symmetry relations in exactly soluble models symmetry relations such as the star triangle or the inverse relation are very useful in determining the partition function of two dimensional exactly soluble models a common construction of the three dimensional equivalents of these symmetry relations is presented they are used to derive in a geometric way applying simultaneously to different kinds of spin models the consequent global properties i e the commutativity of the transfer matrices and the inverse functional equations on the transfer matrix and the partition function the usefulness of the inverse relation is illustrated by an application to the three dimensional ising model

three dimensional integrable models and associated tangle invariants in this paper we show that the boltzmann weights of the three dimensional baxter bazhanov model give representations of the braid group if some suitable spectral limits are taken in the trigonometric case we classify all possible spectral limits which produce braid group representations furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

a search for bilinear equations passing hirota s three soliton condition ii mkdv type bilinear equations in this paper the results of a search for complex bilinear equations with two soliton solutions are presented the following basic types are discussed a the nonlinear schrodinger equation b dx g f 0 a dx dt f f gg and b the benjamin ono equation p dx f f 0 it is found that the existence of two soliton solutions is not automatic but introduces conditions that are like the usual three and four soliton conditions the search was limited by the degree of a 2 and by degree of p 4 the main results are the following 1 iad3x dxdt idy b g f 0 d2xf f gg 2 d2x ad2y idt b g f 0 dxdy f f gg 3 iad3x d2x idt f f 0 and 4 dxdt i adx bdt f f 0

a disorder solution for a cubic ising model the exact expression of the partition function of a three dimensional cubic ising model with nearest neighbour interactions is given when a certain relation between the coupling constants of the model is satisfied this disorder solution is then compared with a partially resummed high temperature expansion of the partition function of the model the constraints on this expansion which result from the existence of the disorder solution and from the inversion relation are discussed

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

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

study of a two dimensional fully frustrated model the authors consider a fully frustrated ising model on a square lattice depending on four parameters the partition function is shown to be equivalent to the two parameter ferromagnetic onsager partition function this result generalises a relation established by southern et al 1980 and can be checked in the particular case of the one parameter villain model in particular the residual entropy of the villain model is linked to the free energy of the onsager model at criticality the reduction from four to two parameters occurring in this mapping is studied in the light of the inverse relation satisfied by the partition function of the frustrated model

on zamolodchikov s solution of the tetrahedron equations the tetrahedron equations arise in field theory as the condition for thes matrix in 2 1 dimensions to be factorizable and in statistical mechanics as the condition that the transfer matrices of three dimensional models commute zamolodchikov has proposed what appear from numerical evidence and special cases to be non trivial particular solutions of these equations but has not fully verified them here it is proved that they are indeed solutions

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

remarks on the star triangle relation in the baxter bazhanov model we show that the restricted star triangle relation introduced by bazhanov and baxter can be obtained either from the star triangle relation of the chiral potts model or from the star square relation proposed by kashaev mangazeev and stroganov and give a response to a guess of bazhanov and baxter

the vertex formulation of the bazhanov baxter model in this paper we formulate an integrable model on the simple cubic lattice then valued spin variables of the model belong to edges of the lattice the boltzmann weights of the model obey the vertex type tetrahedron equation in the thermodynamic limit our model is equivalent to the bazhanov baxter model in the case whenn 2 we reproduce korepanov s and hietarinta s solutions of the tetrahedron equation as special cases

solitons and other solutions for higher order nls equation and quantum zk equation using the extended simplest equation method abstract in this article we apply the extended simplest equation method for constructing the solitons and other solutions of two nonlinear partial differential equations pdes namely the higher order nonlinear schrodinger nls equation with derivative non kerr nonlinear terms and the nonlinear quantum zakharov kuznetsov qzk equation which play an important role in mathematical physics the first equation describes pulse of the propagation beyond ultrashort range in optical communication systems while the second equation arises in quantum magneto plasma comparison of our new results in this article with the well known results is given

qualitative analysis to traveling wave solutions of zakharov kuznetsov burgers equation and its damped oscillatory solutions abstract the theory of planar dynamical systems is applied in this paper to carry out a qualitative analysis to the planar dynamical system corresponding to the bounded traveling wave solution of the zakharov kuznetsov burgers equation and obtain the existence and uniqueness of the bounded traveling wave solutions according to the discussions on the relationships between the shapes of bounded traveling wave solutions and the dissipation coefficient d a critical value d 0 is found for arbitrary traveling wave speed v and integral constant g this equation has a unique monotone kink profile solitary wave solution as the dissipation coefficient d satisfies d d 0 while it has a unique damped oscillatory solution as d d 0 this paper also presents the exact bell profile solitary wave solution as d 0 furthermore we appropriately design the structure of the damped oscillatory solution in light of the evolution relationships of the solution orbit in the global phase portraits to which the damped oscillatory solution corresponds and obtain its approximate solution by means of the undetermined coefficients method finally based on the integral equation that reflects the relationships between the approximate damped oscillatory solution and its exact solution the error estimate is given for the approximate damped oscillatory solution the error is infinitesimal decreasing in exponential form

baxter equations and the zamolodchikov model abstract a summary is given of the significance of the star triangle or yang baxter equations in the solution of two dimensional statistical mechanical models the extension to the three dimensional tetrahedron relations is quoted and it is shown how this can be used to obtain the partition function of the zamolodchikov model for an n lattice the n result differs from that recently obtained by bazhanov and stroganov

new exact solitary wave and multiple soliton solutions of quantum zakharov kuznetsov equation abstract by employing auxiliary equation method and hirota bilinear method the quantum zakharov kuznetsov equation which arises in quantum magnetoplasma is investigated with the aid of symbolic computation both solitary wave solutions and multiple soliton solutions are obtained these new exact solutions will extend previous results and help us explain the properties of multidimensional nonlinear ion acoustic waves in dense magnetoplasma

solitary wave solutions of 3 1 dimensional extended zakharov kuznetsov equation by lie symmetry approach abstract in this paper the solitary wave solutions of 3 1 dimensional extended zakharov kuznetsov ezk equation are constructed which appear in the magnetized two ion temperature dusty plasma and quantum physics lie group of transformation method is proposed to investigate the solution of 3 1 dimensional ezk equation via lie symmetry method the optimal system of one dimensional lie subalgebra is constructed by using lie point symmetries the three dimensional ezk equation reduced into number of ordinary differential equations odes by applying similarity reductions consequently solutions so extracted are more general than erstwhile known results we have obtained twenty one solutions in the explicit form some of them are likewise general and some are new for the best study of us eventually single soliton quasi periodic soliton multisoliton lump type soliton traveling wave and solitary wave interaction behavior are illustrated graphically through numerical simulation for physical affirmation of the results please check whether the affiliations are correct

star triangle relation for a three dimensional model the solvablesl n chiral potts model can be interpreted as a three dimensional lattice model with local interactions to within a minor modification of the boundary conditions it is an ising type model on the body centered cubic lattice with two and three spin interactions the corresponding local boltzmann weights obey a number of simple relations including a restricted star triangle relation which is a modified version of the well known star triangle relation appearing in two dimensional models we show that these relations lead to remarkable symmetry properties of the boltzmann weight function of an elementary cube of the lattice related to the spatial symmetry group of the cubic lattice these symmetry properties allow one to prove the commutativity of the row to row transfer matrices bypassing the tetrahedron relation the partition function per site for the infinite lattice is calculated exactly

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

algebraic invariants in soluble models exhibits on the known solutions of the triangle relation for the exactly solved models some simplifying methods of recovering their parametrisation in terms of algebraic varieties the relation to the automorphy group generated by the inverse and spatial symmetries of the model is also analysed

multiple soliton solutions for the 2 1 dimensional asymmetric nizhnik novikov veselov equation abstract the asymmetric nizhnik novikov veselov equation will be investigated the hirota bilinear method will be used to derive n soliton solutions of this completely integrable equation multiple singular soliton solutions will be developed as well the asymmetric nizhnik novikov veselov equation does not show any resonant phenomenon

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

multiple soliton solutions for the lax kadomtsev petviashvili lax kp equation a new completely integrable dispersive equation is derived the new equation is obtained by extending the lax fifth order equation using the sense of the kadomtsev petviashvili kp equation in extending the kdv equation the newly derived lax kadomtsev petviashvili lax kp equation is investigated by using the tanh coth method and the hirota bilinear method to derive single soliton solution and n soliton solutions respectively the study highlights the multiple soliton solutions of the derived completely integrable equation

paley wiener characterization of kernels for finite rate of innovation sampling exact reconstruction of finite rate of innovation signals can be achieved by employing customized sampling kernels that satisfy certain frequency domain properties we impose compact support in time as an additional constraint considering frequency domain reconstruction we derive conditions for admissible sampling kernels and corresponding sampling rates our constructive kernel design methodology is based on the paley wiener theorem for compactly supported functions the new kernels satisfy generalized strang fix conditions and have specific polynomial modulated exponential reproducing properties unlike exponential splines which have a support that is directly proportional to the number of exponentials they can generate the proposed kernels have a support that is independent of that number to analyze noise robustness we consider a special member of the class that has a sum of modulated splines sms form in the time domain and optimize its parameters to minimize the noise variance the sum of sincs sos kernel reported in the literature is an instance of this construction in noise robustness analysis sms kernels show improvement in mean squared error mse compared with the state of the art alternatives in continuous time noise the improvement in mse is about 2 db for low signal to noise ratio snr and 7 db for high snr in the case of discrete white gaussian noise the mse is lower by as much as 25 db by using a higher order sms kernel compared with the sos kernel for snrs in the range of 10 15 db

tetrahedron equations and the relativistic s matrix of straight strings in 2 1 dimensions the quantums matrix theory of straight strings infinite one dimensional objects like straight domain walls in 2 1 dimensions is considered thes matrix is supposed to be purely elastic and factorized the tetrahedron equations which are the factorization conditions are investigated for the special two colour model the relativistic three strings matrix which apparently satisfies this tetrahedron equation is proposed

multiple soliton solutions of two extended model equations for shallow water waves abstract multiple soliton solutions for two extensions of model equations for shallow water waves presented in m j ablowitz d j kaup a c newell h segur the inverse scattering transform fourier analysis for nonlinear problems stud appl math 53 1974 249 315 r hirota j satsuma n soliton solutions of model equations for shallow water waves j phys soc jpn 40 2 1976 611 612 are obtained the two extensions possess identical dispersion relations but with different structures for the n soliton solutions for n 1 the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these extended equations the tanh coth method is used to obtain single soliton solutions

rational mappings arborescent iterations and the symmetries of integrability we describe a class of nonlinear birational representations of groups generated by a finite number of involutions these groups are symmetries of the yang baxter equations and their higher dimensional generalizations they provide discrete dynamical systems with a variety of behaviors from chaotic to integrable according to the number of invariants of the representation

birational mappings and matrix subalgebra from the chiral potts model we study birational transformations of the projective space originating from lattice statistical mechanics specifically from various chiral potts models associating these models with stable patterns and signed patterns we give general results which allow us to find all chiral q state spin edge potts models when the number of states q is a prime or the square of a prime as well as several q dependent family of models we also prove the absence of monocolor stable signed pattern with more than four states this demonstrates a conjecture about cyclic hadamard matrices in a particular case the birational transformations associated with these lattice spin edge models show complexity reduction in particular we recover a one parameter family of integrable transformations for which we give a matrix representation when the parameter has a suitable value

estimation of sparse mimo channels with common support we consider the problem of estimating sparse communication channels in the mimo context in small to medium bandwidth communications as in the current standards for ofdm and cdma communication systems with bandwidth up to 20 mhz such channels are individually sparse and at the same time share a common support set since the underlying physical channels are inherently continuous time we propose a parametric sparse estimation technique based on finite rate of innovation fri principles parametric estimation is especially relevant to mimo communications as it allows for a robust estimation and concise description of the channels the core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support we show the application of our technique for channel estimation in ofdm uniformly contiguous dft pilots and cdma downlink walsh hadamard coded schemes in the presence of additive white gaussian noise theoretical lower bounds on the estimation of sparse common support scs channel parameters in rayleigh fading conditions are derived finally an analytical spatial channel model is derived and simulations on this model in the ofdm setting show the symbol error rate ser is reduced by a factor 2 0 db of snr to 5 high snr compared to standard non parametric methods e g lowpass interpolation

inverse functional relation on the potts model the two dimensional anisotropic potts model at all temperatures satisfies a local inverse relation leading to an inverse functional equation on the transfer matrix the pertinence of the related functional equation for the partition function is discussed and verified perturbatively by introducing a diagrammatic expansion corresponding to a partial resummation on one parameter of the model possible exploitations of the inverse relation in order to determine the partition functions are sketched this indicates that the inverse relation can be used without referring to a star triangle relation

the new exact solitary and multi soliton solutions for the 2 1 dimensional zakharov kuznetsov equation abstract in this paper by employing two different simplest equation methods the 2 1 dimensional zakharov kuznetsov zk equation derived for describing weakly nonlinear ion acoustic waves in the plasma is investigated with the aid of the bernoulli equation and the coupled burgers equations the electric field potential of zk equation are formally obtained which are presented as the new solitary and multi soliton solutions meanwhile the electric field and magnetic field can be accordingly obtained in addition the significant features of the variable coefficient and parameter are discovered the results show that the solitary and multi soliton solutions are precisely obtained and the efficiency of the methods is demonstrated these new exact solutions will extend previous results and help to explain the features of nonlinear ion acoustic waves in the plasma

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above