the pth moment exponential stability and almost surely exponential stability of stochastic differential delay equations with poisson jump abstract this paper is devoted to study a class of nonlinear stochastic differential delay equations with poisson jump in comparison to the brownian motion the jump leads to the discontinuity of sample paths which makes the analysis more difficult we first introduce the local lipschitz condition and a new nonlinear growth condition which is weaker than those in the previous literature then by virtue of lyapunov function and semi martingale convergence theorem we prove that the considered stochastic system has a unique global solution moreover we also investigate the pth moment exponential stability and the almost surely exponential stability of solutions finally an example is given to illustrate the effectiveness of our theoretical results

stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

degenerations of filippov algebras we consider the variety of filippov n lie algebra structures on an n 1 dimensional vector space the group gln k acts on it and we study the orbit closures with respect to the zariski topology this leads to the definition of filippov algebra degenerations we present some fundamental results on such degenerations including trace invariants and necessary degeneration criteria finally we classify all orbit closures in the variety of complex n 1 dimensional filippov n ary algebras we consider the variety of filippov n lie algebra structures on an n 1 dimensional vector space the group gln k acts on it and we study the orbit closures with respect to the zariski topology this leads to the definition of filippov algebra degenerations we present some fundamental results on such degenerations including trace invariants and necessary degeneration criteria finally we classify all orbit closures in the variety of complex n 1 dimensional filippov n ary algebras

fast reaction limit of a three component reaction diffusion system abstract we consider a three component reaction diffusion system with a reaction rate parameter and investigate its singular limit as the reaction rate tends to infinity the limit problem is given by a free boundary problem which possesses three regions separated by the free boundaries one component vanishes and the other two components remain positive in each region therefore the dynamics is governed by a system of two equations

contractions nijenhuis and saletan tensors for general algebraic structures we study generalizations in many directions of the contraction procedure for lie algebras introduced by saletan we consider products of an arbitrary nature not necessarily lie brackets and we generalize to infinite dimension considering a modification of the approach by nijenhuis tensors to bilinear operations on sections of finite dimensional vector bundles we apply our general procedure to lie algebras lie algebroids and poisson brackets we also present results on contractions of n ary products and coproducts

lasalle type theorems for stochastic differential delay equations the main aim of this paper is to establish the lasalle type asymptotic convergence theorems for the solutions of stochastic differential delay equations these stochastic versions are then applied to establish sufficient criteria for the stochastically asymptotic stability of the delay equations several examples are also given for illustration

deformations and contractions of lie algebras in this contributed presentation we discuss and compare the mutually opposite procedures of deformations and contractions of lie algebras we suggest that with approp riate combinations of both procedures one may construct new lie algebras we first discuss low dimensional lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation the converse is not true in general also we note that some lie algebras belonging to parameterized families are singled out by the irreversibility of defor mations and contractions after reminding that global deformations of the witt virasoro and affine kac moody algebras allow one to retrieve lie algebras of krichever novikov type we contract the latter to find new infinite dimensional lie algebras

smoothness of equisingular families of curves francesco severi 1921 showed that equisingular families of plane nodal curves are t smooth i e smooth of the expected dimension whenever they are non empty for families with more complicated singularities this is no longer true given a divisor d on a smooth projective surface it thus makes sense to look for conditions which ensure that the family v irr d s 1 s r of irreducible curves in the linear system d l with precisely r singular points of types s 1 s r is t smooth considering different surfaces including the projective plane general surfaces in p 3 c products of curves and geometrically ruled surfaces we produce a sufficient condition of the type e t i 1 s i d k 2 where is some invariant of the singularity type and is some constant this generalises the results of greuel lossen and shustin 2001 for the plane case combining their methods and the method of bogomolov instability for many singularity types the invariant leads to essentially better conditions than the invariants used by greuel lossen and shustin 1997 and for most classes of geometrically ruled surfaces our results are the first known for t smoothness at all

almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks stability of numerical solutions to stochastic delay differential equations have received an increasing attention but there has been so far little work on the stability analysis of numerical solutions to stochastic delay hopfield neural networks the aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks by using two approaches the euler method and the backward euler method under some reasonable conditions both the euler scheme and the backward euler scheme are proved to be almost sure exponential stability in particular the euler method and the backward euler method are mainly based on the semimartingale convergence theorem

realization of synchronization in time delayed systems with stochastic perturbation since noise is ubiquitous in both nature and artificial systems the stochastic perturbation influence on the dynamics of the unidirectionally coupled ikeda models is investigated in this paper on the one hand sufficient conditions on the complete synchronization between these noise perturbed and chaotic models are mathematically established and an estimation of the sample transverse lyapunov exponent is rigorously derived on the other hand specific examples and their numerical simulations are provided to illustrate the feasibility of our theoretical results moreover the results on the ikeda models are further generalized to a wide class of coupled nonlinear systems with multiple time delays and a common additive noise it is believed that the idea and approach developed in this paper could be further generalized to investigate some other problems on chaos synchronization and chaos control with stochastic perturbation

adaptive output feedback control for a class of uncertain stochastic non linear systems with time delays in this paper we investigate the adaptive output feedback stabilisation for a class of stochastic non linear systems with time varying time delays first we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non linear systems with time delays and introduce a new stability notion and the related criterion then for a class of stochastic non linear systems with time varying time delays uncertain parameters in both drift and diffusion terms and general constant virtual control coefficients we present a systematic design procedure for a memoryless adaptive output feedback control law by using the backstepping method it is shown that under the control law based on a memoryless observer the closed loop equilibrium of interest is globally stable in probability and moreover the solution process can be regulated to the origin almost surely

numerical solutions of stochastic differential delay equations under the generalized khasminskii type conditions the classical existence and uniqueness theorem of the solution to a stochastic differential delay equation sdde requires the local lipschitz condition and the linear growth condition see e g 11 12 and 20 the numerical solutions under these conditions have also been discussed intensively see e g 4 10 13 16 17 18 21 22 and 24 recently mao and rassias 14 and 15 established the generalized khasminskii type existence and uniqueness theorems for sddes where the linear growth condition is no longer imposed these generalized khasminskii type theorems cover a wide class of highly nonlinear sddes but these nonlinear sddes do not have explicit solutions whence numerical solutions are required in practice however there is so far little numerical theory on sddes under these generalized khasminskii type conditions the key aim of this paper is to close this gap

equivalence of diagonal contractions to generalized iw contractions with integer exponents abstract we present a simple and rigorous proof of the claim by weimar woods e weimar woods contractions generalized inonu wigner contractions and deformations of finite dimensional lie algebras rev math phys 12 2000 1505 1529 that any diagonal contraction e g a generalized inonu wigner contraction is equivalent to a generalized inonu wigner contraction with integer parameter powers

lie algebra of anomalously scaled fluctuations for quantum lattice systems it is proven that anomalously scaled fluctuations have a natural lie algebra structure the harmonic lattice in the ground state is given as an illustration of the general theorem

non solvable contractions of semisimple lie algebras in low dimension the problem of non solvable contractions of lie algebras is analysed by means of a stability theorem the problem is shown to be deeply related to the embeddings among semisimple lie algebras and the resulting branching rules for representations with this procedure we determine all deformations of indecomposable lie algebras having a nontrivial levi decomposition onto semisimple lie algebras of dimension n 8 and obtain the non solvable contractions of the latter class of algebras

contractions of low dimensional lie algebras theoretical background of continuous contractions of finite dimensional lie algebras is rigorously formulated and developed in particular known necessary criteria of contractions are collected and new criteria are proposed a number of requisite invariant and semi invariant quantities are calculated for wide classes of lie algebras including all low dimensional lie algebras an algorithm that allows one to handle one parametric contractions is presented and applied to low dimensional lie algebras as a result all one parametric continuous contractions for both the complex and real lie algebras of dimensions not greater than 4 are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases levels and colevels of low dimensional lie algebras are discussed in detail properties of multiparametric and repeated contractions are also investigated

r matrix lax pair and multiparameter decompositions of lie algebras we construct r operators on the lie algebra x1d524 x1d529 n or more generally hilbert schmidt operators l2 in hilbert space these operators are related to a multiparameter deformation given by a sequence of parameters a1 a2 we determine for which choices of parameters r operators are r matrices we also construct the lax pair for the corresponding hamilton equations

classical and quantum superintegrability with applications a superintegrable system is roughly speaking a system that allows more integrals of motion than degrees of freedom this review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta we present a classification of second order superintegrable systems in two dimensional riemannian and pseudo riemannian spaces it is based on the study of the quadratic algebras of the integrals of motion and on the equivalence of different systems under coupling constant metamorphosis the determining equations for the existence of integrals of motion of arbitrary order in real euclidean space e2 are presented and partially solved for the case of third order integrals a systematic exposition is given of systems in two and higher dimensional space that allow integrals of arbitrary order the algebras of integrals of motions are not necessarily quadratic but close polynomially or rationally the relation between superintegrability and the classification of orthogonal polynomials is analyzed

2 1 kinematical expansions from galilei to de sitter algebras expansion of a lie algebra is the opposite process to contraction starting from a lie algebra the expansion process goes to another algebra which is non isomorphic and less abelian we propose an expansion method based on the casimir invariants of the initial and expanded algebras and where the free parameters involved in the expansion are the curvatures of their associated homogeneous spaces this method is applied for expansions within the family of lie algebras of three dimensional spaces and 2 1 d kinematical algebras we show that these expansions are classed into two types the first type makes the curvature of space or spacetime different from zero i e it introduces a space or universe radius while the other has a similar interpretation for the curvature of the space of worldlines which is non positive and equal to 1 c2 in the kinematical algebras we obtain expansions which go from galilei to either newton hooke or poincarealgebras and from these to de sitter algebras as well as some other examples

non smooth lyapunov function based global stabilization for quantum filters this paper addresses the global stabilization problem for a class of quantum filters via non smooth lyapunov functions due to the intrinsic symmetric topology of filter state space the smooth controls synthesized via the classical lyapunov stochastic stability theory fail to obtain the global stabilizability because of the existence of the so called antipodal eigenstates as such for the first time we introduce a non smooth lyapunov like theory for generic stochastic nonlinear systems which includes a continuous lyapunov like theorem and a discontinuous lyapunov like theorem for stability in probability applying the non smooth lyapunov like theory switching control and continuous control in saturation form are constructed for the quantum filters with consideration of the sliding motion of filter state the non smooth property enables these controls to deal with the symmetric topology of filter state space and to solve the problem of global stabilization for quantum filters the eigenstate transferring is obtained as a special result distinguishing these non smooth lyapunov based controls from classical control approaches for quantum filters the effectiveness of the non smooth lyapunov based controls is illustrated through the control design for the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the controls

projected euler maruyama method for stochastic delay differential equations under a global monotonicity condition abstract in this paper we investigate a projected euler maruyama method for stochastic delay differential equations with variable delay under a global monotonicity condition this condition admits some equations with highly nonlinear drift and diffusion coefficients we appropriately generalize the idea of c stability and b consistency given by beyn et al 2016 to the case with delay moreover the method is proved to be convergent with order one half in a succinct way finally some numerical examples are included to support our theoretical results

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

the almost sure asymptotic stability and p th moment asymptotic stability of nonlinear stochastic differential systems with polynomial growth this note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems sdss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such sdss we also provide the range of the order p a numerical example is provided to illustrate the effectiveness and the benefits of the proposed result

decentralised adaptive output feedback stabilisation for stochastic time delay systems via lasalle yoshizawa type theorem abstractthis paper deals with the decentralised output feedback stabilisation problem for a class of large scale stochastic time delay nonlinear systems a general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time delay systems in addition a stochastic version of the well known lasalle yoshizawa theorem with time varying delay is initially proposed for the controller design and stability analysis then for a class of large scale stochastic systems with time varying delays totally decentralised adaptive delay dependent controllers are designed by using k filter and backstepping approach via lasalle yoshizawa type theorem and constructing a general lyapunov function it is shown that all signals in the closed loop system are bounded almost surely and the solution is almost surely asymptotically stable finally a simulation example is given to illustrate the effectiveness of the results of this paper

synchronization in an array of linearly stochastically coupled networks with time delays abstract in this paper the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays the stochastic coupling term which can reflect a more realistic dynamical behavior of coupled systems in practice is introduced to model a coupled system and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly based on a simple adaptive feedback control scheme and some stochastic analysis techniques several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays finally an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

stochastic differential delay equations of population dynamics in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

almost sure exponential stability of numerical solutions for stochastic delay differential equations using techniques based on the continuous and discrete semimartingale convergence theorems this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations sddes the important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of sddes directly this is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the chebyshev inequality and the borel cantelli lemma

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

bianchi spaces and their three dimensional isometries as s expansions of two dimensional isometries in this paper we show that certain three dimensional isometry algebras specifically those of type i ii iii and v according to bianchi s classification can be obtained as expansions of the isometries in two dimensions in particular we use the so called s expansion method which makes use of the finite abelian semigroups because it is the most general procedure known until now also it is explicitly shown why it is impossible to obtain the algebras of type iv vi ix as expansions from the isometry algebras in two dimensions all the results are checked with computer programs this procedure shows that the problem of how to relate by an expansion two lie algebras of different dimensions can be entirely solved in particular the procedure can be generalized to higher dimensions which could be useful for diverse physical applications as we discuss in our conclusions

welschinger invariants of real del pezzo surfaces of degree 3 we give a recursive formula for purely real welschinger invariants of real del pezzo surfaces of degree k 2 3 where in the case of surfaces of degree 3 with two real components we introduce a certain modification of welschinger invariants and enumerate exclusively the curves traced on the non orientable component as an application we prove the positivity of the invariants under consideration and their logarithmic asymptotic equivalence as well as congruence modulo 4 to genus zero gromov witten invariants

exponential stability of euler maruyama solutions for impulsive stochastic differential equations with delay this paper establishes a method to study the exponential stability of euler maruyama em method for impulsive stochastic differential equations with delay by using the properties of m matrix and stochastic analysis technique some conditions under which the em solution is exponentially mean square stable are obtained some examples are provided to illustrate the results

theta schemes for sddes with non globally lipschitz continuous coefficients this paper establishes the boundedness convergence and stability of the two classes of theta schemes namely split step theta sst scheme and stochastic linear theta slt scheme for stochastic differential delay equations sddes with non globally lipschitz continuous coefficients when the drift f x y satisfies one sided lipschitz condition with respect to the present state x and the diffusion g x y obeys the global lipschitz condition with respect to the present term x but the delay terms y in the drift and diffusion may be highly nonlinear this paper first examines the strong convergence rates of the theta schemes for sddes it is also proved that the two classes of theta schemes for 1 2 1 converge strongly to the exact solution with the order 1 2 but for 0 1 2 the linear growth condition on drift f x y in x is needed for the strong convergence rates the exponential mean square stability of the theta schemes with 1 2 1 is also investigated for highly nonlinear sddes

geometrical aspects of the lie algebra s expansion procedure in this article it is shown that s expansion procedure affects the geometry of a lie group changing it and leading us to the geometry of another lie group with higher dimensionality a method for determining the semigroup which would provide a lie algebra from another is outlined via an example finally it is proved that a lie algebra obtained from another lie algebra via s expansion is a non simple lie algebra

the general solution of the real graded contractions of the general solution of the graded contraction equations for a grading of the real compact simple lie algebra so n 1 is presented in an explicit way it turns out to depend on independent real parameters the structure of the general graded contractions is displayed for the low dimensional cases and kinematical algebras are shown to appear straightforwardly the geometrical or physical meaning of the contraction parameters as curvatures is also analysed in particular for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes

on input to state stability of stochastic nonlinear systems with markovian jumping parameters in this article the input to state stability iss properties of stochastic nonlinear systems with markovian jump parameters are considered firstly the notions of stochastic iss e t weighted integral iss in mean and in the pth mean are introduced then by the lyapunov like function method some corresponding criteria are provided lastly a simulation example is provided to illustrate the effectiveness of our results

contraction of lie algebra representations motivated by an example of inonu and wigner a general procedure for the contraction of irreducible unitary representations of semisimple compact lie algebras is given in this situation contractions mean generalized inonu wigner contractions in particular this means that by a simple limiting process one obtains representations of nonsemisimple noncompact lie algebras as examples a general treatment of so 3 is given as well as some results for su 3

dimension theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes introduction let k be an algebraically closed ground field of characteristic zero the following result is well known see severi 1 anhang f p 317 if en d is a complete i e maximal irreducible algebraic system defined over k of plane algebraic not necessarily irreducible curves of a given order n such that the general curve c of en d k has d nodes and no other singularities then the dimension of en d is equal to 3n p 1 where p n 1 n 2 2 d is the effective genus of c we note that 3n p 1 is equal to n n 3 2 d here n n n 3 2 is the dimension of the linear system of all plane curves of order n this is in agreement with the intuitive expectation that the requirement that a curve of order n possess d nodes in non assigned position imposes d independent algebraic non linear conditions on the curve the above result is easily proved and will be included by us in a more general theorem the proof of which is the main object of this paper theorem 2 section 3 and which deals with irreducible algebraic systems e of curves of order n in which the general curve c of e k has arbitrary singularities but is free from multiple components equivalently c is a reduced curve this theorem asserts that if p is the effective genus of c the definition of the effective genus of a reducible but reduced curve is given in section 3 formula 2 then dim e c 3n p 1 with equality if and only if c has only nodes as singularities it is easily seen see severi loc cit that if 0 c d n n 1 2 then there always exists curves of order n having d nodes the maximum

lowest dimensional example on non universality of generalized inonu wigner contractions abstract we prove that there exists just one pair of complex four dimensional lie algebras such that a well defined contraction among them is not equivalent to a generalized iw contraction or to a one parametric subgroup degeneration in conventional algebraic terms over the field of real numbers this pair of algebras is split into two pairs with the same contracted algebra the example we constructed demonstrates that even in the dimension four generalized iw contractions are not sufficient for realizing all possible contractions and this is the lowest dimension in which generalized iw contractions are not universal moreover this is also the first example of nonexistence of generalized iw contraction for the case when the contracted algebra is not characteristically nilpotent and therefore admits nontrivial diagonal derivations the lower bound equal to three of nonnegative integer parameter exponents which are sufficient to realize all generalized iw contractions of four dimensional lie algebras is also found

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

plane curves of minimal degree with prescribed singularities we prove that there exists a positive such that for any integer d 3 and any topological types s1 sn of plane curve singularities satisfying

graded contractions of the lie algebra e 2 1 the graded contractions of pseudo euclidean lie algebra are studied the non equivalent gradings of of type and a are extended to the entire lie algebra using the action of on the abelian ideal the translations the graded contractions embed into a large family of six dimensional lie algebras the family includes solvable nilpotent and nonsolvable lie algebras both decomposable and indecomposable ones the distinction between graded and inonu wigner contractions is analysed the physically most interesting lie algebras obtained by the contractions are the inhomogeneous galilei and pseudo galilei

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

geometry of families of nodal curves on the blown up projective plane let p2r be the projective plane blown up at r generic points denote by e0 e1 er the strict transform of a generic straight line on p2 and the exceptional divisors of the blown up points on p2r respectively we consider the variety virr of all irreducible curves c with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness irreducibility and non emptiness moreover we extend our conditions for the smoothness and the irreducibility on families of reducible curves for r 9 we give the complete answer concerning the existence of nodal curves in virr

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

on almost sure stability of hybrid stochastic systems with mode dependent interval delays this note develops a criterion for almost sure stability of hybrid stochastic systems with mode dependent interval time delays which improves an existing result by exploiting the relation between the bounds of the time delays and the generator of the continuous time markov chain the improved result shows that the presence of markovian switching is quite involved in the stability analysis of delay systems numerical examples are given to verify the effectiveness

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

output feedback stabilization using small gain method and reduced order observer for stochastic nonlinear systems this technical note further investigates more general stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and focuses on solving the following problems 1 a class of counterexamples which are different from that in are reconstructed to discuss the relationship between two small gain type conditions on siiss and 2 under the weaker conditions on nonlinearities based on a reduced order observer small gain type condition on siiss and stochastic lasalle theorem an output feedback controller is constructed to guarantee the global asymptotical stability in probability of the closed loop stochastic system

adaptive synchronization between two different noise perturbed chaotic systems with fully unknown parameters abstract this paper investigates adaptive synchronization between two different noise perturbed chaotic systems with fully unknown parameters based on lyapunov stability theory the general expression of the suitable nonlinear adaptive synchronization controller is developed at the same time the noise perturbed update laws of parameters are proposed to guarantee the synchronization of two different unknown chaotic systems theoretical analysis and numerical simulations on adaptive synchronization between rossler system and noise perturbed chua s circuits lorenz system and noise perturbed chen system with fully unknown parameters show the efficiency of the proposed adaptive scheme

brief paper smc design for robust h control of uncertain stochastic delay systems recently sliding mode control method has been extended to accommodate stochastic systems however the existing results employ an assumption that may be too restrictive for many stochastic systems this paper aims to remove this assumption and present in terms of lmis a sliding mode control design method for stochastic systems with state delay in some cases the proposed method provides a control scheme for finite time stabilization of stochastic delay systems

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

contractions of lie algebras generalized inonu wigner contractions versus graded contractions recently a new notion of contraction has been introduced the purely algebraically defined graded contractions that fall into two disjoint classes continuous and discrete our main result is that all continuous graded contractions can be realized by generalized inonu wigner contractions furthermore we give a complete characterization of the discrete graded contractions via certain higher order identities inherent to the grading group

on the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps this paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps by the ito formula stochastic inequality and semi martingale convergence theorem we study the asymptotic stability in the p th moment and almost sure exponential stability of solutions under the local lipschitz condition and nonlinear growth condition on the other hand we also show the convergence in probability of numerical schemes under nonlinear growth condition finally an example is provided to illustrate the theory

global stability and stabilization of more general stochastic nonlinear systems abstract this paper considers the global stability and stabilization of more general stochastic nonlinear systems due to the absence of the conventional assumptions e g lipschitz condition the stochastic nonlinear systems under investigation may have more than one weak solution however the most associated results are only applicable to the stochastic systems having a unique strong solution and therefore it is meaningful to refine and extend the relevant concepts and methods to the more general case in this paper the concepts of stochastic stability in the more general sense are first introduced to cover the stochastic nonlinear systems having more than one weak solution then the generalized stochastic barbashin krasovskii theorem and lasalle theorem are established which present the criterions of stochastic stability for more general stochastic nonlinear systems as one of the main contributions in this paper we rigorously prove the generalized stochastic barbashin krasovskii theorem moreover based on the generalized theorems the output feedback and state feedback stabilization are accomplished respectively for two classes of high order stochastic nonlinear systems under rather weaker assumptions comparing to the existing literature

existence of curves with prescribed topological singularities throughout this paper we study the existence of irreducible curves c on smooth projective surfaces with singular points of prescribed topological types s 1 s r there are necessary conditions for the existence of the type r i 1 s i c 2 c k for some fixed divisor k on and suitable coefficients and and the main sufficient condition that we find is of the same type saying it is asymptotically proper ten years ago general results of this quality were not known even for the case e p 2 c an important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up e of the form o d r i 1 m i e i deduced from the kawamata vieweg vanishing theorem its proof covers the first part of the paper while the middle part is devoted to the existence theorems in the last part we investigate our conditions on ruled surfaces products of elliptic curves surfaces in p 3 c and k3 surfaces

existence uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps in this paper we are concerned with neutral stochastic functional differential equations driven by pure jumps nsfdewpjs we prove the existence and uniqueness of the solution to nsfdewpjs whose coefficients satisfying the local lipschitz condition in addition we establish the p th exponential estimations and almost surely asymptotic estimations of the solution for nsfdewjs

convergence rate and stability of the truncated euler maruyama method for stochastic differential equations abstract recently mao 2015 developed a new explicit method called the truncated euler maruyama em method for the nonlinear sde and established the strong convergence theory under the local lipschitz condition plus the khasminskii type condition in his another follow up paper mao 2016 he discussed the rates of l q convergence of the truncated em method for q 2 and showed that the order of l q convergence can be arbitrarily close to q 2 under some additional conditions however there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated em method would be inapplicable the key aim of this paper is to establish the convergence rate without these restrictions the other aim is to study the stability of the truncated em method the advantages of our new results will be highlighted by the comparisons with the results in mao 2015 2016 as well as others on the tamed em and implicit methods

irreducibility of equisingular families of curves in 1985 joe harris proved the long standing claim of severi that equisingular families of plane nodal curves are irreducible whenever they are nonempty for families with more complicated singularities this is no longer true given a divisor d on a smooth projective surface it thus makes sense to look for conditions which ensure that the family v irr d s 1 s r of irreducible curves in the linear system d l with precisely r singular points of types s 1 s r is irreducible considering different surfaces including general surfaces in p 3 c and products of curves we produce a sufficient condition of the type r i 1 deg x s i 2 d k 2 where is some constant and x s i some zero dimensional scheme associated to the singularity type our results carry the same asymptotics as the best known results in this direction in the plane case even though the coefficient is worse for most of the surfaces considered these are the only known results in that direction

families of nodal curves on projective threefolds and their regularity via postulation of nodes the main purpose of this paper is to introduce a new approach to study families of nodal curves on projective threefolds precisely given x a smooth projective threefold e a rank two vector bundle on x l a very ample line bundle on x and k 0 0 integers and denoted by v e l k the subscheme of p h 0 e l k parametrizing global sections of e l k whose zero loci are irreducible and nodal curves on x we present a new cohomological description of the tangent space t s v e l k at a point s 2 v e l k this description enable us to determine effective and uniform upper bounds for which are linear polynomials in k such that the family v e lk is smooth and of the expected dimension regular for short the almost sharpness of our bounds is shown by some interesting examples furthermore when x is assumed to be a fano or a calaby yau threefold we study in detail the regularity property of a point s 2 v e lk related to the postulation of the nodes of its zero locus c v s x roughly speaking when the nodes of c are assumed to be in general position either on x or on an irreducible divisor of x having at worst log terminal singularities or to lie on a l c i and subcanonical curve in x we find upper bounds onwhich are respectively cubic quadratic and linear polynomials in k ensuring the regularity of v e l k at s finally when x p 3 we also discuss some interesting geometric properties of the curves given by sections parametrized by v e ox k

adaptive complete synchronization of the noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch in this paper we design an adaptive feedback controller to synchronize a class of noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch based on invariance principle of stochastic time delay differential equations some sufficient conditions of adaptive complete synchronization are given comparing with other papers here we consider the effect of internal noise time delay and parametric mismatch in the synchronized process as the illustrative examples the famous lorenz system and rossler system are considered here in order to validate the proposed scheme numerical simulations are performed and the numerical results show that our scheme is very effective

the three dimensional real lie algebras and their contractions in this paper the general contractions of the three dimensional real lie algebras are determined a short summary will be given of the history definitions properties examples and applications of contractions of lie algebras so far mostly simple or generalized inonu wigner contractions have been used the three dimensional real lie algebras are classified in such a way that their general contractions can be easily read off all these contractions can be realized by generalized inonu wigner contractions which supports the argument that these are the interesting objects to study

anti de sitter poincare symmetries and representations from poincare galilei through a classical deformation approach a classical deformation procedure based on universal enveloping algebras casimirs and curvatures of symmetrical homogeneous spaces is applied to several cases of physical relevance starting from the 3 1 d galilei algebra we describe at the level of representations the process leading to its two physically meaningful deformed neighbours the poincare algebra is obtained by introducing a negative curvature in the flat galilean phase space or space of worldlines while keeping a flat spacetime to be precise starting from a representation of the galilei algebra with both casimirs different from zero we obtain a representation of the poincare algebra with both casimirs necessarily equal to zero the poincare angular momentum pauli lubanski components position and velocity operators etc are expressed in terms of galilean operators through some expressions deforming the proper galilean ones similarly the newton hooke algebras appear by endowing spacetime with a nonzero curvature while keeping a flat phase space the same approach starting from the 3 1 d poincare algebra provides representations of the anti de sitter as poincare deformations

general properties of the expansion methods of lie algebras the study of the relation between lie algebras and groups and especially the derivation of new algebras from them is a problem of great interest in mathematics and physics because finding a new lie group from an already known one also means that a new physical theory can be obtained from a known one one of the procedures that allow us to do so is called expansion of lie algebras and has been recently used in different physical applications particularly in gauge theories of gravity here we report on further developments of this method required to understand in a deeper way their consequences in physical theories we have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and more specifically as necessary conditions to know if two arbitrary lie algebras can be related by some expansion mechanism formal aspects such as the cartan decomposition of the expanded algebras are also discussed finally an instructive example that allows us to check explicitly all our theoretical results is also provided

synchronization of stochastic competitive neural networks with different timescales and reaction diffusion terms we propose a feedback controller for the synchronization of stochastic competitive neural networks with different timescales and reaction diffusion terms by constructing a proper lyapunov krasovskii functional as well as employing stochastic analysis theory the lashall type invariance principle for stochastic differential delay equations and a linear matrix inequality lmi technique a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks a simulation example is given to show the effectiveness of the theoretical results

exponential stability in p th mean of solutions and of convergent euler type solutions of stochastic delay differential equations one concept of the stability of a solution of an evolutionary equation relates to the sensitivity of the solution to perturbations in the initial data there are other stability concepts notably those concerned with persistent perturbations results are presented on the stability in p th mean of solutions of stochastic delay differential equations with multiplicative noise and of stochastic delay difference equations the difference equations are of a type found in numerical analysis and we employ our results to obtain mean square stability criteria for the solution of the euler maruyama discretization of stochastic delay differential equations the analysis proceeds as follows we show that an inequality of halanay type derivable via comparison theory can be employed to derive conditions for p th mean stability of a solution we then produce a discrete analogue of the halanay type theory that permits us to develop a p th mean stability analysis of analogous stochastic difference equations the application of the theoretical results is illustrated by deriving mean square stability conditions for solutions and numerical solutions of a constant coefficient linear test equation

the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching and with polynomial growth abstract this paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching sdswmss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques we propose some conditions under which such sdswmss are asymptotically stable and exponentially stable nontrivial examples are provided to illustrate our results