasi hemiregular hemirings are investigated by these kinds of fuzzy h ideals

characterizations of hemirings by their h ideals in this paper we characterize hemirings in which all h ideals or all fuzzy h ideals are idempotent it is proved among other results that every h ideal of a hemiring r is idempotent if and only if the lattice of fuzzy h ideals of r is distributive under the sum and h intrinsic product of fuzzy h ideals or equivalently if and only if each fuzzy h ideal of r is intersection of those prime fuzzy h ideals of r which contain it we also define two types of prime fuzzy h ideals of r and prove that a non constant h ideal of r is prime in the second sense if and only if each of its proper level set is a prime h ideal of r

isomorphism theorems and fuzzy k ideals of k semirings we define and study the fuzzy maximal k ideal of a k semiring also we characterize the quotient k semiring r a of a k semiring r by a fuzzy maximal k ideal a and we have some isomorphism theorems in commutative k semirings and further we have some properties of the quotient k semiring r a of all cosets of a fuzzy semiprimary semiprime primary prime k ideal a in a commutative k semiring r

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

soft semirings molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we initiate the study of soft semirings by using the soft set theory the notions of soft semirings soft subsemirings soft ideals idealistic soft semirings and soft semiring homomorphisms are introduced and several related properties are investigated

exponential stabilization of neural networks with various activation functions and mixed time varying delays this paper presents some results on the global exponential stabilization for neural networks with various activation functions and time varying continuously distributed delays based on augmented time varying lyapunov krasovskii functionals new delay dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities a numerical example is given to illustrate the feasibility of our results

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

the intrinsic product of fuzzy subsets of a ring abstract the sup min product which is defined through the expressions of the type x a1b1 ambm for the element x of a ring is called the intrinsic product the definition has been critically studied for all fuzzy subsets of a ring and its organic connection with structures like fuzzy subrings and fuzzy ideals has been investigated this product has been successfully applied to a regular ring which characterizes such a ring in the fuzzy setting

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

inductive semirings one of the most well known induction principles in computer science is the fixed point induction rule or least pre fixed point rule inductive semirings are partially ordered semirings equipped with a star operation satisfying the fixed point equation and the fixed point induction rule for linear terms inductive semirings are extensions of continuous semirings and the kleene algebras of conway and kozen we develop in a systematic way the rudiments of the theory of inductive semirings in relation to automata languages and power series in particular we prove that if s is an inductive semiring then so is the semiring of matrices sn n for any integer n 0 and that if s is an inductive semiring then so is any semiring of power series s a as shown by kozen the dual of an inductive semiring may not be inductive in contrast we show that the dual of an iteration semiring is an iteration semiring kuich proved a general kleene theorem for continuous semirings and bloom and esik proved a kleene theorem for all conway semirings since any inductive semiring is a conway semiring and an iteration semiring as we show there results a kleene theorem applicable to all inductive semirings we also describe the structure of the initial inductive semiring and conjecture that any free inductive semiring may be given as a semiring of rational power series with coefficients in the initial inductive semiring we relate this conjecture to recent axiomatization results on the equational theory of the regular sets

fuzzy soft set theory applied to bck bci algebras abstract in the paper p k maji r biswas a r roy fuzzy soft sets j fuzzy math 9 3 2001 589 602 maji et al introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem the aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in bck bci algebras the notions of fuzzy soft bck bci algebras closed fuzzy soft ideals and fuzzy soft p ideals are introduced and related properties are investigated

the semiring of matrices over a finite chain let l m denote the chain 0 1 2 m 1 with the usual ordering and m n l m the matrix semiring of all nxn matrices with elements in l m we firstly introduce some order preserving semiring homomorphisms from m n l m to m l k by using these homomorphisms we show that a matrix over the finite chain l m can be decomposed into the sum of some matrices over the finite chain l k where k

on computational complexity of clifford algebra after a brief discussion of the computational complexity of clifford algebras we present a new basis for even clifford algebra cl 2m that simplifies greatly the actual calculations and without resorting to the conventional matrix isomorphism formulation obtains the same complexity in the last part we apply these results to the clifford algebra formulation of the np complete problem of the maximum clique of a graph introduced by budinich and budinich a spinorial formulation of the maximum clique problem of a graph j math phys 47 043502 2006

fuzzy h ideals of hemirings a characterization of an h hemiregular hemiring in terms of a fuzzy h ideal is provided some properties of prime fuzzy h ideals of h hemiregular hemirings are investigated it is proved that a fuzzy subset z of a hemiring s is a prime fuzzy left right h ideal of s if and only if z is two valued z 0 1 and the set of all x in s such that z x 1 is a prime left right h ideal of s finally the similar properties for maximal fuzzy left right h ideals of hemirings are considered

on prime quasi prime weakly quasi prime fuzzy left ideals of semigroups in this paper we introduce and study the prime quasi prime and weakly quasi prime fuzzy left ideals of a semigroup s we give characterizations of the largest fuzzy ideal i f contained in a fuzzy left ideal f of a semigroup s and the largest fuzzy subsemigroup i f such that f is a fuzzy ideal of i f finally strongly semisimple semigroups are characterized by quasi prime fuzzy left ideals

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained