exact ltp representation of the generalized periodic reference fxlms algorithm the analysis of the filtered x least mean square fxlms algorithm can be based either on a stochastic or deterministic approach one of the drawbacks of the stochastic analysis is that it relies on several assumptions which are not justified if the reference signal is time periodic to overcome these limitations several deterministic methods have been suggested however useful results have been reported only for setups with certain filter length secondary path model or reference signal in this paper an exact linear time periodic ltp representation is proposed assuming only that the reference is synchronously sampled the representation is derived for a general fxlms system which also covers the multichannel topology of several parallel filters and its common narrowband modification the representation is found to have a linear time invariant lti form if the filter length is suitably chosen the usability of the method is demonstrated in a numerically computed example by comparing it to an approximate lti model

a confluence matrix condition for exponential error convergence in overparametrized adaptive systems many practical adaptive feedforward systems are overparametrized and for this reason will not satisfy persistent excitation pe conditions for these systems a weaker pe condition is proposed under which it is shown that the while parameters may not converge the cancellation error the error between the desired and estimated outputs still converges exponentially bounds are given on the exponential rate of convergence useful for understanding the various tradeoffs and for systematic optimization and design purposes the convergence rate is determined by properties of the confluence matrix defined herein that plays a role similar to that played by the autocorrelation matrix for fully pe systems as a case study the structure of the confluence matrix is examined in detail for adaptive systems with a tap delay line tdl regressor and sinusoid excitation

universal role of correlation entropy in critical phenomena in statistical physics if we divide successively an equilibrium system into two parts we will face a situation that to a certain length the physics of a subsystem is no longer the same as the original one the extensive property of the thermal entropy s a boolean or b s a s b is then violated this observation motivates us to introduce a concept of correlation entropy between two points as measured by the mutual information in information theory to study the critical phenomena a rigorous relation is established to display some drastic features of the non vanishing correlation entropy of a subsystem formed by any two distant particles with long range correlation this relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena we also verify these analytical studies in terms of two well studied models for both the thermal and quantum phase transitions the two dimensional ising model and the one dimensional transverse field ising model therefore the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory

steady state mse convergence of lms adaptive filters with deterministic reference inputs with applications to biomedical signals we analyze the steady state mean square error mse convergence of the lms algorithm when deterministic functions are used as reference inputs a particular adaptive linear combiner is presented where the reference inputs are any set of orthogonal basis functions the adaptive orthogonal linear combiner aolc several authors have applied this structure always considering in the analysis a time average behavior over one signal occurrence we make a more precise analysis using the deterministic nature of the reference inputs and their time variant correlation matrix two different situations are considered in the analysis orthogonal complete expansions and incomplete expansions the steady state misadjustment is calculated using two different procedures with equivalent results the classical one analyzing the transient behavior of the mse and as the residual noise at the output of the equivalent time variant transfer function of the system the latter procedure allows a very simple formalism being valid for colored noise as well the derived expressions for steady state misadjustment are contrasted with experimental results in electrocardiographic ecg signals giving exact concordance for any value of the step size

wigner analysis and casimir operators of sa 4 r in theories involving gravity including qcd generated gravitylike effects in hadrons sa 4 r plays a role its single casimir invariant and that of its sa 2 r and sa 3 r subgroups are evaluated the group orbits are studied and the unitary irreducible representations are classified

the residual spectrum of an inner form of sp_8 supported in the minimal parabolic subgroup the part of the residual spectrum of an inner form of the split group sp 8 supported in the minimal parabolic subgroup is decomposed since the considered inner form is not quasi split the normalization of the standard intertwining operators required for the calculation of the poles of the eisenstein series is out of the reach of the langlands shahidi method hence a normalization technique based on the transfer of the plancherel measure between the split group and its inner form is applied the obtained decomposition reveals certain features of the residual spectrum of the inner form which do not appear for the split group

sinusoidal interference rejection analysis of an lms adaptive feedforward controller with a noisy periodic reference this paper applies a new vector subspace model to determine the non wiener solutions of the lms algorithm when the reference input is an arbitrary noisy periodic signal the lms weights are modeled as a deterministic time varying mean plus a zero mean fluctuating part for the mean weight each harmonic component of the periodic reference is shown to excite only a two dimensional 2 d subspace of the n dimensional tap weight space the fluctuating part of the weight is due to the reference noise that excites the full n dimensional space the power spectrum of the error is computed using the correlation function of the weight fluctuations the error is shown to be primarily the sum of a white noise and the canceled periodic residual for an independent noise vector model when the effects of the tapped delay line are incorporated in the model the noise becomes colored with a spectrum centered about the canceled sinusoidal frequency this weight model significantly simplifies the understanding of the non wiener behavior and can be applied to active noise cancellation problems when filters appear in the cancellation loop

spinor fields and the gl 4 r gauge structure in the nonsymmetric theory of gravitation the spinor structure associated with the local gauge group gl 4 r of the nonsymmetric gravitation theory ngt is based on a spinor wave equation constructed from a vierbein a gl 4 r spin connection and the infinite dimensional irreducible representations of the universal covering group sl 4 r of the noncompact group sl 4 r the multiplicity free irreducible representations of sl 4 r correspond to bivalued spinorial representations of sl 4 r that contain an infinite number of half odd integer spin particles by adjoining the translations t4 the extended group a t4 gl 4 r replaces the poincare group p the properties of the mass spectrum are obtained from an infinite component wave equation and the physical spinor field consists of an infinite sum of finite nonunitary representations of the lorentz group

all sl 3 r ladder representations all unitary and nonunitary ladder multiplicity free with respect to the so 3 maximal compact subgroup representations of the double covering group sl 3 r of the sl 3 r group are cataloged and presented explicitly the list of nonunitary representations is corrected and completed and a new insight concerning the j 2 ladder representation starting with j 3 2 is obtained

non wiener solutions for the lms algorithm a time domain approach a time domain analysis of the lms algorithm is presented for a sinusoidal deterministic reference input for the sinusoidal reference input only the n dimensional time varying linear matrix recursion for the weight vector is solved using a 2 d orthogonal subspace decomposition using this weight vector solution it is shown that there exists a linear time invariant relationship between the desired input and the filter output

density matrix renormalization group study of the correlation function of the bilinear biquadratic spin 1 chain using the recently developed density matrix renormalization group approach we study the correlation function of the spin 1 chain with quadratic and biquadratic interactions this allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue combining our results with other studies we predict three phases in the region where the quadratic and biquadratic terms are both positive

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

singular vectors of representations of quantum groups the author gives explicit formulae for singular vectors of verma modules over uq g they give the general formula for g an for some cases when g dn and for some rank two subalgebras of g not an dn for this he uses a special basis of uq g where g is the negative root subalgebra of g which was introduced in his earlier work on the case q 1 this basis seems more economical than the poincare birkhoff witt type of basis used by malikov feigin and fuchs 1986 for the construction of singular vectors of verma modules in the case q 1 furthermore this basis turns out to be part of a general basis introduced recently for other reasons by lusztig 1988 for uq b where b is a borel subalgebra of g

spinorial infinite equations fitting metric affine gravity two different approaches are used to construct infinite component spinor equations based on the multiplicity free irreducible representations of sl 4 r these manifield equations are sl 2 c invariant they exist in special relativity and can directly be coupled to gravitation in the metric affine theory i e in einstein s general relativity with nonpropagating torsion and nonmetricity in the first approach the maximal compact subgroup s 4 of sl 4 r is physical a vector operator x is constructed directly in the infinite dimensional reducible representation ddisc 1 2 0 ddisc 0 1 2 in the second approach sl 2 c and a vector operator are embedded directly in sl 4 r via the dirac representation a manifield equation is then constructed in a manner analogous to the majorana equation by taking an infinite dimensional irreducible multiplicity free representation of sl 4 r spinorial in j1 in the j1 j2 reduction over s 4 both manifields can fit the observed ma

residual automorphic forms and spherical unitary representations of exceptional groups arthur has conjectured that the unitarity of a number of representations can be shown by nding appropriate automorphic realizations this has been veried for classical groups by mglin and for the exceptional chevalley group g2 by kim in this paper we extend their results on spherical representations to the remaining exceptional groups e6 e7 e8 and f4 in particular we prove arthur s conjecture that the spherical constituent of an unramied principal series of a chevalley group over any local eld of characteristic zero is unitarizable if its langlands parameter coincides with half the weighted marking of a coadjoint nilpotent orbit of the langlands dual lie algebra

a general theory of linear time invariant adaptive feedforward systems with harmonic regressors establishes necessary and sufficient conditions for an adaptive system with a harmonic regressor i e a regressor comprised exclusively of sinusoidal signals to admit an exact linear time invariant lti representation these conditions are important because a large number of adaptive systems used in practice have sinusoidal regressors and the stability and performance of such systems having lti representations can be completely analyzed by well known methods the theory is extended to applications where the lti conditions do not hold in which case the harmonic adaptive system can be written as the parallel connection of a purely lti subsystem and a linear time varying ltv subsystem an explicit upper bound is established on the induced two norm of the ltv block which allows systematic treatment using emerging robust control methods applicable to lti systems with norm bounded ltv perturbations

elementary representations and intertwining operators for su 2 2 i the structure of the group su 2 2 and of its lie algebra is studied in detail the results will be applied in subsequent parts devoted to the explicit construction of elementary representations of su 2 2 induced from different parabolic subgroups and of the intertwining operators between these representations a summary of some results of parts ii and iii is given

entropy energy and negativity in fermi resonance coupled states of substituted methanes several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities the dynamics of entropy energy and negativity is studied for fermi resonance coupled vibrations in substituted methanes with three kinds of initial mixed states which are the mixed density matrices of binomial states thermal states and squeezed states on two vibrational modes respectively it is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti correlated in the same oscillatory frequency so do the energies for each kind of state with small magnitudes whereas the entropies exhibit positive correlations with the corresponding energies furthermore for small magnitudes quantum mutual entropy is positively correlated with the interacting energy analytic forms of entropies and energies are provided with initial conditions in which they are stationary and the agreement between analytic and numerical simulations is satisfactory the dynamical entanglement measured by negativity is examined for those states and conditions it is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes and the time averaged negativity has the minimal value under the conditions of stationary entropies and energies moreover negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes those are useful for molecular quantum information processing and dynamical entanglement

on overline gl 4 mathbb r covariant extensions of the dirac equation infinite component generalizations of both massless and massive dirac equations are constructed which are covariant with respect to the double covering of the general linear group in four dimensions these generalized dirac equations can be made covariant with respect to the full diffeomorphism group of the spacetime manifold by replacing ordinary derivatives by covariant derivatives in the usual way

an sl 4 r lie algebraic treatment of the first family of poschl teller potentials an sl 4 r dynamical potential algebra containing the so 4 potential algebra is constructed for the two parameter poschl teller potentials of the first kind for this purpose the relation between the wigner rotation matrices and the solutions of the first poschl teller equation is used explicit expressions are given for the sl 4 r generators as well as for their action on the normalised solutions all the hamiltonian eigenstates corresponding to the family of potentials with quantised potential strengths m m differing by integers are proved to belong to a single sl 4 r unitary irreducible representation of the ladder series for integral values of m and m the latter is dladd 0 0 eta while for half integral values it is dladd 1 2 1 2 eta where eta is some real parameter both irreducible representations are also shown to be characterised by generalised young pattern labels pqr0 where p 2 1 2i eta and q r 0

algebra and physics of the unitary multiplicity free representations of sl 4 r the systematics of the multiplicity free unitary irreducible representations of sl 4 r are restudied and an amended list is presented an automorphism essential to the physical application for particles and fields in minkowski space is described

novel fxlms convergence condition with deterministic reference a novel analysis of fxlms convergence when the reference signal is deterministic is presented in this paper the simple case of a sinusoidal reference is considered first to be later extended to any combination of multiple sinusoids in both cases we derive an upper bound for the algorithm step size which ensures convergence in the derivation of this result there is no need of any of the usual approximations such as independence between reference and weights or slow convergence which are not suitable for deterministic references instead we consider the common cases where the adaptive system shows linear time invariant behavior the upper bound obtained for the step size is in good agreement with empirical measurements

structural analysis and elementary representations of sl 4 r and gl 4 r and their covering groups the structure of the groups sl 4 r and gl 4 r and their universal cover ing groups sl 4 r and gl 4 r respectively and lie algebras sl 4 r and gl 4 r respectively are studied the parabolic subgroups and subalgebras are identified and the cuspidal parabolic subgroups singled out the iwasawa and bruhat decompositions are given explicitly all elementary representations er of sl 4 r are explicitly given in two equivalent realizations using the preceding detailed structural analysis the sl 4 r constructions are used for the explicit realization of all er of sl 4 r gl 4 r and gl 4 r the results shall be applied among other things elsewhere for the construction of all irreducible representations of the above groups

an external approach to unitary representations the principal ideas of harmonic analysis on a locally compact group g which is not necessarily compact or commutative were developed in the 1940 s and early 1950 s in this theory the role of the classical fundamental harmonics is played by the irreducible unitary representations of g the set of all equivalence classes of such representations is denoted by and is called the dual object of g or the unitary dual of g since the 1940 s an intensive study of the foundations of harmonic analysis on complex and real reductive groups has been in progress for a definition of reductive groups the reader may consult the appendix at the end of the second section the motivation for this development came from mathematical physics differential equations differential geometry number theory etc through the 1960 s progress in the direction of the plancherel formula for real reductive groups was great due mainly to harish chandra s monumental work while at the same time the unitary duals of only a few groups had been parametrized with f mautner s work ma a study of harmonic analysis on reductive groups over other locally compact non discrete fields was started we shall first describe such fields in the sequel a locally compact non discrete field will be called a local field if we have a non discrete absolute value on the field q of rational numbers then it is equivalent either to the standard absolute value and the completion is the field r of real numbers or to a p adic absolute value for some prime number p for r 2 q write r pa b where a and b are integers and neither a nor b are divisible by p then the p adic absolute value of r is jrjp p a completion of q with respect to the p adic absolute value is denoted by qp it is called a field of p adic numbers each finite dimensional extension f of qp has a natural topology of a vector space over qp with this topology f becomes a local field the topology of f can be also introduced with an absolute value which is denoted by j jf in the fifth section we shall fix a natural absolute value the fields of real and complex numbers together with the finite extensions of p adic numbers exhaust all local fields of characteristic zero up to isomorphisms we let f be a finite field denote by f x the field of formal power series over f elements of this field are series of the form f p n k anx an 2 f for some integer k fix q 1

entropy correlation and entanglement for mixed states in an algebraic model as an alternative with potential connections to actual experiments other than the systems more usually used in the field of entanglement the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well established algebraic model with parameters extracted from fitting to highly excited spectral experimental results for molecules h2o and so2 is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode for a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti correlation and the linear entropy of each mode is positively correlated with the negativities just for the mixed squeezed states with small parameters in h2o while they do not display any correlation in other cases for the mixed squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy the differences in the linear entropy and the negativities between h2o and so2 are discussed as well those are useful for molecular quantum computing and quantum information processing

critical behaviors of mutual information in the one dimensional spin 1 bilinear biquadratic model the critical behaviors of the mutual information in the one dimensional spin 1 bilinear biquadratic model are studied it is found that all the quantum phase transition points including the order disorder ones and the infinite order ones in the system can be quantified from the singularity analysis of the mutual information of two sites with the longest distance because the mutual information captures the correlation properties about the critical fluctuations more interestingly the special structure of the wavefunction and the special symmetric property of the system can be indicated by the entropy correlation behaviors the finite size scaling laws of the mutual information and its derivative are also studied