analytic results related to magneto hydrodynamic turbulence abstract analytic results are provided for topics related to the magneto hydrodynamic turbulence scaling exponents of general structure functions geometric criteria for singularity formation and dissipative solutions

on the universality of geometrical and transport exponents of rigidity percolation we develop a three parameter position space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity vector percolation in two dimensions to do this we study site bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb respectively the global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class and possibly that of random scalar percolation however if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation we find them to be very different although the corresponding values of the correlation length exponent are the same this indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal which is consistent with some of the recent numerical simulations

rigidity of random networks of stiff fibers in the low density limit rigidity percolation is analyzed in two dimensional random networks of stiff fibers as fibers are randomly added to the system there exists a density threshold q q min above which a rigid stress bearing percolation cluster appears this threshold is found to be above the connectivity percolation threshold q q c such that q min 1 1698 0 0004 q c the transition is found to be continuous and in the universality class of the two dimensional central force rigidity percolation on lattices at percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters whose number diverges in the limit of infinite system size when a critical bond is removed the scaling with system size of the average size of these clusters was found to give a new scaling exponent delta 1 61 0 04

the euclid algorithm and the fast computation of cross covariance and autocovariance sequences a simple linear procedure is given to compute the cross covariance sequence associated with the outputs of two rational digital transfer functions driven by the same white noise sequence such a computation often appears in the study of digital filters in wiener filtering in noise variance estimation in the study of low order approximations and in the study of multichannel systems a fast algorithm based on the euclid algorithm is introduced to solve the linear system of equations involved in the computation and a detailed analysis of the matrix is given the special case of the autocovariance computation is reviewed and the same study is performed alternate polynomial presentations are given and are shown to involve the same matrices and similar fast algorithms

existence theorem and blow up criterion of the strong solutions to the two fluid mhd equation in r3 abstract we first give the local well posedness of strong solutions to the cauchy problem of the 3d two fluid mhd equations and then study the blow up criterion of the strong solutions by means of the fourier frequency localization and bony s paraproduct decomposition it is proved that the strong solution u b can be extended after t t if either u l t q b p 0 with 2 q 3 p 1 and b l t 1 b 0 or j l t q b p 0 with 2 q 3 p 2 where t u denotes the vorticity of the velocity and j b stands for the current density

3d euler equations and ideal mhd mapped to regular systems probing the finite time blowup hypothesis abstract we prove by an explicit construction that solutions to incompressible 3d euler equations defined in the periodic cube 0 l 3 can be mapped bijectively to a new system of equations whose solutions are globally regular we establish that the usual beale kato majda criterion for finite time singularity or blowup of a solution to the 3d euler system is equivalent to a condition on the corresponding regular solution of the new system in the hypothetical case of euler finite time singularity we provide an explicit formula for the blowup time in terms of the regular solution of the new system the new system is amenable to being integrated numerically using similar methods as in euler equations we propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite time singularity problem of euler equations based on the conservation of quantities directly related to energy and circulation the method of mapping to a regular system can be extended to any fluid equation that admits a beale kato majda type of theorem e g 3d navier stokes 2d and 3d magnetohydrodynamics and 1d inviscid burgers we discuss briefly the case of 2d ideal magnetohydrodynamics in order to illustrate the usefulness of the mapping we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1d inviscid burgers equation

two regularity criteria for the 3d mhd equations this work establishes two regularity criteria for the 3d incompressible mhd equations the first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction

on the energy of inviscid singular flows abstract it is known that the energy of a weak solution to the euler equation is conserved if it is slightly more regular than the besov space b 3 1 3 when the singular set of the solution is or belongs to a smooth manifold we derive various l p space regularity criteria dimensionally equivalent to the critical one in particular if the singular set is a hypersurface the energy of u is conserved provided the one sided non tangential limits to the surface exist and the non tangential maximal function is l 3 integrable while the maximal function of the pressure is l 3 2 integrable the results directly apply to prove energy conservation of the classical vortex sheets in both 2d and 3d at least in those cases where the energy is finite

rigidity percolation in a field rigidity percolation with g degrees of freedom per site is analyzed on randomly diluted erdos renyi graphs with average connectivity gamma in the presence of a field h in the gamma h plane the rigid and flexible phases are separated by a line of first order transitions whose location is determined exactly this line ends at a critical point with classical critical exponents analytic expressions are given for the densities n f of uncanceled degrees of freedom and gamma r of redundant bonds upon crossing the coexistence line gamma r and n f are continuous although their first derivatives are discontinuous we extend for the case of nonzero field a recently proposed hypothesis namely that the density of uncanceled degrees of freedom is a free energy for rigidity percolation analytic expressions are obtained for the energy entropy and specific heat some analogies with a liquid vapor transition are discussed particularizing to zero field we find that the existence of a g 1 core is a necessary condition for rigidity percolation with g degrees of freedom at the transition point gamma c maxwell counting of degrees of freedom is exact on the rigid cluster and on the g 1 rigid core i e the average coordination of these subgraphs is exactly 2g although gamma c the average coordination of the whole system is smaller than 2g gamma c is found to converge to 2g for large g i e in this limit maxwell counting is exact globally as well

remarks on global regularity of 2d generalized mhd equations abstract in this paper we investigate the global regularity of 2d generalized mhd equations in which the dissipation term and magnetic diffusion term are u and b respectively let u 0 b 0 h s with s 2 it is showed that the smooth solution u x t b x t is globally regular for the case 0 1 2 3 2

a superfast solver for sylvester s resultant linear systems generated by a stable and an anti stable polynomial abstract we develop a superfast method for the solution of n m n m sylvester s resultant linear systems associated with two real polynomials a z and c z of degree n and m respectively where a z is a stable polynomial i e all its roots lie inside the unit circle whereas c z is an anti stable polynomial i e z m c z 1 is stable the proposed scheme proceeds by iteratively constructing a sequence of increasing approximations of the solution it is based on a blend of ideas from structured numerical linear algebra computational complex analysis and linear operator theory each iterative step can be performed in o n m log n m arithmetic operations by combining fast polynomial arithmetic based on fft with displacement rank theory for structured matrices in addition the resulting process is shown to be quadratically convergent right from the start since the approximation error at the j th iteration is o r 2 j where r max a i 0 i min c i 0 i denotes the separation ratio between the spectrum of a z and c z finally we report and discuss the results of many numerical experiments which confirm the effectiveness and the robustness of the proposed algorithm

application of logical transport to determine the directed and isotropic percolation thresholds the authors present a monte carlo algorithm based on logical transport which determines the effective isotropic percolation and directed percolation thresholds of finite size lattices they apply the algorithm to bond and site directed percolation in two dimensions and determine the asymptotic percolation thresholds by finite size scaling

besov spaces and the multifractal hypothesis parisi and frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis i e they conjecture that the velocity field has local holder exponents in a range hmin hmax with exponents h occurring on a sets h with a fractal dimensiond h heuristic reasoning led them to an expression for the scaling exponentz p ofpth order as the legendre transform of the codimensiond d h we show here that a part of the multifractal hypothesis is correct under even weaker assumptions namely if the velocity field hasl p mean holder indexs i e if it lies in the besov spaceb p s then local holder regularity is satisfied ifs d p then the hypothesis is true in a generalized sense of holder space with negative exponents and we discuss the proper definition of local holder classes of negative index finally if a certain box counting dimension exists then the legendre transform of its codimension gives the scaling exponentz p and more generally the maximal besov index of order p ass p z p p our method of proof is derived from a recent paper of s jaffard using compactly supported orthonormal wavelet bases and gives an extension of his results we discuss implications of the theorems for ensemble average scaling and fluid turbulence

nonlocal percolation and partial ordering in the dilute baxter wu model the zero temperature limit of the dilute baxter wu model is studied in the context of percolation theory the percolation model describing the propagation of order is identified and shown to possess a nonlocal mechanism for the propagation of that order a monte carlo study of this model is performed using the nonlocal cluster identification algorithm developed by fried and schick 1992 the author also shows that the mechanism responsible for nonlocal percolation allows for the possibility of the propagation of partial order at intermediate impurity concentration a partially ordered phase is found and its structure is discussed

a mean field theory of the elastic granular disc model in two dimensions the author has constructed a stephen type mean field theory for the elastic granular disc model in two dimensions and calculated the mean field value of two crossover exponents phi 1 and phi 2 which describe the ways in which the two point elastic susceptibility and the angle angle correlation function scale with the distance respectively the author has found that phi 1 2 and phi 2 1 the possible relation of phi 1 and phi 2 to the bulk modulus exponent f is discussed

least squares approximation of perfect reconstruction filter banks designing good causal filters for perfect reconstruction pr filter banks is a challenging task due to the unusual nature of the design constraints we present a new least squares ls design methodology for approximating prfbs that avoids most of these difficult constraints the designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters then given some desired reconstruction delay this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a prfb this technique is built on a multi input multi output mimo system model for filter banks derived from the filter bank polyphase representation using this model we frame the ls approximation problem for prfbs as a causal ls equalization problem for mimo systems we derive the causal ls solution to this design problem and present an algorithm for computing this solution the resulting algorithm includes a mimo spectral factorization that accounts for most of the complexity and computational cost for this design technique finally we consider some design examples and evaluate their performance

on approximate solutions of the equations of incompressible magnetohydrodynamics abstract inspired by an approach proposed previously for the incompressible navier stokes ns equations we present a general framework for the a posteriori analysis of the equations of incompressible magnetohydrodynamics mhd on a torus of arbitrary dimension d this setting involves a sobolev space of infinite order made of c vector fields with vanishing divergence and mean on the torus given any approximate solution of the mhd cauchy problem its a posteriori analysis with the method of the present work allows one to infer a lower bound on the time of existence of the exact solution and to bound from above the sobolev distance of any order between the exact and the approximate solution in certain cases the above mentioned lower bound on the time of existence is found to be infinite so one infers the global existence of the exact mhd solution we present some applications of this general scheme the most sophisticated one lives in dimension d 3 with the abc flow perturbed magnetically as an initial datum and uses for the cauchy problem a galerkin approximate solution in 124 fourier modes we illustrate the conclusions arising in this case from the a posteriori analysis of the galerkin approximant these include the derivation of global existence of the exact mhd solution with the abc datum when the dimensionless viscosity and resistivity are equal and stay above a critical value

remarks on the blow up criteria for three dimensional ideal magnetohydrodynamics equations in this paper we establish some improved regularity conditions for the three dimensional 3d magnetohydrodynamics equations we proved the logarithmically improved caflisch klapper steele s criteria remarks on sigularities dimension and energy dissipation for ideal hydrodynamics and mhd commun math phys 184 443 1997 as well as the logarithmically improved he xin s on the regularity of weak solutions to the magnetohydrodynamic equations j differ equ 23 235 2005 and wu s bounds and new approach for the 3d mhd equations j nonlinear sci 12 395 2002 results for 3d ideal mhd equations

synthesis of accurate fractional gaussian noise by filtering this paper describes a method for generating long sample paths of accurate fractional gaussian noise fgn the increment process of fractional brownian motion fbm the method is based on a wold decomposition in which fgn is expressed as the output of a finite impulse response filter with discrete white gaussian noise as input the form of the ideal filter is derived analytically in the continuous time case for the finite length discrete time case an iterative projection algorithm incorporating a newton raphson step is described for computing the coefficients of a length n filter in a time approximately proportional to n fast convolution of discrete white gaussian noise with the computed filter impulse response yields arbitrarily long sequences which exactly match the correlation structure of fgn over a finite range of lags for values of the hurst parameter h smaller than a critical value hcritap0 85 and large n the finite length autocorrelation sequence of fgn is positive definite and this range of lags can be as large as the filter autocorrelation length when h h crit the finite length autocorrelation sequence of fgn is no longer positive definite and a modification is made to allow a wold decomposition the generated sequences then exactly match the autocorrelation structure of fgn over a more restricted range of lags which becomes smaller as h approaches unity

critical behaviour of anisotropic superelastic central force percolation the authors study central force percolation on a triangular lattice where the bonds are springs that can freely rotate around the nodes all bonds in one preferred direction are infinitely rigid in the other two directions a proportion p of the springs chosen at random are infinitely rigid while the rest have a finite strength for this specific problem the threshold at which the network becomes infinitely rigid corresponds to the usual bond percolation threshold of a square lattice and is therefore exactly equal to 0 5 they use a transfer matrix algorithm to study the elastic modulus of strips of width ranging from 2 to 32 and length 105 they obtain an estimate of the critical exponent relative to the scaling of the elastic moduli with the strip width 0 99 or 0 03 close to s v for the corresponding isotropic electric problem

rigid animals in three dimensions the number of rigid clusters c n is enumerated for the central force model on a site diluted fcc lattice the exponent vr governing the growth of the radius of gyration of the rigid animal is also calculated it is found that c n approximately n0 333n and vr 0 32 or 0 02

rigidity transition in two dimensional random fiber networks rigidity percolation is analyzed in two dimensional random fibrous networks the model consists of central forces between the adjacent crossing points of the fibers two strategies are used to incorporate rigidity adding extra constraints between second nearest crossing points with a probability p sn and welding individual crossing points by adding there four additional constraints with a probability p weld and thus fixing the angles between the fibers these additional constraints will make the model rigid at a critical probability p sn p sn c and p weld p weld c respectively accurate estimates are given for the transition thresholds and for some of the associated critical exponents the transition is found in both cases to be in the same universality class as that of the two dimensional central force rigidity percolation in diluted lattices

a geometrical interpretation of the chaotic state of inhomogeneous deterministic cellular automata abstract we propose a geometrical interpretation of the chaotic state of inhomogeneous cellular automata from the rules of the cellular automaton we construct a network the percolating phase of this network coincides with the chaotic phase of the cellular automaton we also report numerical tests of these ideas on several cellular automata

optimal differentiation based on stochastic signal models the problem of estimating the time derivative of a signal from sampled measurements is addressed the measurements may be corrupted by colored noise a key idea is to use stochastic models of the signal to be differentiated and of the measurement noise two approaches are suggested the first is based on a continuous time stochastic process as a model of the signal the second uses a discrete time arma model of the signal and a discrete time approximation of the derivative operator digital differentiators are presented in a shift operator polynomial form they minimize the mean square estimation error and are calculated from a linear polynomial equation and a polynomial spectral factorization the three obstacles to perfect differentiation namely a finite smoothing lag measurement noise and aliasing effects due to sampling are discussed

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

scalar and vectorial percolation in compressed expanded graphite dc electrical conductivity and elastic moduli of cubic samples made of two kinds of compressed expanded graphite are measured as a function of their apparent density different percolation thresholds at which the physical properties under study are found to vanish are determined the accuracy of the values is confirmed by the application of the usual scaling laws above but near these thresholds the corresponding critical exponents are indeed found to be very close to their universal values the relationships between the connectivity dc i e scalar and rigidity dr i e vectorial critical densities are discussed it is shown that the ratio dr dc is always almost equal to 8 5 which fact may be accounted by the so called kirkwood keating kk model to our knowledge it is the first time that such a constant value is observed in real materials the kk model is also consistent with critical exponents of elasticity found in both kind of samples hence compressed expanded graphite appears to behave like a disordered heterogeneous medium in which elastic forces are mostly of central nature but include also bond bending contributions

rigid backbone a new geometry for percolation understood in both cases from the nodes linksblobs picture of percolation clusters in fact it is fair to say that in the vast majority of percolation problems encountered to date even continuum percolation 6 the basic geometric features of the percolation clusters such as the scaling of the number of singly connected bonds are identical and the differences arise only at the level of the dynamics for the class of models of interest here however geometric connection the existence of a bond does not imply complete elastic connection because the number of constraints associated with the existence of a bond is smaller than the number of degrees of freedom associated with the sites it connects the percolation threshold is higher8 than that of the corresponding standard percolation problem thorpe6 has suggested the name rigidity percolation for this class of models distinguishing it from the elasticity percolation universality class mentioned above in this paper we study the simplest rigidity percolation model namely the two dimensional central force model 8 ex

onsager s conjecture in bounded domains for the conservation of entropy and other companion laws we show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy and other respective companion laws if they possess a certain fractional differentiability of order one third in the interior of the domain and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary this extends various recent results of the authors

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

tracking of time varying mobile radio channels 1 the wiener lms algorithm adaptation algorithms with constant gains are designed for tracking smoothly time varying parameters of linear regression models in particular channel models occurring in mobile radio communications in a companion paper an application to channel tracking in the is 136 tdma system is discussed the proposed algorithms are based on two key concepts first the design is transformed into a wiener filtering problem second the parameters are modeled as correlated arima processes with known dynamics this leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information the algorithms can be realized as wiener filters called learning filters or as lms newton updates complemented by filters that provide predictions or smoothing estimates the simplest algorithm named the wiener lms is presented all parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known the computational complexity is of the same order of magnitude as that of lms for regressors which are either white or have autoregressive statistics the tracking performance is however substantially improved

spectral factorization by optimal gain iteration an iterative algorithm for spectral factorization is presented the algorithm has the form of a frequency domain version of the newton raphson solution of the corresponding riccati equation although results are established without reference to an underlying state variable model application is made to a distributed filtering problem

remarks on singularities dimension and energy dissipation for ideal hydrodynamics and mhd for weak solutions of the incompressible euler equations there is energy conservation if the velocity is in the besov space b 3 s with s greater than 1 3 b 3 s consists of functions that are lip s i e holder continuous with exponent s measured in the l p norm here this result is applied to a velocity field that is lip 0 except on a set of co dimension on which it is lip agr 1 with uniformity that will be made precise below we show that the frisch parisi multifractal formalism is valid at least in one direction for such a function and that there is energy conservation if analogous conservation results are derived for the equations of incompressible ideal mhd i e zero viscosity and resistivity for both energy and helicity in addition a necessary condition is derived for singularity development in ideal mhd generalizing the beale kato majda condition for ideal hydrodynamics

theory and design of optimum fir compaction filters the problem of optimum fir energy compaction filter design for a given number of channels m and a filter order n is considered the special cases where n m and n spl infin have analytical solutions that involve eigenvector decomposition of the autocorrelation matrix and the power spectrum matrix respectively we deal with the more difficult case of m n spl infin for the two channel case and for a restricted but important class of random processes we give an analytical solution for the compaction filter that is characterized by its zeros on the unit circle this also corresponds to the optimal two channel fir filter bank that maximizes the coding gain under the traditional quantization noise assumptions with a minor extension this can also be used to generate optimal wavelets for the arbitrary m channel case we provide a very efficient suboptimal design method called the window method the method involves two stages that are associated with the above two special cases as the order increases the suboptimality becomes negligible and the filter converges to the ideal optimal solution we compare the window method with a previously introduced technique based on linear programming

a spectral tchebychev solution for three dimensional dynamics of curved beams under mixed boundary conditions abstract this paper presents the application of the spectral tchebychev st technique for solution of three dimensional dynamics of curved beams structures having variable and arbitrary cross section under mixed boundary conditions to accurately capture the vibrational behavior of curved structures a three dimensional 3d solution approach is required since these structures generally exhibit coupled motions in this study the integral boundary value problem ibvp governing the dynamics of the curved structures is found using extended hamilton s principle where the strain energy is expressed using 3d linear elasticity equation to solve the ibvp numerically the 3d spectral tchebychev 3d st approach is used to evaluate the integral and derivative operations defined by the ibvp and to render the complex geometry into an equivalent straight beam with rectangular cross section a series of coordinate transformations are applied to validate and assess the performance of the presented solution approach two case studies are performed i curved beam with rectangular cross section ii curved and pretwisted beam with airfoil cross section in both cases the results natural frequencies and mode shapes are also found using a finite element fe solution approach it is shown that the difference in predicted natural frequencies are less than 1 and the mode shapes are in excellent agreement based on the modal assurance criteria mac analyses however the presented spectral tchebychev solution approach significantly reduces the computational burden therefore it can be concluded that the presented solution approach can capture the 3d vibrational behavior of curved beams as accurately as an fe solution but for a fraction of the computational cost

the diffusion limit for reversible jump processes on z d with ergodic random bond conductivities we consider a reversible jump process on d whose jump rates themselves are random we show mean square convergence of this process under diffusion scaling to a limiting brownian motion with a certain diffusion matrix characterizing effective conductivity

a remark on global regularity of 2d generalized magnetohydrodynamic equations abstract in this paper we study the global regularity of the following 2d two dimensional generalized magnetohydrodynamic equations u t u u p b b u b t u b b u b and get global regular solutions when 0 1 2 1 3 2 3 which improves the results in 5 in particular we obtain the global regularity of the 2d generalized mhd when 0 and 3 2

an analysis of optimal modal regulation convergence and stability this paper treats the linear quadratic regulator problem for infinite dimensional second order in time linear oscillators we solve the problem approximately by modeling a finite number of mode

regularity criteria for the 3d generalized mhd equations in terms of vorticity abstract we prove regularity criteria for the 3d generalized mhd equations these criteria impose assumptions on the vorticity only in addition we also prove a result of global existence for smooth solution under some special conditions

bond diluted rigid animals for central force model an exact enumeration of rigid clusters is analysed using pade approximants the number of bond diluted rigid clusters with n b bonds is found to grow like n theta b b 2 165 or 0 005 n b with theta b 0 988 a value different from that of site diluted rigid animals

continuum modeling of flexible structures with application to vibration control in this paper we consider the construction of hybrid models for flexible structures including both the natural spatially distributed dynamics of low mass density structures and the lumped models associated with rigid body dynamics for the purposes of active control of structural vibrations we argue that by using transform methods the standard approach to transfer function or mechanical impedance modeling can be extended to provide a complete formulation of a hybrid model with localized control we proceed to give a systematic procedure for obtaining the required transfer functions and green s functions for the hybrid model dynamics consisting of one dimensional elastic elements such as beams rods and cables together with rigid body lumped models we focus on a well known family of models for elastic elements together with various reductions and indicate the construction of well posed state space models for these systems using the resulting state space we next demonstrate the construction of a complete frequency domain characterization of the elemental system response using transfer functions and green s functions hybrid constructions are discussed for various interconnections of distributed and lumped elements and a simple illustrative example is given we highlight the extent to which the required computations can be performed automatically on a digital computer using a computer algebra system

higher order commutator estimates and local existence for the non resistive mhd equations and related models this paper establishes the local in time existence and uniqueness of strong solutions in hs for s n 2 to the viscous non resistive magnetohydrodynamics mhd equations in rn n 2 3 as well as for a related model where the advection terms are removed from the velocity equation the uniform bounds required for proving existence are established by means of a new estimate which is a partial generalisation of the commutator estimate of kato ponce comm pure appl math 41 7 891 907 1988

global cauchy problem of 2d generalized magnetohydrodynamic equations abstract in this paper we prove the global in time existence of smooth solutions of the 2d generalized magnetohydrodynamic equations with zero viscosity when the power of the laplacian operator in the dissipation term of the induction equation is between 1 and 2 we also show a regularity criterion on the direction of the magnetic field b 0 b b when 1

solving the linear quadratic optimal control problem for infinite dimensional systems abstract calculation of the solutions to linear quadratic optimal control problems for infinite dimensional systems is considered the sequence of solutions to a sequence of approximating finite dimensional problems converges to the optimal control for the infinite dimensional system if certain assumptions such as uniform stabilizability are satisfied we use this result to calculate controllers for the infinite dimensional system that are arbitrarily close to optimal a one dimensional heat equation and a problem of acoustic noise control are used to illustrate the algorithm the numerical results are discussed

rigid clusters enumeration animal counting techniques suggest that the fraction of rigid animals among all animals with s sites on a triangular lattice varied roughly as s1 2 0 46 or 0 01 s

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

an efficient algorithm for testing the generic rigidity of graphs in the plane given a structure made up of n sites connected by b bars the problem of recognizing which subsets of sites form rigid units is not a trivial one because of the non local character of rigidity in central force systems even though this is a very old problem of statics no simple algorithms are available for it so the most usual approach has been to solve the elastic equations which is very time consuming for large systems recently an integer algorithm was proposed for this problem in two dimensions using matching methods from graph theory and laman s theorem for two dimensional graphs the method is relatively simple but its time complexity grows as in the worst case and almost as fast on practical cases so that an improvement is highly desirable in this paper we describe a further elaboration of that procedure which relies upon the description of the system as a collection of rigid bodies connected by bars instead of sites connected by bars sets of rigidly connected objects are replaced by a unique body and this is done recursively as more rigid connections between bodies are discovered at larger scales as a consequence of this rescaling transformation our algorithm has much improved average behaviour even when its worst case complexity remains the time complexity of the body bar algorithm is found to scale as for the randomly diluted triangular lattice while the original site bar version scales as for the same problem

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

global regularity criterion for the 3d navier stokes equations involving one entry of the velocity gradient tensor in this paper we provide a sufficient condition in terms of only one of the nine entries of the gradient tensor that is the jacobian matrix of the velocity vector field for the global regularity of strong solutions to the three dimensional navier stokes equations in the whole space as well as for the case of periodic boundary conditions

a newton raphson method for moving average spectral factorization using the euclid algorithm an implementation of the newton raphson approach to compute the minimum phase moving average spectral factor of a finite positive definite correlation sequence is presented each step in the successive approximation method involves a system of linear equations that is solved using either the levinson algorithm backwards the jury stability test or a symmetrized version of the euclid algorithm various properties of the newton raphson map are studied the algorithm is generalized to other symmetries other than with respect to the unit circle the special case of the symmetry with respect to the imaginary axis is presented and related to the routh hurwitz stability test for continuous time transfer function

computations with infinite toeplitz matrices and polynomials we relate polynomial computations with operations involving infinite band toeplitz matrices and show applications to the numerical solution of markov chains of nonlinear matrix equations to spectral factorizations and to the solution of finite toeplitz systems in particular two matrix versions of graeffe s iteration are introduced and their convergence properties are analyzed correlations between graeffe s iteration for matrix polynomials and cyclic reduction for block toeplitz matrices are pointed out the paper contains a systematic treatment of known topics and presentation of new results improvements and extensions

root finding by expansion with independent constraints elimination methods are highly effective for the solution of linear and nonlinear systems of equations but reversal of the elimination principle can be beneficial as well competent incorporation of additional independent constraints and variables or more generally immersion of the original computational problem into a larger task defined by a larger number of independent constraints and variables can improve global convergence of iterative algorithms that is their convergence from the start a well known example is the dual linear and nonlinear programming which enhances the power of optimization algorithms we believe that this is just an ad hoc application of general principle of expansion with independent constraints it should be explored systematically for devising iterative algorithms for the solution of equations and systems of equations and for optimization at the end of this paper we comment on other applications and extensions of this principle presently we show it at work for the approximation of a single zero of a univariate polynomial p of a degree n empirical global convergence of the known algorithms for this task is much weaker than that of the algorithms for all n zeros such as weierstrass durand kerner s root finder which reduces its root finding task to viete s vieta s system of n polynomial equations with n unknowns we adjust this root finder to the approximation of a single zero of p preserve its fast global convergence and decrease the number of arithmetic operations per iteration from quadratic to linear together with computing a zero of a polynomial p the algorithm deflates this polynomial as by product and then could be reapplied to the quotient to approximate the next zero of p alternatively by using m processors that exchange no data one can concurrently approximate up to m zeros of p our tests confirm the efficiency of the proposed algorithms technically our root finding boils down to computations with structured matrices polynomials and partial fraction decompositions our study of these links can be of independent interest e g as by product we express the inverse of a sylvester matrix via its last column thus extending the celebrated result of gohberg and sementsul 1972 22 from toeplitz to sylvester matrix inverses

regularity criteria in terms of the pressure for the three dimensional mhd equations in this paper we consider the cauchy problem for the 3d incompressible mhd equations a regularity criterion by providing sufficient condition in terms of the pressure is established more precisely we show that if p l 0 t l r 3 with 3 2 7 4 and 12 5 4 then any weak solutions u b of the 3d mhd equations is regular on 0 t

elastic property of the self avoiding random walk calculates the end to end elastic susceptibility for the bond bending model on the self avoiding random walk the numerical result shows clearly that the central force term is irrelevant when the bond bending term is present the result also indicates that when the elastic constant of the bond bending term is set equal to infinity the elastic network is governed by the conductivity exponent of the random resistor network

global regularity of the two dimensional incompressible generalized magnetohydrodynamics system abstract in this paper we consider the global regularity of the two dimensional generalized incompressible magnetohydrodynamics system with velocity dissipation exponent 1 4 and magnetic diffusion exponent 1 based on the improved integrability in terms of vorticity this result is a further improvement of very recent works jiu and zhao 2014 and yamazaki 2013 which require 1 3 and 1 therefore our result is more closer to the resolution of the well known global regularity issue on the 2d magnetohydrodynamics system 0 1

nonexistence of self similar singularities in the viscous magnetohydrodynamics with zero resistivity abstract we are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in r n n 2 3 namely the mhd with positive viscosity and zero resistivity in the special case of zero magnetic field the system reduces to the navier stokes equations in r n in this paper we exclude the scenario of finite time singularity in the form of self similarity under suitable integrability conditions on the velocity and the magnetic field we also prove the nonexistence of asymptotically self similar singularity this provides us information on the behavior of solutions near possible singularity of general type as described in corollary 1 1

new progress in real and complex polynomial root finding matrix methods are increasingly popular for polynomial root finding the idea is to approximate the roots as the eigenvalues of the companion or generalized companion matrix associated with an input polynomial the algorithms also solve secular equation qr algorithm is the most customary method for eigen solving but we explore the inverse rayleigh quotient iteration instead which turns out to be competitive with the most popular root finders because of its excellence in exploiting matrix structure to advance the iteration we preprocess the matrix and incorporate newton s linearization repeated squaring homotopy continuation techniques and some heuristics the resulting algorithms accelerate the known numerical root finders for univariate polynomial and secular equations and are particularly well suited for the acceleration by using parallel processing furthermore even on serial computers the acceleration is dramatic for numerical approximation of the real roots in the typical case where they are much less numerous than all complex roots

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

scalars convected by a two dimensional incompressible flow we provide a test for numerical simulations for several two dimensional incompressible flows that appear to develop sharp fronts we show that in order to have a front the velocity has to have uncontrolled velocity growth 2001 john wiley sons inc

optimal vibration control of curved beams using distributed parameter models abstract the design of linear quadratic optimal controller using spectral factorization method is studied for vibration suppression of curved beam structures modeled as distributed parameter models the equations of motion for active control of the in plane vibration of a curved beam are developed firstly considering its shear deformation and rotary inertia and then the state space model of the curved beam is established directly using the partial differential equations of motion the functional gains for the distributed parameter model of curved beam are calculated by extending the spectral factorization method moreover the response of the closed loop control system is derived explicitly in frequency domain finally the suppression of the vibration at the free end of a cantilevered curved beam by point control moment is studied through numerical case studies in which the benefit of the presented method is shown by comparison with a constant gain velocity feedback control law and the performance of the presented method on avoidance of control spillover is demonstrated

on global regularity of 2d generalized magnetohydrodynamic equations abstract in this article we study the global regularity of 2d generalized magnetohydrodynamic equations 2d gmhd in which the dissipation terms are u and b we show that smooth solutions are global in the following three cases 1 2 1 0 1 2 2 2 2 0 we also show that in the inviscid case 0 if 1 then smooth solutions are global as long as the direction of the magnetic field remains smooth enough

global regularity for the 2d mhd equations with mixed partial dissipation and magnetic diffusion abstract whether or not classical solutions of the 2d incompressible mhd equations without full dissipation and magnetic diffusion can develop finite time singularities is a difficult issue a major result of this paper establishes the global regularity of classical solutions for the mhd equations with mixed partial dissipation and magnetic diffusion in addition the global existence conditional regularity and uniqueness of a weak solution is obtained for the 2d mhd equations with only magnetic diffusion

decomposition of fir digital filters for realization via the cascade connection of subfilters a method is presented for decomposing even order linear phase fir filters with distinct roots into the cascade connection of second and fourth order subfilters the technique consists of of finding roots of the z domain filter transfer function by searching a finite region in the complex z plane due to symmetry in the impulse response only the perimeter the real axis and boundary and interior of the upper half of the unit circle need to be searched for real and complex values of roots from which the impulse response coefficients of the corresponding subfilters can be directly determined the root finding algorithm tests for existence of a root at each interval in a finite grid and then utilizes the newton raphson method to refine the final estimate of each root value in the two dimensional 2 d search the cauchy riemann relations are exploited to reduce computations and speed convergence this method has been tested on fir filters with orders ranging to over 120 and has proven effective in decomposing filters to the cascade realization with identical frequency response characteristics an example is presented that illustrates the use of this technique

energy and cross helicity conservation for the three dimensional ideal mhd equations in a bounded domain abstract in this paper we prove the energy and cross helicity conservation of weak solutions to the three dimensional ideal mhd equations in a bounded domain under the interior besov regularity conditions which are exactly same as the three dimensional periodic domain case in 3 and the boundedness and the besov type continuity conditions for both the velocity and magnetic fields near the boundary which seem crucial for the bounded domain case due to the boundary effect note that our besov type continuity conditions near the boundary are consistent with the interior besov regularity conditions

computing theoretical autocovariances of multivariate autoregressive moving average models by using a block levinson method a closed form expression relating the theoretical autocovariances of a multivariate autoregressive moving average arma model to the arma parameters in terms of a system of linear equations has been presented recently using this result and the special hankel plus toeplitz structure of the coefficient matrix obtained after suitable partitioning this paper presents a method for computing multivariate autocovariance functions that is based on a block levinson procedure the method is particularly advantageous for models with high order autoregressive components and or a large number of variables

mesh independence of kleinman newton iterations for riccati equations in hilbert space in this paper we consider the convergence of the infinite dimensional version of the kleinman newton algorithm for solving the algebraic riccati operator equation associated with the linear quadratic regulator problem in a hilbert space we establish mesh independence for this algorithm and apply the result to systems governed by delay equations numerical examples are presented to illustrate the results

synthesis of extremal wavelet generating filters using gaussian quadrature orthogonal wavelets can be generated from finite impulse response quadrature mirror filters these filters are also used in perfect reconstruction filter banks this paper addresses the problem of efficiently synthesizing such filters a class of extremal filters is defined by the property that their magnitude spectrum maximizes an integral criterion it is found that these filters are characterized by their zeros on the unit circle which frequently can be obtained from a set of orthogonal polynomials a family of filters is constructed that minimize the subband aliasing energy and can generate wavelets with an arbitrary number of vanishing moments the algorithm for generating these filters makes use of the levinson recursions gaussian quadrature and a fast version of euclid s algorithm similar to other methods for constructing quadrature mirror filters the spectral factorization of a polynomial is the computationally expensive part of this algorithm

partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations in this paper we study the local behavior of the solutions to the three dimensional magnetohydrodynamic equations we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions it is shown that in some neighborhood of x0 t0 the gradients of the velocity field u and the magnetic field b are locally uniformly bounded in l norm as long as that either the scaled local l2 norm of the gradient or the scaled local total energy of the velocity field is small and the scaled local total energy of the magnetic field is uniformly bounded these estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory as an immediately corollary we can derive an estimates of hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid various partial regularity results are obtained as consequences of our blow up estimates

on the well posedness of the ideal mhd equations in the triebel lizorkin spaces in this paper we prove the local well posedness for the ideal mhd equations in the triebel lizorkin spaces and obtain a blow up criterion of smooth solutions specifically we fill a gap in a step of the proof of the local well posedness part for the incompressible euler equation in chae comm pure appl math 55 654 678 2002

1 d expansion for k core percolation the physics of k core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon examples of such a phenomenon range from orientational ordering in solid ortho para mathrm h 2 mixtures to the onset of rigidity in bar joint networks to dynamical arrest in glass forming liquids unlike ordinary k 1 and biconnected k 2 percolation the mean field k ensuremath geqslant 3 core percolation transition is both continuous and discontinuous i e there is a jump in the order parameter accompanied with a diverging length scale to determine whether or not this hybrid transition survives in finite dimensions we present a 1 d expansion for k core percolation on the d dimensional hypercubic lattice we show that to order 1 d 3 the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability this result suggests that the unusual hybrid nature of the mean field k core transition survives in high dimensions

a new regularity criterion for the 3d incompressible mhd equations in terms of one component of the gradient of pressure abstract in this paper we study the global regularity issue for the 3d incompressible mhd equations it is proved that if the pressure p satisfies 3 p l 0 t l r 3 with 2 3 2 3 and 1 then the corresponding weak solution u b is regular on 0 t

the bond bending model in three dimensions the author discusses the bond bending model in three dimensions he argues that for this model loops are very important in all length scales and the rigidity percolation is non local exhibiting similar behaviour to the central force model

exact relations between elastic and electrical response of d dimensional percolating networks with angle bending forces arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity e and the macroscopic elastic stiffness moduli c e of percolating systems of any dimensionality using the notation e p t c e p t for the critical behavior of a randomly diluted system slightly above the percolation threshold p c p p p c 0 and e p s c e p s for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold p p p c 0 we show that t t 2 and s s where is the percolation correlation length critical exponent p p 0

linear statistical models for stationary sequences and related algorithms for cholesky factorization of toeplitz matrices we review the levinson durbin recursions for computing the cholesky factors of the inverse of a toeplitz correlation matrix r and the schur recursions for computing the cholesky factors of r itself we show that both algorithms may be imbedded in a single vector lattice recursion then depending only on how the initial conditions are set one gets either the levinson durbin or the leroux gueguen recursions for computing reflection coefficients we extend the analysis to treat the toeplitz nonsymmetric case and place the corresponding algorithms into the same framework we also review the relation between the vector lattice recursions and their implementations in a serial lattice structure then we show how the factorizations may be run backwards to compute the cholesky factors and correlations from the reflection coefficients this generalizes a result usually attributed to robinson and treitel one of our main purposes is to emphasize that the levinson durbin recursions for going back and forth between correlations reflection coefficients and autoregressive filter parameters may be replaced with a dual set of recursions for going back and forth between correlations reflection coefficients and moving average filter parameters when the correlation sequence is arma p p then we show how the schur recursions simplify to the morf sidhu kailath algorithm for computing kalman gains finally the msk algorithm may be specialized to the rissanen algorithm for factoring a pure ma correlation sequence

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

mean square error analysis of nonuniform subband adaptive filters for system modeling nonuniform filterbanks have recently been proposed for subband adaptive filters safs however nonuniform safs have not yet been given a thorough performance analysis this paper gives a comprehensive mean square error mse analysis of system modeling nonuniform and degeneratively uniform safs after convergence for a specified filterbank using the equivalent polyphase representation suggested by ono et al minimum mse mmse estimates for the individual subband errors are presented with respect to a given filterbank for finite length fir infinite length causal iir and infinite noncausal adaptive filters using these subband mmse estimators an mmse estimator is derived for the overall fullband error finally the derived mmse estimators are verified by a numerical simulation the intent of this paper is not to compare nonuniform and uniform saf performance but merely to present a unified mathematical methodology to predict their mmses

accelerated approximation of the complex roots and factors of a univariate polynomial the known algorithms approximate the roots of a complex univariate polynomial in nearly optimal arithmetic and boolean time they are however quite involved and require a high precision of computing when the degree of the input polynomial is large which causes numerical stability problems we observe that these difficulties do not appear at the initial stages of the algorithms and in our present paper we extend one of these stages analyze it and avoid the cited problems still achieving the solution within a nearly optimal complexity estimates provided that some mild initial isolation of the roots of the input polynomial has been ensured the resulting algorithms promise to be of some practical value for root finding and can be extended to the problem of polynomial factorization which is of interest on its own right we conclude with outlining such an extension which enables us to cover the cases of isolated multiple roots and root clusters

on the statistics of the estimated reflection coefficients of an autoregressive process the exact statistics of the estimated reflection coefficients for an autoregressive process are difficult to determine however since almost all the common methods for estimating the reflection coefficients are maximum likelihood estimates for large data records the asymptotic distribution of the estimates is multivariate gaussian with a covariance matrix given by the cramer rao bound a recursive means of computing the covariance matrix bound is described simulation results show that the asymptotic expressions are accurate for large data records however for relatively short data records the asymptotic expressions are accurate only for spectra with a small dynamic range

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence