the use and efficiency of the theorems of structural variation for finite element analysis this paper describes how the theorems of structural variation may be used in finite element analysis the efficiency of the theorems is examined and their application to structural and geotechnical problems illustrated

equivalence of hardy submodules generated by polynomials abstract in this paper we obtain a complete classification under unitary equivalence for hardy submodules on the polydisk which are generated by ideals of polynomials let i be an ideal of polynomials in n variables since i is generated by finitely many polynomials i has a greatest common divisor p so i can be uniquely written as i p l which is called the beurling form of i let i 1 p 1 l 1 i 2 p 2 l 2 we prove that i 1 and i 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n and p 1 l 1 p 1 l 2 consequently two principal submodules p 1 and p 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n furthermore we give a complete similarity classification for submodules generated by homogeneous ideals finally we point out that in the case of the hardy module on the unit ball i 1 and i 2 are unitarily equivalent if and only if they are equal if i 1 and i 2 are homogeneous ideals then i 1 and i 2 are quasi similar if and only if i 1 i 2

on the support of mse optimal fixed rate scalar quantizers this paper determines how the support regions of optimal and asymptotically optimal fixed rate scalar quantizers with respect to mean squared error depend on the number of quantization points n and the probability density of the variable being quantized it shows that for asymptotic optimality it is necessary and sufficient that the support region grow fast enough that the outer or overload distortion decreases as o 1 n sup 2 formulas are derived for the minimal support of asymptotically optimal quantizers for generalized gamma densities including gaussian and laplacian interestingly these turn out to be essentially the same as for the support of optimal fixed rate uniform scalar quantizers heuristic arguments are then used to find closed form estimates for the support of truly optimal quantizers for generalized gamma densities these are found to be more accurate than the best prior estimates as computed by numerical algorithms they demonstrate that the support of an optimal quantizer is larger than the minimal asymptotically optimal support by a factor depending on the density but not n and that the outer distortion of optimal quantizers decreases as 1 n sup 3

design and analysis of optimal noisy channel quantization with random index assignment this paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance given a tandem source channel coding system with vector quantization block channel coding and random index assignment a closed form formula is first derived for computing the average end to end distortion eed of the system which reveals a structural factor called the scatter factor of a noisy channel quantizer based on this formula we propose a noisy channel quantization design method by minimizing the eed experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the eed when compared with quantizers designed separately without reference to channel conditions which reveals a practical and effective design for noisy channel quantization as to simplify the channel model by considering a random index assignment furthermore we have presented the high rate asymptotic analysis of the eed for the tandem system while convergence analysis of the iterative algorithm is included in the appendix

essentially normal homogeneous quotient modules on the polydisc abstract in the present paper we give a complete characterization of all essentially normal homogeneous quotient modules of the hardy space on the unit polydisc it turns out that our approach also applies to quotients of weighted bergman modules

optimal quantizer design for noisy channels an approach to combined source channel coding we present an analysis of the zero memory quantization of memoryless sources when the quantizer output is to be encoded and transmitted across a noisy channel necessary conditions for the joint optimization of the quantizer and the encoder decoder pair are presented and an iterative algorithm for obtaining a locally optimum system is developed the performance of this locally optimal system obtained for the class of generalized gaussian distributions and the binary symmetric channel is compared against the optimum performance theoretically attainable using rate distortion theoretic arguments as well as against the performance of lloyd max quantizers encoded using the natural binary code and the folded binary code it is shown that this optimal design could result in substantial performance improvements the performance improvements are more noticeable at high bit rates and for broad tailed densities

performance of quantized equal gain transmission with noisy feedback channels in this paper new results and insights are derived for the performance of multiple input single output systems with beamforming at the transmitter when the channel state information is quantized and sent to the transmitter over a noisy feedback channel it is assumed that there exists a per antenna power constraint at the transmitter hence the equal gain transmission egt beamforming vector is quantized and sent from the receiver to the transmitter the loss in received signal to noise ratio snr relative to perfect beamforming is analytically characterized and it is shown that at high rates the overall distortion can be expressed as the sum of the quantization induced distortion and the channel error induced distortion and that the asymptotic performance depends on the error rate behavior of the noisy feedback channel as the number of codepoints gets large the optimum density of codepoints also known as the point density that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel i e the uniform density the binary symmetric channel with random index assignment is a special case of the analysis and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming the accuracy of the theoretical expressions obtained are verified through monte carlo simulations

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

structural modifications simulated by virtual distortions a numerical strategy for the simulation of structural modifications by virtual distortions is proposed two cases of structural modification are considered the first concerns modifications of material distribution and the second modifications of local constitutive relations e g unilateral constraints for stresses or deformations a formaulation of the fundamental equations of the simulation method is presented these equations are applicable to the general structural modification problem of a truss like structure then numerical algorithms which refer to particular applications such as progressive collapse analysis or the analysis of structures with gaps are discussed the versatility of the method is illustrated with a number of examples and the computational advantages of structural modification by the virtual distortion method are discussed

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

quantization of memoryless and gauss markov sources over binary markov channels joint source channel coding for stationary memoryless and gauss markov sources and binary markov channels is considered the channel is an additive noise channel where the noise process is an mth order markov chain two joint source channel coding schemes are considered the first is a channel optimized vector quantizer optimized for both source and channel the second scheme consists of a scalar quantizer and a maximum a posteriori detector in this scheme it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise these two schemes are then compared against two schemes which use channel interleaving numerical results show that the proposed schemes outperform the interleaving schemes for very noisy channels with high noise correlation gains of 4 5 db in signal to noise ratio are possible

essential normality of polynomial generated submodules hardy space and beyond abstract recently douglas and wang proved that for each polynomial q the submodule q of the bergman module generated by q is essentially normal 11 using improved techniques we show that the hardy space analogue of this result holds and more

tradeoff between source and channel coding on a gaussian channel consider a system that quantizes and encodes analog data for transmission across an additive noise gaussian channel to minimize distortion the channel code rate must be chosen to optimally allocate the available transmission rate between lossy source coding and block channel coding we establish tight upper and lower bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a gaussian channel thus extending some recently obtained results for the binary symmetric channel the upper hounds are obtained by averaging whereas the lower bounds are uniform over all possible index assignments analytic expressions are derived for large and small signal to noise ratios and also for large source vector dimension as in the binary symmetric channel the optimal channel code rate is often substantially smaller than the channel capacity and the distortion decays exponentially with the number of channel uses exact exponents are derived

bounds on the performance of vector quantizers under channel errors vector quantization vq is an effective and widely known method for low bit rate communication of speech and image signals a common assumption in the design of vq based communication systems is that the compressed digital information is transmitted through a perfect channel under this assumption quantization distortion is the only factor in output signal fidelity moreover the assignment of channel symbols to the vq reconstruction vectors is of no importance however under physical channels errors may be present causing degradation in overall system performance in such a case the effect of channel errors on the coding system performance depends on the index assignment of the reconstruction vectors the index assignment problem is a special case of the quadratic assignment problem qap and is known to be np complete for a vq with n reconstruction vectors there are n possible assignments meaning that an exhaustive search over all possible assignments is practically impossible to help the vq designer we present in this correspondence lower and upper bounds on the performance of vq systems under channel errors over all possible assignments the bounds coincide with a general bound for the qap nevertheless the proposed derivation allows us to compare the bounds with published results on vq index assignment a related expression for the average performance is also given and discussed special cases and numerical examples are given in which the bounds and average performance are compared with index assignments obtained by known algorithms

on the design of mean square error channel coding systems using cyclic codes channel coding systems that employ linear block codes can be designed according to a mean square error criterion the optimum encoder and decoder pair is determined by selecting special elements in a generalized frequency domain based upon the values of key parameters called ratio weights systems may be designed that employ either hard or soft decision variables in the decoder when cyclic codes are used a minimal ideal decomposition of the code space shows that the ratio weights possess constant values on certain subsets in the frequency domain this permits a drastic reduction in the number of ratio weights that need to be computed for a cyclic code with t minimal ideals this design procedure narrows the search for constancy subsets of the ratio weights to 2 t 1 subsets of the general space only one ratio weight needs to be computed for each constancy subset

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

an analytical investigation of shape control of large space structures by applied temperatures an analytical procedure for the static shape control of flexible space structures subjected to thermal distortions is developed which is based on prescribing temperatures in control elements having much higher coefficients of thermal expansion than the main structure the temperatures at the control elements are defined so as to minimize the overall thermal distortion of the structure from its ideal shape and a matrix equation is obtained which can be solved for the set of optimum control temperatures a formulation of the procedure for continuous structures governed by differential equations and a formulation for discrete finite element modeled structures governed by matrix equations are presented the equations from the continuous formulation are employed for the shape control of a simple beam distorted by nonuniform heating and the discrete formulation is applied in a general purpose finite element structural analysis computer program for the shape control of a 750 m radiometer antenna reflector dish subjected to orbital heating a reduction in thermal distortion by a factor of nearly 50 was obtained with the use of only seven control elements results for four different sets of control locations for the antenna are presented in which reductions in distortion of up to a factor of four were obtained

the elastic plastic analysis of frames by the theorems of structural variation the theorems of structural variation for rigidly jointed frames are extended to cover the nonlinear elastic plastic analysis of frames to collapse strain hardening and other material changes are included in the analysis it is shown that the entire load deflection history of a frame following the successive formation of plastic hinges up to and including collapse is obtained from a single initial elastic analysis the manner in which these theorems are used to insert real or plastic hinges to a frame is presented and details of the manual calculations involved in the elastic plastic analysis of a portal is given to demonstrate the simplicity of the method this is followed by a comparison of the results with those obtained experimentaly by baker and charlton the versatility of the method is then demonstrated by altering the shape of a frame before its elastic plastic analysis

a harmonic analysis approach to essential normality of principal submodules guo and the second author have shown that the closure i in the drury arveson space of a homogeneous principal ideal i in c z1 zn is essentially normal in this note the authors extend this result to the closure of any principal polynomial ideal in the bergman space in particular the commutators and cross commutators of the restrictions of the multiplication operators are shown to be in the schatten p class for p n the same is true for modules generated by polynomials with vector valued coefficients further the maximal ideal space xi of the resulting c algebra for the quotient module is shown to be contained in z i bn where z i is the zero variety for i and to contain all points in bn that are limit points of z i bn finally the techniques introduced enable one to study a certain class of weight bergman spaces on the ball

beurling type quotient modules over the bidisk and boundary representations this paper mainly concerns beurling type quotient modules of h2 d2 over the bidisk by establishing a theorem of function theory over the bidisk it is shown that a beurling type quotient module is essentially normal if and only if the corresponding inner function is a rational inner function having degree at most 1 1 furthermore we apply this result to the study of boundary representations of toeplitz algebras over quotient modules it is proved that the identity representation of c sz sw is a boundary representation of b sz sw in all nontrivial cases this extends a result of arveson to toeplitz algebras on beurling type quotient modules over the bidisk cf w arveson subalgebras of c algebras acta math 123 1969 141 224 w arveson subalgebras of c algebras ii acta math 128 1972 271 308 the paper also establishes k homology defined by beurling type quotient modules over the bidisk

hilbert polynomials and arveson s curvature invariant abstract we define and study hilbert polynomials for certain holomorphic hilbert spaces we obtain several estimates for these polynomials and their coefficients our estimates inspire us to investigate the connection between the leading coefficients of hilbert polynomials for invariant subspaces of the symmetric fock space and arveson s curvature invariant for coinvariant subspaces we are able to obtain some formulas relating the curvature invariant with other invariants in particular we prove that arveson s version of the gauss bonnet chern formula is true when the invariant subspaces are generated by any polynomials

alphabet constrained data compression the optimal data compression problem is posed in terms of an alphabet constraint rather than an entropy constraint solving the optimal alphabet constrained data compression problem yields explicit source encoder decoder designs which is in sharp contrast to other approaches the alphabet constrained approach is shown to have the additional advantages that 1 classical waveform encoding schemes such as pulse code modulation pcm differential pulse code modulation dpcm and delta modulation dm as well as rate distortion theory motivated tree trellis coders fit within this theory 2 the concept of preposterior analysis in data compression is introduced yielding a rich new class of coders and 3 it provides a conceptual framework for the design of joint source channel coders for noisy channel applications examples are presented of single path differential encoding delayed or tree encoding preposterior analysis and source coding over noisy channels

the isomorphism problem for some universal operator algebras abstract this paper addresses the isomorphism problem for the universal non self adjoint operator algebras generated by a row contraction subject to homogeneous polynomial relations we find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables and that this happens if and only if the associated subproduct systems are isomorphic the proof makes use of the complex analytic structure of the character space together with some recent results on subproduct systems restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry these commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties we prove a projective nullstellensatz connecting closed ideals and their zero sets under some technical assumptions we find that two such algebras are isomorphic as algebras if and only if they are similar and we obtain a clear geometrical picture of when this happens this result is obtained with tools from algebraic geometry reproducing kernel hilbert spaces and some new complex geometric rigidity results of independent interest the c envelopes of these algebras are also determined the banach algebraic and the algebraic classification results are shown to hold for the wot closures of these algebras as well

essential normality essential norms and hyperrigidity abstract let s s 1 s d denote the compression of the d shift to the complement of a homogeneous ideal i of c z 1 z d arveson conjectured that s is essentially normal in this paper we establish new results supporting this conjecture and connect the notion of essential normality to the theory of the c envelope and the noncommutative choquet boundary the unital norm closed algebra b i generated by s 1 s d modulo the compact operators is shown to be completely isometrically isomorphic to the uniform algebra generated by polynomials on v z i b d where z i is the variety corresponding to i consequently the essential norm of an element in b i is equal to the sup norm of its gelfand transform and the c envelope of b i is identified as the algebra of continuous functions on v b d which means it is a complete invariant of the topology of the variety determined by i in the ball motivated by this determination of the c envelope of b i we suggest a new more qualitative approach to the problem of essential normality we prove the tuple s is essentially normal if and only if it is hyperrigid as the generating set of a c algebra which is a property closely connected to arveson s notion of a boundary representation we show that most of our results hold in a much more general setting in particular for most of our results the ideal i can be replaced by an arbitrary not necessarily homogeneous invariant subspace of the d shift

the hadamard transform a tool for index assignment we show that the channel distortion for maximum entropy encoders due to noise on a binary symmetric channel is minimized if the vector quantizer can be expressed as a linear transform of a hypercube the index assignment problem is regarded as a problem of linearizing the vector quantizer we define classes of index assignments with related properties within which the best index assignment is found by sorting not searching two powerful algorithms for assigning indices to the codevectors of nonredundant coding systems are presented one algorithm finds the optimal solution in terms of linearity whereas the other finds a very good but suboptimal solution in a very short time

high rate vector quantization for noisy channels with applications to wideband speech spectrum compression this paper considers the high rate performance of source coding for noisy discrete symmetric channels with random index assignment ia accurate analytical models are developed to characterize the expected distortion performance of vector quantization vq for a large class of distortion measures it is shown that when the point density is continuous the distortion can be approximated as the sum of the source quantization distortion and the channel error induced distortion expressions are also derived for the continuous point density that minimizes the expected distortion next for the case of mean squared error distortion a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component the extent of the singularity is also characterized these results provide analytical models for the expected distortion performance of both conventional vq as well as for channel optimized vq as a practical example compression of the linear predictive coding parameters in the wideband speech spectrum is considered with the log spectral distortion as performance metric the theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion

the application of the theorems of structural variation to finite element problems in this paper the application of the theorems of structural variation to finite element problems is presented and a simplified procedure for constant strain triangular elements is developed applications for these techniques are discussed

asymptotic bounds on optimal noisy channel quantization via random coding asymptotically optimal zero delay vector quantization in the presence of channel noise is studied using random coding techniques first an upper bound is derived for the average rth power distortion of channel optimized k dimensional vector quantization at transmission rate r on a binary symmetric channel with bit error probability spl epsiv the upper bound asymptotically equals 2 sup rrg spl epsiv k r where k k r 1 log sub 2 l 2 spl radic spl epsiv 1 spl epsiv spl les g spl epsiv k r spl les 1 for all spl epsiv spl ges 0 lim sub spl epsiv spl rarr 0 g spl epsiv k r 1 and lim sub k spl rarr spl infin g spl epsiv k r 1 numerical computations of g spl epsiv k r are also given this result is analogous to zador s 1982 asymptotic distortion rate of 2 sup rr for quantization on noiseless channels next using a random coding argument on nonredundant index assignments a useful upper bound is derived in terms of point density functions on the minimum mean squared error of high resolution regular vector quantizers in the presence of channel noise the formula provides an accurate approximation to the distortion of a noisy channel quantizer whose codebook is arbitrarily ordered finally it is shown that the minimum mean squared distortion of a regular noisy channel vq with a randomized nonredundant index assignment is in probability asymptotically bounded away from zero

channel optimized soft trellis waveform coding we provide a new fuzzy relaxation trellis codebook search algorithm over noisy channels the new algorithm solves the problems associated with the lbg algorithm in the sense of delivering relatively lower distortion configurations using short training sequences furthermore the new approach is significantly less sensitive to the initialization process the algorithm minimizes a weighted distortion measure averaged over both the source and the channel statistics the weights are soft distortion related reliability information which are delivered by a soft trellis vector quantization algorithm stvq the concept of soft compression is introduced by haddad and yongacoglu see proc globecom rio de janeiro brazil dec 1999 in another paper using the forward backward symbol map algorithm the work introduced in this paper is an extension of the work established for the noiseless channel case by haddad and yongacoglu see proc ieee icassp istanbul turkey june 2000 in yet another paper testing is performed using first and second order gauss markov sources over several trellis structures vector dimensions and compression rates moreover the robustness of the optimal configurations is tested under channel mismatch conditions and compared with tandem coding systems

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

joint source and noisy channel trellis encoding corresp in a trellis encoding communication system the decoder is a time invariant nonlinear filter with finite memory sliding block code and the encoder is a trellis search algorithm matched to the decoder a coding theorem is established for a trellis encoding of a stationary and ergodic source over a discrete memoryless noisy channel which shows that such communication systems can perform arbitrarily close to the source distortion rate function evaluated at the channel capacity

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

an analytic grothendieck riemann roch theorem we extend the boutet de monvel toeplitz index theorem to complex manifolds with isolated singularities following the relative k homology theory of baum douglas and taylor for manifolds with boundary we apply this index theorem to study the arveson douglas conjecture let bmbm be the unit ball in cmcm and i an ideal in the polynomial algebra c z1 zm c z1 zm we prove that when the zero variety zizi is a complete intersection space with only isolated singularities and intersects with the unit sphere s2m 1s2m 1 transversely the representations of c z1 zm c z1 zm on the closure of i in la2 bm and also the corresponding quotient space qiqi are essentially normal furthermore we prove an index theorem for toeplitz operators on qiqi by showing that the representation of c z1 zm c z1 zm on the quotient space qiqi gives the fundamental class of the boundary zi s2m 1zi s2m 1 in the appendix we prove with kai wang that if f la2 bm vanishes on zi bmzi bm then f is contained inside the closure of the ideal i in la2 bm

multiplier algebras of complete nevanlinna pick spaces dilations boundary representations and hyperrigidity abstract we study reproducing kernel hilbert spaces on the unit ball with the complete nevanlinna pick property through the representation theory of their algebras of multipliers we give a complete description of the representations in terms of the reproducing kernels while representations always dilate to representations of the ambient c algebra we show that in our setting we automatically obtain coextensions in fact we show that in many cases this phenomenon characterizes the complete nevanlinna pick property we also deduce operator theoretic dilation results which are in the spirit of work of agler and several other authors moreover we identify all boundary representations compute the c envelopes and determine hyperrigidity for certain analogues of the disc algebra finally we extend these results to spaces of functions on homogeneous subvarieties of the ball

essential normality for quotient modules and complex dimensions abstract for analytic sets m introduced in 9 we show that the corresponding quotient module q of the bergman module is p essentially normal for all p dim c m which verifies the geometric arveson douglas conjecture in this case this result makes it possible to study the helton howe trace invariants on both q and the corresponding submodule r

quotient modules for some hilbert modules over the bidisk in this note we will prove the essential normality of some type of quotient hilbert modules over the bidisk moreover we will study some properties of the compression of the multiplication operators to the quotient hilbert modules

essentially normal hilbert modules and k homology this paper mainly concerns the essential normality of graded submodules essentially all of the basic hilbert modules that have received attention over the years are p essentially normal including the d shift hilbert module the hardy and bergman modules of the unit ball arveson conjectured graded submodules over the unit ball inherit this property and provided motivations to seek an affirmative answer some positive results have been obtained by arveson and douglas however the problem has been resistant in dimensions d 2 3 this paper shows that the arveson s conjecture is true in any dimension the paper also gives an affirmative answer in the case of the graded principal submodule finally the paper is associated with k homology invariants arising from graded quotient modules by which geometry of the quotient modules and geometry of algebraic varieties are connected in dimensions d 2 3 it is shown that k homology invariants determined by graded quotients are nontrivial the paper also establishes results on p smoothness of k homology elements and gives an explicit expression for k homology invariant in dimension d 2

samuel multiplicity and the structure of semi fredholm operators abstract two numerical invariants refining the fredholm index are introduced for any semi fredholm operator in such a way that their difference calculates the fredholm index these two invariants are inspired by samuel multiplicity in commutative algebra and can be regarded as the stabilized dimension of the kernel and cokernel a geometric interpretation of these invariants leads naturally to a 4 4 uptriangular matrix model for any semi fredholm operator on a separable hilbert space this model can be regarded as a refined local version of the apostol s 3 3 triangular representation for arbitrary operators some classical results such as gohberg s punctured neighborhood theorem can be read off directly from our matrix model banach space operators are also considered

quotients of standard hilbert modules we initiate a study of hilbert modules over the polynomial algebra that are obtained by completing with respect to an inner product having certain natural properties a standard hilbert module is a finite multiplicity version of one of these standard hilbert modules occupy a position analogous to that of free modules of finite rank in commutative algebra and their quotients by submodules give rise to universal solutions of nonlinear relations essentially all of the basic hilbert modules that have received attention over the years are standard including the hilbert module of the shift the hardy and bergman modules of the unit ball modules associated with more general domains in and those associated with projective algebraic varieties we address the general problem of determining when a quotient of an essentially normal standard hilbert module is essentially normal this problem has been resistant our main result is that it can be linearized in that the nonlinear relations defining the submodule can be reduced appropriately to linear relations through an iteration procedure and we give a concrete description of linearized quotients

geometric arveson douglas conjecture abstract we prove the arveson douglas essential normality conjecture for graded hilbert submodules that consist of functions vanishing on a given homogeneous subvariety of the ball smooth away from the origin our main tool is the theory of generalized toeplitz operators of boutet de monvel and guillemin

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

the structure of inner multipliers on spaces with complete nevanlinna pick kernels let k be the reproducing kernel for a hilbert space h k of analytic functions on bd the open unit ball in cd d 1 k is called a complete np kernel if k0 1 and if 1 1 k z is positive definite on bd bd let d be a separable hilbert space and consider h k d h k d and think of it as a space of d valued h k functions a theorem of mccullough and trent j funct anal 178 2000 226 249 partially extends the beurling lax halmos theorem for the invariant subspaces of the hardy space h2 d they show that if k is a complete np kernel and if d is a separable hilbert space then for any scalar multiplier invariant subspace m of h k d there exists an auxiliary hilbert space e and a multiplication operator h k e h k d such that is a partial isometry and m h k e such multiplication operators are called inner multiplication operators and they satisfy the orthogonal projection onto m in this paper we shall show that for many interesting complete np kernels the analogy with the beurling lax halmos theorem can be strengthened we show that for almost every z bd the nontangential limit z of the multiplier bd b e d associated with an inner multiplication operator is a partial isometry and that rank z is equal to a constant almost everywhere the result applies to certain weighted dirichlet spaces and to the space h2d which is determined by the kernel k z 11 z d z bd in particular our result implies that the curvature invariant of arveson proc natl acad sci usa96 1999 11 096 11 099 of a pure contractive hilbert module of finite rank is an integer this answers a question of w arveson proc natl acad sci usa96 1999 11096 11099

dixmier trace for toeplitz operators on symmetric domains abstract for toeplitz operators on bounded symmetric domains of higher rank there is no obvious way to define the dixmier trace within the toeplitz c algebra since commutators are in general not compact in this paper we solve this problem by constructing a hilbert quotient module corresponding to partitions of length 1 which leads to commutators in the macaev class l n we also obtain an explicit formula for the dixmier trace of such commutators in terms of the underlying boundary geometry which involves a new type of flag manifold defined in jordan theoretic terms

binary lattice vector quantization with linear block codes and affine index assignments we determine analytic expressions for the performance of some low complexity combined source channel coding systems the main tool used is the hadamard transform in particular we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments linear block channel coding and a binary symmetric channel the distortion formulas are specialized to nonredundant channel codes for a binary symmetric channel and then extended to affine index assignments on a binary asymmetric channel various structured index assignments are compared our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes one interesting result shown is that for a uniform source and uniform quantizer the natural binary code is never optimal for a nonsymmetric channel even though it is known to be optimal for a symmetric channel

performance of quantizers on noisy channels using structured families of codes achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers it is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end to end distortion decays to zero exponentially fast as a function of the overall transmission rate and is achieved by choosing a channel code rate that is independent of the overall transmission rate we show that for certain families of practical channel codes and binary lattice vector quantizers the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate this is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows explicit channel code rate schedules are obtained for several well known families of channel codes

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

pseudo gray coding a pseudo gray code is an assignment of n bit binary indexes to 2 points in a euclidean space so that the hamming distance between two points corresponds closely to the euclidean distance pseudo gray coding provides a redundancy free error protection scheme for vector quantization vq of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise a globally optimal solution to this problem is generally intractable due to an inherently large computational complexity a locally optimal solution the binary switching algorithm is introduced based on the objective of minimizing a useful upper bound on the average system distortion the algorithm yields a significant reduction in average distortion and converges in reasonable running times the sue of pseudo gray coding is motivated by the increasing need for low bit rate vq based encoding systems that operate on noisy channels such as in mobile radio speech communications

source and channel rate allocation for channel codes satisfying the gilbert varshamov or tsfasman vladut zink bounds we derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the gilbert varshamov or tsfasman vladut zink 1984 bounds formulas giving the high resolution vector quantizer distortion of these systems are also derived in addition we give bounds on how far below the channel capacity the transmission rate should be for a given delay constraint the bounds obtained depend on the relationship between channel code rate and relative minimum distance guaranteed by the gilbert varshamov bound and do not require sophisticated decoding beyond the error correction limit we demonstrate that the end to end mean squared error decays exponentially fast as a function of the overall transmission rate which need not be the case for certain well known structured codes such as hamming codes

quantizers with uniform decoders and channel optimized encoders scalar quantizers with uniform decoders and channel optimized encoders are studied for a uniform source on 0 1 and binary symmetric channels two families of affine index assignments are considered the complemented natural code cnc introduced here and the natural binary code nbc it is shown that the nbc never induces empty cells in the quantizer encoder whereas the cnc can nevertheless we show that the asymptotic distributions of quantizer encoder cells for the nbc and the cnc are equal and are uniform over a proper subset of the source s support region empty cells act as a form of implicit channel coding an effective channel code rate associated with a quantizer designed for a noisy channel is defined and computed for the codes studied by explicitly showing that the mean squared error mse of the cnc can be strictly smaller than that of the nbc we also demonstrate that the nbc is suboptimal for a large range of transmission rates and bit error probabilities this contrasts with the known optimality of the nbc when either both the encoder and decoder are not channel optimized or when only the decoder is channel optimized

a sequence based approximate mmse decoder for source coding over noisy channels using discrete hidden markov models in previous work on source coding over noisy channels it was recognized that when the source has memory there is typically residual redundancy between the discrete symbols produced by the encoder which can be capitalized upon by the decoder to improve the overall quantizer performance sayood and borkenhagen 1991 and phamdo and farvardin see ieee trans inform theory vol 40 p 186 93 1994 proposed detectors at the decoder which optimize suitable criteria in order to estimate the sequence of transmitted symbols phamdo and farvardin also proposed an instantaneous approximate minimum mean squared error iammse decoder these methods provide a performance advantage over conventional systems but the maximum a posteriori map structure is suboptimal while the iammse decoder makes limited use of the redundancy alternatively combining aspects of both approaches we propose a sequence based approximate mmse sammse decoder for a markovian sequence of encoder produced symbols and a discrete memoryless channel we approximate the expected distortion at the decoder under the constraint of fixed decoder complexity for this simplified cost the optimal decoder computes expected values based on a discrete hidden markov model using the wellknown forward backward f b algorithm performance gains for this scheme are demonstrated over previous techniques in quantizing gauss markov sources over a range of noisy channel conditions moreover a constrained delay version is also suggested

asymptotic quantization error of continuous signals and the quantization dimension extensions of the limiting qnanfizafion error formula of bennet are proved these are of the form d s k n f n beta b where n is the number of output levels d s k n f is the s th moment of the metric distance between quantizer input and output beta b 0 k s beta is the signal space dimension and f is the signal distribution if a suitably well behaved k dimensional signal density f x exists b b s k int f rho x dx 1 rho rho k s k and b s k does not depend on f for k 1 s 2 this reduces to bennett s formula if f is the cantor distribution on 0 1 0 and this k equals the fractal dimension of the cantor set 12 13 random quantization optimal quantization in the presence of an output information constraint and quantization noise in high dimensional spaces are also investigated

structural reanalysis for general layout modifications a procedure for reanalysis of structures subjected to various layout modifications is presented the procedure is based on exact analysis of the initial design it is suitable for all types of layout changes including the general case in which some members and joints are added other members and joints are deleted and some joint coordinates are modified in the particular and challenging case of addition of joints where the number of degrees of freedom is increased a simple reanalysis of a modified initial design is first carried out further changes are then applied to the latter design it is shown that for changes in a limited number of members of a truss structure an exact solution is readily achieved for changes in numerous members of a general structure an approximate solution can be efficiently obtained high quality approximations are demonstrated for various types of layout modifications

outage behavior of slow fading channels with power control using partial and erroneous csit this work investigates high snr outage behavior of slow fading channels with quantized feedback and partial power control when feedback indices are error prone we propose a quantizer structure with continuous voronoi regions and derive its optimality conditions using probability analysis our design involves construction of a novel bit mapping scheme the optimized power control codebook resembles channel optimized scalar quantizers cosqs also the diversity gain of the communication system under study is characterized with both nonzero and vanishing feedback error probabilities

a method to derive approximate explicit solutions for structural mechanics problems the availability of explicit solutions i e analytical relationships between the structural response and the design variables allows a more direct and plain treatment of several structural problems this paper is devoted to derive approximate explicit solutions in the framework of linear static analysis of finite element modeled structures with a given layout fixed node positions the proposed procedure is based on a factorization of the element stiffness matrix following the unimodal components concept which allows a non conventional assembly of the global stiffness matrix the exact inversion of that matrix is a trivial task for the case of statically determinate structures structures with few redundancies or few design variables an approximate inverse of the stiffness matrix is herein derived for more general structural problems by resorting to the sherman morrison woodbury formula 2006 elsevier ltd all rights reserved