on optimal gaussian signaling in mimo relay channels with partial decode and forward for gaussian multiple input multiple output mimo relay channels with partial decode and forward the optimal type of input distribution is still an open question in general recent research has revealed that in some other scenarios with unknown optimal input distributions e g interference channels improper i e noncircular gaussian distributions can outperform proper circular gaussian distributions in this paper we show that this is not the case for partial decode and forward in the gaussian mimo relay channel with gaussian transmit signals i e we show that a proper gaussian input distribution is the optimal one among all gaussian distributions in order to prove this property an innovation covariance matrix is introduced and a decomposition is performed by considering the optimization over this matrix as an outer problem a key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two user mimo broadcast channel under a sum covariance constraint for which the optimality of proper signals can be shown

design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

continuity conditions for finite element analysis of solids in conventional finite element formulations the concept of node a point where one of the shape functions is unitary and all others are nil is used to advantage as it simplifies the definition of interelement continuity conditions this constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and in particular of equilibrium elements in the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes interelement continuity conditions are imposed a posteriori as in hybrid elements the derivation of the element matrices is based upon the equations expressing equilibrium compatibility and the constitutive relations without explicitly using variational principles this results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and or to use conforming or non conforming elements as the approach used is independent of the choice of basic functions and of the shape of the elements it is perfectly general it allows the parallel analysis of kinematically and statically admissible formulations as proposed by fraeijs de veubeke 1 as the interelement continuity conditions are imposed a posteriori new variables are used to express this condition

efficient scalar quantization of exponential and laplacian random variables this paper presents solutions to the entropy constrained scalar quantizer ecsq design problem for two sources commonly encountered in image and speech compression applications sources having the exponential and laplacian probability density functions we use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design we show how to obtain the optimal ecsq either with or without an additional constraint on the number of levels in the quantizer in contrast to prior methods which require a multidimensional iterative solution of a large number of nonlinear equations the new method needs only a single sequence of solutions to one dimensional nonlinear equations in some laplacian cases one additional two dimensional solution is needed as a result the new method is orders of magnitude faster than prior ones we show that as the constraint on the number of levels in the quantizer is relaxed the optimal ecsq becomes a uniform threshold quantizer utq for exponential but not for laplacian sources we then further examine the performance of the utq and optimal ecsq and also investigate some interesting alternatives to the utq including a uniform reconstruction quantizer urq and a constant dead zone ratio quantizer cdzrq

a conforming solution to curved plate bending problems a curved triangular element for plate bending is developed using the displacement method of formulation the element has one outwardly curved side and conforms on an arbitrary quadratic boundary to the user the element appears as a single curved triangle internally however the element is subdivided into a straight sided triangle and a curved segment the straight sided triangle is extensively documented in the literature2 5 and is referred to in the paper as the cowper triangle the curved segment is a two noded element with 12 degrees of freedom it has one straight side and one curved side independent expansions are assumed in each domain and explicit shape functions derived the theoretical solution to a few practical problems is contained in each of the two expansions in such cases the curved triangle produces perfect results otherwise the accuracy is of the same order as that obtained in similar problems with straight boundaries the method is easily extended to elements of higher order

a higher order triangular plate bending element revisited a new formulation of an eighteen degrees of freedom higher order triangular plate bending element using triangular area co ordinates is presented the displacement function w is taken as the complete fifth order polynomial in area co ordinates the normal slope along an edge of the triangle is constrained to vary cubically the twenty one constants are expressed explicity in terms of eighteen degrees of freedom the element stiffness matrix is expressed as a product of component matrices for which explicit expressions are developed and presented no numerical inversion or integration is necessary the formulation is expected to be useful specially for microcomputers

a bit allocation method for sparse source coding in this paper we develop an efficient bit allocation strategy for subband based image coding systems more specifically our objective is to design a new optimization algorithm based on a rate distortion optimality criterion to this end we consider the uniform scalar quantization of a class of mixed distributed sources following a bernoulli generalized gaussian distribution this model appears to be particularly well adapted for image data which have a sparse representation in a wavelet basis in this paper we propose new approximations of the entropy and the distortion functions using piecewise affine and exponential forms respectively because of these approximations bit allocation is reformulated as a convex optimization problem solving the resulting problem allows us to derive the optimal quantization step for each subband experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform based coding application

joint optimization of the transmit covariance and relay precoder in general gaussian amplify and forward relay channels the maximum data rate that can be achieved by the strictly causal full duplex amplify and forward af scheme in general gaussian relay channels is achieved by gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder this problem possesses an intricate nonconvex structure and is hence difficult to solve to circumvent this difficulty the relay precoder is assumed to be given and then the karush kuhn tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder these expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the af scheme at any source transmit power in addition to significantly reducing the effort expended in searching for the optimal relay precoder this observation enables us to find the optimal precoders at low and high source transmit powers for asymptotically low transmit powers the optimal relaying mechanism is shown to possess an interlacing structure thereby resembling half duplex operation in contrast for asymptotically high transmit powers it is optimal for the relay to be silent the asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that at intermediate source transmit powers are shown numerically to outperform asymptotically optimal precoders

the capacity of the semideterministic relay channel corresp the capacity of the class of relay channels with sender x 1 a relay sender x 2 a relay receiver y 1 f x 1 x 2 and ultimate receiver y is proved to be c max min p x 1 x 2 i x 1 x 2 y h y 1 x 2 i x 1 y x 2 y 1

eigenvalue convergence in the finite element method in static force deflection applications of the finite element method convergence rates for the p version in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed are superior to those for the h version in which the element degree remains fixed while the mesh is refined so that element size approaches zero in structural dynamics applications one does not seek to approximate a single solution as in static applications but seeks estimates for a number of the lower system eigenvalues this paper identifies factors responsible for poorer accuracy in higher computed eigenvalues in addition it explains why the p version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h version numerical examples demonstrate the superiority of the p version over the h version they also show the effects of various mechanisms limiting eigenvalue convergence

an mcmc approach to universal lossy compression of analog sources motivated by the markov chain monte carlo mcmc approach to the compression of discrete sources developed by jalali and weissman we propose a lossy compression algorithm for analog sources that relies on a finite reproduction alphabet which grows with the input length the algorithm achieves in an appropriate asymptotic sense the optimum shannon theoretic tradeoff between rate and distortion universally for stationary ergodic continuous amplitude sources we further propose an mcmc based algorithm that resorts to a reduced reproduction alphabet when such reduction does not prevent achieving the shannon limit the latter algorithm is advantageous due to its reduced complexity and improved rates of convergence when employed on sources with a finite and small optimum reproduction alphabet

low resolution scalar quantization for gaussian sources and absolute error this correspondence considers low resolution scalar quantization for a memoryless gaussian source with respect to absolute error distortion it shows that slope of the operational rate distortion function of scalar quantization is infinite at the point dmax where the rate becomes zero thus unlike the situation for squared error distortion or for laplacian and exponential sources with squared or absolute error distortion for a gaussian source and absolute error scalar quantization at low rates is far from the shannon rate distortion function i e far from the performance of the best lossy coding technique

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

bilayer low density parity check codes for decode and forward in relay channels this paper describes an efficient implementation of binning for decode and forward df in relay channels using low density parity check ldpc codes bilayer ldpc codes are devised to approach the theoretically promised rate of the df relaying strategy by incorporating relay generated parity bits in specially designed bilayer graphical code structures while conventional ldpc codes are sensitively tuned to operate efficiently at a certain channel parameter the proposed bilayer ldpc codes are capable of working at two different channel parameters and two different rates that at the relay and at the destination to analyze the performance of bilayer ldpc codes bilayer density evolution is devised as an extension of the standard density evolution algorithm based on bilayer density evolution a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming further in order to approach to the theoretical df rate for a wide range of channel parameters this paper proposes two different forms of bilayer codes the bilayer expurgated and bilayer lengthened codes it is demonstrated that the rate of a properly designed bilayer ldpc code can closely approach the theoretical df limit finally it is shown that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

a seventh order numerical method for solving boundary value nonlinear ordinary differential equations a numerical method for solving two point boundary value problems associated with systems of first order nonlinear ordinary differential equations is described it needs three function evaluations for each sub interval and is of order o h7 where h is the space chop results of computational experiments comparing this method with other known methods are given

new results on optimal entropy constrained quantization given h 0 the problem is considered of finding an n level quantizer q which is optimal in the sense of encoding a given continuously distributed random variable x with minimum expected squared error subject to the constraint h q x

gaussian orthogonal relay channels optimal resource allocation and capacity a gaussian orthogonal relay model is investigated where the source transmits to the relay and destination in channel 1 and the relay transmits to the destination in channel 2 with channels 1 and 2 being orthogonalized in the time frequency plane in order to satisfy practical constraints the total available channel resource time and bandwidth is split into the two orthogonal channels and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized the main focus of the analysis is on the case where the source to relay link is better than the source to destination link which is the usual scenario encountered in practice a lower bound on the capacity achievable rate is derived and optimized over the parameter spl theta which represents the fraction of the resource assigned to channel 1 it is shown that the lower bound achieves the max flow min cut upper bound at the optimizing spl theta the common value thus being the capacity of the channel at the optimizing spl theta furthermore it is shown that when the relay to destination signal to noise ratio snr is less than a certain threshold the capacity at the optimizing spl theta is also the maximum capacity of the channel over all possible resource allocation parameters spl theta finally the achievable rates for optimal and equal resource allocations are compared and it is shown that optimizing the resource allocation yields significant performance gains

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

on the relay channel with receiver transmitter feedback an achievable rate for the discrete memoryless relay channel with receiver transmitter feedback is proposed based on block markov superposition encoding the achievable rate can also be extended to gaussian channels a second achievable rate for the gaussian relay channel based on a schalkwijk kailath type scheme is presented for some channels both achievable rates strictly improve upon all previously known achievable rates for the discrete memoryless relay channel also a converse result is provided

a general degree hybrid equilibrium finite element for kirchhoff plates summary we present a family of hybrid equilibrium finite elements for the quasistatic linear elastic analysis of plates governed by kirchhoff theory the moments are approximated by self balanced polynomial fields of general degree and in order to impose strong codiffusivity the normal boundary rotations are approximated with complete polynomials of the same degree whereas the transverse deflections use polynomials one degree lower furthermore it is also necessary to include an independent approximation of the vertex translations we show that the triangular form of this element is stable that is free from spurious kinematic modes and the formulation that we present allows these elements to be used as a standard displacement element examples of computed values and convergence of the solutions are presented which demonstrate the performance of these elements copyright 2013 john wiley sons ltd

a solution to the c1 continuity problem in plate bending a family of high order conforming triangles for the finite element analysis of plate bending problems is developed using the displacement method of formulation the development proceeds in two steps a family of non conforming triangles based on polynomial expansions of order 4 is first generated and its performance found to be unacceptable nodal variables for the non conforming family are selected from the set w wx wy wn the elements are then made to conform by adding a twist nodal variable wnt at the mid side nodes rational functions define the three additional degrees of freedom simple and very accurate procedures solve the problems associated with the use of such functions numerical results are presented for the conforming triangles of order 4 and 7 following a brief description of the two elements a listing of the explicit shape functions for the quartic triangle is included the numerical results are very good in particular they are superior per degree of freedom to the results predicted by the various non conforming and conforming cubic and related elements at present used in computer packages together with a similar performance by the quintic member10 of the family they validate the proposed theoretical solution

practical quantizer design for half duplex estimate and forward relaying we propose a quantizer design method for practical half duplex estimate and forward ef relaying first we identify the regime in which ef relaying yields substantial gains where the snr is low and the relay destination link is strong then we discover design simplifications that reduce complexity with little loss in the above regime for relay quantizer design we first consider mean squared distortion minimization to illustrate the unsuitability of the approach we present an example with awgn links and a bpsk source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate a distortion minimizing quantizer attempts to preserve the received signal at the relay the quantizer should instead preserve source information in information theoretical terms the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint the above conclusion derived from information theoretical principles is then translated to a quantizer design method for the low snr regime using ldpc codes of blocklength 100000 bpsk modulation and quantizers designed using the proposed criterion we observe performance less than a decibel away from the achievable rate at a ber of 10 4

concentric permutation source codes permutation codes are a class of structured vector quantizers with a computationally simple encoding procedure based on sorting the scalar components using a codebook comprising several permutation codes as subcodes preserves the simplicity of encoding while increasing the number of rate distortion operating points improving the convex hull of operating points and increasing design complexity we show that when the subcodes are designed with the same composition optimization of the codebook reduces to a lower dimensional vector quantizer design within a single cone heuristics for reducing design complexity are presented including an optimization of the rate allocation in a shape gain vector quantizer with gain dependent wrapped spherical shape codebook

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

on the reliability function of the discrete memoryless relay channel bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types two achievable error exponents are derived based on partial decode forward and compress forward which are well known superposition block markov coding schemes the derivations require combinations of the techniques involved in the proofs of csiszar korner marton s packing lemma for the error exponent of channel coding and marton s type covering lemma for the error exponent of source coding with a fidelity criterion the decode forward error exponent is evaluated on sato s relay channel from this example it is noted that to obtain the fastest possible decay in the error probability for a fixed effective coding rate one ought to optimize the number of blocks in the block markov coding scheme assuming the blocklength within each block is large an upper bound on the reliability function is also derived using ideas from haroutunian s lower bound on the error probability for point to point channel coding with feedback

curved composite boundary elements for second order two dimensional problems finite elements with a curved edge often require relatively large numerical effort to form 1 4 relatively simple triangular elements with a single curved edge are developed in this paper for second order two dimensional problems a convex boundary element is formed as a composite of two straight edged triangles and a circular sector application of the convex composite boundary element results in less numerical effort for a comparable error in circular and elliptical domain test problems than the application of straight edged elements in all cases shown and in most cases when compared to the curved isoparametric elements for domains with concave boundaries the application of straight edged concave composite boundary and curved isoparametric elements give comparable accuracies and numerical efforts because of a fortuitous cancellation of error that occurs with straight edged elements in this case

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

balance laws and centro velocity in dissipative systems starting with a density that is conserved for a dynamical system when dissipation is ignored a local conservation law is derived for which the total flux integrated over the spatial domain is unique when dissipation is incorporated the conservation law becomes a balance law the contribution due to dissipation in this balance law is split in a unique way in a part that is proportional to the density and in a divergence expression that adds to the original conservative flux density the total additional flux is uniquely defined it is shown that these total fluxes appear in the expression for the centro velocity i e in the velocity of the center of gravity of the density which shows that this velocity can be defined in a unique way in contrast to a local velocity applications to the korteweg de vries burgers equations and to the incompressible navier stokes equations are given

interpolated boundary conditions in plate bending problems using c1 curved finite elements abstract the purpose of this paper is to construct high order c 1 curved finite elements which are useful for the approximate solutions of plate bending problems with clamp or simply support boundary conditions over nonpolygon domains this kind of finite elements is defined over the exact domain of the problem and the corresponding approximate solution is also obtained over the original domain moreover the effect of the numerical quadrature schemes is studied

a linear encoding approach to index assignment in lossy source channel coding we present a general scheme for the lossy transmission of a source with arbitrary statistics through a noisy channel under the mean square error fidelity criterion our approach is based on transform coding scalar quantization of the transform coefficients and linear encoding of the quantization indices entropy coding and channel coding are merged into a single linear encoding function such that the catastrophic behavior of conventional entropy coding is avoided and the full power of modern coding techniques and iterative belief propagation decoding can be exploited we show that this approach is asymptotically optimal in the limit of large block length for arbitrary source statistics and binary input output symmetric channel in the practical regime of finite block length and low decoding complexity we show through the explicit construction of codes for the lossy transmission of digital images over a binary symmetric channel that our approach yields significant improvements with respect to previously proposed channel optimized quantization schemes and also with respect to the conventional concatenation of state of the art image coding with state of the art channel coding although our constructive example focuses on a special case the approach is general and can be applied to other classes of sources of practical interest

compress forward coding with bpsk modulation for the half duplex gaussian relay channel this paper studies compress forward cf coding with bpsk modulation for the half duplex gaussian relay channel in cf relaying wyner ziv coding is applied at the relay to exploit the joint statistics between signals at the relay and the destination we propose slepian wolf coded nested scalar quantization swcnsq for practical wyner ziv coding at the relay we first provide the achievable rate of swcnsq based cf relaying as a performance benchmark and then present a practical code design using low density parity check ldpc codes for error protection at the source and nested scalar quantization plus irregular repeat accumulation ira codes for cf coding at the relay the degree distributions of the ldpc and ira codes are optimized using extrinsic information transfer charts and gaussian approximation under discretized density evolution for asymptotically large block lengths our optimized code design operates 0 11 0 21 db away from the swcnsq limit for cf relaying simulations with ldpc ira codes of length 2 times 105 bits show a performance gap of 0 27 0 38 db from the achievable rate

diversity analysis of randomized linear dispersion codes in a half duplex amplify and forward multiple relay system a point to point multiple relay communication system with half duplex constraints is considered the relays operate under the amplify and forward paradigm and implement a linear dispersion distributed space time code with randomized dispersion matrices of independent and identically distributed entries the large signal to noise ratio behavior of the asymptotically large deterministic system is studied for both the optimum maximum likelihood receiver and the linear minimum mean squared error lmmse receiver the diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices more specifically when the linear dispersion matrices are sufficiently tall both receivers achieve the maximum diversity order i e the total number of relays plus one conversely when the linear dispersion matrices are fat in the sense that relays linearly compress the information received from the source the optimum receiver is shown to achieve an asymptotic diversity order of two whereas the lmmse receiver is totally unable to exploit the available spatial diversity

bounds on capacity and minimum energy per bit for awgn relay channels upper and lower bounds on the capacity and minimum energy per bit for general additive white gaussian noise awgn and frequency division awgn fd awgn relay channel models are established first the max flow min cut bound and the generalized block markov coding scheme are used to derive upper and lower bounds on capacity these bounds are never tight for the general awgn model and are tight only under certain conditions for the fd awgn model two coding schemes that do not require the relay to decode any part of the message are then investigated first it is shown that the side information coding scheme can outperform the block markov coding scheme it is also shown that the achievable rate of the side information coding scheme can be improved via time sharing in the second scheme the relaying functions are restricted to be linear the problem is reduced to a single letter nonconvex optimization problem for the fd awgn model the paper also establishes a relationship between the minimum energy per bit and capacity of the awgn relay channel this relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy per bit that do not differ by more than a factor of 1 45 for the fd awgn relay channel model and 1 7 for the general awgn model

variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations radiation boundary conditions are derived for partial differential equations which describe wave phenomena assuming the evolution of the system to be governed by a lagrangian variational principle boundary conditions are obtained with noether s theorem from the requirement that they transmit some appropriate density such as the energy density as well as possible the theory is applied to a nonlinear version of the klein gordon equation for this application numerical test results are presented in an accompanying paper the theory is applied to a two dimensional wave equation

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

a two level finite element discretization of the stream function form of the navier stokes equations abstract we analyze a two level method of discretizing the stream function form of the navier stokes equations this report presents the two level algorithm and error analysis for the case of conforming elements the two level algorithm consists of solving a small nonlinear system on the coarse mesh then solving a linear system on the fine mesh the basic result states that the error between the coarse and fine meshes are related superlinearly via as an example if the clough tocher triangles or the bogner fox schmit rectangles are used then the coarse and fine meshes are related by h o h 3 2 ln h 1 4

a joint time invariant filtering approach to the linear gaussian relay problem in this paper the linear gaussian relay problem is considered under the linear time invariant lti model the rate maximization problem in the linear gaussian relay channel is formulated in the frequency domain based on the toeplitz distribution theorem under the further assumption of realizable input spectra the rate maximization problem is converted to the problem of joint source and relay filter design with two power constraints one at the source and the other at the relay and a practical solution to this problem is proposed based on the adaptive projected sub gradient method numerical results show that the proposed method yields a considerable gain over the instantaneous amplify and forward af scheme in inter symbol interference isi channels also the optimality of the af scheme within the class of one tap relay filters is established in flat fading channels

wyner ziv coding based on tcq and ldpc codes this paper considers trellis coded quantization tcq and low density parity check ldpc codes for the quadratic gaussian wyner ziv coding problem after tcq of the source x ldpc codes are used to implement slepian wolf coding of the quantized source q x with side information y at the decoder assuming 256 state tcq and ideal slepian wolf coding in the sense of achieving the theoretical limit h q x y we experimentally show that slepian wolf coded tcq performs 0 2 db away from the wyner ziv distortion rate function dwz r at high rate this result mirrors that of entropy constrained tcq in classic source coding of gaussian sources furthermore using 8 192 state tcq and assuming ideal slepian wolf coding our simulations show that slepian wolf coded tcq performs only 0 1 db away from dwz r at high rate these results establish the practical performance limit of slepian wolf coded tcq for quadratic gaussian wyner ziv coding practical designs give performance very close to the theoretical limit for example with 8 192 state tcq irregular ldpc codes for slepian wolf coding and optimal non linear estimation at the decoder our performance gap to dwz r is 0 20 db 0 22 db 0 30 db and 0 93 db at 3 83 bit per sample b s 1 83 b s 1 53 b s and 1 05 b s respectively when 256 state 4 d trellis coded vector quantization instead of tcq is employed the performance gap to dwz r is 0 51 db 0 51 db 0 54 db and 0 80 db at 2 04 b s 1 38 b s 1 0 b s and 0 5 b s respectively

vector quantization with complexity costs vector quantization is a data compression method by which a set of data points is encoded by a reduced set of reference vectors the codebook a vector quantization strategy is discussed that jointly optimizes distortion errors and the codebook complexity thereby determining the size of the codebook a maximum entropy estimation of the cost function yields an optimal number of reference vectors their positions and their assignment probabilities the dependence of the codebook density on the data density for different complexity functions is investigated in the limit of asymptotic quantization levels how different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression the wavelet coefficients of gray level images are quantized and the reconstruction error is measured the approach establishes a unifying framework for different quantization methods like k means clustering and its fuzzy version entropy constrained vector quantization or topological feature maps and competitive neural networks

full explicit interpolation formulas for the argyris triangle abstract explicit interpolation formulas are presented in terms of area coordinates for the argyris triangle with 21 degrees of freedom so that c 1 continuity is clearly observed it is further shown that 5 unisolvency can be proved in a very direct manner

basis functions for general hsieh clough tocher triangles complete or reduced in this note we give the basis functions shape functions for hsieh clough tocher triangles complete or reduced in order to take the best advantage of symmetry and for simplicity we derive these functions for a general triangle by using simultaneously the area co ordinates and the so called eccentricity parameters we conclude with some remarks concerning the implementation

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

a new c1 finite element full heptic a new c1 finite element complete in 7th degree polynomial basis is described and compared with other c1 elements in an eigen elements analysis

entropy of highly correlated quantized data this paper considers the entropy of highly correlated quantized samples two results are shown the first concerns sampling and identically scalar quantizing a stationary continuous time random process over a finite interval it is shown that if the process crosses a quantization threshold with positive probability then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity the second result provides an upper bound to the rate at which the joint entropy tends to infinity in the case of an infinite level uniform threshold scalar quantizer and a stationary gaussian random process specifically an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived at high sampling rates these results indicate a sharp contrast between the large encoding rate in bits sec required by a lossy source code consisting of a fixed scalar quantizer and an ideal sampling rate adapted lossless code and the bounded encoding rate required by an ideal lossy source code operating at the same distortion

a general formulation of equilibrium macro elements with control of spurious kinematic modes the exorcism of an old curse this paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner the effects of spurious kinematic modes present to some extent in all primitive equilibrium elements are eliminated by judicious assembly into macro equilibrium elements these macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable such a family of macro elements is a new development and results for polynomials of degree greater than two have not been seen before the quality of results for macro equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples

some notes on statically admissible fe solution of the thin plate bending problem with a posteriori error estimation by paulina światkiewicz and zdzislaw wiȩckowski international journal for numerical methods in engineering 2020

state dependent relay channel achievable rate and capacity of a semideterministic class this paper considers the problem of communicating over a relay channel with state when noncausal state information is partially available at the nodes we first establish a lower bound on the achievable rates based on noisy network coding and gelfand pinsker coding and show that it provides an alternative characterization of a previously known bound we then introduce the class of state decoupled relay channels and show that our lower bound is tight for a subclass of semideterministic channels we also compute the capacity for two specific examples of this subclass a channel with multiplicative binary fading and a channel with additive gaussian interference these examples are not special cases of previous classes of semideterministic relay channels with known capacity

time asymptotics and the self organization hypothesis for 2d navier stokes equations in this paper we study the long time behaviour of solutions with a two dimensional structure of the navier stokes equations on a periodic grid from a rigorous investigation of the decrease of the energy e and the enstrophy w it follows that the rayleigh quotient image is monotonically decreasing on solutions this is shown to imply that the spatial structure of any solution tends to a critical point of q which is the structure of some planar vortex and that all these structures are unstable except for the fundamental one which has the longest wavelength the time dependence of the approach towards this self organized state is investigated in some detail in the spectral plane the mean squared wave numbers of both the spectral energy and enstrophy density are shown to decrease as a function of time for the enstrophy this implies that the normal cascade does not match the discriminating effect of the viscous dissipation

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

study of gaussian relay channels with correlated noises in this paper we consider the full duplex and half duplex gaussian relay channels where the noises at the relay and destination are arbitrarily correlated we first derive the capacity upper bound and the achievable rates with three existing schemes decode and forward df compress and forward cf and amplify and forward af we present two capacity results under specific noise correlation coefficients one being achieved by df and the other being achieved by direct link transmission or a special case of cf the channel for the former capacity result is equivalent to the traditional gaussian degraded relay channel and the latter corresponds to the gaussian reversely degraded relay channel for cf and af schemes we show that their achievable rates are strictly decreasing functions of the correlation coefficient when the correlation coefficient is negative moreover when the noise correlation coefficient is positive the cf achievable rate may also outperform the independent noise case if the noise correlation coefficient is within a certain range through numerical comparisons under different channel settings we observe that although df completely disregards the noise correlation while the other two can potentially exploit such extra information none of the three relay schemes always outperforms the others over different correlation coefficients moreover the exploitation of noise correlation by cf and af accrues more benefit when the source relay link is weak this paper also considers the optimal power allocation problem under the correlated noise channel setting with individual power constraints at the relay and the source it is shown that the relay should use all its available power to maximize the achievable rates under any correlation coefficient with a total power constraint across the source and the relay the achievable rates are proved to be concave functions over the power allocation factor for af and cf under full duplex mode where the closed form power allocation strategy is derived

analysis of the generalized df cf for gaussian relay channels decode or compress we consider a three node quasi static communication system with a full duplex relay the goal is to determine the relaying mode that enables rate efficient communication under given channel conditions to achieve this goal we consider a generalized scheme that subsumes the decode and forward df and compress and forward cf schemes as special cases the generalized scheme is considered when the source and relay signals are synthesized from commonly used gaussian codebooks which are shown to be capacity achieving in two asymptotic cases perfect relay destination link and broken source destination link studying the generalized df cf scheme it is shown that for two non asymptotic cases in which the signal to noise ratios snrs of the links satisfy certain conditions this scheme reduces to either df or cf for another set of non asymptotic snrs the generalized scheme is shown to yield strictly higher rates than both df and cf despite the complexity of the generalized scheme its rate advantage over df and cf is shown to be upper bounded by 0 5 bits per channel use this indicates that the practical benefit of the analysis of this scheme is to enable selecting the relaying mode that suits a given channel realization numerical results show that under rayleigh fading conditions this selection yields significant gains over fixed df and cf

on instantaneous relaying the gaussian three node relay channel with orthogonal receive components i e the transmitted signals from the source and the relay do not interfere with each other is investigated for such channels linear relaying is a suboptimal strategy in general this is because a linear scheme merely repeats the received noisy signal and does not utilize the available degrees of freedom efficiently at this background nonlinear symbol wise as opposed to block wise relaying strategies are developed to compensate for the shortcomings of the linear strategy optimal strategies are presented for two special cases of the general scenario and it is shown that memoryless relaying can achieve the capacity furthermore for the general gaussian relay channel a parametric piecewise linear pl mapping is proposed and analyzed the achievable rates obtained by the pl mapping are computed numerically and optimized for a certain number of design parameters it is concluded that optimized pl relaying always outperforms conventional instantaneous linear relaying amplify and forward it is also illustrated that the proposed pl relaying scheme can improve on sophisticated block markov encoding i e decode and forward when the source relay link is ill conditioned relative to other links furthermore pl relaying can work at rates close to those achieved by side information encoding i e compress and forward but at a much lower complexity

explicit interpolation formulas for the bell triangle abstract explicit interpolation formulas are presented mainly using area coordinates for the bell triangle with 18 degrees of freedom so that c 1 continuity is clearly observed the bell triangle is derived by imposing the p 4 admissible constraints on the argyris triangle by which the 4 unisolvency is proved variable node expressions combining the argyris and bell triangles are further developed

slepian wolf coded nested lattice quantization for wyner ziv coding high rate performance analysis and code design nested lattice quantization provides a practical scheme for wyner ziv coding this paper examines the high rate performance of nested lattice quantizers and gives the theoretical performance for general continuous sources in the quadratic gaussian case as the rate increases we observe an increasing gap between the performance of finite dimensional nested lattice quantizers and the wyner ziv distortion rate function we argue that this is because the boundary gain decreases as the rate of the nested lattice quantizers increases to increase the boundary gain and ultimately boost the overall performance a new practical wyner ziv coding scheme called slepian wolf coded nested lattice quantization swc nq is proposed where slepian wolf coding is applied to the quantization indices of the source for the purpose of compression with side information at the decoder theoretical analysis shows that for the quadratic gaussian case and at high rate swc nq performs the same as conventional entropy coded lattice quantization with the side information available at both the encoder and the decoder furthermore a nonlinear minimum mean square error mse estimator is introduced at the decoder which is theoretically proven to degenerate to the linear minimum mse estimator at high rate and experimentally shown to outperform the linear estimator at low rate practical designs of one and two dimensional nested lattice quantizers together with multilevel low density parity check ldpc codes for slepian wolf coding give performance close to the theoretical limits of swc nq

low resolution scalar quantization for gaussian sources and squared error this correspondence analyzes the low resolution performance of entropy constrained scalar quantization it focuses mostly on gaussian sources for which it is shown that for both binary quantizers and infinite level uniform threshold quantizers as d approaches the source variance spl sigma sup 2 the least entropy of such quantizers with mean squared error d or less approaches zero with slope log sub 2 e 2 spl sigma sup 2 as the shannon rate distortion function approaches zero with the same slope this shows that in the low resolution region scalar quantization with entropy coding is asymptotically as good as any coding technique

curved finite elements of class implementation and numerical experiments part 1 construction and numerical tests of the interpolation properties the aim of this work is to show how to implement some of the methods of curved finite elements of class c1 introduced and analyzed in a previous work by the first author these methods use curved finite elements which are c1 compatible with the argyris triangle a careful description of the implementation is completed by some numerical experiments which show the very high degree of accuracy of the associated interpolation subsequently in a second part we will show the efficiency of such methods for solving thin plate or thin shell problems set on curved boundary domains

powell sabin b splines and unstructured standard t splines for the solution of the kirchhoff love plate theory exploiting bezier extraction the equations that govern kirchhoff love plate theory are solved using quadratic powell sabin b splines and unstructured standard t splines bezier extraction is exploited to make the formulation computationally efficient because quadratic powell sabin b splines result in inline image continuous shape functions they are of sufficiently high continuity to capture kirchhoff love plate theory when cast in a weak form unlike non uniform rational b splines nurbs which are commonly used in isogeometric analysis powell sabin b splines do not necessarily capture the geometry exactly however the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to nurbs as no bending strip method for joined nurbs patches is needed this paper further illustrates how unstructured t splines can be modified such that they are inline image continuous around extraordinary points and that the blending functions fulfil the partition of unity property the performance of quadratic nurbs unstructured t splines powell sabin b splines and nurbs to nurps non uniform rational powell sabin b splines which are obtained by a transformation from a nurbs patch is compared in a study of a circular plate

information rates of densely sampled data distributed vector quantization and scalar quantization with transforms for gaussian sources this paper establishes rates attainable by several lossy schemes for coding a continuous parameter source to a specified mean squared error distortion based on sampling at asymptotically large rates first a densely sampled spatiotemporal stationary gaussian source is distributively encoded the berger tung bound to the distributed rate distortion function and three convergence theorems are used to obtain an upper bound expressed in terms of the source spectral density to the smallest attainable rate at asymptotically large sampling rates the bound is tighter than that recently obtained by kashyap both indicate that with ideal distributed lossy coding dense sensor networks can efficiently sense and convey a field in contrast to the negative result obtained by marco for encoders based on scalar quantization and slepian wolf distributed lossless coding the second scheme is transform coding with scalar coefficient quantization a new generalized transform coding analysis as well as the aforementioned convergence theorems is used to find the smallest attainable rate at asymptotically large sampling rates in terms of the source spectral density and the operational rate distortion function of the family of quantizers which in contrast to previous analyses need not be convex the result shows that when a transform is used scalar quantization need not cause the poor performance found by marco as a corollary the final result pursues an approach originally proposed by berger to show that the inverse water pouring formula for the rate distortion function can be attained at high sampling rates by transform coding with ideal vector quantization to encode the coefficients also established in the paper are relations between operational rate distortion and distortion rate functions for a continuous parameter source and those for the discrete parameter source that results from sampling

a method for creating a class of triangular c1 finite elements finite elements providing a c1 continuous interpolation are useful in the numerical solution of problems where the underlying partial differential equation is of fourth order such as beam and plate bending and deformation of strain gradient dependent materials although a few c1 elements have been presented in the literature their development has largely been heuristic rather than the result of a rational design to a predetermined set of desirable element properties therefore a general procedure for developing c1 elements with particular desired properties is still lacking this paper presents a methodology by which c1 elements such as the tuba 3 element proposed by argyris et al can be constructed in this method which to the best of our knowledge is the first one of its kind a class of finite elements is first constructed by requiring a polynomial interpolation and prescribing the geometry the location of the nodes and the possible types of nodal dofs a set of necessary conditions is then imposed to obtain appropriate interpolations generic procedures are presented which determine whether a given potential member of the element class meets the necessary conditions the behaviour of the resulting elements is checked numerically using a benchmark problem in strain gradient elasticity

the stability of stars of triangular equilibrium plate elements equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models but when formulating equilibrium models questions of stability or admissibility of loads are of major concern this paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and or flexural actions patches of elements that share a common vertex are considered and such patches are termed stars stars may be used in global analyses as assemblies of elements forming macro elements or in local analyses the conditions for stability or the existence and number of spurious kinematic modes are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration the procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links copyright 2008 john wiley sons ltd

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

capacity of a class of multicast tree networks in this paper we characterize the capacity of a new class of discrete memoryless multicast networks having a tree topology for achievability a novel coding scheme is constructed where some relays employ a combination of decode and forward and compress and forward and the other relays perform a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology for converse a new technique of iteratively manipulating inequalities exploiting the tree topology is used this class of multicast tree networks includes the class of diamond networks studied by kang and ulukus as a special case

on the uniform quantization of a class of sparse sources we consider the uniform scalar quantization of a class of mixed distributed memoryless sources namely sources having a bernoulli generalized gaussian bgg distribution both for low and high resolutions asymptotic expressions of the distortion for a pth order moment error measure and close approximations of the entropy are provided for these sources operational rate distortion functions at high bit rate and their slope factors at low bit rate are derived the dependence of these results on p and the distribution parameters as well as the relation to the shannon optimal rate distortion bound are then discussed the application of these results to transform coding in two simple cases is finally highlighted

on universal quantization the quantization of n dimensional vectors in r n with an arbitrary probability measure under a mean square error constraint is discussed it is demonstrated that a uniform one dimensional quantizer followed by a noiseless digital variable rate encoder entropy encoding can yield a rate that is for any n no more than 0 754 bit per sample higher than the rate associated with the optimal n dimensionai quantizer regardless of the probabilistic characterization of the input n vector for the allowable mean square error

high order methods for elliptic partial differential equations with singularities this paper reports on an experimental study of the effectiveness of high order numerical methods applied to linear elliptic partial differential equations whose solutions have singularities or similar difficulties e g boundary layers sharp peaks three specific hypotheses are established with high levels of statistical confidence to support the general conclusion there is a strong correlation between the order of a method and its efficiency higher order is better

filter and forward relay design for mimo ofdm systems in this paper the filter and forward ff relay design for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated due to the considered mimo structure the ff relay design is investigated in the framework of joint design together with the linear mimo transceiver as the design criterion first the minimization of weighted sum mean square error mse is considered the joint design in this case is approached based on alternating optimization that iterates between the optimal design of the ff relay for given mimo precoding and decoding matrices and the optimal design of mimo precoding and decoding matrices for a given ff relay filter second a more advanced problem of joint design for rate maximization is considered the second problem is approached based on the obtained result regarding the first problem of weighted sum mse minimization and the existing result regarding the relationship between weighted mse minimization and rate maximization numerical results show the effectiveness of the proposed ff relay design method and significant performance improvement by the proposed ff relay over widely considered simple af relays for mimo ofdm systems

generalization of the c1 tuba plate finite elements to the geometrically exact kirchhoff love shell model abstract the finite element implementation of a geometrically exact thin shell model is reported in the present paper the shell kinematics is based on the kirchhoff love assumption and is characterized by the deformation gradient which yielded the generalized cross section strain measures stretches and curvatures written in terms of first and second order derivatives of displacements the energetically conjugate quantity the first piola kirchhoff stress tensor is used to define the generalized stresses the shell s initial geometry is exactly represented using a mapping from a reference configuration a neo hookean material functional supplemented by the plane stress condition is incorporated in the constitutive level of the model both configuration dependent and independent forces are considered for the domain and boundary loading the consistent linearization of the rendered weak form is addressed the tuba family of plate finite elements is adopted for the discretization of the displacement vector field these triangular elements with necessarily straight sides in the reference configuration provide c 1 continuous approximations a sine qua non property for a consistent discretization of the kirchhoff love model the family contains 3 pairs of elements primary and reduced which provide polynomial approximants of degrees k 5 6 and 7 respectively the reduced elements have a simpler structure and a smaller number of nodes but still guarantee c 1 continuity the boundary normal derivative of the approximation in these elements is constrained such that its order is reduced by one unit from k 1 at the primary elements to k 2 due to complexity of the elements degrees of freedom which are the function value its normal first and second order derivatives the imposition of the essential boundary conditions requires some preliminary analysis of the boundary behavior such study is presented for the most common practical cases six benchmark examples are presented to demonstrate the model usefulness and efficiency

asymptotic analysis of amplify and forward relaying in a parallel mimo relay network this paper studies the setup of a parallel mimo relay network in which k relays each equipped with n antennas assist in transmitting data between a source and a destination each equipped with m antennas m n in the half duplex mode it is assumed that there is no direct source destination link and the communication is performed in two hops an amplify and forward relaying scheme called incremental cooperative beamforming scheme icbs is introduced and shown to achieve the capacity of the network in the asymptotic case of k with a gap scaling of at most log k 4 k this result is shown to hold as long as the power of each relay is significantly larger than log3 k log log k k in addition in the case that the source power is equal to the relays power and both tend to infinity the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays simulation results confirm the validity of analytical arguments

extended finite element methods for thin cracked plates with kirchhoff love theory a modelization of cracked plates under bending loads in the xfem framework is addressed the kirchhoff love model is considered it is well suited for very thin plates commonly used for instance in aircraft structures reduced hct and fvs elements are used for the numerical discretization two kinds of strategies are proposed for the enrichment around the crack tip with for both of them an enrichment area of xed size i e independant of the mesh size parameter in the rst one each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip the second strategy consists in introducing these functions in the nite element basis with a single degree of freedom for each one an integral matching is then used in order to ensure the c1 continuity of the solution at the interface between the enriched and the non enriched areas finally numerical convergence results for these strategies are presented and discussed

wave diffusion dualism of the neutral fractional processes in this paper a neutral fractional equation is introduced and analyzed in contrast to the general time and space fractional diffusion equation the neutral fractional equation contains fractional derivatives of the same order 1 2 both in space and in time as it has been shown earlier solutions of the neutral fractional equation can be interpreted as damped waves with the constant propagation velocities that means that this equation inherits some characteristics of the wave equation otherwise the first fundamental solution of the one dimensional neutral fractional equation is known to be a spatial probability density function evolving in time and is thus related to the diffusion processes in this paper we investigate the entropy and the entropy production rate of the neutral fractional equation and show that both of them are strongly connected to those of the diffusion processes thus a wave diffusion dualism of the processes described by the neutral fractional equation is established

isoparametric hermite elements isoparametric hermite elements are created using bogner fox schmit rectangles on a reference domain and mapping these numerically onto the computational domain the difficulties involved in devising explicit c1 shape functions for isoparametric elements are thus avoided and the resulting elements have all the benefits of full c1 continuity the simplicity of the bogner fox schmit element and the geometrical flexibility expected from higher order isoparametric elements the numerical mapping consists in the finite element solution of a linear boundary value problem which is inexpensive and is carried out as a preprocessing operation the required derivatives of the mapping then being supplied to the main analysis as data some care is required in defining the differential boundary conditions and guidance on this is provided examples are given showing the success of the mapping procedure and the use of the resulting elements in the solution of some boundary value problems the numerical results confirm a convergence analysis provided for the new isoparametric hermite element

on the c1 continuous discretization of non linear gradient elasticity a comparison of nem and fem based on bernstein bezier patches in gradient elasticity the appearance of strain gradients in the free energy density leads to the need of c 1 continuous discretization m ethods in the present work the performances of c 1 finite elements and the c 1 natural element method nem are compared the triangular argyris and hsieh clough tocher finite elements are reparametrized in terms of the bernstein polynomials the quadrilateral bogner fox schmidt element is used in an isoparametric framework for which a preprocessing algorithm is presented additionally the c 1 nem is applied to non linear gradient elasticity several numerical examples are analyzed to compare the convergence behavior of the different methods it will be illustrated that the isoparametric elements and the nem show a significantly better performance than the triangular elements

optimal entropy constrained scalar quantization of a uniform source optimal scalar quantization subject to an entropy constraint is studied for a wide class of difference distortion measures including rth power distortions with r 0 it is proved that if the source is uniformly distributed over an interval then for any entropy constraint r in nats an optimal quantizer has n e sup r interval cells such that n 1 cells have equal length d and one cell has length c spl les d the cell lengths are uniquely determined by the requirement that the entropy constraint is satisfied with equality based on this result a parametric representation of the minimum achievable distortion d sub h r as a function of the entropy constraint r is obtained for a uniform source the d sub h r curve turns out to be nonconvex in general moreover for the squared error distortion it is shown that d sub h r is a piecewise concave function and that a scalar quantizer achieving the lower convex hull of d sub h r exists only at rates r log n where n is a positive integer