hyponormal operators with finite rank self commutators and quadrature domains this paper studies some classes of pure hyponormal operators with finite rank self commutators satisfying the condition that their spectra are unions of a finite collection of the closures of quadrature domains

the denjoy wolff theorem in cn abstract if d is a bounded and strictly convex domain in c n and f d d is holomorphic and fixed point free then there exists d such that the sequence f n of the iterates of f converges in the compact open topology to the constant mapping taking the value

using combinatorial optimization to design good unit memory convolutional codes a method for designing good unit memory convolutional codes is presented the method is based on the decomposition of the original problem into two easier subproblems that can be formulated as optimization problems and solved by efficient heuristic search algorithms the efficacy of this method is demonstrated by a table containing 33 new unit memory convolutional codes n k with 5

a directed search approach for unit memory convolutional codes a set of heuristic algorithms to numerically search for binary unit memory convolutional codes umc are presented along with a large number of new codes for 2 spl les k spl les 8 and code rate 1 4 spl les r 1 combinatorial optimization is used which involves selecting and then pairwise matching column vectors of the two n k umc tap weight matrices the column selection problem is that of finding the best 2n k binary linear block code bc in this correspondence the best bc generator matrix g is found by successively refining g using directed local exhaustive searches in particular the set of minimum weight codewords are used to find a subset of g to exhaustively search the umc search strategy pairwise matching problem uses a directed local exhaustive search similar to the bc directed search by using the concept of the terminated bc of the umc the heuristic algorithms developed in this correspondence are very robust and converge relatively quickly to the optimal or near optimal umc in addition although it is generally possible to achieve the block code upper bound for free distance we give a class of umcs which cannot achieve this bound

perturbation expansion for a one dimensional anderson model with off diagonal disorder the weak disorder expansion for a random schrodinger equation with off diagonal disorder in one dimension is studied the invariant measure the density of states and the lyapunov exponent are computed the most interesting feature in this model appears at the band center where the differentiated density of states diverges while the lyapunov exponent vanishes the invariant measure approaches an atomic measure concentrated on zero and infinity the results extend previous work of markos to all orders of perturbation theory

bounds on the free distance of systematic convolutional codes asymptotic bounds on the free distance of binary time varying systematic convolutional codes are developed from a unified point of view it is found that this unified approach provides some insight into the relationship between the distances of systematic versus nonsystematic codes it is also helpful from a constructive point of view the free distance bounds of systematic unit memory codes are also discussed

the denjoy wolff theorem for condensing holomorphic mappings if b is the open unit ball of a strictly convex banach space x and f b b is holomorphic condensing with respect to and fixed point free then there exists b such that the sequence lcub fn of the iterates of f converges in the compact open topology to the constant map taking the value

analytic structure of the one dimensional random bond ising model the quenched average of the one dimensional random bond or j ising model in a magnetic field is studied using a technique based on the transformation of a product of random 2 2 matrices to an iterated conformal map this approach allows for the underlying analytic structure of the random matrix product to appear as a natural consequence of the conformal mapping of the extended complex plane the quenched average of the characteristic exponent i e the free energy is obtained by averaging over a specified probability distribution of nearest neighbour coupling the evaluation of the quenched average of the characteristic exponent is performed within the isoentropic approximation the isoentropic approximation treats all bond configurations with the same number of antiferromagnetic domains having the same entropy and enables the enumeration of equivalent configurations combinatorial methods can then be used to express the average over all realizations of the random matrix product as a combinatorial sum the combinatorial sum is evaluated using resummation methods and an explicit expression for the quenched average of the characteristic exponent is thereby obtained for the case of the random bond ising model the explicit expression for the free energy is dependent on constants which are calculated numerically

dynamical localization for the random dimer schrodinger operator we study the one dimensional random dimer model with hamiltonian h v where for all x mathbb z v 2x v 2x 1 and where the v 2x are i i d bernoulli random variables taking the values v v 0 we show that for all values of vand with probability one in the spectrum of his pure point if v 1 and v 1 sqrt 2 the lyapunov exponent vanishes only at the two critical energies given by e v for the particular value v 1 sqrt 2 respectively v sqrt 2 we show the existence of new additional critical energies at e 3 sqrt 2 respectively e 0 on any compact interval inot containing the critical energies the eigenfunctions are then shown to be semi uniformly exponentially localized and this implies dynamical localization for all q 0 and for all ell 2 mathbb z with sufficiently rapid decrease mathop sup limits t r psi i left q right kern 1pt left t right mathop sup limits t left langle p i left h omega right psi t left x right q p i left h omega right psi t right rangle infty here psi t e ih omega t psi and pi h is the spectral projector of h onto the interval i in particular if v 1 and v sqrt 2 these results hold on the entire spectrum so that one can take i h

local correlations in one and two dimensional disordered systems in one dimensional disordered systems all states are localized but when you add local correlations such as a dimer impurity some states become delocalized in this paper a wide range of correlations are studied leading to a delocalization of states moreover second nearest neighbour models which also have extended states are investigated finally a new approach to the case of two dimensions is presented using a matrix transfer technique where explicit extended states are found

quasi cyclic unit memory convolutional codes unit memory convolutional codes with generator matrices which are composed of circulant submatrices are introduced this structure facilitates the analysis of efficient search for good codes equivalences among such codes and some of the basic structural properties are discussed in particular catastrophic encoders and minimal encoders are characterized and dual codes treated further various distance measures are discussed and a number of good codes some of which result from efficient computer search and some of which result from known block codes are presented

concatenated codes with convolutional inner codes the minimum distance of concatenated codes with reed solomon outer codes and convolutional inner codes is studied for suitable combinations of parameters the minimum distance can be lower bounded by the product of the minimum distances of the inner and outer codes for a randomized ensemble of concatenated codes a lower bound of the gilbert varshamov type is proved

inequalities for proper contractions and strictly dissipative operators abstract some inequalities for proper contractions and strictly dissipative operators on a hilbert space are proved these inequalities for operators are related to the classical harnack s inequalities for analytic functions with a positive real part

perturbation theory for the random dimer model the authors study a one dimensional tight binding model with a random potential taking two values or nu with the restriction that on pairs of two neighbouring sites the potentials take the same value this random dimer model proposed by dunlap phillips and wu 1990 has a vanishing lyapunov exponent for the energy e or nu they compute the lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism

bounded distance decoding of unit memory codes we discuss minimum distance decoding of convolutional codes the relevant distance functions are defined and the set of correctable error patterns is described by a sequence of weight constraints decoding methods for error patterns of bounded weight are described and it is demonstrated that these methods offer a favorable combination of performance and complexity exact values and upper bounds on the error probability are calculated from finite state models of the decoding process

bounded minimum distance decoding of unit memory codes we propose an algorithm for bounded minimum distance decoding of partial unit memory codes up to half the designed extended row distance it makes use of a reduced trellis with the nodes found by bounded minimum distance decoding of the block codes used in the unit memory code the results can be extended to general multimemory codes the complexity of this algorithm is upper bounded by 2 d sub 1sup r 2d sub spl alpha times the complexity of the bounded minimum distance decoder of the block codes in the unit memory code here d sub spl alpha is the linear increase of the designed extended row distance d sub isup r

iteration of holomorphic maps in hilbert spaces abstract previous work gong ning chen j math anal appl 98 1984 305 313 on iteration of holomorphic maps of cn is continued the purpose of this note is to extend results given in the above mentioned reference to the case of complex hilbert spaces other comments are appended

strongly mds convolutional codes maximum distance separable mds convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree in this paper a class of mds convolutional codes is introduced whose column distances reach the generalized singleton bound at the earliest possible instant such codes are called strongly mds convolutional codes they also have a maximum or near maximum distance profile the extended row distances of these codes will also be discussed briefly

symbolic dynamics of fully developed chaos i statistics and characteristics of two symbol sequences abstract by discerning levels k of statistical description it is shown that the level k boltzmann entropy h k log possibilities on level k of two symbol sequences equals the information theoretical conditional entropy ks k k 1 s k 1 with s k the average shannon entropy on level k a mixing measure is introduced by means of an appropriate demixing procedure from the properties of the two symbol sequence an expression for a symbolic 2 x 2 correlation matrix is derived

bounds on distances and error exponents of unit memory codes binary unit memory codes originally introduced by lee are investigated a few examples of constant unit memory codes are given and bounds on the distance profile and the free distances are discussed for time varying codes asymptotic lower bounds on the distance profile and the free distance are given the error probability for the codes used on a memoryless binary input output symmetric channel is asymptotically upper bounded the asymptotic results for the free distance and the error probability which are in some respects better than for conventional convolutional codes are interpreted by forney s inverse concatenation construction

random iterations fixed points and invariant crf horospheres in complex banach spaces abstract for holomorphic noncontractive maps on not necessarily bounded domains in complex banach spaces we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations in particular we show that the problem concerning the existence of the horospheres determined by caratheodory reiffen finsler pseudometrics defined on unbounded domains has the solution and we prove new results of type of julia s lemma and wolff s theorem

correlation induced metal insulator transition in the one dimensional anderson model abstract we study the nature of the electronic states in tight binding one dimensional models with long range correlated disorder in particular we study both diagonal and off diagonal chains the energies are considered to be in such a sequency to describe the trace of a fractional brownian motion with a specified spectral density s k 1 k using a renormalization group technique we show that for random on site energy sequences with anti persistent increments 2 the lyapunov coefficient inverse localization length vanishes within a finite range of energy values revealing the presence of an anderson like metal insulator transition in the case of off diagonal disorder a phase of delocalized states becomes stable for any 1

active distances for convolutional codes a family of active distance measures for general convolutional codes is defined these distances are generalizations of the extended distances introduced by thommesen and justesen 1983 for unit memory convolutional codes it is shown that the error correcting capability of a convolutional code is determined by the active distances the ensemble of periodically time varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble the active distances are very useful in the analysis of concatenated convolutional encoders

random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces conditions which guarantee the uniform convergence of random iterations of holomorphic contractions on unbounded domains in complex hausdorff locally convex and sequentially complete topological vector spaces are established also conditions concerning the convergence of random iterations of weaker contractions in hausdorff uniform spaces are given

unit memory codes for continuous phase modulation in an awgn channel the combination of unit memory codes and continuous phase modulation in an additive white gaussian noise channel is considered our motivation is based on the fact that when rouanne and costello s 1988 free distance lower bound is applied to unit memory codes an improved lower bound is obtained specific constructions are considered for 4 level modulation schemes with full response and weak partial response heuristic design rules are used for defining the subsets of codes within which an exhaustive search is conducted the coding gains of the best codes within these subsets are better than those of best previously known multi memory codes

reflectionless modes in chains with large size homogeneous impurities the authors study the spectra and localization properties of tight binding chains with randomly distributed binary blocks of arbitrary size m one having site energies epsilon a and the other epsilon b respectively they demonstrate that for block size m greater than one and delta mod epsilon a epsilon b less than a critical value delta c m perfect transmission resonance modes exist in the band their number is proportional to m and they occur via dominant 1 e2 divergencies of the localization length no transmission is found for delta delta c m the results are understood by solving exactly the scattering problem from a single homogeneous impurity block of arbitrary size m in the limit of hard impurities m to infinity transmission stops only when delta delta c infinity 4v v being the intersite matrix element that is when the pure a and b bands become detached

the nature of electronic states in a disordered chain with long ranged hopping amplitudes abstract in this work we investigate the nature of the electronic states in a one dimensional tight binding model with on site energetic disorder and long ranged hopping amplitudes these are assumed to follow a power law decay behavior with distance in the form h r 1 r with 1 direct numerical diagonalization finite size scaling and a spectral statistics analysis show that as 1 the localization length exhibits an exponential growth as the upper band edge is approached strong finite size corrections are present in this regime near the upper band edge with the one electron states displaying a strong level repulsion even at large although finite chains

singular behavior of the density of states and the lyapunov coefficient in binary random harmonic chains we study the integrated density of statesh 2 of a chain of harmonic oscillators with a binary random distribution of the masses we show in particular that there is a dense set of values of the squared frequency for which the differenceh 2 h 2 has a singularity of the type 2 multiplied by a periodic function of ln where the exponent and the period depend continuously on 2 in the region where 1 2 h is not differentiate on a dense set of points the same type of singularities is also present in the lyapunov coefficient

convolutional codes in rank metric with application to random network coding random network coding recently attracts attention as a technique to disseminate information in a network this paper considers a noncoherent multishot network where the unknown and time variant network is used several times in order to create dependence between the different shots particular convolutional codes in rank metric are used these codes are so called partial unit memory p um codes i e convolutional codes with memory one first distance measures for convolutional codes in rank metric are shown and two constructions of p um codes in rank metric based on the generator matrices of maximum rank distance codes are presented second an efficient error erasure decoding algorithm for these codes is presented its guaranteed decoding radius is derived and its complexity is bounded finally it is shown how to apply these codes for error correction in random linear and affine network coding

absence of localization in disordered systems with local correlation in an early work by dunlap et al 1990 it was conjectured using a matrix transfer approach that diagonal disordered systems with local correlation dimer models exhibit an absence of anderson localization in this letter we find explicitly these delocalized states and energies using a suitable unitary transformation and the symmetries related to the model moreover we expand these states around the critical energy and find a new 1 square root e ec divergence