a time dependent theory of quantum resonances in this paper we further develop a general theory of metastable states resulting from perturbation of unstable eigenvalues we apply this theory to many body schrouml dinger operators and to the problem of quasiclassical tunneling

second order perturbation theory for embedded eigenvalues we study second order perturbation theory for embedded eigenvalues of an abstract class of self adjoint operators using an extension of the mourre theory under assumptions on the regularity of bound states with respect to a conjugate operator we prove upper semicontinuity of the point spectrum and establish the fermi golden rule criterion our results apply to massless pauli fierz hamiltonians for arbitrary coupling

lowest energy states in nonrelativistic qed atoms and ions in motion within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and n electrons coupled to the radiation field since the total momentum p is conserved the hamiltonian h admits a fiber decomposition with respect to p with fiber hamiltonian h p a stable atom resp ion means that the fiber hamiltonian h p has an eigenvalue at the bottom of its spectrum we establish the existence of a ground state for h p under i an explicit bound on p ii a binding condition and iii an energy inequality the binding condition is proven to hold for a heavy nucleus and the energy inequality for spinless electrons

synchronization in an array of output coupled boolean networks with time delay this brief presents an analytical study of synchronization in an array of coupled deterministic boolean networks bns with time delay two kinds of models are considered in one model the outputs contain time delay while in another one the outputs do not one restriction in this brief is that the state delay and output delay are restricted to be equal by referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices some necessary and sufficient conditions are derived for the synchronization of delay coupled bns examples including a practical epigenetic example are given for illustration

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

two supercharacter theories for the parabolic subgroups in orthogonal and symplectic groups abstract we construct two supercharacter theories in the sense of p diaconis and i m isaacs for the parabolic subgroups in orthogonal and symplectic groups for each supercharacter theory we obtain a supercharacter analog of the a a kirillov formula for irreducible characters of finite unipotent groups

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

the quantum n body problem this selective review is written as an introduction to the mathematical theory of the schrodinger equation for n particles characteristic for these systems are the cluster properties of the potential in configuration space which are expressed in a simple geometric language the methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of a number of basic and by now classical results the central theme is the interplay between the spectral theory of n body hamiltonians and the space time and phase space analysis of bound states and scattering states

quantum mechanical resonance and limiting absorption the many body problem we introduce a notion of quantum mechanical resonance that does not rely on analytic continuation of resolvent or scattering matrix and relate it to slow temporal decay of certain distinguished resonant states we proceed to prove existence of resonances for the generalized many body schrodinger operator for a rather large class of potentials containing coulomb and yukawa but also nonsymmetric and nonanalytic potentials with coulomblike singularities at the origin and certain differentiability and decay properties

stability analysis and stabilization of 2 d switched systems under arbitrary and restricted switchings in this paper the problems of stability analysis and stabilization are investigated for discrete time two dimensional 2 d switched systems which are formulated by the well known fornasini marchesini local state space model firstly by using the switched quadratic lyapunov function approach a sufficient stability condition is established for such systems under arbitrary switching signal then the extended average dwell time technique combining with the piecewise lyapunov function approach is developed and it is utilized for the stability analysis of the 2 d switched systems for the restricted switching case based on the stability analysis results sufficient conditions are presented to stabilize the 2 d switched systems finally two examples are provided to illustrate the effectiveness of the proposed new design techniques

on the periodic trajectories of boolean control networks abstract in this note we first characterize the periodic trajectories or equivalently the limit cycles of a boolean network and their global attractiveness we then investigate under which conditions all the trajectories of a boolean control network may be forced to converge to the same periodic trajectory if every trajectory can be driven to such a periodic trajectory this is possible by means of a feedback control law

positive commutators in non equilibrium quantum statistical mechanics the method of positive commutators developed for zero temperature problems over the last twenty years has been an essential tool in the spectral analysis of hamiltonians in quantum mechanics we extend this method to positive temperatures i e to non equilibrium quantum statistical mechanics we use the positive commutator technique to give an alternative proof of a fundamental property of a certain class of large quantum systems called return to equilibrium this property says that equilibrium states are asymptotically stable if a system is slightly perturbed from its equilibrium state then it converges back to that equilibrium state as time goes to infinity

scattering metrics and geodesic flow at infinity any compact manifold with boundary admits a riemann metric on its interior taking the form x 4 dx 2 x 2 h near the boundary where x is a boundary defining function and h is a smooth symmetric 2 cotensor restricting to be positive definite and hence a metric h on the boundary the scattering theory associated to the laplacian for such a scattering metric was discussed by the first author and here it is shown as conjectured that the scattering matrix is a fourier integral operator which quantizes the geodesic flow on the boundary for the metric h at time to prove this the poisson operator of the associated generalized boundary problem is constructed as a fourier integral operator associated to a singular legendre manifold

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

irreducible characters of groups associated with finite nilpotent algebras with involution abstract an algebra group is a group of the form p 1 j where j is a finite dimensional nilpotent associative algebra a theorem of z halasi asserts that in the case where j is defined over a finite field f every irreducible character of p is induced from a linear character of an algebra subgroup of p if j is a nilpotent algebra with involution then naturally defines a group automorphism of p 1 j and we may consider the fixed point subgroup c p assuming that f has odd characteristic p we show that every irreducible character of c p is induced from a linear character of a subgroup of the form c q where q is a invariant algebra subgroup of p as a particular case the result holds for the sylow p subgroups of the finite classical groups of lie type

variational methods in relativistic quantum mechanics this review is devoted to the study of stationary solutions of lin ear and nonlinear equations from relativistic quantum mechanics involving the dirac operator the solutions are found as critical points of an energy func tional contrary to the laplacian appearing in the equations of nonrelativistic quantum mechanics the dirac operator has a negative continuous spectrum which is not bounded from below this has two main consequences first the energy functional is strongly indefinite second the euler lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap between the negative and positive continuous spectra moreover since we work in the space domain r 3 the palais smale condition is not satisfied for these reasons the problems discussed in this review pose a challenge in the calculus of variations the existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems in the first part we consider the fixed eigenvalue problem for models of a free self interacting relativistic particle they allow to describe the localized state of a spin 1 2 particle a fermion which propagates without changing its shape this includes the soler models and the maxwell dirac or klein gordon dirac equations the second part is devoted to the presentation of min max principles al lowing to characterize and compute the eigenvalues of linear dirac operators with an external potential in the gap of their essential spectrum many con sequences of these min max characterizations are presented among them a new kind of hardy like inequalities and a stable algorithm to compute the eigenvalues in the third part we look for normalized solutions of nonlinear eigenvalue problems the eigenvalues are lagrange multipliers lying in a spectral gap we review the results that have been obtained on the dirac fock model which is a nonlinear theory describing the behavior of n interacting electrons in an external electrostatic field in particular we focus on the problematic definition of the ground state and its nonrelativistic limit in the last part we present a more involved relativistic model from quan tum electrodynamics in which the behavior of the vacuum is taken into ac count it being coupled to the real particles the main interesting feature of this model is that the energy functional is now bounded from below providing us with a good definition of a ground state

asymptotic completeness for long range many particle systems with stark effect ii we prove the existence and the asymptotic completeness of the dollard type modified wave operators for many particle stark hamiltonians with long range potentials

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

leader following consensus of a class of stochastic delayed multi agent systems with partial mixed impulses in this paper the exponential leader following consensus problem is investigated for a class of nonlinear stochastic networked multi agent systems with partial mixed impulses and unknown time varying but bounded delays the main feature of partial mixed impulses is that time varying impulses are not only composed of synchronizing and desynchronizing impulses simultaneously but they are also injected into a fraction of nodes in multi agent systems three kinds of partial mixed impulses are proposed fixed partial mixed impulses periodic partial mixed impulses and try once discard like partial mixed impulses by means of the lyapunov function theory and the comparison principle conditions are derived for ensuring global exponential leader following consensus under the presented three kinds of partial mixed impulses simulations of leader following consensus of robotic systems are provided to validate the effectiveness of the proposed results and to show the advantages of the proposed partial mixed impulses

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

simultaneous stabilization for a set of boolean control networks abstract this paper investigates simultaneous stabilization of a collection of boolean control networks bcns by using the semi tensor product method and presents a number of new results first an algebraic expression of the bcns is obtained by the semi tensor product based on which some necessary and sufficient conditions are presented to solve the simultaneous stabilization problem by a free control sequence a state feedback control and an output feedback control respectively second using the column stacking form of matrices a new procedure is established to design both state feedback and output feedback controllers for the simultaneous stabilization problem the study of two illustrative examples shows that the new results obtained in this paper are very effective in solving simultaneous stabilization of a collection of bcns

supercharacters and superclasses for algebra groups we study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups these groups generalize the unimodular upper triangular groups over a finite field and the supercharacter theory we develop extends results of carlos andre and ning yan that were originally proved in the upper triangular case this theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table we discuss connections with the kirillov orbit method and with gelfand pairs and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class respectively we also show that products of supercharacters are positive integer combinations of supercharacters

controllability of probabilistic boolean control networks based on transition probability matrices in this paper we propose a new approach to investigate the controllability and reachability of probabilistic boolean control networks pbcns with forbidden states we first give a simple algebraic formula for the transition probability between two states in a given number of time step while avoiding a set of forbidden states then we construct the controllability matrix based on a new operator and some necessary and sufficient conditions are obtained for the controllability and reachability of pbcns a numerical example is given to illustrate the efficiency of the obtained results

set stabilization for switched boolean control networks this paper studies the set stabilization of switched boolean control networks in which a feedback control design algorithm is presented by a constructive method necessary and sufficient conditions of the set stabilization of switched boolean control networks under arbitrary switching signals are presented for the cases of the control input relying on switching signals or not respectively furthermore the corresponding switching signal independent and switching signal dependent controllers are provided for these two cases respectively it is shown that the condition of the switching signal dependent controller is less conservative than the one of the switching signal independent controller finally examples are given to illustrate the effectiveness of the proposed results

cycles of periodically time variant boolean networks this paper investigates cycles of periodically time variant boolean networks ptvbns some properties of cycles of ptvbns and the relationship between ptvbns and time invariant boolean networks tibns are revealed it is shown that each cycle of a ptvbn corresponds to a common cycle of some tibns and all the cycles of a ptvbn can be constructed by those of the corresponding tibns moreover some results on lengths of cycles of ptvbns are derived finally some examples are given to illustrate the obtained theoretical results

absence of singular continuous spectrum for certain self adjoint operators we give a sufficient condition for a self adjoint operator to have the following properties in a neighborhood of a pointe of its spectrum a its point spectrum is finite b its singular continuous spectrum is empty c its resolvent satisfies a class of a priori estimates

exponential bounds and semifiniteness of point spectrum for n body schrodinger operators for a large class ofn body schrodinger operatorsh we prove that eigenvalues ofh cannot accumulate from above at any threshold ofh our proof relies onl2 exponential upper bounds for eigenfunctions ofh with explicit constants obtained by modifying methods of froese and herbst

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

phase space analysis on some black hole manifolds abstract the schwarzschild and reissner nordstrom solutions to einstein s equations describe space times which contain spherically symmetric black holes we consider solutions to the linear wave equation in the exterior of a fixed black hole space time of this type we show that for solutions with initial data which decay at infinity and at the bifurcation sphere a weighted l 6 norm in space decays like t 1 3 this weight vanishes at the event horizon but not at infinity to obtain this control we require only an loss of angular derivatives

on the regularity of the electronic schrodinger equation in hilbert spaces of mixed derivatives the electronic schrodinger equation describes the motion of electrons under coulomb interaction forces in the field of clamped nuclei and forms the basis of quantum chemistry the present article is devoted to the regularity properties of the corresponding wavefunctions that are compatible with the pauli principle it is shown that these wavefunctions possess certain square integrable mixed weak derivatives of order up to n 1 with n the number of electrons across the singularities of the interaction potentials the result is of particular importance for the analysis of approximation methods that are based on the idea of sparse grids or hyperbolic cross spaces it indicates that such schemes could represent a promising alternative to current methods for the solution of the electronic schrodinger equation and that it may even be possible to reduce the computational complexity of an n electron problem to that of a one electron problem

solutions of the multiconfiguration equations in quantum chemistry the multiconfiguration methods are the natural generalization of the well known hartree fock theory for atoms and molecules by a variational method we prove the existence of a minimum of the energy and of infinitely many solutions of the multiconfiguration equations a finite number of them being interpreted as excited states of the molecule our results are valid when the total nuclear charge z exceeds n 1 n is the number of electrons and cover most of the methods used by chemists the saddle points are obtained with a min max principle we use a palais smale condition with morse type information and a new and simple form of the euler lagrange equations

disturbance decoupling control design for switched boolean control networks abstract this paper investigates a kind of disturbance decoupling problems ddps for switched boolean control networks bcns that is the disturbance independent output decoupling problem via the semi tensor product of matrices by converting the dynamics of switched bcns into an algebraic form and using the redundant variable separation technique all possible state feedback controllers are designed for the disturbance independent output decoupling problem then based on the obtained state feedback disturbance decoupling controllers and the system s output equation a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers the study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched bcns

algebraic formulation and topological structure of boolean networks with state dependent delay abstract this paper investigates the algebraic formulation topological structure and set stability of boolean networks with state dependent delay sdd firstly using the algebraic state space representation assr method the dynamics of boolean networks with sdd is converted into an equivalent augmented system secondly based on the equivalent augmented system some necessary and sufficient conditions are presented to calculate fixed points and cycles of boolean networks with sdd thirdly it is proved that the set stability of boolean networks with sdd is equivalent to the set stability of augmented system and a necessary and sufficient condition is presented by constructing a kind of set stability matrix finally the obtained results are applied to the strategy consensus of networked evolutionary games with memories

asymptotic stability of differential systems with impulsive effects suffered by logic choice in this paper we investigate the asymptotic stability of differential systems with impulsive effects suffered by logic choice first we give the expression of system with logic selected impulsive effects which is a hybrid system second by using semi tensor product a criterion of asymptotic stability for the system is provided third we study the linearly coupled system with impulsive effects under logic choice and give a sufficient condition for asymptotic stability finally a numerical simulation is given to illustrate the effectiveness of our results

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

supercharacters symmetric functions in noncommuting variables and related hopf algebras we identify two seemingly disparate structures supercharacters a useful way of doing fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field and the ring of symmetric functions in noncommuting variables each is a hopf algebra and the two are isomorphic as such this allows developments in each to be transferred the identification suggests a rich class of examples for the emerging field of combinatorial hopf algebras

propagation estimates for n body schroedinger operators we prove propagation estimates of strong type for long rangen body hamiltonians emphasis is on phase space analysis in the free channel region

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

maximal velocity of photons in non relativistic qed abstract we consider the problem of propagation of photons in the quantum theory of non relativistic matter coupled to electromagnetic radiation which is presently the only consistent quantum theory of matter and radiation assuming that the matter system is in a localized state i e for energies below the ionization threshold we show that the probability to find photons at time t at the distance greater than c t where c is the speed of light vanishes as t as an inverse power of t

stability of schrodinger eigenvalue problems we derive a general stability criterion for discrete eigenvalues of schrodinger operators such asa p 2 v x using only strong continuity ofa anda in the perturbation parameter the theory is developed for non selfadjoint operators and illustrated with examples like the anharmonic oscillator the stark and the zeeman effect the principal tools are weyl s criterion for the essential spectrum and a construction due to enss 5 they are also used to extend the classical invariance theorems for the essential spectrum to certain singular perturbations including some local perturbations of the laplacian by differential operators of arbitrary high order

super characters of finite unipotent groups of types b n c n and d n abstract we define and study super characters over the complex field of the classical finite unipotent groups of types b n c n and d n under the assumption that the prime is sufficiently large we extend the known results for the unitriangular group proved by the first author in the papers c a m andre basic characters of the unitriangular group j algebra 175 1995 287 319 and c a m andre basic characters of the unitriangular group for arbitrary primes proc amer math soc 130 7 2002 1943 1954 in particular we prove that every irreducible complex character occurs as a constituent of a unique super character we also give a combinatorial description of all the irreducible characters of maximum degree

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

sparse grid spaces for the numerical solution of the electronic schrodinger equation this article complements the author s recent work numer math 98 731 759 2004 on the regularity of the electronic schrodinger equation in hilbert spaces of mixed derivatives it has been shown there that the solutions of this equation are surprisingly smooth and possess square integrable mixed weak derivatives of order up to n 1 with n the number of electrons across the singularities of the interaction potentials and it has been claimed that this result can help to break the complexity barriers in computational quantum mechanics using correspondingly antisymmetrized sparse grid trial functions a construction of this kind that can be interpreted as a sparse grid sampling theorem is sketched here

exponential bounds and absence of positive eigenvalues for n body schrodinger operators for a large class ofn body potentialsv we prove that if is an eigenfunction of v with eigenvaluee then sup 2 e 0 exp x l2 is either a threshold or consequences of this result are the absence of positive eigenvalues and optimal l2 exponential lower bounds

regularity of eigenstates in regular mourre theory abstract the present paper gives an abstract method to prove that possibly embedded eigenstates of a self adjoint operator h lie in the domain of the kth power of a conjugate operator a conjugate means here that h and a have a positive commutator locally near the relevant eigenvalue in the sense of mourre the only requirement is c k 1 a regularity of h regarding integer k our result is optimal under a natural boundedness assumption of the multiple commutators we prove that the eigenstate dilated by exp i a is analytic in a strip around the real axis in particular the eigenstate is an analytic vector with respect to a natural applications are dilation analytic systems satisfying a mourre estimate where our result can be viewed as an abstract version of a theorem due to balslev and combes 1971 3 as a new application we consider the massive spin boson model

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

spectral analysis of n body schrodinger operators for a large class of two body potentials we solve two of the main problems in the spectral analysis of multiparticle quantum hamiltonians explicitly we prove that the point spectrum lies in a closed countable set and describe that set in terms of the eigenvalues of hamiltonians of subsystems and that there is no singular continuous spectrum we accomplish this by extending mourre s work on three body problems to n body problems

perturbation of embedded eigenvalues in the generalized n body problem we discuss the perturbation of continuum eigenvalues without analyticity assumptions among our results we show that generally a small perturbation removes these eigenvalues in accordance with fermi s golden rule thus generically in a baire category sense the schrodinger operator has no embedded non threshold eigenvalues

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

exponential decay and ionization thresholds in non relativistic quantum electrodynamics abstract spatial localization of the electrons of an atom or molecule is studied in models of non relativistic matter coupled to quantized radiation we give two definitions of the ionization threshold one in terms of spectral data of cluster hamiltonians and one in terms of minimal energies of non localized states we show that these two definitions agree and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood the latter result is derived from a new general result on exponential decay tailor made for our problem but applicable to many non relativistic quantum systems outside quantum electrodynamics as well

finite time stability analysis and h control for a class of nonlinear time delay hamiltonian systems this paper investigates the finite time stability fts analysis and finite time h control design for a class of nonlinear time delay hamiltonian systems and proposes some delay dependent results on both the fts and finite time control design first a criterion on the fts is proposed for general time delay nonlinear systems via the razumikhin approach then based on the criterion some delay independent and delay dependent conditions on the fts are derived for the nonlinear time delay hamiltonian systems by constructing a suitable lyapunov function third we use the obtained fts results to investigate the finite time h control problem and present a control design procedure for a class of nonlinear time delay port controlled hamiltonian systems by the energy shaping approach study of two illustrative examples shows that the results obtained in this paper work very well in the fts analysis and control design of some nonlinear time delay hamiltonian systems

a supercharacter theory for involutive algebra groups if j is a finite dimensional nilpotent algebra over a finite field k the algebra group p 1 j admits a standard supercharacter theory as defined in 16 if j is endowed with an involution then naturally defines a group automorphism of p 1 j and we may consider the fixed point subgroup cp x p x x 1 assuming that k has odd characteristic p we use the standard supercharacter theory for p to construct a supercharacter theory for cp in particular we obtain a supercharacter theory for the sylow p subgroups of the finite classical groups of lie type and thus extend in a uniform way the construction given by andre and neto in 7 8 for the special case of the symplectic and orthogonal groups

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

asymptotic completeness of long range n body quantum systems where x is a euclidean space and lra a e a is a finite family of projections onto certain subspaces xa of x we will always assume that the family xa a e a is closed with respect to the algebraic sum and contains xamin 0 the class of operators of the form 0 2 is a generalization of 0 1 up to a linear change of coordinates in the configuration space x they usually go under the name of generalized n body schrbdinger operators and were first considered in a in what follows we will drop the word generalized we refer the reader to rsi vol iii for a general introduction to n body schr6dinger operators defined as in equation 0 1 we will consistently use the definition 0 2 and assume that the reader is familiar with the physical meaning of various objects under study

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

controllability and observability of boolean control networks with time variant delays in states this brief investigates the controllability and observability of boolean control networks with not necessarily bounded time variant delays in states after a brief introduction to converting a boolean control network to an equivalent discrete time bilinear dynamical system via the semi tensor product of matrices the system is split into a finite number of subsystems constructed forest with no time delays by using the idea of splitting time that is proposed in this brief then the controllability and observability of the system are investigated by verifying any so called controllability constructed path and any so called observability constructed paths in the above forest respectively which generalize some recent relevant results matrix test criteria for the controllability and observability are given the corresponding control design algorithms based on the controllability theorems are given we also show that the computing complexity of our algorithm is much less than that of the existing algorithms

strategy optimization for static games based on stp method abstract in this paper we consider the choice behavior of players in a static game and discuss solutions to static games of complete information problem via semi tensor product stp method some properties of the dominant behaviors are obtained based on which choosing the dominant strategies deleting the dominated strategies are used to optimize the strategy sets so as to obtain solutions to the considered game examples are given to show the effectiveness of the results

set stability and set stabilization of boolean control networks based on invariant subsets this study addresses the set stability of boolean networks bns and set stabilization of boolean control networks bcns set stability determines whether a bn converges to a given subset whereas set stabilizability addresses the issue of whether a bcn can be stabilized to a given subset many problems can be viewed as special cases of set stability and set stabilization including synchronization partial stability and partial stabilization problems the concepts of invariant subset and control invariant subset are introduced then algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed based on the invariant subsets obtained the necessary and sufficient conditions for set stability and set stabilizability are established and formulae are provided to calculate the shortest transient periods for respective initial states a design procedure is proposed for finding all the time optimal set stabilizers finally an example is used to show the application of the proposed results to the synchronization problem of bns

a supercharacter theory for the sylow p subgroups of the finite symplectic and orthogonal groups abstract we define the superclasses for a classical finite unipotent group u of type b n q c n q or d n q and show that together with the supercharacters defined in c a m andre a m neto supercharacters of the sylow p subgroups of the finite symplectic and orthogonal groups pacific j math 239 2 2009 201 230 they form a supercharacter theory in the sense of p diaconis i m isaacs supercharacters and superclasses for algebra groups trans amer math soc 360 5 2008 2359 2392 in particular we prove that the supercharacters take a constant value on each superclass and evaluate this value as a consequence we obtain a factorization of any superclass as a product of elementary superclasses in addition we also define the space of superclass functions and prove that it is spanned by the supercharacters as a consequence we re obtain the decomposition of the regular character as an orthogonal linear combination of supercharacters finally we define the supercharacter table of u and prove various orthogonality relations for supercharacters similar to the well known orthogonality relations for irreducible characters

geometric methods for nonlinear many body quantum systems abstract geometric techniques have played an important role in the seventies for the study of the spectrum of many body schrodinger operators in this paper we provide a formalism which also allows to study nonlinear systems we start by defining a weak topology on many body states which appropriately describes the physical behavior of the system in the case of lack of compactness that is when some particles are lost at infinity we provide several important properties of this topology and use them to write a simple proof of the famous hvz theorem in the repulsive case in the second step we recall the method of geometric localization in fock space as proposed by derezinski and gerard and we relate this tool to our weak topology we then provide several applications we start by studying the so called finite rank approximation which consists in imposing that the many body wavefunction can be expanded using finitely many one body functions we thereby emphasize geometric properties of hartree fock states and prove nonlinear versions of the hvz theorem in the spirit of works of friesecke in the last section we study translation invariant many body systems comprising a nonlinear term which effectively describes the interactions with a second system as an example we prove the existence of the multi polaron in the pekar tomasevich approximation for certain values of the coupling constant

synchronization of kauffman networks we analyze the synchronization transition for a pair of coupled identical kauffman networks in the chaotic phase the annealed model for kauffman networks shows that synchronization appears through a transcritical bifurcation and provides an approximate description for the whole dynamics of the coupled networks we show that these analytical predictions are in good agreement with numerical results for sufficiently large networks and study finite size effects in detail preliminary analytical and numerical results for partially disordered networks are also presented