a general stability theorem for linear discrete time systems the strongest sufficient conditions for constraining zeros to be on or within a circular region in the z plane in terms of weighted absolute norms are derived using elementary geometry it is shown that the weighted l 1 norm yields the strongest result

robust stability of neutral delay differential systems abstract in this paper we consider the robust stability problem for a neutral delay differential system where the characteristic equations involve a polytope of quasi polynomials first the edge theorem is developed for robust stability analysis of a polytope of neutral quasi polynomials based on the edge theorem the robust stability of neutral systems with commensurate delays will be reduced to the checking of the h hurwitz stability of all the edges of a polytope of quasi polynomials and the schur stability of all the edges of the subpolytope of neutral terms then an effective graphical test is made for checking the robust stability of a polytope of neutral quasi polynomials finally we show that checking vertic quasi polynomials is sufficient for the asymptotic stability of the entire family of first order quasi polynomials of the neutral type

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

note on the absolute value of the roots of a polynomial some simple formulas are derived which give bounds for the absolute value of the roots of a polynomial with complex coefficients a conjecture on the condition for some roots to be located in certain circular regions is also proposed

an analytical method of estimating the domain of attraction for polynomial differential equations a system of nth order differential equations with polynomial right hand sides is considered and a simple analytical method of estimating the domain of attraction is developed the method involves an ordinary quadratic lyapunov function spl upsi x sup t q y x with a certain parameter vector y from the same state space all linear factors in the expression for spl upsi spl dot are bounded in the domain spl upsi spl les 1 and the derivative is bounded by a quadratic function the negativeness of which determines the restrictions for y the domain of attraction is estimated through a simple scaling of the obtained area or through its nonlinear transformation with optimization the method allows for obtaining domains for example with infinite volume that are comparable with ones obtained by complicated computational procedures a set of examples is presented

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

construction of a non trivial planar field theory with ultraviolet stable fixed point we study a 4 4 planar euclidean quantum field theory with propagator 1 p 2 2 0 with the help of the tree expansion of gallavotti and nicolo 1 this non renormalizable theory is shown to have a non trivial ultraviolet stable fixed point at negative coupling constant the vicinity of the fixed point is discussed

a note on a classical bound for the moduli of all zeros of a polynomial considers the monic polynomial f z z sup n a sub n 1 z sup n 1 a sub 0 in the complex variable z with complex coefficients under the assumption that the nonleading coefficients of f lie in the disk mod z mod

an efficient algorithm for finding the d stability bound of discrete singularly perturbed systems with multiple time delays in this paper we present an original work on the d stabilization problem of discrete singularly perturbed systems with multiple time delays a new robust d stability criterion in terms of stability radius is first derived to guarantee that all poles of the discrete multiple time delay systems remain inside the specific disk d alpha r uncertainties then by using the technique of time scale separation we derive the corresponding slow and fast subsystems of a discrete multiple time delay singularly perturbed system the state feedback controls for the d stabilization of the slow and the fast subsystems are separately designed and a composite state feedback control for the original system is subsequently synthesized from these state feedback controls thereafter we derive a frequency domain epsilon dependent dstability criterion for the original discrete multiple time delay singularly perturbed system under the composite state feedback control if any one of the conditions of this criterion is fulfilled

the lipatov argument for φ 3 4 perturbation theory we extend to 3 4 the work of s breen on the leading behavior at large order of 2 4 perturbation theory using a phase space expansion to obtain new estimates on the high energy behavior of 3 4 feynman graphs and a rigorous semiclassical expansion we prove that the radius of convergence of the borel transform of the pertubative series for 3 4 euclidean field theory is the one computed by the lipatov method

a renormalisation group method v a single renormalisation group step this paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and or fermion fields and comprises the core of the method in the renormalisation group method increasingly large scales are studied in a progressive manner with an interaction parametrised by a field polynomial which evolves with the scale under the renormalisation group map in our context the progressive analysis is performed via a finite range covariance decomposition perturbative calculations are used to track the flow of the coupling constants of the evolving polynomial but on their own perturbative calculations are insufficient to control error terms and to obtain mathematically rigorous results in this paper we define an additional non perturbative coordinate which together with the flow of coupling constants defines the complete evolution of the renormalisation group map we specify conditions under which the non perturbative coordinate is contractive under a single renormalisation group step our framework is essentially combinatorial but its implementation relies on analytic results developed earlier in the series of papers the results of this paper are applied elsewhere to analyse the critical behaviour of the 4 dimensional continuous time weakly self avoiding walk and of the 4 dimensional n component varphi 4 model in particular the existence of a logarithmic correction to mean field scaling for the susceptibility can be proved for both models together with other facts about critical exponents and critical behaviour

bifurcations in the frequency response of nonlinear feedback control systems the bifurcation theory is applied to bifurcations and accompanying jump phenomena which appear in the frequency response of nonlinear feedback control systems it is also shown by a numerical example that such complicated structures exist in the frequency response of a simple nonlinear feedback control system

a modal decomposition of the hopf normal form coefficient the local stability of a nonlinear dynamical system at an equilibrium point with a pair of purely imaginary eigenvalues can be assessed through the computation of a cubic hopf normal form coefficient assuming the remaining eigenvalues have negative real parts in this paper a modal decomposition of the hopf coefficient is proved the decomposition provides a new methodology for analyzing the hopf cubic normal form coefficient in a formal way the framework is illustrated by nonlinear stability analysis of two control designs where it is shown that the hopf coefficient can be stabilized through modal nonlinear feedbacks

further results on the bounds of the zeros of quasi critical polynomials on the basis of the relationship of the mth power of a polynomial and its modular form polynomial whose coefficients are the moduli of the coefficients of that polynomial we derive a necessary and sufficient condition for the modulus of the mth power of a polynomial for contacting its modular form on the boundary of a disc combined with the result about distribution of zeros of analytic function some new sufficient conditions are derived which give bounds of the absolute values of the roots of a quasi critical polynomial these results extend certain earlier similar tests for linear discrete time systems finally four examples are given to demonstrate the results example 2 1 gives a state feedback application examples 2 2 and 2 4 deal with r stability and example 2 3 display that our theorems give better results when m increases but at the cost of increasing complexity

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

analysis of a coupled fluid structure model with applications to hemodynamics we propose and analyze a simplified fluid structure coupled model for flows with compliant walls as in f nobile and c vergara siam j sci comput 30 2008 pp 731 763 the wall reaction to the fluid is modeled by a small displacement viscoelastic shell where the tangential stress components and displacements are neglected we show that within this small displacement approximation a transpiration condition can be used which does not require an update of the geometry at each time step for pipe flow at least such simplifications lead to a model which is well posed and for which a semi implicit time discretization can be shown to converge we present some numerical results and a comparison with a standard test case taken from hemodynamics the model is more stable and less computer demanding than full models with moving mesh we apply the model to a three dimensional arterial flow with a stent

a lipatov bound for φ 4 4 euclidean field theory we bound the large order behavior of these pieces of the renormalized perturbation expansion for 4 4 which do not contain renormalons 1 the bound we obtain has the form of the leading asymptotic behavior computed by the lipatov method with the exact value of the lipatov constant therefore this paper is a step towards the rigorous study of the large order behavior of 4 4 and towards a proof of existence of the first renormalon singularity which should prevent the theory from being borel summable using the results of this paper and the techniques of 15 one can for instance improve 17 the estimate 18 on the finiteness of the radius of convergence of the borel transform of renormalized 4 4 and obtain that this radius is at least the exact value conjectured in 1

the stress tensor conformal anomaly and analytic regularizations in this paper the stress tensor conformal anomaly of a conformally coupled scalar field defined in a d dimensional riemannian manifold is derived with or without a boundary using the zeta function analytic regularization method it is found that the scalar anomaly is independent of any massless limit in an odd dimensional manifold with a boundary the anomaly is not zero owing the boundary condition dependent term after briefly discussing the cutoff method it is proven that the zeta function method is equivalent to the cutoff method with a subtraction of the polar terms

periodicity and chaos from switched flow systems contrasting examples of discretely controlled continuous systems two examples of the discrete control of a continuous variable system are analyzed these examples exhibit what may be regarded as the two extremes of complexity of the closed loop behavior one is eventually periodic the other is chaotic the examples are derived from sampled deterministic flow models these are of interest in their own right but have also been used as models for certain aspects of manufacturing systems in each case the authors give a precise characterization of the closed loop behavior

analytic regularization of the ψiψi d2 model at finite temperature and density simultaneously using the dimensional and analytic regularization methods we reexamine the gross neveu model at finite temperature and density chemical potential in a d dimensional space time the regularized effective potential is presented at the 1 n large n approximation it is found that in d 3 the effective potential is finite

a simple criterion for stability of linear discrete systems abstract a simple sufficient condition is presented for confining the poles of a linear discrete system on an arbitrarily specified circular region in the z plane

boundary conditions involving pressure for the stokes problem and applications in computational hemodynamics pressure driven flows typically occur in hydraulic networks e g oil ducts water supply biological flows microfluidic channels etc however stokes and navier stokes problems are most often studied in a framework where dirichlet type boundary conditions on the velocity field are imposed thanks to the simpler settings from the theoretical and numerical points of view in this work we propose a novel formulation of the stokes system with pressure boundary condition together with no tangential flow on a part of the boundary in a standard stokes functional framework using lagrange multipliers to enforce the latter constraint on velocity more precisely we carry out i a complete analysis of the formulation from the continuous to discrete level in two and three dimensions ii the description of our solution strategy iii a verification of the convergence properties with an analytic solution and finally iv three dimensional simulations of blood ow in the cerebral venous network that are in line with in vivo measurements and the presentation of some performance metrics with respect to our solution strategy

on the bounds for the roots of a polynomial some new sufficient conditions are presented which give bounds for the absolute values of the roots of a polynomial these results extend certain earlier stability tests for linear discrete systems

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

bounds on completely convergent euclidean feynman graphs letg be a euclidean feynman graph containingl g lines we prove that ifg has massive propagators and does not contain any divergent subgraphs its value is bounded bykl g we also prove the infrared analogue of this bound

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

convergent perturbation expansions for euclidean quantum field theory mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of greens functions in euclidean quantum field theory to arbitrary accuracy including nonperturbative contributions from large field fluctuations here we describe the expansions at the example of 3 dimensional 4 theory in continuous space they are not essentially more complicated than standard perturbation theory the nth order term is expressed in terms of o n dimensional integrals and is of order k if 4k 3 n 4k

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

a simple sufficient condition for the stability of linear discrete time systems the condition is found by finding the largest hypersphere which is interior to the stability boundaries in parameter space

loop vertex expansion for φ2k theory in zero dimension in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction

zeta function continuation and the casimir energy on odd and even dimensional spheres the zeta function continuation method is applied to compute the casimir energy on spheressn both odd and even dimensional spheres are studied for the appropriate conformally modified laplacian the casimir energy is shown to be finite for all dimensions even though generically it should diverge in odd dimensions due to the presence of a pole in the associated zeta function s the residue of this pole is computed and shown to vanish in our case an explicit analytic continuation of s is constructed for all values ofn this enables us to calculate exactly and we find that the casimir energy vanishes in all even dimensions for odd dimensions is never zero but alternates in sign asn increases through odd values some results are also derived for the casimir energy of other operators of laplacian type