holonomic functions of several complex variables and singularities of anisotropic ising n fold integrals focusing on examples associated with holonomic functions we try to bring new ideas on how to look at phase transitions for which the critical manifolds are not points but curves depending on a spectral variable or even fill higher dimensional submanifolds lattice statistical mechanics often provides a natural holonomic framework to perform singularity analysis with several complex variables that would in the most general mathematical framework be too complex or simply could not be defined in a learn by example approach considering several picard fuchs systems of two variables above calabi yau odes associated with double hypergeometric series we show that d finite holonomic functions are actually a good framework for finding properly the singular manifolds the singular manifolds are found to be genus zero curves we then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics the n fold integrals n corresponding to the n particle decomposition of the magnetic susceptibility of the anisotropic square ising model in this anisotropic case we revisit a set of so called nickelian singularities that turns out to be a two parameter family of elliptic curves we then find the first set of non nickelian singularities for 3 and 4 that also turns out to be rational or elliptic curves we underline the fact that these singular curves depend on the anisotropy of the ising model or equivalently that they depend on the spectral parameter of the model this has important consequences on the physical nature of the anisotropic n s which appear to be highly composite objects we address from a birational viewpoint the emergence of families of elliptic curves and that of calabi yau manifolds on such problems we also address the question of singularities of non holonomic functions with a discussion on the accumulation of these singular curves for the non holonomic anisotropic full susceptibility this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

a multicarrier architecture based upon the affine fourier transform recently innovative multicarrier schemes have been proposed that exploit the transmission of chirp shaped waves e sup j2 spl pi ct2 by optimally choosing the chirp parameter c on the basis of the channel characteristics and are more robust to time varying channels than ordinary ofdm schemes this concept was applied to continuous time and to discrete time systems in the present paper we aim at developing those ideas using the affine fourier transform aft which is a very general formulation of chirp transforms we present a multicarrier modulation based upon the discrete form of the aft that is therefore inherently discrete and strictly invertible moreover it allows to define a circular prefix concept that is coherent with the chirp nature of the transmission the system can be efficiently implemented by adding a simple phase correction block to standard ofdm modulators demodulators and can effectively combat interchannel interference when the propagation channel is made of few multipath components affected by independent frequency offsets our discrete time multicarrier scheme is an improved version of martone s approach as we also show by simulation results and exhibits analogous characteristics to barbarossa s continuous time system

hyperbolic coxeter groups for triangular potts models the symmetry groups generated by the inversion relations of lattice models of statistical mechanics on triangular lattices are analysed for vertex models and for the standard scalar potts model with two and three site interactions these groups are generated by three inversion relations and are seen to be generically very large ones hyperbolic groups two situations for which the representations of these groups degenerate into smaller ones hopefully compatible with integrability are considered the first reduction for the vertex triangular model corresponds to the situation where the vertex of the triangular model coincides with the left or right hand side of a yang baxter relation in this case the representation of the group is isomorphic up to a semi direct product by a finite group to z z the second reduction for q state ports models occurs for particular values of q the so called tutte beraha numbers for this model algebraic varieties including the known ferromagnetic critical variety happen to be invariant under such large groups of symmetries as a byproduct this analysis provides nice birational representations of hyperbolic coxeter groups

on the phase diagram of the chiral potts model the authors study the phase diagram of the isotropic three state chiral potts model monte carlo simulations performed on twisted square lattices with different sizes up to 64 64 indicate different types of critical curves in particular a floating phase seems to occur finite size scaling analyses are performed at some specific critical points the phase diagram they propose is discussed using exact results

stability analysis of diagonally equipotent matrices diagonally equipotent matrices are diagonally dominant matrices for which dominance is never strict in any coordinate they appear e g as laplacian matrices of signed graphs we show in this paper that for this class of matrices it is possible to provide a complete characterization of the stability properties based only on the signs of the entries of the matrices

a necessary and sufficient condition for the stability of nonnegative interval discrete systems the stability of nonnegative discrete systems with interval uncertainty is discussed for this class of system a necessary and sufficient condition for the stability is provided when all elements of the system matrix are assumed to be specified by intervals an illustrative example is used as a guideline to demonstrate the effectiveness of the result simple computational tests are suggested and their usefulness in this framework is discussed the possible extension of this result to more general classes of systems is addressed

sufficient conditions on stability of interval matrices connections and new results the stability properties of interval matrices are discussed sufficient conditions are given for these properties based upon gershgorin s theorem and its extension and they are shown to improve previous results the derivation helps clarify relations between certain previously available results and shows they can be derived using gershgorin s theorem furthermore the problem of determining the stability of interval matrices is related to that of characterizing certain nonsingular m matrices

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

two channel paraunitary filter banks based on linear canonical transform in this correspondence we propose a two channel paraunitary filter bank which is based on linear canonical transform lct instead of the fourier transform input output relations for such a filter bank are derived in terms of polyphase matrices and modulation matrices it is shown that like conventional filter banks the lct based paraunitary filter banks need only one filter to be designed and the rest of the filters can be obtained from it it is also shown that lct based paraunitary filter banks can be designed by using conventional power symmetric filter design in the fourier domain

comment on stability of interval matrices liao xiao xin 1987 gave necessary and sufficient conditions for the stability of a class of interval matrices it can easily be shown that these results follow directly from a theorem relating stable metzler matrices and quasidominant negative diagonal matrices by mckenzie 1966 which states see also siljak 1978 a metzler matrix a is stable if and only if it is quasidominant negative diagonal as the author considers metzler matrices theorems 1 2 and 3 are obvious also a theorem by fiedler and ptak 1962 concerning a pair of minkowski matrices see also siljak 1978 leads to the same results

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

necessary and sufficient conditions for componentwise stability of interval matrix systems in the asymptotic stability as analysis of interval matrix systems some results are available that operate only as sufficient conditions based on a unique test matrix adequately built from the interval matrix our note reveals the complete role of this test matrix for fully characterizing the componentwise asymptotic stability cwas of interval matrix systems cwas is a special type of as which ensures the flow invariance of certain time dependent sets with respect to the state space trajectories hence the sufficient conditions for as get a new and deeper meaning by their reformulation as necessary and sufficient conditions with respect to the stronger property of cwas

stability of a polytope of matrices counterexamples while there have been significant breakthroughs for the stability of a polytope of polynomials since v l kharitonov s 1978 seminal result on interval polynomials for a polytope of matrices the stability problem is considered far from completely resolved counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case these counterexamples illustrate the fundamental differences between polynomial stability and matrix stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail

robust stability of discrete time systems under parametric perturbations stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable in this paper two methods are presented to estimate the stability robustness region of a linear time invariant discrete time system under multiparameter additive perturbations an inherent difficulty which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region is resolved by transforming the problem to stability of a higher order continuous time system this allows for application of the available results on stability robustness of continuous time systems to discrete time systems the results are also applied to stability analysis of discrete time interconnected systems where the interconnections are treated as perturbations on decoupled stable subsystems

triangular lattice potts models in this paper we study the 3 state potts model on the triangular lattice which has two and three site interactions using a peierls argument we obtain a rigorous bound on the transition temperature thereby disproving a conjecture on the location of its critical point low temperature series are generated and analyzed for three particular choices of the coupling constants a phase diagram is then drawn on the basis of these considerations our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order implying the existence of a multicritical point in the ferromagnetic region relation of the triangularq state potts model with other lattice statistical problems is also discussed in particular an ashkin teller model and the hard hexagon lattice gas solved by baxter emerge as special cases in appropriate limits

on stability of interval matrices new sufficient and sometimes necessary and sufficient conditions are obtained for schur and hurwitz stability of interval matrices by relying on the concept of connective stability and m matrices the necessity part is broadened to include interval matrices with mixed signs of the off diagonal elements provided the sign patterns follow that of the morishima matrix the obtained results are extended to cover convex combinations of interval matrices

explicit formulas for stability radii of nonnegative and metzlerian matrices we address stability issues pertaining to uncertain nonnegative and metzlerian matrices the problem under consideration is the computation of the stability radius when matrix perturbations are both unstructured and structured we show that the stability radius can be obtained in the former case by computing the largest singular value of a constant matrix and in the latter case by computing the spectral radius of a constant matrix

on the simultaneous diagonal stability of linear discrete time systems abstract this paper studies the set of time invariant linear discrete time systems in which each system has a diagonal quadratic lyapunov function first it is shown that there is generally no common diagonal quadratic lyapunov function for such a set of systems even if the set is assumed to be commutative it is also shown that the commutativity assures the existence of a common diagonal quadratic lyapunov function inside the set of 2 2 systems or the set of nonnegative systems then two simple topological results are presented concerning the simultaneous diagonal stability on the set of nonnegative systems the first is a measure of the difference of matrices that assures the simultaneous diagonal stability the second is a measure of the commutativity of matrices

analytic properties of the partition function for statistical mechanical models the author explains with examples the relationship between zeros of the partition function analyticity and degeneracy of absolute magnitude of eigenvalues of the transfer matrix for statistical mechanical models it is shown how to write down a polynomial representation of the partition function for any model with a two sheet largest eigenvalue the staggered ice model representation of the q state potts model on a sequence of semi infinite strips is solved and it is shown that for 0 q 4 the potts model result is only projected out by special boundary conditions the non potts part of the result is obtained for a 4 infinity strip and gives baxter s antiferromagnetic critical curve 1982

diagonal stability of interval matrices and applications abstract let a i a r n n a a a be an interval matrix and 1 p we introduce the concept of schur and hurwitz diagonal stability relative to the holder p norm of a i abbreviated as sds p and hds p respectively this concept is formulated in terms of a matrix inequality using the p norm which must be satisfied by the same positive definite diagonal matrix for all a a i the inequality form is different for sds p and hds p the particular case of p 2 is equivalent to the condition of quadratic stability of a i the sds 2 inequality is equivalent to the stein inequality a a i a t pa p 0 and the hds 2 inequality is equivalent to the lyapunov inequality a a i a t p pa 0 in both cases p is a positive definite diagonal matrix and the notation 0 means negative definite the first part of the paper provides sds p and hds p criteria presents methods for finding the positive definite diagonal matrix requested by the definition of sds p and hds p analyzes the robustness of sds p and hds p and explores the connection with the schur and hurwitz stability of a i the second part shows that the sds p or hds p of a i is equivalent to the following properties of a discrete or continuous time dynamical interval system whose motion is described by a i the existence of a strong lyapunov function defined by the p norm and the existence of exponentially decreasing sets defined by the p norm that are invariant with respect to system s trajectories

signal extrapolation in wavelet subspaces the papoulis gerchberg pg algorithm is well known for band limited signal extrapolation the authors consider the generalization of the pg algorithm to signals in the wavelet subspaces in this research the uniqueness of the extrapolation for continuous time signals is examined and sufficient conditions on signals and wavelet bases for the generalized pg gpg algorithm to converge are given a discrete gpg algorithm is proposed for discrete time signal extrapolation and its convergence is investigated numerical examples are given to illustrate the performance of the discrete gpg algorithm

a fast convergence algorithm for band limited extrapolation by sampling in this paper an algorithm for band limited extrapolation is presented this uses shannon s sampling theorem and fourier series error analysis is given by proof the convergence rate is much faster than that of the papoulis gerchberg algorithm the procedure of the fast convergence algorithm is described in detail the result is demonstrated by numerical examples

three state chiral potts models on the triangular lattice a monte carlo study abstract the phase transition of the three state chiral potts model is investigated by monte carlo simulations performed on two types of isotropic triangular lattices of various linear sizes up to 128 these two types of model are shown to have different phase diagrams in addition the critical antifferomagnetic point is analyzed in detail

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

quadratic stability and stabilization of dynamic interval systems this note presents necessary and sufficient conditions for the quadratic stability and stabilization of dynamic interval systems the results are obtained in terms of linear matrix inequalities lmis and extended to the quadratic stability and stabilization of linear systems with uncertain parameters with the powerful lmi toolbox it is very convenient to solve these problems the illustrative examples show that this method is effective and less conservative to check the robust stability and to design the stabilizing controller for dynamic interval systems

comments on assessing the stability of linear time invariant continuous interval dynamic systems the first part of this note identifies and analyzes two weak points of the commented paper i example 1 reports an incorrect result for which we provide a complete explanation and correction ii the practical use of theorem 1 reveals major drawbacks such as a severe limitation in the applicability due to the restrictive conditions requested by the hypothesis and a relatively low accuracy of the results i e rough values for the right outer bounds of the eigenvalue ranges of interval matrices the second part of the note presents three methods that circumvent the use of theorem 1 and provide the following information about the eigenvalue range of an interval matrix a right outer bound relying on an inequality proved by j rohn see references the right end point by solving a constrained global maximization problem a right outer bound for arbitrary interval matrices and the right end point for some classes of interval matrices by calculating the spectral abscissa of a constant matrix that majorizes the considered interval matrix for illustration by numerical examples throughout the note we use three interval matrices related to example 1 from the commented paper

extrapolation of bandlimited signals in linear canonical transform domain the linear canonical transform lct has been shown to be a powerful analyzing tool in signal processing many results of this transform are already known including bandlimited extrapolation the existing algorithm for solving the problem of lct bandlimited extrapolation is based on signal expansion into a series of generalized prolate spheroidal wave functions gpswfs however the requirement to compute and store the gpswfs and the errors due to the series truncation render this algorithm ill suitable for a practical implementation in this correspondence we first propose a new formulation of the gerchberg papoulis gp algorithm for lct bandlimited extrapolation then we present a fast convergence algorithm for the new formulation the classical gp algorithm related to fourier bandlimited signals is noted as a special case moreover the comparison between the proposed algorithm and the one based on gpswfs expansion is provided and the validity of the theoretical derivations is demonstrated via simulations several potential applications of the achieved theory are also presented

uncertainty principle for real signals in the linear canonical transform domains the linear canonical transform lct is a generalization of the fractional fourier transform frft having applications in several areas of signal processing and optics in this paper we extend the uncertainty principle for real signals in the fractional fourier domains to the linear canonical transform domains giving us the tighter lower bound on the product of the spreads of the signal in two specific lct domains than the existing lower bounds in the lct domains it is seen that this lower bound can be achieved by a gaussian signal the effect of time shifting and scaling the signal on the uncertainty principle is also discussed it is shown here that a signal bandlimited in one lct domain can be bandlimited in some other lct domains also the exceptions to the uncertainty principle in the lct domains arising out of this are also discussed

relations between fractional operations and time frequency distributions and their applications the fractional fourier transform frft is a useful tool for signal processing it is the generalization of the fourier transform many fractional operations such as fractional convolution fractional correlation and the fractional hilbert transform are defined from it in fact the frft can be further generalized into the linear canonical transform lct and we can also use the lct to define several canonical operations in this paper we discuss the relations between the operations described above and some important time frequency distributions tfds such as the wigner distribution function wdf the ambiguity function af the signal correlation function and the spectrum correlation function first we systematically review the previous works in brief then some new relations are derived and listed in tables then we use these relations to analyze the applications of the frpt lct to fractional canonical filter design fractional canonical hilbert transform beam shaping and then we analyze the phase amplitude problems of the frft lct for phase amplitude problems we find as with the original fourier transform that in most cases the phase is more important than the amplitude for the frft lct we also use the wdf to explain why fractional canonical convolution can be used for space variant pattern recognition

convergence of adaptive control schemes using least squares parameter estimates the stability convergence asymptotic optimality and self tuning properties of stochastic adaptive control schemes based on least squares estimates of the unknown parameters are examined it is assumed that the additive noise is i i d and gaussian and that the true system is of minimum phase the bayesian embedding technique is used to show that the recursive least squares parameter estimates converge in general the normal equations of least squares are used to establish that all stable control law designs used in a certainty equivalent i e indirect procedure generally yield a stable adaptive control system four results are given to characterize the limiting behavior precisely a certainty equivalent self tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one even without any excitation in the reference trajectory

some results on quadratic stability of switched systems with interval uncertainty in this paper we present some results on the quadratic stability of switched systems with uncertain parameters we show that the quadratic stability of a class of switched uncertain systems may be readily verified using simple algebraic conditions

three state chiral potts models in two dimensions integrability and symmetry abstract symmetry and integrability relations for the three state chiral potts model on two dimensional lattices are reviewed our detailed and systematic analysis leads to new integrability varieties for specific chiral potts models including new integrable points for the standard antiferromagnetic potts model we also describe a three state vertex model representation of the chiral potts model and write down the associated fundamental invariants for three coordinated lattices