switched nonlinear systems with state dependent dwell time the asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied the system switches among a family of integral input to state stable systems the time between two consecutive switchings is not less than a value d this dwell time d is allowed to take different values according to a function whose argument is the state of the system at the switching times we propose a dwell time function which depends on the comparison functions which characterize the integral input to state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with bounded energy the main feature of the analysis is that it does not rely on the property for the switching to stop in finite time the two important cases of locally exponentially stable and feedforward systems are analyzed in detail

quantum groups via hall algebras of complexes we describe quantum enveloping algebras of symmetric kac moody lie algebras via a nite eld hall algebra construction involving z2 graded complexes of quiver representations

input to state stabilization of switched nonlinear systems this note derives some sufficient conditions to ensure that the whole switched nonlinear system is input to state stabilizable iss when each mode is iss both cases that the switchings of system modes coincide exactly and that they do not coincide with those of the corresponding controllers are considered for the latter a model based identification scheme is used to identify the system modes the proposed scheme can overcome the finite escape time that may happen in this case

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

a commutative algebra on degenerate cp1 and macdonald polynomials we introduce a unital associative algebra a associated with degenerate cp1 we show that a is a commutative algebra and whose poincare series is given by the number of partitions thereby we can regard a as a smooth degeneration limit of the elliptic algebra introduced by feigin and odesskii int math res notices 11 531 1997 then we study the commutative family of the macdonald difference operators acting on the space of symmetric functions a canonical basis is proposed for this family by using a and the heisenberg representation of the commutative family studied by shiraishi commun math phys 263 439 2006 it is found that the ding iohara algebra lett math phys 41 183 1997 provides us with an algebraic framework for the free field construction an elliptic deformation of our construction is discussed showing connections with the drinfeld quasi hopf twisting leningrad math j 1 1419 1990 in the sence of babelon bernard billey phys lett b 375 89 1996 the ruijsenaar

the bridgeland s ringel hall algebra associated to an algebra with global dimension at most two abstract for any finite dimensional associative algebra with global dimension 2 we show that there is an embedding from the twisted ringel hall algebra to the bridgeland s ringel hall algebra in particular this result is true for tilted algebras and canonical algebras

buckling and vibrations of polar orthotropic circular plates of linearly varying thickness resting on an elastic foundation abstract axisymmetric vibrations of polar orthotropic circular plates of linearly varying thickness subjected to hydrostatic in plane force and resting on an elastic foundation winkler type are discussed on the basis of the classical plate theory an approximate solution of the problem is obtained by a ritz method frequency parameters of plates with different edge conditions for the first three modes of vibration are presented as computed for various values of the taper parameter the rigidity parameter the foundation parameter the flexibility parameter and the in plane force parameter

triangular decomposition of the composition algebra of the kronecker algebra abstract letabe a finite dimensional hereditary algebra over a finite field and let h a and c a be respectively the ringel hall algebra and the composition algebra ofa definerdto be the element m h a where m runs over the isomorphism classes of the regulara modules with dimension vectord we prove thatrdand the exceptionala modules all lie in c a letkbe the kronecker algebra p resp i the subalgebra of c k generated by the preprojective resp preinjective k modules and t the subalgebra generated byr n n forn 0 then we prove that c k p t i and then t is just the subalgebra of c k generated by all regular elements

stabilizing switching signals a transition from point wise to asymptotic conditions abstract characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature this article collects a multitude of stabilizing switching signals under an umbrella framework we achieve this in two steps firstly given a family of systems possibly containing unstable dynamics we propose a new and general class of stabilizing switching signals secondly we demonstrate that prior results based on both point wise and asymptotic characterizations follow our result this is the first attempt in the switched systems literature where these switching signals are unified under one banner

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

global stability results for switched systems based on weak lyapunov functions in this paper we study the stability of nonlinear and time varying switched systems under restricted switching we approach the problem by decomposing the system dynamics into a nominal like part and a perturbation like one most stability results for perturbed systems are based on the use of strong lyapunov functions i e functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state however switched systems under restricted switching may not admit strong lyapunov functions even when asymptotic stability is uniform over the set of switching signals considered the main contribution of the current paper consists in providing stability results that are based on the stability of the nominal like part of the system and require only a weak lyapunov function these results may have wider applicability than results based on strong lyapunov functions the results provided follow two lines first we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal like and the perturbation like parts of the system second we provide input to state stability iss results for the case when the nominal like part is switched linear time varying we provide two types of iss results standard iss that involves the essential supremum norm of the input and a modified iss that involves a power type norm

input output to state stability and state norm estimators for switched nonlinear systems in this paper the concepts of input output to state stability ioss and state norm estimators are considered for switched nonlinear systems under average dwell time switching signals we show that when the average dwell time is large enough a switched system is ioss if all of its constituent subsystems are ioss moreover under the same conditions a non switched state norm estimator exists for the switched system furthermore if some of the constituent subsystems are not ioss we show that still ioss can be established for the switched system if the activation time of the non ioss subsystems is not too big again under the same conditions a state norm estimator exists for the switched system however in this case the state norm estimator is a switched system itself consisting of two subsystems we show that this state norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for

on the hall algebra of an elliptic curve i these rings admit numerous algebraic and geometric realizations but one of the historically first constructions dating to the work of steinitz in 1900 completed later by hall was given in terms of what is now called the classical hall algebra h see ma chapter ii this algebra has a basis consisting of isomorphism classes of abelian q groups where q is a fixed prime power and the structure constants are defined by counting extensions between such abelian groups in fact these structure constants are polynomials in q and we can therefore consider h as a c q 1 algebra a theorem of steinitz and hall provides an isomorphism h q c q x1 x2 under this isomorphism the natural basis of h resp the natural scalar product is mapped to the basis of hall littlewood polynomials resp the hall littlewood scalar product in addition zelevinsky z endowed q with a structure of a cocommutative hopf algebra and the whole algebra q c q 1

a realisation of the quantum supergroup u glm n abstract we reconstruct the quantum enveloping superalgebra u gl m n over q via finite dimensional quantum schur superalgebras in particular we obtain a new basis containing the standard generators for u gl m n and explicit multiplication formulas of an arbitrary basis element by a generator

modified ringel hall algebras green s formula and derived hall algebras abstract in this paper we define the modified ringel hall algebra m h a of a hereditary abelian category a from the category c b a of bounded z graded complexes two main results are obtained one is to give a new proof of green s formula on ringel hall numbers by using the associative multiplication of the modified ringel hall algebra the other is to show that in certain twisted cases the derived hall algebra can be embedded in the modified ringel hall algebra as a consequence of the second result we get that in certain twisted cases the modified ringel hall algebra is isomorphic to the tensor algebra of the derived hall algebra and the torus of acyclic complexes and therefore the modified ringel hall algebra is invariant under derived equivalences

bridgeland s hall algebras of tilted algebras and lusztig s symmetries abstract for each finite dimensional algebra a of finite global dimension over a finite field bridgeland considered the ringel hall algebra of 2 cyclic complexes of projective a modules and achieved an algebra called bridgeland s hall algebra by taking some localization and reduction in this paper we show that there exist homomorphisms of algebras from quantum groups to bridgeland s hall algebras of tilted algebras in particular for apr tilting this homomorphism provides a realization of lusztig s symmetries of quantum groups via bridgeland s hall algebras

triangular decomposition of tame non simply laced composition algebras let a be a finite dimensional hereditary algebra over a finite field and let c a be the composition algebra of a let p resp i be the subalgebra of c a generated by the preprojective resp preinjective a modules and let t be the subalgebra generated by rd where rd m h a m runs over the isomorphism classes of the regular a modules with dimension vector d and h a is the ringel hall algebra of a then we prove that c a p t i if a is one of the types bn cn bcn bdn cdn f41 f42 g21 g22 or a11

stabilizing switching signals for switched systems this article deals with stability of continuous time switched systems under constrained switching given a family of systems possibly containing unstable dynamics we characterize a new class of switching signals under which the switched system generated by it and the family of systems is globally asymptotically stable our characterization of such stabilizing switching signals involves the asymptotic frequency of switching the asymptotic fraction of activation of the constituent systems and the asymptotic densities of admissible transitions among them our techniques employ multiple lyapunov like functions and extend preceding results both in scope and applicability

drinfeld double and ringel green theory of hall algebras abstract as a continuation of the work of ringel and green on hall algebras the hopf algebra structure of a extended twisted hall algebra is presented here by introducing the ringel pairing of hall algebras the drinfeld double of a hall algebra is constructed the reduced form of this drinfeld double is applicable to the generic composition algebra which gives a complete realization of quantum group this ringel green theory makes it possible to give the formulae for the computation of commutators in quantum groups in terms of hall algebras

representations of cohomological hall algebras and donaldson thomas theory with classical structure groups we introduce a new class of representations of the cohomological hall algebras of kontsevich and soibelman which we call cohomological hall modules or cohm for short these representations are constructed from self dual representations of a quiver with contravariant involution sigma and provide a mathematical model for the space of bps states in orientifold string theory we use the cohm to define a generalization of the cohomological donaldson thomas theory of quivers in which the quiver representations have orthogonal or symplectic structure groups the associated invariants are called orientifold donaldson thomas invariants we prove the orientifold analogue of the integrality conjecture for sigma symmetric quivers we also formulate precise conjectures regarding the geometric meaning of orientifold donaldson thomas invariants and the freeness of the cohm of a sigma symmetric quiver we prove the freeness conjecture for disjoint union quivers loop quivers and the affine dynkin quiver of type widetilde a 1 we also verify the geometric conjecture in a number of examples finally we construct explicit poincare birkhoff witt type bases of the cohm of finite type quivers

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

indecomposable vector bundles and stable higgs bundles over smooth projective curves we prove that the number of geometrically indecomposable vector bundles of xed rank r and degree d over a smooth projective curve x dened over a nite eld is given by a polynomial depending only on r d and the genus g of x in the weil numbers of x we provide a closed formula expressed in terms of generating series for this polynomial we also show that the same polynomial computes the number of points of the moduli space of stable higgs bundles of rank r and degree d over x this entails a closed formula for the poincar e polynomial of the moduli spaces of stable higgs bundles over a compact riemann surface and hence also for the poincar e polynomials of the twisted character varieties for the groups gl r

buckling and vibrations of polar orthotropic annular plates of variable thickness abstract the effect of an hydrostatic in plane force together with the orthotropy on the axisymmetric vibrations of an annular plate of linearly varying thickness in the radial direction has been analyzed on the basis of classical theory of plates the numerical solution of the governing differential equation for two boundary conditions inner and outer both clamped inner clamped and outer simply supported at the periphery has been obtained by a spline technique transverse displacements moments in normalized form for a particular set of plate parameters and buckling loads in compression with thickness variation and various values of rigidity ratios have been computed for first two modes of vibrations a comparison of present results with those available in the literature shows a very good agreement

on derived hall numbers for tame quivers abstract in the present paper we study the derived hall algebra for the bounded derived category of the finite dimensional nilpotent representations of a dynkin or tame quiver over a finite field we show that for any three given objects in the bounded derived category the associated derived hall numbers are given by a rational function in the cardinalities of ground fields

hall algebras hereditary algebras and quantum groups let r be an associative hereditary algebra over a finite field k and let r fin be the full subcategory of r mod whose objects are those left r modules x which are finite as sets ix oc assume also that r isfinitary in c ringel s sense i e that iext l s s c for all simple s s in r fin this condition is met for example if r is finitely generated as k algebra 4 pp 435 436 let be the set of all isomorphism classes in r fin if 2 e then u will denote an r module in class 2 the class of all zero left r modules is denoted 0 let i c be the set of all isomorphism classes of simple modules in r fin thus u i e i is a complete set of simple finite left r modules we identify the grothendieck group k0 r fin with the free abelian group e1 v i v e 7z having i as free basis so that if x e r fin then the corresponding element of k0 r fin is the dimension vector dimx y i vii where for each i e vi is the multiplicity of the simple module u in any composition series of x clearly d imx lies in the subsemigroup

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

double hall algebras and derived equivalences abstract we show that the reduced drinfeld double of the ringel hall algebra of a hereditary category is invariant under derived equivalences by associating an explicit isomorphism to a given derived equivalence we also extend the results of burban and schiffmann 5 6 sevenhant and van den bergh 1999 25 and xiao and yang 2001 31

generalized switching signals for input to state stability of switched systems this article deals with input to state stability iss of continuous time switched nonlinear systems given a family of systems with exogenous inputs such that not all systems in the family are iss we characterize a new and general class of switching signals under which the resulting switched system is iss our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval unlike in the case of average dwell time switching we also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results

a note on bridgeland s hall algebra of two periodic complexes we show that the hall algebra of two periodic complexes which is recently introduced by t bridgeland coincides with the drinfeld double of the ordinary hall bialgebra

pbw bases of the twisted generic composition algebras of affine valued quivers abstract pbw type bases of the twisted generic composition algebras of the affine valued quivers are constructed by using the frobenius morphism

input to state stability for nonlinear systems with stochastic impulses abstract in this study the problem of input to state stability iss is systematically investigated for nonlinear systems with stochastic impulses first the iss problem is considered for systems where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval then the iss problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density several different cases are considered i e cases where the impulsive instants are satisfied by a renewal process poisson process semi markov chain and markov chain an example of coordination of multi agent systems is provided to illustrate the effectiveness of the proposed new stability criteria

a q γ analog of the w1 algebra a q analog of the w1 algebra is introduced irreducible quasifinite highest weight modules of this algebra and r matrices acting on a tensor product of these modules are investigated a connection with the q deformed virasoro and wn algebras is also discussed

toen s formula and green s formula abstract let a be a finitary hereditary abelian category in this note we show that green s formula on hall numbers of a can be deduced from the associativity of the derived hall algebra of a whose multiplication structure constants are given by the so called toen s formula

hall algebras associated to triangulated categories by counting triangles and applying the octahedral axiom we find a direct way to prove the formula of toen in t section 5 1 for a triangulated category satisfying the left homological finiteness condition

derived hall algebras the purpose of this work is to define a derived hall algebra mathcal dh t associated to any dg category t under some finiteness conditions our main theorem states that mathcal dh t is associative and unital it is shown that mathcal dh t contains the usual hall algebra mathcal h t when t is an abelian category we will also prove an explicit formula for the derived hall numbers purely in terms of invariants of the triangulated category associated to t as an example we describe the derived hall algebra of an hereditary abelian category

axisymmetric vibrations of polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of polar orthotropic annular plates of linearly varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates frequencies mode shapes and moments have been computed for three different boundary conditions for various values of the rigidity ratios the radii ratio and the taper parameter for the first two modes of vibration the results for isotropic annular plates of uniform and non uniform thickness show good agreement with those available in the literature