asymptotically stable oscillations in systems with hysteresis nonlinearities abstract we present some sufficient conditions for the asymptotic stability of oscillations in nonlinear ode systems with respect to small hysteretic perturbations

a second variational theory for optimal periodic processes a sufficiency condition for a periodic process with free period to be a weak local minimum is given by making detailed use of the properties of the monodromy matrix the transition matrix calculated over a closed orbit previous results are corrected extended and clarified a necessary condition for a real valued periodic riccati matrix to exist is that there be no distinct eigenvalues of the monodromy matrix on the unit circle for local sufficiency it is required that no eigenvalues of the monodromy matrix except a double root at unity lie on the unit circle

mathematical analysis and numerical solution of models with dynamic preisach hysteresis abstract hysteresis is a phenomenon that is observed in a great variety of physical systems which leads to a nonlinear and multivalued behavior making their modeling and control difficult even though the analysis and mathematical properties of several rate independent and rate dependent hysteresis models are known this is not the case for the bertotti s rate dependent extension of the classical preisach model the so called dynamic preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics both being crucial in practice this paper deals with the description and mathematical analysis of the dynamic preisach hysteresis model toward that end we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field h and the magnetic induction b in which the values of b not only depends on the present values of h but also on the past history and its velocity we first analyze mathematically some important properties of the model and compare them with known results for the static preisach model then we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations under suitable assumptions we prove the existence of a solution of a weak formulation of the problem and solve it numerically finally we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic preisach model

generalized polar coordinates on lie groups and numerical integrators motivated by developments in numerical lie group integrators we introduce a family of local coordinates on lie groups denoted generalized polar coordinates fast algorithms are derived for the computation of the coordinate maps their tangent maps and the inverse tangent maps in particular we discuss algorithms for all the classical matrix lie groups and optimal complexity integrators for n spheres

generalized green s functions and spectral densities in the complex energy plane the titchmarsh weyl theory is applied to the schrodinger equation in the case when the asymptotic form of the solution is not known it is assumed that the potential belongs to the weyl s limit point classification a rigorous analytical continuation of the green s function obtained from the solution regular at the origin and the square integrable weyl s solution regular at infinity to the unphysical riemann energy sheet is carried out it is demonstrated how the green s function can be uniquely constructed from the titchmarsh weyl m function and its nevanlinna representation the behavior of the m function in the neighborhood of poles is investigated the m function is decomposed in a so called generalized real part reg and a generalized imaginary part img reg m is found to have a significant argument change upon pole passages img m is found to be a generalized spectral density from the generalized spectral density a spectral resolution of the differential operator and its resolvent i

two stage lotteries without the reduction axiom preference relations over two stage lotteries are analyzed empirical evidence indicates that decisionmakers do not always behave in accordance with the reduction of compound lotteries axiom but they seem to satisfy a compound independence axiom although the reduction and the compound independence axioms together with continuity imply expected utility theory each of them by itself is compatible with all possible preference relations over simple lotteries using these axioms the author analyzes three different versions of expected utility for two stage lotteries the author suggests several different compound dominance axioms as possible replacements of the reduction axiom which are strictly weaker than the reduction of compound lotteries axiom copyright 1990 by the econometric society

an ℏ brownian motion and the existence of stochastic option prices abstract we introduce a particular type of brownian motion i e a brownian motion with a diffusion coefficient containing we show that under classical black scholes methodology we can obtain a pde with a stochastic rate of return in this environment of non classical uncertainty valued preferences for risk may exist

spectral concentration and rapidly decaying potentials abstract we consider the spectral function 0 for the sturm liouville equation y q y 0 on 0 with a boundary condition y 0 cos y 0 sin 0 and where q l 0 a point 0 is called a point of spectral concentration if has a local maximum there we give a new formula for in terms of the prufer transformation angle and we identify a rapid transitional property of in the neighbourhood of points of spectral concentration this property provides a sensitive test of the existence of such points and lends itself to a detailed computational investigation which reveals such points in greater profusion than shown by for example sledge our approach also leads to the possibility of a theoretical investigation

fast elliptic solvers in cylindrical coordinates and the coulomb collision operator in this paper we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates r q z with free space radiation conditions by combining integral equation methods in the radial variable r with fourier methods in q and z we show that high order accuracy can be achieved in both the governing potential and its derivatives a weak singularity arises in the fourier transform with respect to z that is handled with special purpose quadratures we show how these solvers can be applied to the evaluation of the coulomb collision operator in kinetic models of ionized gases

brief paper oscillations and transfer properties of relay feedback systems with time delay linear plants oscillations and transfer properties of relay feedback systems with linear plants having a dead time time delay are considered poincare maps are found explicitly in terms of the system parameters the oscillatory and transfer properties are presented in the format of the locus of a perturbed relay system lprs which represents the continuum of all possible periodic solutions and transfer properties of the system with a given linear plant conditions of local orbital asymptotic stability are found in terms of the system parameters the proposed approach is illustrated by examples

titchmarsh weyl theory and its relations to scattering theory spectral densities and cross sections theory and applications the radial equation or set of equations derived in scattering theory is analyzed by means of titchmarsh weyl theory for singular second order differential equations in particular we have focused on the spectral density concept and the corresponding relation to the scattering cross section the method of complex deformations is brought in as a necessary ingredient in the evaluation of the underlying pole strings which together with the background build up the actual dispersion relation data the analysis is supported by numerical applications to a centrifugal family of simple potentials

weyl titchmarsh type formula for periodic schrodinger operator with wigner von neumann potential the schrodinger operator on the half line with periodic background potential perturbed by a certain potential of wigner von neumann type is considered the asymptotics of generalized eigenvectors for lambda is an element of c and on the absolutely continuous spectrum is established the weyl titchmarsh type formula for this operator is proven

eigenvalue and eigenfunction asymptotics for regular sturm liouville problems abstract in this paper we obtain asymptotic formulas for eigenvalues eigenfunctions and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general sturm liouville equation pu r q u 0 having regular endpoints the method is based on a conversion to liouville normal form and an iterative procedure of solving the associated volterra integral equation producing an asymptotic expansion of the solution in higher powers of 1 1 2 as

eigenvalues of fourth order singular sturm liouville boundary value problems abstract in this paper by establishing a new comparison theorem and constructing upper and lower solutions some sufficient conditions of existence of positive solutions for the following nonlinear fourth order singular sturm liouville eigenvalue problem 1 p t p t u t f t u t 0 1 u 0 u 1 0 u 0 lim t 0 p t u t 0 u 1 lim t 1 p t u t 0 are established due to the schauder s fixed point theorem for large enough where 0 0 f and p can be singular at t 0 and or 1 moreover f can also be singular at u 0 in addition some peculiar cases are discussed and some further results are obtained

first results on applying a non linear effect formalism to alliances between political parties and buy and sell dynamics we discuss a non linear extension of a model of alliances in politics recently proposed by one of us the model is constructed in terms of operators describing the interest of three parties to form or not some political alliance with the other parties the time evolution of what we call the decision functions is deduced by introducing a suitable hamiltonian which describes the main effects of the interactions of the parties amongst themselves and with their environments which are generated by their electors and by people who still have no clear idea for which party to vote or even if to vote the hamiltonian contains some non linear effects which takes into account the role of a party in the decision process of the other two parties moreover we show how the same hamiltonian can also be used to construct a formal structure which can describe the dynamics of buying and selling financial assets without however implying a specific price setting mechanism

spectral concentrations and resonances of a second order block operator matrix and an associated λ rational sturm liouville problem this paper studies the resonances and points of spectral concentration of the block operator matrix egin pmatrix frac d 2 d x 2 q sqrt tw sqrt tw u end pmatrix in the space l 2 0 1 oplus l 2 0 1 in particular we study the dynamics of the resonance eigenvalue t showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points a connection is also established between resonances and points of spectral concentration finally some numerical examples are given which show that each of the above theoretical possibilities can be realized

global stability of relay feedback systems for a large class of relay feedback systems rfs there will be limit cycle oscillations conditions to check existence and local stability of limit cycles for these systems are well known global stability conditions however are practically nonexistent the paper presents conditions in the form of linear matrix inequalities lmis that when satisfied guarantee global asymptotic stability of limit cycles induced by relays with hysteresis in feedback with linear time invariant lti stable systems the analysis consists in finding quadratic surface lyapunov functions for poincare maps associated with rfs these results are based on the discovery that a typical poincare map induced by an lti flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state moreover level sets of this function are convex subsets of linear manifolds the search for quadratic lyapunov functions on switching surfaces is done by solving a set of lmis although this analysis methodology yields only a sufficient criterion of stability it has proved very successful in globally analyzing a large number of examples with a unique locally stable symmetric unimodal limit cycle in fact it is still an open problem whether there exists an example with a globally stable symmetric unimodal limit cycle that could not be successfully analyzed with this new methodology examples analyzed include minimum phase systems systems of relative degree larger than one and of high dimension such results lead us to believe that globally stable limit cycles of rfs frequently have quadratic surface lyapunov functions

boundary value method for inverse sturm liouville problems in this paper we present a method to recover symmetric and non symmetric potential functions of inverse sturm liouville problems from the knowledge of eigenvalues the linear multistep method coupled with suitable boundary conditions known as boundary value method bvm is the main tool to approximate the eigenvalues in each iteration step of the used newton method the bvm was extended to work for neumann neumann boundary conditions moreover a suitable approximation for the asymptotic correction of the eigenvalues is given numerical results demonstrate that the method is able to give good results for both symmetric and non symmetric potentials

econophysics and individual choice abstract the subjectivist theory of probability specifies certain axioms of rationality which together lead to both a theory of probability and a theory of preference the theory of probability is used throughout the sciences while the theory of preferences is used in economics results in quantum physics challenge the adequacy of the subjectivist theory of probability as we show answering this challenge requires modifying an archimedean axiom in the subjectivist theory but changing this axiom modifies the subjectivist theory of preference and therefore has implications for economics as this paper notes these implications are consistent with current empirical findings in psychology and economics as we show these results also have implications for pricing in securities markets this suggests further directions for research in econophysics

generating self excited oscillations for underactuated mechanical systems via two relay controller a tool for the design of a periodic motion in an underactuated mechanical system via generating a self excited oscillation of a desired amplitude and frequency by means of the variable structure control is proposed first an approximate approach based on the describing function method is given which requires that the mechanical plant should be a linear low pass filter the hypothesis that usually holds when the oscillations are relatively fast the method based on the locus of a perturbed relay systems provides an exact model of the oscillations when the plant is linear finally the poincare map s design provides the value of the controller parameters ensuring the locally orbitally stable periodic motions for an arbitrary mechanical plant the proposed approach is shown by the controller design and experiments on the furuta pendulum

numerical approximation of high dimensional fokker planck equations with polynomial coefficients this paper is concerned with the numerical solution of high dimensional fokker planck equations related to multi dimensional diffusion with polynomial coefficients or pearson diffusions classification of multi dimensional pearson diffusion follows from the classification of one dimensional pearson diffusion there are six important classes of pearson diffusion three of them possess an infinite system of moments gaussian gamma beta while the other three possess a finite number of moments inverted gamma student and fisher snedecor numerical approximations to the solution of the fokker planck equation are generated using the spectral method the use of an adaptive reduced basis technique facilitates a significant reduction in the number of degrees of freedom required in the approximation through the determination of an optimal basis using the singular value decomposition svd the basis functions are constructed dynamically so that the numerical approximation is optimal in the current finite dimensional subspace of the solution space this is achieved through basis enrichment and projection stages numerical results with different boundary conditions are presented to demonstrate the accuracy and efficiency of the numerical scheme

distribution of poles for scattering on the real line abstract the density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential in the case of a potential with finite singularities at the endpoints of the support asymptotic formulae for the poles are given while in the c 0 case an example of a potential with infinitely many scattering poles on i r is constructed the scattering amplitude of a compactly supported potential is also characterized

relay based identification of a class of nonminimum phase siso processes a set of general expressions is derived from a single symmetrical relay feedback test for identification of a class of process transfer functions using these expressions the parameters of open loop stable nonminimum phase transfer function models may be obtained from simple measurements made on the limit cycle for comparison the conventional describing function based identification formulae are presented fourier series based curve fitting with the options of nonlinear least squares method and trust region algorithm is used to measure limit cycle parameters in the presence of measurement noise examples are given to illustrate the value of the proposed method

a direct method for the boltzmann equation based on a pseudo spectral velocity space discretization a deterministic method is proposed for solving the boltzmann equation the method employs a galerkin discretization of the velocity space and adopts as trial and test functions the collocation basis functions based on weights and roots of a gauss hermite quadrature this is defined by means of half and or full range hermite polynomials depending whether or not the distribution function presents a discontinuity in the velocity space the resulting semi discrete boltzmann equation is in the form of a system of hyperbolic partial differential equations whose solution can be obtained by standard numerical approaches the spectral rate of convergence of the results in the velocity space is shown by solving the spatially uniform homogeneous relaxation to equilibrium of maxwell molecules as an application the two dimensional cavity flow of a gas composed of hard sphere molecules is studied for different knudsen and mach numbers although computationally demanding the proposed method turns out to be an effective tool for studying subsonic slightly rarefied gas flows

singular second order operators the maximal and minimal operators and selfadjoint operators in between differential operators arising from the differential equation py qy lambda wy are put in the hilbert space setting l 2 a b w a new and simpler characterization of the minimal operator is exhibited selfadjoint operators which lie in between the minimal and maximal operator are easily described in terms of conditions on boundary coefficients which look like and indeed are the same as those imposed on regular problems examples drawn from mathematical physics include the legendre laguerre hermite and bessel problems

evolutionary quantum game we present a study of a dynamical quantum game each agent has a memory of her performance over the previous m timesteps and her strategy can evolve in time the game exhibits distinct regimes of optimality for small m the classical game performs better while for intermediate m the relative performance depends on whether the source of qubits is corrupt for large m the quantum players dramatically outperform the classical players by freezing the game into high performing attractors in which evolution ceases

nonlinear resonance in systems with hysteresis a general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis this approach uses a special property of nonlinear terms which is valid for many important classes of hysteresis operators for systems with such hysteresis nonlinearities we introduce a method to derive conditions for the existence of forced oscillations and for systems with a parameter of nonlinear resonance at infinity

absence of high energy spectral concentration for dirac systems with divergent potentials it is known that one dimensional dirac systems with potentials q which tend to or at infinity such that 1 q is of bounded variation have a purely absolutely continuous spectrum covering the whole real line we show that for the system on a half line there are no local maxima of the spectral density points of spectral concentration above some value of the spectral parameter if q satisfies certain additional regularity conditions these conditions admit thrice differentiable potentials of power or exponential growth the eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end point

oscillations and transfer properties of relay servo systems with integrating plants asymmetric limit cycles and input output properties of relay feedback systems with integrating plants are studied in the technical note it is noted that an integrating plant introduces significantly different dynamics so that a different than traditional system representation is needed to obtain a fixed point of poincare map conditions of orbital asymptotic stability are obtained the infinite set of possible periodic solutions and transfer characteristics is presented in the form of the locus of a perturbed relay system lprs a formula of lprs is derived an example of analysis of oscillations and transfer properties is given

absolute continuity and spectral concentration for slowly decaying potentials abstract we consider the spectral function 0 for the sturm liouville equation y qq y 0 on 0 with the boundary condition y 0 0 and where q has slow decay o x a a 0 as x we develop our previous methods of locating spectral concentration for q with rapid exponential decay this journal 81 1997 333 348 to deal with the new theoretical and computational complexities which arise for slow decay

a gaussian quadrature procedure for use in the solution of the boltzmann equation and related problems abstract a new gaussian quadrature procedure is developed for integrals of the form 0 e y 2 y p y dy for p 0 1 and 2 recursion relations are derived for the coefficients in the general three term recurrence relation for the polynomials whose roots are the quadrature abscissae a comparison with the gauss laguerre quadrature procedure is presented solutions of the chemical kinetic boltzmann equation are obtained with a discrete ordinate method based on this gaussian quadrature procedure the results are compared with previous solutions obtained with a polynomial expansion method

on counter examples to aizerman and kalman conjectures counter examples to aizerman s and kalman s conjectures are considered investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done the simultaneous exis

spectral concentration and perturbed discrete spectra abstract we examine spectral concentration for a class of sturm liouville problems on 0 a typical example being y x x cx2 y x 0 the discrete spectrum for c 0 leads to spectral concentration in the continuous spectrum for c 0 and we use a new formula for the spectral function to make a detailed computational investigation of the way in which spectral concentration occurs in particular we find that as c decreases spectral concentration arises first from the lowest unperturbed eigenvalue and then in turn from these eigenvalues in increasing order of size

efficient calculation of spectral density functions for specific classes of singular sturm liouville problems new families of approximations to sturm liouville spectral density functions are derived for cases where the potential function has one of several specific forms this particular form dictates the type of expansion functions used in the approximation error bounds for the residuals are established for each case in the case of power potentials the approximate solutions of an associated terminal value problem at are shown to be asymptotic power series expansions of the exact solution numerical algorithms have been implemented and several examples are given demonstrating the utility of the approach

on the location of resonances of exponentially decaying sturm liouville potentials the paper is concerned with analytic continuation into the unphysical sheet for sturm liouville potentials whose decay at infinity is no faster than o e ax a resonance free region is found and the existence of a natural boundary is discussed an example related to the bessel equation is examined in some detail

quantum mechanical and human violations of compound probability principles toward a generalized heisenberg uncertainty principle a key central tenet of decision theory is that decomposing an uncertain event into sub events should not change the overall probability assigned to that uncertain event as we show both quantum physics and behavioral decision theory appear to systematically violate this principle in very similar ways these results suggest that the structuring phase of decision analysis which specifies how various events are decomposed helps shape the subjective probabilities which will ultimately be assigned to those events

on subordinacy and analysis of the spectrum of one dimensional schrodinger operators abstract by considering the behaviour as n of the ratio of l2 0 n norms of solutions of d 2 dr 2 v r u xu 0 r x r a characterisation of the absolutely continuous and singular spectra of one dimensional schrodinger operators is deduced the analysis is applicable to all operators for which l d 2 dr 2 v r is regular at 0 and in the limit point case at infinity with v r locally integrable

a phase field model with temperature dependent constraint this paper is concerned with a phase field model with temperature dependent constraint for the order parameter in the kinetic equation of the order parameter we take account of diffusion as well as undercooled superheated state which is modelled by means of a hysteresis input output relation the input is the temperature field and the output is the order parameter in this paper we shall show that there exists a solution globally in time in a physically reasonable sense when the coefficient of interfacial energy is sufficiently small

mathematical models for hysteresis the various existing classical models for hysteresis preisach ishlinskii duhem madelung are surveyed as well a more modern treatments by contemporary workers the emphasis is on a clear mathematical description of the formulation and properties of each model in addition the authors try to make the reader aware of the many open questions in the study of hysteresis

parabolic pdes with hysteresis and quasivariational inequalities w0 being prescribed as an initial output of w its input output relation is illustrated in fig 1 1 see 1 part i iii 2 for the precise de nition in the gure fa and fd are continuous and nondecreasing functions on r such that fa fd on r we refer for some results on this sort of model to 1 4 as is well known 1 part i iii 2 1 2 is equivalent to the following variational inequality wt x t iu x t w x t 3 0 x t qt 1 3

the m function for hamiltonians with wigner von neumann potentials hamiltonians with strong wigner von neumann potentials are known to possess bound states in the continuous spectrum for smaller couplings these bound states become resonances which appear as singularities of the m function these singularities are intimately connected with the decay of the corresponding subordinate eigenfunction for coulomb type potentials with schrodinger operators this has recently be shown by atkinson the author and hinton klaus and shaw here these results are extended to a general class of wigner von neumann potentials for dirac and schrodinger operators

on a computer assisted proof of the existence of eigenvalues below the essential spectrum of the sturm liouville problem abstract there is considerable interest in determining the existence of eigenvalues of the sturm liouville problem py qy wy where the independent variable x 0 and p q and w are real valued functions and is the spectral parameter in general an analytic attack on this problem is quite difficult and usually requires the use of the variational principal together with choice of suitable test functions we show how results from functional analysis together with interval analysis and interval arithmetic can be used not only to determine the existence of such eigenvalues but also to compute provably correct bounds on their values

quantum dating market abstract we consider the dating market decision problem under the quantum mechanics point of view quantum states whose associated amplitudes are modified by men strategies are used to represent women the grover quantum search algorithm is used as a playing strategy success is more frequently obtained by playing quantum than playing classic

computing the spectral function for singular sturm liouville problems algorithms for computing sturm liouville spectral density functions are developed based on several mathematical characterizations convergence and error bounds are derived and methods are tested on several examples the results are compared with those from the existing software package sledge

a spectral transform method for singular sturm liouville problems with applications to energy diffusion in plasma physics we develop a spectrally accurate numerical method to compute solutions of a model pde used in plasma physics to describe diffusion in velocity space due to fokker planck collisions the solution is represented as a discrete and continuous superposition of normalizable and nonnormalizable eigenfunctions via the spectral transform associated with a singular sturm liouville operator we present a new algorithm for computing the spectral density function of the operator that uses chebyshev polynomials to extrapolate the value of the titchmarsh weyl m function from the complex upper half plane to the real axis the eigenfunctions and density function are rescaled and a new formula for the limiting value of the m function is derived to avoid amplification of roundoff errors when the solution is reconstructed the complexity of the algorithm is also analyzed showing that the cost of computing the spectral density function at a point grows less rapidly than any fractional inverse power of the desired acc

bounded solutions and absolute continuity of sturm liouville operators this work is a contribution to the theory of the absolutely continuous spectrum of one dimensional schriidinger operators i e sturm liouville operators generated by differential expressions of the form ru u qu in proofs of absolute continuity for such operators and also for the closely related dirac systems always asymptotic properties of solutions of zu lu for real or complex values of 1 have played an important role see for example 18 19 8 4 9 lo in these works and a number of others particular classes of potentials q were treated using properties of solutions in the course of the proof of absolute continuity somewhat more recently the connection between asymptotic properties of solutions and absolute continuity was given a theory i e results of the following form were proved let the solutions of zu lu satisfy some specific asymptotic property for a varying in some subset of r no or almost no a priori assumptions on q then operators generated by z are absolutely continuous in this set a first result of this type was given by carmona 3 who proved that local uniform boundedness of solutions together with their derivatives in some open a set implies pure absolute continuity in this set here we will mostly rely on the concept of non or racy of solutions which was shown by gilbert and pearson 7 12 61 to be a powerful tool in the investigation of the continuous spectrum of sturm liouville operators in section 2 we give some consequences of their results whi ch are useful in proofs of absolute continuity these consequences range from non existence of imbedded eigenvalues and the existence of absolutely continuous parts to pure absolute continuity and the existence of transient 210 0022 247x 92 5 00

quantum barro gordon game in monetary economics abstract classical game theory addresses decision problems in multi agent environment where one rational agent s decision affects other agents payoffs game theory has widespread application in economic social and biological sciences in recent years quantum versions of classical games have been proposed and studied in this paper we consider a quantum version of the classical barro gordon game which captures the problem of time inconsistency in monetary economics such time inconsistency refers to the temptation of weak policy maker to implement high inflation when the public expects low inflation the inconsistency arises when the public punishes the weak policy maker in the next cycle we first present a quantum version of the barro gordon game next we show that in a particular case of the quantum game time consistent nash equilibrium could be achieved when public expects low inflation thus resolving the game

bounds on scattering poles in one dimension for the class of super exponentially decaying potentials on the real line sharp upper bounds on the counting function of the poles in discs are derived and the density of the poles in strips is estimated in the case of nonnegative potentials explicit estimates for the width of a pole free strip are obtained

dynamics of relay relaxation oscillators relaxation oscillators can usually be represented as a feedback system with hysteresis the relay relaxation oscillator consists of relay hysteresis and a linear system in feedback the objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators in particular we give a complete analysis for the case of unimodal periodic orbits and illustrate the presence of degenerate and asymmetric orbits we also discuss how complex orbits can arise from bifurcation of unimodal orbits finally we focus on oscillators with an integrator as the linear component and study the entrainment under external forcing and phase locking when such oscillators are coupled in a ring

analytic continuation and resonance free regions for sturm liouville potentials with power decay the analytic continuation of the jost solution into a sector of the unphysical sheet is established for analytic potentials with power decay the method also yields resonance free regions which in the case of super exponential decay are confirmed to be the best possible of their kind by the known asymptotic distribution of resonances

bifurcation of periodic orbits in a class of planar filippov systems abstract in this paper we discuss the perturbations of a general planar filippov system with exactly one switching line when the system has a limit cycle we give a condition for its persistence when the system has an annulus of periodic orbits we give a condition under which limit cycles are bifurcated from the annulus we also further discuss the stability and bifurcations of a nonhyperbolic limit cycle when the system has an annulus of periodic orbits we show via an example how the number of limit cycles bifurcated from the annulus is affected by the switching

hysteresis and periodic solutions of semilinear and quasilinear wave equations on demontre l existence de solutions periodiques pour les problemes u tt u xx f u g t x u t o u t 0 u tt f u x x g t x u x t o u x t 0 pour chaque g periodique ou f est l operateur d ishlinskii et 0 arbitraire

asymptotic distribution of resonances in one dimension abstract we determine the leading asymptotics of the resonance counting function for a class of schrodinger operators in one dimension whose potentials may have non compact support

quantum social game theory abstract most game theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis this paper explores the effects of non independence on strategic interaction two types of non independence effects are considered first the paper considers subjective non independence at the level of the individual actor by looking at how choice ambivalence shapes the decision making process specifically how do alternative individual choices superpose with one another to constructively destructively shape each other s role within an actor s decision making process this process is termed as quantum superposition of alternative choices second the paper considers how inter subjective non independence across actors engenders collective strategies among two or more interacting actors this is termed as quantum entanglement of strategies taking into account both types of non independence effect makes possible the emergence of a new collective equilibrium without assuming signaling prior contract agreement or third party moderation or even cheap talk i apply these ideas to analyze the equilibrium possibilities of a situation wherein n actors play a quantum social game of cooperation i consider different configurations of large n quantum entanglement using the approach of density operator i specifically consider the following configurations star shaped nearest neighbors and full entanglement

the hurwitz theorem for bessel functions and antibound states in spectral theory an 1889 result of hurwitz is that the bessel function j v c v 0 c 0 has no zeros for 2 n v n 1 with integer n a new application of this result is given which describes the behaviour of jost functions and antibound states for one dimensional schrodinger equations with exponentially decaying potential a new hurwitz type theorem with similar applications is developed for hypergeometric functions extensions are obtained where the power series are terminated after 2 n 1 terms and larger zero free intervals 2 n v are found

accurate spectral numerical schemes for kinetic equations with energy diffusion we examine the merits of using a family of polynomials that are orthogonal with respect to a non classical weight function to discretize the speed variable in continuum kinetic calculations we consider a model one dimensional partial differential equation describing energy diffusion in velocity space due to fokker planck collisions this relatively simple case allows us to compare the results of the projected dynamics with an expensive but highly accurate spectral transform approach it also allows us to integrate in time exactly and to focus entirely on the effectiveness of the discretization of the speed variable we show that for a fixed number of modes or grid points the non classical polynomials can be many orders of magnitude more accurate than classical hermite polynomials or finite difference solvers for kinetic equations in plasma physics we provide a detailed analysis of the difference in behavior and accuracy of the two families of polynomials for the non classical polynomials if the initial condition is not smooth at the origin when interpreted as a three dimensional radial function the exact solution leaves the polynomial subspace for a time but returns up to roundoff accuracy to the same point evolved to by the projected dynamics in that time by contrast using classical polynomials the exact solution differs significantly from the projected dynamics solution when it returns to the subspace we also explore the connection between eigenfunctions of the projected evolution operator and non normalizable eigenfunctions of the full evolution operator as well as the effect of truncating the computational domain

modeling interactions between political parties and electors abstract in this paper we extend some recent results on an operatorial approach to the description of alliances between political parties interacting among themselves and with a basin of electors in particular we propose and compare three different models deducing the dynamics of their related decision functions i e the attitude of each party to form or not an alliance in the first model the interactions between each party and their electors are considered we show that these interactions drive the decision functions toward certain asymptotic values depending on the electors only this is the perfect party which behaves following the electors suggestions the second model is an extension of the first one in which we include a r u l e which modifies the status of the electors and of the decision functions as a consequence at some specific time step in the third model we neglect the interactions with the electors while we consider cubic and quartic interactions between the parties and we show that we get slightly oscillating asymptotic values for the decision functions close to their initial values this is the real party which does not listen to the electors several explicit situations are considered in details and numerical results are also shown

parabolic problems with the preisach hysteresis operator in boundary conditions parabolic initial boundary value problems coupled via the boundary condition with ordinary differential equations whose right hand side contains the preisach hysteresis operator are considered in particular these problems model thermocontrol processes in chemical reactors climate control systems biological cells etc for the preisach operator with and without time delay solvability periodicity of solutions and global b attractors are studied

fast switches in relay feedback systems relays are common in automatic control systems even linear systems with relay feedback are however far from fully understood new results are given about the behavior of these systems via a state space approach it is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing markov parameter of the linear system is positive fast switches are shown to occur as part of stable limit cycles an analysis is developed for these limit cycles that illustrates how they can be predicted

resonances and analytic continuation for exponentially decaying sturm liouville potentials abstract the sturm liouville equation on the half line 0 is considered with a potential which decays exponentially at infinity it is known that green s function has an analytic continuation into part of the unphysical sheet im here it is shown that analytic continuation into the whole of this sheet is possible for certain types of decay the methods are constructive and they also provide a new and rigorous way of locating resonances

periodic solutions to a heat equation with hysteresis in the source term this paper is concerned with a parabolic problem with hysteresis effects in the heat source which models the feedback control the existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time more precisely with the help of the subdifferential operator theory and the poincare map the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage to limit procedure

new characterizations of spectral density functions for singular sturm liouville problems a generalization is given for a characterization of the spectral density function of weyl and titchmarsh for a singular sturm liouville problem having absolutely continuous spectrum in 0 a recurrent formulation is derived that generates a family of approximations based on this scheme proofs of convergence for these new approximations are supplied and a numerical method is implemented the computational results show more rapid rates of convergence which are in accord with the theoretical rates