a study on the dimension of global sections of adjoint bundles for polarized manifolds abstract let x be a smooth complex projective variety of dimension n and let l be an ample line bundle on x in this paper in order to investigate the dimension of h 0 k x t l more systematically we introduce the invariant a i x l for every integer i with 0 i n furthermore we study this invariant for the case where l is ample and spanned by global sections as applications we get a lower bound resp an upper bound for the dimension of h 0 k x t l if l is ample and spanned by global sections resp very ample

a theoretical and computational framework for anisotropic continuum damage mechanics at large strains abstract the main objective of this work is the formulation and algorithmic treatment of anisotropic continuum damage mechanics at large strains based on the concept of a fictitious isotropic undamaged configuration an additional linear tangent map is introduced which allows the interpretation as a damage deformation gradient then the corresponding finger tensor denoted as damage metric constructs a second order internal variable due to the principle of strain energy equivalence with respect to the fictitious effective space and the standard reference configuration the free energy function can be computed via push forward operations within the nominal setting referring to the framework of standard dissipative materials associated evolution equations are constructed which substantially affect the anisotropic nature of the damage formulation the numerical integration of these ordinary differential equations is highlighted whereby two different schemes and higher order methods are taken into account finally some numerical examples demonstrate the applicability of the proposed framework

modeling and analysis of a phase field system for damage and phase separation processes in solids abstract in this work we analytically investigate a multi component system for describing phase separation and damage processes in solids the model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function the main aim of this paper is to show existence of weak solutions for the introduced model where in contrast to existing damage models in the literature different elastic properties of damaged and undamaged material are regarded to prove existence of weak solutions for the introduced model we start with an approximation system then by passing to the limit existence results of weak solutions for the proposed model are obtained via suitable variational techniques

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

a gradient enhanced large deformation continuum damage model for fibre reinforced materials a non local gradient based damage formulation within a geometrically non linear setting is presented the hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre reinforced material respectively the inelastic constitutive response is governed by a scalar 1 d type damage formulation where only the anisotropic elastic part is assumed to be affected by the damage following the concept in dimitrijevic and hackl 28 the local free energy function is enhanced by a gradient term this term essentially contains the gradient of the non local damage variable which itself is introduced as an additional independent variable in order to guarantee the equivalence between the local and non local damage variable a penalisation term is incorporated within the free energy function based on the principle of minimum total potential energy a coupled system of euler lagrange equations i e the balance of linear momentum and the balance of the non local damage field is obtained and solved in weak form the resulting coupled highly non linear system of equations is symmetric and can conveniently be solved by a standard incremental iterative newton raphson type solution scheme several three dimensional displacement and force driven boundary value problems partially motivated by biomechanical application highlight the mesh objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

efficient iteration schemes for anisotropic hyperelasto plasticity numerical issues arising when integrating hyperelasto plastic constitutive equations with elastic anisotropy stemming from anisotropic damage and plastic anisotropy as represented by kinematic hardening are discussed in particular solution algorithms for the corresponding non linear system of equations due to implicit integration algorithms are addressed it is shown that algorithms like staggered iteration and quasi newton techniques are superior to a pure newton technique when the cpu time is compared however the drawback of the staggered and the quasi newton technique is that rather small time steps must be taken to ensure convergence which can be of importance when applying complex constitutive models in a finite element programme copyright 2005 john wiley sons ltd

on the spatial formulation of anisotropic multiplicative elasto plasticity abstract this contribution aims at a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto plasticity embedded in the well established framework of non standard dissipative materials we adopt as a key ingredient the introduction of additional symmetric arguments typically structural tensors into the relevant scalar valued isotropic tensor functions on this basis the fundamental covariance relation leads us to a formulation which allows itself to be set up directly in terms of spatial arguments and thus guarantees a convenient implementation within a finite element setting

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

on sectional genus of quasi polarized 3 folds let x be a smooth projective variety over c and l a nef big resp ample divisor on x then x l is called a quasi polarized resp polarized manifold then we conjecture that g l q x where g l is the sectional genus of l and q x dim h1 ox is the irregularity of x in general it is unknown whether this conjecture is true or not even in the case of dim x 2 for example this conjecture is true if dim x 2 and dim ho l 0 but it is unknown if dimx 3 and dimh l 0 in this paper we prove g l q x if dimx 3 and dimh l 2 furthermore we classify polarized manifolds x l with dim x 3 dim h l 3 and g l q x

khatri rao space time codes space time st coding techniques exploit the spatial diversity afforded by multiple transmit and receive antennas to achieve reliable transmission in scattering rich environments st block codes are capable of realizing full diversity and spatial coding gains at relatively low rates st trellis codes can achieve better rate diversity tradeoffs at the cost of high complexity on the other hand v blast supports high rates but has no built in spatial coding and does not work well with fewer receive than transmit antennas we propose a novel linear block coding scheme based on the khatri rao matrix product the proposed scheme offers flexibility for achieving full rate or full diversity or a desired rate diversity tradeoff and it can handle any transmit receive antenna configuration or signal constellation the proposed codes are shown to have numerous desirable properties including guaranteed unique linear decodability built in blind channel identifiability and efficient near maximum likelihood decoding

on the dual variable of the logarithmic strain tensor the dual variable of the cauchy stress tensor and related issues the paper discusses relations related to the dual variables of the cauchy stress tensor and the logarithmic strain tensor we give a new proof that the logarithmic strain is dual to the cauchy stress tensor in the isotropic hyperelastic case corresponding relations are given in the case of multiplicative finite strain elasto viscoplasticity for the material eshelby like stress tensor and the rotated material stress tensor as well the general case of anisotropic response is discussed the dual variable of the logarithmic strain tensor is derived and some new expressions are given specifically it is proven that the skew symmetric part of the eshelby tensor is determined by the commutator of the logarithmic strain tensor and its conjugate variable the question of the existence of dual variables for the cauchy stress tensor and its material counterparts is rigorously answered where it is shown that in the general case a dual variable does not exist

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

blind ml detection of orthogonal space time block codes identifiability and code construction the blind maximum likelihood ml detection of a general space time block code stbc is considered a challenging implementation problem recent work has revealed that for the orthogonal stbcs ostbcs their special code structures can be exploited to formulate highly effective blind ml based algorithms attracted by this realization merit this paper investigates the blind ml identifiability of ostbcs with an emphasis on the binary psk bpsk and quaternary psk qpsk constellations we find a class of ostbcs called the nonrotatable ostbcs that can be uniquely identified up to a sign uiuts almost surely under a few mild assumptions for example for an independently distributed rayleigh channel with any number of receiver antennas a nonrotatable ostbc can be uiuts with probability 1 while this identifiability looks appealing already we further examine a subclass of nonrotatable ostbcs called the nonintersecting subspace nis ostbcs we prove that nis ostbcs are uiuts for any nonzero channel however nis ostbcs are not available in the existing literature to fill this gap we devise a code construction procedure that can convert any bpsk or qpsk ostbc to an nis ostbc

on maximum likelihood detection and the search for the closest lattice point maximum likelihood ml decoding algorithms for gaussian multiple input multiple output mimo linear channels are considered linearity over the field of real numbers facilitates the design of ml decoders using number theoretic tools for searching the closest lattice point these decoders are collectively referred to as sphere decoders in the literature in this paper a fresh look at this class of decoding algorithms is taken in particular two novel algorithms are developed the first algorithm is inspired by the pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the viterbo boutros sphere decoder the connection between the proposed algorithm and the stack sequential decoding algorithm is then established this connection is utilized to construct the second algorithm which can also be viewed as an application of the schnorr euchner strategy to ml decoding aided with a detailed study of preprocessing algorithms a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near ml detection performance this claim is supported by intuitive arguments and simulation results in many relevant scenarios

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

orthogonal space time block codes maximum likelihood detection for unknown channels and unstructured interferences space time coding stc schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention the so called orthogonal space time block codes ostbcs have been of particular interest due to their good performance and low decoding complexity in this paper we take a systematic maximum likelihood ml approach to the decoding of ostbc for unknown propagation channels and unknown noise and interference conditions we derive a low complexity ml decoding algorithm based on cyclic minimization and assisted by a minimum amount of training data furthermore we discuss the design of optimal training sequences and optimal information transfer to an outer decoder numerical examples demonstrate the performance of our algorithm

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

a counterexample for the open problem on the minimal delays of orthogonal designs with maximal rates x liang systematically investigated orthogonal designs with maximal rates gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates he also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates and proved that the problem is correct for less than or equal to six transmit antennas in this correspondence we give a counterexample for the open problem for n 8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56 hence we give a negative answer for the open problem

blind ml detection of orthogonal space time block codes efficient high performance implementations orthogonal space time block codes ostbcs have attracted much attention owing to their simple code construction maximal diversity gain and low maximum likelihood ml detection complexity when channel state information csi is available at the receiver this paper addresses the problem of ml ostbc detection with unknown csi focusing on the binary and quaternary psk constellations we show that blind ml ostbc detection can be simplified to a boolean quadratic program bqp from an optimization viewpoint the bqp is still a computationally hard problem and we propose two alternatives for dealing with this inherent complexity first we consider the semidefinite relaxation sdr approach which leads to a suboptimal but accurate blind ml detection algorithm with an affordable worst case computational cost we also consider the sphere decoding approach which leads to an exact blind ml detection algorithm that remains computationally expensive in the worst case but generally incurs a reasonable average computational cost for the two algorithms we study implementation methods that can significantly reduce the computational complexity simulation results indicate that the two blind ml detection algorithms are competitive in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors moreover numerical studies show that the sdr algorithm provides better complexity performance than the sphere decoder in the worst case sense and vice versa in the average sense

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

on the second sectional h arithmetic genus of polarized manifolds let x l be a polarized variety defined over the complex number field with dim x n in this paper we introduce the notion of the i th sectional h arithmetic genus hi x l for every integer i with 0 i n we expect that this invariant has a property similar to the euler poincare characteristic of the structure sheaf of i dimensional varieties in this paper we consider the case where x is smooth and i 2 and we study a polarized version of some results in the theory of surfaces

young measure quasi static damage evolution an existence result for the quasi static evolution of incomplete damage in elastic materials is presented the absence of gradient terms in the damage variable causes a critical lack of compactness therefore the analysis is developed in the framework of young measures where a notion of solution is defined presenting some improvements with respect to previous contributions the main new feature in the proof of the existence result regards a delicate construction of the joint recovery sequence

a consistent time fe method for large strain elasto plasto dynamics in the present paper energy consistent momentum conserving time stepping schemes for geometrically nonlinear multiplicative elasto plasto dynamics referred to as ecmc cg methods are developed in this context the entire discretisation procedure of the global equations of motion is based on galerkin methods in space and time whereby special emphasis is placed on the desired conservation properties related to the approximation of time integrals to guarantee energy consistency also for higher order finite elements in time a thermodynamically motivated enhanced stress tensor which defines a non standard quadrature rule is derived for elasto plastic material behaviour concerning the integration of the local evolution equations in time exemplarily a well established first order accurate exponential update is applied and adapted according to the global time stepping scheme based on linear finite elements in time the performance of the resulting scheme is demonstrated by means of several representative numerical examples whereby it is shown that global energy consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts

geometrically non linear anisotropic inelasticity based on fictitious configurations application to the coupling of continuum damage and multiplicative elasto plasticity the objective of this contribution is the formulation and algorithmic treatment of a phenomenological framework to capture anisotropic geometrically non linear inelasticity in addition to the intermediate configuration of multiplicative elasto plasticity we further introduce two microscopic configurations of lagrangian and eulerian type which characterize the so called fictitious undamaged material this kinematical framework enables us to apply two well established postulates based on standard terminology in non linear continuum mechanics concerning the free energy function the postulate of strain energy equivalence is adopted and in view of the plastic dissipation potential the concept of effective stress is a natural outcome of the underlying kinematical assumptions finally we focus on the integration technique for the class of obtained evolution equations and present numerical examples for a prototype model to underline the applicability of the proposed framework copyright 2003 john wiley sons ltd

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold