irreductible representations of the simple jordan superalgebra of grassmann poisson bracket abstract we obtain classification of the irreducible bimodules over the jordan superalgebra kan n the kantor double of the grassmann poisson superalgebra g n on n odd generators for all n 2 and an algebraically closed field of characteristic 2 this generalizes the corresponding result of c martinez and e zelmanov announced in 12 for n 4 and a field of characteristic zero

invariance properties for a class of quasipolynomials when a time delay system involves multiple imaginary roots mirs the stability analysis will become much more complicated than that in the case with only simple imaginary roots sirs an mir may exhibit different splitting behaviors and to the best of the authors knowledge their properties have not been fully investigated in this paper we focus on characterizing the invariance properties for mirs with any multiplicity furthermore the proposed methodology makes it possible to also cover some degenerate cases already encountered and discussed in the literature in addition we propose an easily implemented frequency sweeping method making it possible to derive the asymptotic behavior without invoking the puiseux series

residue harmonic balance solution procedure to nonlinear delay differential systems abstract this paper develops the residue harmonic balance solution procedure to predict the bifurcated periodic solutions of some autonomous delay differential systems at and after hopf bifurcation in this solution procedure the zeroth order solution employs just one fourier term the unbalanced residues due to fourier truncation are considered by solving linear equation iteratively to improve the accuracy the number of fourier terms is increased automatically the well known sunflower equation and van der pol equation with unit delay are given as numerical examples their solutions are verified for a wide range of system parameters comparison with those available shows that the residue harmonic balance method is effective to solve the autonomous delay differential equations moreover the present method works not only in determining the amplitude but also the frequency at bifurcation

irreducible bimodules over alternative algebras and superalgebras the irreducible alternative superbimodules are studied the complete classification is obtained for even bimodules of arbitrary dimension and for finite dimensional irreducible superbimodules over an algebraically closed field

representation theory of jordan superalgebras i we complete the classification of irreducible bimodules over simple finite dimensional jordan superalgebras

hopf bifurcation analysis of integro differential equation with unbounded delay abstract the complexity of a nonlinear dynamical system is controllable via a selection of system parameters one representative behavior of such a complex system can be illustrated by hopf bifurcation this paper presents a hopf bifurcation analysis of a kind of integro differential equations with unbounded delay based on the hopf bifurcation principle a set of relationships among system parameters are obtained when a periodic orbit exists in the system a numerical analysis is applied to solve the integro differential delay equation this paper proves the existence of hopf bifurcation in the corresponding difference equations under the same system parameters as that in the integro differential delay equations

global dynamics of nicholsonʼs blowflies equation revisited onset and termination of nonlinear oscillations abstract we revisit nicholson s blowflies model with natural death rate incorporated into the delay feedback we consider the delay as a bifurcation parameter and examine the onset and termination of hopf bifurcations of periodic solutions from a positive equilibrium we show that the model has only a finite number of hopf bifurcation values and we describe how branches of hopf bifurcations are paired so the existence of periodic solutions with specific oscillation frequencies occurs only in bounded delay intervals the bifurcation analysis and the matlab package dde biftool developed by engelborghs et al guide some numerical simulations to identify ranges of parameters for coexisting multiple attractive periodic solutions

retarded differential equations retarded differential equations rdes are differential equations having retarded arguments they arise in many realistic models of problems in science engineering and medicine where there is a time lag or after effect numerical techniques for such problems may be regarded as extensions of dense output methods for ordinary differential equations odes but scalar rdes are inherently infinite dimensional with a richer structure than their ode counterparts we give background material develop a theoretical foundation for the basic numerics and give some results not previously published

lower bounds for quartic anharmonic and double well potentials rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the schrodinger equation with quartic anharmonic and symmetric double well potentials of the form v a b ax2 2 bx4 b 0 are presented this procedure exploits some exactly soluble model potentials and appears to be of quite general utility

bifurcations and multiple traffic jams in a car following model with reaction time delay we investigate an optimal velocity car following model for n cars on a circular singlelane road where reaction time delay of drivers is taken into account the stability of the uniform ow equilibrium is studied analytically while bifurcating periodic solutions for difierent wave numbers are investigated with numerical continuation techniques this reveals that the periodic solution with the smallest wave number may be stable and all other periodic solutions are unstable as n is increased periodic solutions develop stop and go fronts that correspond to rapid deceleration and acceleration between regions of uniformly owing and stagnant tra c in terms of the positions of all cars on the ring these fronts are associated with tra c jams all tra c jams form a tra c pattern that evolves under time due to slow motion of the fronts the tra c pattern corresponding to the stable periodic motion of cars is the only stable one however we flnd that other periodic orbits may be unstable only so weakly that they give rise to transient tra c jams that may persist for long times eventually such tra c jams either merge with one another or disperse until the stable tra c pattern is reached

accelerated landweber iterations for the solution of ill posed equations in this paper the potentials of so calledlinear semiiterative methods are considered for the approximate solution of linear ill posed problems and ill conditioned matrix equations several efficient two step methods are presented most of which have been introduced earlier in the literature stipulating certain conditions concerning the smoothness of the solution a notion of optimal speed of convergence may be formulated various direct and converse results are derived to illustrate the properties of this concept if the problem s right hand side data are contaminated by noise semiiterative methods may be used asregularization methods assuming optimal rate of convergence of the iteration for the unperturbed problem the regularized approximations will be of order optimal accuracy to derive these results specific properties of polynomials are used in connection with the basic theory of solving ill posed problems rather recent results onfast decreasing polynomials are applied to answer an open question of brakhage numerical examples are given including a comparison to the method of conjugate gradients

estimates of the bistable region in metal cutting the classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics the standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature the proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point in the case of the one degreeof freedom model of orthogonal cutting the existence of unstable self excited vibrations is proven along the stability limits which is strongly related to the force characteristic at its inflexion point an analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist it is shown how this domain of bistability depends on the theoretical chip thickness the comparison of these results with the experimental observations and also with the subcritical hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity

approximate analytical solutions for primary chatter in the non linear metal cutting model this paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non linear differential equations of motion the process model is based upon the established mechanics of orthogonal cutting and results in a pair of non linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution the chosen solution technique is the perturbation method of multiple time scales and approximate closed form solutions are generated for the most important non resonant case numerical data are then substituted into the analytical solutions and key results are obtained and presented some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given it is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used these being chosen to represent a real orthogonal cutting process in an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co ordinates

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

numerical stability analysis and computation of hopf bifurcation points for delay differential equations we present a numerical technique for the stability analysis and the computation of branches of hopf bifurcation points in nonlinear systems of delay differential equations with several constant delays the stability analysis of a steady state solution is done by a numerical implementation of the argument principle which allows to compute the number of eigenvalues with positive real part of the characteristic matrix the technique is also used to detect bifurcations of higher singularity hopf and fold bifurcations during the continuation of a branch of hopf points this allows to trace new branches of hopf points and fold points

unital bimodules over the simple jordan superalgebra d t we classify indecomposable finite dimensional bimodules over jordan superalgebras d t t 1 0 1

representations of simple noncommutative jordan superalgebras i abstract in this article we begin the study of representations of simple finite dimensional noncommutative jordan superalgebras in the case of degree 3 we show that any finite dimensional representation is completely reducible and depending on the superalgebra quasiassociative or jordan then we study representations of superalgebras d t and k 3 and prove the kronecker factorization theorem for superalgebras d t in the last section we use a new approach to study noncommutative jordan representations of simple jordan superalgebras

numerical bifurcation analysis of immunological models with time delays in recent years a large number of mathematical models that are described by delay differential equations ddes have appeared in the life sciences to analyze the models dynamics numerical methods are necessary since analytical studies can only give limited results in turn the availability of efficient numerical methods and software packages encourages the use of time delays in mathematical modelling which may lead to more realistic models we outline recently developed numerical methods for bifurcation analysis of ddes and illustrate the use of these methods in the analysis of a mathematical model of human hepatitis b virus infection

efficient computation of characteristic roots of delay differential equations using lms methods we aim at the efficient computation of the rightmost stability determining characteristic roots of a system of delay differential equations the approach we use is based on the discretization of the time integration operator by a linear multistep lms method the size of the resulting algebraic eigenvalue problem is inversely proportional to the steplength we summarize theoretical results on the location and numerical preservation of roots furthermore we select nonstandard lms methods which are better suited for our purpose we present a new procedure that aims at computing efficiently and accurately all roots in any right half plane the performance of the new procedure is demonstrated for small and large scale systems of delay differential equations

lie superalgebras graded by p n and q n abstract in this article we study lie superalgebras graded by the root systems p n and q n

classification of linearly compact simple jordan and generalized poisson superalgebras abstract we classify all linearly compact simple jordan superalgebras over an algebraically closed field of characteristic zero as a corollary we deduce the classification of all linearly compact unital simple generalized poisson superalgebras

robust stability optimization for linear delay systems in a probabilistic framework abstract this paper is concerned with an eigenvalue based stabilization method for linear autonomous delay systems with uncertain parameters modeled by a random vector the dependence of the characteristic matrix on the uncertain parameters can be nonlinear also delay values can be subject to uncertainty unlike the stability optimization methods for deterministic problems which minimize the spectral abscissa our approach shows better robust properties based on a more realistic model where the uncertainty is taken into account by minimizing an objective function consisting of the mean of the spectral abscissa with a variance penalty the properties of the spectrum of delay differential algebraic equations of retarded type are analyzed and an integration method to compute the mean and variance of the spectral abscissa which describes the stability property of the system is presented subsequently the analysis of the behavior of the gradient of the characteristic roots is addressed and a suitable explicit formula of the gradient of the objective function is presented finally for designing the controller a suitable optimization routine requiring the objective function and its gradient is presented the efficacy of the method is illustrated with numerical examples including a model of an experimental heat exchanger the algorithms developed are publicly available

on the tits kantor koecher construction of unital jordan bimodules abstract in this paper we explore relationship between representations of a jordan algebra j and the lie algebra g obtained from j by the tits kantor koecher construction more precisely we construct two adjoint functors l i e j mod 1 g mod 1 and j o r g mod 1 j mod 1 where j mod 1 is the category of unital j bimodules and g mod 1 is the category of g modules admitting a short grading using these functors we classify j such that the semisimple part is of clifford type and the category j mod 1 is tame

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

structurable superalgebras of cartan type abstract we describe the simple lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of cartan type we give a classification of simple structurable superalgebras of cartan type over an algebraically closed field f of characteristic 0 together with the faulkner theorem on the classification of classical such superalgebras it gives a classification of the simple structurable superalgebras over f

real time dynamic substructuring in a coupled oscillator pendulum system real time dynamic substructuring is a powerful testing method which brings together analytical numerical and experimental tools for the study of complex structures it consists of replacing one part of the structure with a numerical model which is connected to the remainder of the physical structure the substructure by a transfer system in order to provide reliable results this hybrid system must remain stable during the whole test a primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system in this paper we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator the oscillator is modelled numerically and the transfer system is an actuator the system dynamics is governed by two coupled second order neutral delay differential equations we carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system we then perform a series of hybrid experimental tests for a pendulum oscillator system the results give excellent qualitative and quantitative agreement when compared to the analytical stability results

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

on the analysis of the double hopf bifurcation in machining processes via centre manifold reduction the single degree of freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double hopf bifurcation point centre manifold reduction and normal form calculations are performed to investigate the long term dynamics of the cutting process the normal form of the four dimensional centre subsystem is derived analytically and the possible topologies in the infinite dimensional phase space of the system are revealed it is shown that bistable parameter regions exist where unstable periodic and in certain cases unstable quasi periodic motions coexist with the equilibrium taking into account the non smoothness caused by loss of contact between the tool and the workpiece the boundary of the bistable region is also derived analytically the results are verified by numerical continuation the possibility of transient chaotic motions in the global non smooth dynamics is shown

periodic solutions in a model of recurrent neural feedback an equation which plant used to model recurrent neural feedback with delay is analyzed to determine its periodic solution structure as a two parameter hopf bifurcation problem the model exhibits

reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method spectral discretization methods are well established methods for the computation of characteristic roots of time delay systems in this paper a method is presented for computing all characteristic roots in a given right half plane in particular a procedure for the automatic selection of the number of discretization points is described this procedure is grounded in the connection between a spectral discretization and a rational approximation of exponential functions first a region that contains all desired characteristic roots is estimated second the number of discretization points is selected in such a way that in this region the rational approximation of the exponential functions is accurate finally the characteristic roots approximations obtained from solving the discretized eigenvalue problem are corrected up to the desired precision by a local method the effectiveness and robustness of the procedure are illustrated with several examples and compared with dde biftool

wild two point algebras abstract the representation type of two point algebras is determined it is also shown that a two point algebra is wild if and only if it is controlled wild moreover it turns out that a minimal wild two point algebra is strongly minimal wild if and only if it is not strictly wild

numerical hopf bifurcation for a class of delay differential equations abstract in this paper we consider discretization of parameter dependent delay differential equations of the form x t f x t x t r we show that if the delay differential equation undergoes a hopf bifurcation then the discrete scheme undergoes a hopf bifurcation of the same type the results of this paper extend the results of our previous analysis relating to the discretization of the delay logistic equation to a wider class of problems

representations of exceptional simple alternative superalgebras of characteristic 3 we study representations of simple alternative superalgebras b 1 2 and b 2 4 the irreducible bimodules and bimodules with superinvolution over these superalgebras are classified and some analogues of the kronecker factorization theorem are proved for alternative superalgebras that contain b 1 2 and b 4 2

modular representations of the jordan superalgebras d t and k3 abstract up to the irreducible representations of the simple three dimensional lie algebra s l 2 we classify the unital finite dimensional irreducible jordan representations of the simple superalgebra d t in the case of an algebraically closed field of characteristic p 2 as a corollary we obtain a classification of the finite dimensional irreducible representations of the kaplansky superalgebra k 3 in the case of characteristic p 2

jordan bimodules over the superalgebras p n and q n we extend the jacobson s coordinatization theorem to jordan superalgebras using it we classify jordan bimodules over superalgebras of types q n and jp n n 3 then we use the tits kantor koecher construction and representation theory of lie superalgebras to treat the remaining case q 2

arnoldi methods for image deblurring with anti reflective boundary conditions image deblurring with anti reflective boundary conditions and a non symmetric point spread function is considered several iterative methods based on krylov subspace projections as well as arnoldi tikhonov regularization methods with reblurring right or left preconditioners are compared the aim of the preconditioner is not to accelerate the convergence but to improve the quality of the computed solution and to increase the robustness of the regularization method right preconditioning in conjunction with methods based on the arnoldi process are found to be robust and give high quality restorations in particular when the observed image is contaminated by motion blur our new method is much more effective than other approaches described in the literature such as range restricted arnoldi methods and the conjugate gradient method applied to the normal equations implemented with the reblurring approach

image reconstruction and restoration using the simplified topological e algorithm in order to compute meaningful approximations of the solutions of large scale linear inverse ill posed problems some form of regularization should be employed cimmino and landweber methods are well known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems despite their usually slow convergence the goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods in particular we provide insight and algorithmic details about the simplified topological e algorithm applied to slow converging iterative regularization methods the results of many numerical experiments and comparisons with other methods are also displayed

an abstract framework in the numerical solution of boundary value problems for neutral functional differential equations we consider the numerical solution of boundary value problems for general neutral functional differential equations the problems are restated in an abstract form and then a general discretization of the abstract form is introduced and a convergence analysis of this discretization is developed

the simplified topological varepsilon algorithms for accelerating sequences in a vector space when a sequence of numbers is slowly converging it can be transformed into a new sequence which under some assumptions converges faster to the same limit one of the best known sequence transformations is the shanks transformation which can be recursively implemented by the varepsilon algorithm of wynn this transformation and this algorithm have been extended in two different ways to a sequence of elements of a topological vector space e in this paper we present new algorithms for implementing these topological shanks transformations they no longer require the manipulation of elements of the algebraic dual space e of e nor do they use the duality product inside the rules of the algorithms they need the storage of fewer elements of e and the stability is improved they also allow us to prove convergence and acceleration results for some types of sequences various applications involving sequences of vectors or matrices show the interest of the new algorithms

some special cases in the stability analysis of multi dimensional time delay systems using the matrix lambert w function this paper revisits a recently developed methodology based on the matrix lambert w function for the stability analysis of linear time invariant time delay systems by studying a particular yet common second order system we show that in general there is no one to one correspondence between the branches of the matrix lambert w function and the characteristic roots of the system furthermore it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system and that the principal branch can be used to find several roots and not the dominant root only as stated in previous works the results are first presented analytically and then verified by numerical experiments

representations of simple jordan superalgebras abstract this paper completes description of categories of representations of finite dimensional simple unital jordan superalgebras over algebraically closed field of characteristic zero

wedderburn principal theorem for jordan superalgebras i abstract we consider finite dimensional jordan superalgebras j over an algebraically closed field of characteristic 0 with solvable radical n such that n 2 0 and j n is a simple jordan superalgebra of one of the following types kac k 10 kaplansky k 3 superform or d t we prove that an analogue of the wedderburn principal theorem wpt holds if certain restrictions on the types of irreducible subbimodules of n are imposed where n is considered as a j n bimodule using counterexamples it is shown that the imposed restrictions are essential

computing unstable manifolds of periodic orbits in delay differential equations we present the first algorithm for computing unstable manifolds of saddle type periodic orbits with one unstable floquet multiplier in systems of autonomous delay differential equations ddes with one fixed delay specifically we grow the one dimensional unstable manifold wu q of an associated saddle fixed point q of a poincare map defined by a suitable poincare section starting close to q along the linear approximation to wu q given by the associated eigenfunction our algorithm grows the manifold as a sequence of points where the distance between points is governed by the curvature of the one dimensional intersection curve wu q of wu q with our algorithm makes it possible to study global bifurcations in ddes we illustrate this with the break up of an invariant torus and a subsequent crisis bifurcation to chaos in a dde model of a semiconductor laser with phase conjugate feedback