strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

some new characters on the wire tap channel of type ii the noiseless wire tap channel of type ii with coset coding scheme was provided by ozarow and wyner in this correspondence the user is split into multiple parties who are coordinated in coding their data symbols by using the same encoder the adversary can tap not only partial transmitted symbols but also partial data symbols we are interested in the equivocation of the data symbols to this adversary who has more power than that of ozarow and wyner the generalized hamming weight of wei and the dimension length profile dlp of forney are extended to two code formats relative generalized hamming weight and relative dimension length profile rdlp upper and lower bounds of the new concepts are investigated they are useful to design a perfect secrecy coding scheme for the coordinated multiparty model under a general secrecy standard the coordinated model can provide a higher transmission rate than an uncoordinated time sharing model

on the dimension of subfield subcodes a new lower bound for the dimension of a subfield subcode is given this bound improves the well known lower bound of p delsarte 1975 and coincides in many cases with the true dimension of the code alternant codes and geometric goppa codes are discussed as special cases

linear authentication codes bounds and constructions in this paper we consider a new class of unconditionally secure authentication codes called linear authentication codes or linear a codes we show that a linear a code can be characterized by a family of subspaces of a vector space over a finite field we then derive an upper bound on the size of the source space when other parameters of the system that is the sizes of the key space and the authenticator space and the deception probability are fixed we give constructions that are asymptotically close to the bound and show applications of these codes in constructing distributed authentication systems

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

parity equations based unknown input reconstruction for mimo stochastic systems with an application in this paper an approach for reconstructing an unknown input for multiple input multiple output systems is presented it is assumed that the system is affected by process noise whereas the available system inputs are contaminated by measurement noise the novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors a modification of the algorithm is also provided which allows the approach to deal with systems whose zero is close to unity the order of the parity space can be treated as a tuning parameter allowing for a trade off between the smoothness of the reconstructed unknown input and a phase lag an analytical solution of the overall problem is obtained by making use of a lagrange multiplier method the utility of the scheme is demonstrated when applied to a practical hydrological system

maximum rank array codes and their application to crisscross error correction a mu n n k array code c over a field f is a k dimensional linear space of n n matrices over f such that every nonzero matrix in c has rank or mu it is first shown that the dimension of such array codes must satisfy the singleton like bound k

from mixture theory to biot s approach for porous media abstract two apparently different approaches are used in dealing with the mechanics of a deformable porous medium mixture theories on the one hand and purely macroscale theories which are mainly associated with the work of biot on the other hand in the mixture theories the porous medium is represented by spatially superposed interacting media while macroscale theories assume that standard concepts of continuum mechanics are still relevant at the macro level the aim of this paper is two fold first it is shown that the macroscale field equations derived from mixture theories can be reformulated in terms of the measurable quantities involved in the macroscale theories second it is demonstrated how these field equations including the fundamental inequality obtained from the second law entail the existence of a macroscale c potential upon which a thermo dynamically consistent formulation of the constitutive equations can be firmly founded

brief extension of minimum variance estimation for systems with unknown inputs in this paper we address the problem of minimum variance estimation for discrete time time varying stochastic systems with unknown inputs the objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs it extends the results of darouach and zasadzinski automatica 33 1997 717 where the unknown inputs are only present in the model the main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises this fact leads generally to suboptimal filters necessary and sufficient conditions for the unbiasedness of this filter are established then conditions under which the estimation error and the system noises are uncorrelated are presented and an optimal estimator and a predictor filters are derived sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time invariant case a numerical example is given in order to illustrate the proposed method

relative generalized hamming weights of one point algebraic geometric codes security of linear ramp secret sharing schemes can be characterized by the relative generalized hamming weights of the involved codes 26 24 in this paper we elaborate on the implication of these parameters and we devise a method to estimate their value for general one point algebraic geometric codes as it is demonstrated for hermitian codes our bound is often tight furthermore for these codes the relative generalized hamming weights are often much larger than the corresponding generalized hamming weights

minimal delay fir delayed left inverses for systems with zero nonzero zeros abstract this paper considers finite time input reconstruction for discrete time linear time invariant systems in the case where the initial condition is unknown there are three main results first a specific construction of finite impulse response fir delayed left inverse with the minimal delay for systems with zero nonzero zeros is presented next it is shown that in the presence of an arbitrary unknown initial condition finite time input reconstruction is possible using a delayed left inverse h if and only if h is fir finally it is shown that a transfer function with full column normal rank has an fir delayed left inverse with the minimal delay if and only if the system has zero nonzero zeros

moving horizon numerical observers of nonlinear control systems in this note we develop moving horizon numerical observers and analyze the error in the error estimation we take into consideration both the integration error and the optimization error the design facilitates the use of a variety of numerical algorithms to form different observers as a special case an euler newton observer is introduced the numerical observer is independent of any optimization software or toolbox furthermore the observer is formulated in a way that is especially efficient for systems with sampled measurement

variationally consistent derivation of the stress partitioning law in saturated porous media abstract the linearized version of a recently formulated variational macroscopic theory of biphasic isotropic porous media vmtpm is employed to derive a general stress partitioning law for media undergoing flow conditions under prevented fluid seepage and negligible inertia effects typically met in biphasic specimens subjected to jacketed tests the principle of virtual work relevant to the specialization of vmtpm to such characteristic flow conditions naturally yields a stress partitioning law between solid and fluid phase of a saturated medium that exactly matches with the celebrated terzaghi s principle it is also shown that the stress tensor of the solid phase work associated with the strain measure of the vmtpm naturally corresponds to the terzaghi s effective stress accordingly under undrained conditions terzaghi s law is proved to be a completely general stress partitioning law for a saturated biphasic medium irrespective of its constitutive and or microstructural features as well as of the compressibility of its constituent phases since the developments reported are obtained ruling out thermodynamic constraints and any assumption on the internal microstructure and on the compressibility of the phases the results obtained indicate that terzaghi s law could more generally apply to a broader class of biphasic media and be not restricted within the context of geomechanics

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

boundary conditions at fluid permeable interfaces in porous media a variational approach abstract a general set of boundary conditions at fluid permeable interfaces between dissimilar fluid filled porous matrices is established starting from an extended hamilton rayleigh principle these conditions do include friction and inertial effects once linearized they encompass boundary conditions relative to volume darcy brinkman and to surface saffman beavers joseph dissipation effects

network generalized hamming weight in this work we extend the notion of generalized hamming weight for classical linear block codes to linear network codes by introducing the network generalized hamming weight nghw for a given network with respect to a fixed linear network code the basic properties of nghw are studied we further show that nghw can be used as a tool to characterize the security performance of a linear network code on a wiretap network we also introduce the notion of network maximum distance separable code nmds code by extending the notion of maximum distance separable code in classical algebraic coding theory we prove that nmds codes play an important role in minimizing the information that an eavesdropper can obtain from the network

on metrics for error correction in network coding the problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model for coherent network coding where knowledge of the network topology and network code is assumed at the source and destination nodes the error correction capability of an outer code is succinctly described by the rank metric as a consequence it is shown that universal network error correcting codes achieving the singleton bound can be easily constructed and efficiently decoded for noncoherent network coding where knowledge of the network topology and network code is not assumed the error correction capability of a subspace code is given exactly by a new metric called the injection metric which is closely related to but different than the subspace metric of koumltter and kschischang in particular in the case of a non constant dimension code the decoder associated with the injection metric is shown to correct more errors then a minimum subspace distance decoder all of these results are based on a general approach to adversarial error correction which could be useful for other adversarial channels beyond network coding

new constructions of subspace codes using subsets of mrd codes in several blocks a basic problem for the constant dimension subspace coding is to determine the maximal possible size mathrm a q n d k of a set of k dimensional subspaces in mathrm f q n such that the subspace distance satisfies d u v 2k 2 dim u cap v geq d for any two different subspaces u and v in this set we present two new constructions of constant dimension subspace codes using subsets of maximum rank distance mrd codes in several blocks this method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting mrd codes in these two constructions subsets of mrd codes with bounded ranks play an essential role the delsarte theorem about the rank distribution of mrd codes is an important ingredient to count codewords in our constructed constant dimension subspace codes we give many new lower bounds for mathrm a q n d k more than 110 new constant dimension subspace codes better than previously best known codes are constructed

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

relative generalized matrix weights of matrix codes for universal security on wire tap networks universal security over a network with linear network coding has been intensively studied however previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network which restricts the possible packet lengths of optimal universal secure codes does not allow to apply known list decodable rank metric codes and requires performing operations over a large field in this paper we introduce new parameters relative generalized matrix weights and relative dimension rank support profile for code pairs that are linear over the field used in the network and show that they measure the universal security performance of these code pairs for one code and non square matrices generalized matrix weights coincide with the existing delsarte generalized weights hence we prove the connection between these latter weights and secure network coding which was left open as main applications the proposed new parameters enable us to 1 obtain optimal universal secure linear codes on noiseless networks for all possible packet lengths in particular for packet lengths not considered before 2 obtain the first universal secure list decodable rank metric code pairs with polynomial sized lists based on a recent construction by guruswami et al and 3 obtain new characterizations of security equivalences of linear codes finally we show that our parameters extend relative generalized hamming weights and relative dimension length profile respectively and relative generalized rank weights and relative dimension intersection profile respectively

on the similarities between generalized rank and hamming weights and their applications to network coding rank weights and generalized rank weights have been proved to characterize error and erasure correction and information leakage in linear network coding in the same way as hamming weights and generalized hamming weights describe classical error and erasure correction and information leakage in wire tap channels of type ii and code based secret sharing although many similarities between both the cases have been established and proved in the literature many other known results in the hamming case such as bounds or characterizations of weight preserving maps have not been translated to the rank case yet or in some cases have been proved after developing a different machinery the aim of this paper is to further relate both weights and generalized weights show that the results and proofs in both cases are usually essentially the same and see the significance of these similarities in network coding some of the new results in the rank case also have new consequences in the hamming case

rank minimization over finite fields fundamental limits and coding theoretic interpretations this paper establishes information theoretic limits for estimating a finite field low rank matrix given random linear measurements of it these linear measurements are obtained by taking inner products of the low rank matrix with random sensing matrices necessary and sufficient conditions on the number of measurements required are provided it is shown that these conditions are sharp and the minimum rank decoder is asymptotically optimal the reliability function of this decoder is also derived by appealing to de caen s lower bound on the probability of a union the sufficient condition also holds when the sensing matrices are sparse a scenario that may be amenable to efficient decoding more precisely it is shown that if the n n sensing matrices contain on average nlog n entries the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field analogies are drawn between the aforementioned results and rank metric codes in the coding theory literature in fact we are also strongly motivated by understanding when minimum rank distance decoding of random rank metric codes succeeds to this end we derive minimum distance properties of equiprobable and sparse rank metric codes these distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one

state and unknown input estimation for linear discrete time systems in this paper a state and unknown input delayed estimator is designed for discrete time linear systems even if some well known matching condition does not hold this result is obtained using a constructive algorithm that analyzes the state observability and the left invertibility of the systems with unknown inputs and that provides a suitable canonical transformation for the design of the estimator

an arbitrary lagrangian eulerian finite element formulation for a poroelasticity problem stemming from mixture theory abstract a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid the governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue the formulation is based on the adoption of an arbitrary lagrangian eulerian ale perspective we focus on a flow regime in which inertia forces are negligible the stability and convergence of the formulation is discussed and numerical results demonstrate agreement with the theory

relative generalized rank weight of linear codes and its applications to network coding by extending the notion of minimum rank distance this paper introduces two new relative code parameters of a linear code mathcal c 1 of length n over a field extension mathbb f q m and its subcode mathcal c 2 subsetneqq mathcal c 1 one is called the relative dimension intersection profile rdip and the other is called the relative generalized rank weight rgrw we clarify their basic properties and the relation between the rgrw and the minimum rank distance as applications of the rdip and the rgrw the security performance and the error correction capability of secure network coding guaranteed independently of the underlying network code are analyzed and clarified we propose a construction of secure network coding scheme and analyze its security performance and error correction capability as an example of applications of the rdip and the rgrw silva and kschischang showed the existence of a secure network coding in which no part of the secret message is revealed to the adversary even if any dim mathcal c 1 1 links are wiretapped which is guaranteed over any underlying network code however the explicit construction of such a scheme remained an open problem our new construction is just one instance of secure network coding that solves this open problem

superposition and chain rule for bounded hessian functions abstract we study the properties of superposition of bounded hessian functions establishing the validity of a second order chain rule we prove rectifiability properties of all noncritical level sets ofbh functions by showing a geometric measure theory analogous of dini s theorem

homogenization of the navier stokes equations in open sets perforated with tiny holes i abstract framework a volume distribution of holes this paper treats the homogenization of the stokes or navier stokes equations with a dirichlet boundary condition in a domain containing many tiny solid obstacles periodically distributed in each direction of the axes for example in the three dimensional case the obstacles have a size of e3 and are located at the nodes of a regular mesh of size e a suitable extension of the pressure is used to prove the convergence of the homogenization process to a brinkman type law in which a linear zero order term for the velocity is added to a stokes or navier stokes equation

optimal filtering for systems with unknown inputs an optimal filtering formula is derived for linear time varying discrete systems with unknown inputs by making use of the well known innovations filtering technique the derivation is an extension of a new observer design method for time invariant deterministic systems with unknown inputs the systems under consideration have the most general form the derived optimal filter has a similar form to the standard kalman filter with some modified covariance and gain matrices

on randomized linear network codes and their error correction capabilities randomized linear network code for single source multicast was introduced and analyzed in ho et al ieee transactions on information theory october 2006 where the main results are upper bounds for the failure probability of the code in this paper these bounds are improved and tightness of the new bounds is studied by analyzing the limiting behavior of the failure probability as the field size goes to infinity in the linear random coding setting for single source multicast the minimum distance of the code defined in zhang ieee transactions on information theory january 2008 is a random variable taking nonnegative integer values that satisfy the inequality in the singleton bound recently established in yeung and cai communications in information and systems 2006 for network error correction codes we derive a bound on the probability mass function of the minimum distance of the random linear network code based on our improved upper bounds for the failure probability codes having the highest possible minimum distance in the singleton bound are called maximum distance separable mds the bound on the field size required for the existence of mds codes reported in zhang ieee transactions on information theory january 2008 and matsumoto arxiv cs it 0610121 oct 2006 suggests that such codes exist only when field size is large define the degradation of a code as the difference between the highest possible minimum distance in the singleton bound and the actual minimum distance of the code the bound for the probability mass function of the minimum distance leads to a bound on the field size required for the existence of network error correction codes with a given maximum degradation the result shows that allowing minor degradation reduces the field size required dramatically

unknown state unknown input reconstruction in discrete time nonminimum phase systems geometric methods the complete solution to the unknown state unknown input reconstruction problem in systems with invariant zeros is inherently conditioned by the fact that for any invariant zero at least one initial state exists such that the output is not affected when the mode of the invariant zero is properly injected into the system despite this intrinsic limitation the problem of reconstructing the initial state and the inaccessible inputs from the available measurements has recently attracted remarkable interest owing to its impact on the synthesis of enhanced reliability control systems this contribution consists of a geometric method which solves the unknown state unknown input reconstruction problem in discrete time systems with invariant zeros anywhere in the complex plane except the unit circumference the case of systems with the invariant zeros in the open set outside the unit disc is regarded as the basic one the difficulties related to the presence of those invariant zeros are overcome by accepting a reconstruction delay commensurate to the invariant zero time constants and the accuracy required for reconstruction the solution devised for that case also applies to systems without invariant zeros however in this case reconstruction is exact and the delay depends on the number of iterations needed for a certain conditioned invariant algorithm to converge finally the more general case of systems with invariant zeros lying anywhere in the complex plane with the sole exception of the unit circumference is reduced to the fundamental one through the synthesis of an appropriate filter

convolutional codes with maximum column sum rank for network streaming the column hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels we introduce a metric known as the column sum rank that parallels the column hamming distance when streaming over a network with link failures we prove the rank analogues of several known column hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory our construction involves finding a class of super regular matrices that preserve this property after multiplication with non singular block diagonal matrices in the ground field

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

optimal ferrers diagram rank metric codes optimal rank metric codes in ferrers diagrams are considered such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space first we consider rank metric anticodes and prove a code anticode bound for ferrers diagram rank metric codes the size of optimal linear anticodes is given four techniques and constructions of ferrers diagram rank metric codes are presented each providing optimal codes for different diagrams and parameters for which no optimal solution was known before the first construction uses maximum distance separable codes on the diagonals of the matrices the second one takes a subcode of a maximum rank distance code and the last two combine codes in small diagrams to a code in a larger diagram the constructions are analyzed and compared and unsolved diagrams are identified

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

coding for errors and erasures in random network coding the problem of error control in random linear network coding is considered a ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic motivated by the property that linear network coding is vector space preserving information transmission is modeled as the injection into the network of a basis for a vector space v and the collection by the receiver of a basis for a vector space u a metric on the projective geometry associated with the packet space is introduced and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space v capu is sufficiently large if the dimension of each codeword is restricted to a fixed integer the code forms a subset of a finite field grassmannian or equivalently a subset of the vertices of the corresponding grassmann graph sphere packing and sphere covering bounds as well as a generalization of the singleton bound are provided for such codes finally a reed solomon like code construction related to gabidulin s construction of maximum rank distance codes is described and a sudan style ldquolist 1rdquo minimum distance decoding algorithm is provided

deadbeat unknown input state estimation and input reconstruction for linear discrete time systems abstract this paper considers discrete time input reconstruction and state estimation assuming that the system has no invariant zeros without assuming that the initial condition is known and without assuming that at least one markov parameter has full column rank algorithms based on the generalized inverse of a block toeplitz matrix are given for unknown input state estimation and simultaneous input reconstruction and state estimation in both cases the unknown input is an arbitrary signal both algorithms are deadbeat which means that exact input reconstruction and state estimation are achieved in a finite number of steps

a novel approach to unknown input filter design for discrete time linear systems in this paper a new h filter design approach is proposed for discrete time linear systems with unknown inputs the proposed lyapunov based approach free of any similarity transformations designs a linear filter for the modified model of the plant and then extracts the original states of the system the designed filter estimates both the system states and the unknown input simultaneously and does not have many of the restrictive assumptions and restrictions that the existing unknown input filters do in the end simulation results are used to illustrate the effectiveness of the proposed filter

state observers for discrete time linear systems with unknown inputs in the paper the problem of designing a full order state observer for a general discrete time linear system with unknown inputs is analyzed necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided and a constructive design procedure together with some examples are discussed finally the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved

error correcting codes in projective spaces via rank metric codes and ferrers diagrams coding in the projective space has received recently a lot of attention due to its application in network coding reduced row echelon form of the linear subspaces and ferrers diagram can play a key role for solving coding problems in the projective space in this paper we propose a method to design error correcting codes in the projective space we use a multilevel approach to design our codes first we select a constant weight code each codeword defines a skeleton of a basis for a subspace in reduced row echelon form this skeleton contains a ferrers diagram on which we design a rank metric code each such rank metric code is lifted to a constant dimension code the union of these codes is our final constant dimension code in particular the codes constructed recently by koetter and kschischang are a subset of our codes the rank metric codes used for this construction form a new class of rank metric codes we present a decoding algorithm to the constructed codes in the projective space the efficiency of the decoding depends on the efficiency of the decoding for the constant weight codes and the rank metric codes finally we use puncturing on our final constant dimension codes to obtain large codes in the projective space which are not constant dimension

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

on the equations governing the motion of an anisotropic poroelastic material we address biot s equations governing the motion of an anisotropic fluid saturated poroelastic material with certain properties first we investigate the uniqueness in solutions of the three dimensional governing equations for the regular region of the poroelastic material and enumerate the conditions sufficient for the uniqueness next by applying hamilton s principle to the motion of the region we obtain a variational principle that generates only the biot newton equations and the associated natural boundary conditions then by extending the variational principle for the region with an internal fixed surface of discontinuity through legendre s transformation we derive a six field variational principle that operates on all the poroelastic field variables the variational principle leads as its euler lagrange equations to all the governing equations including the jump conditions but the initial conditions as a generalized version of the hellinger reissner variational principle moreover we consider the free vibrations of the region and we discuss some basic properties of eigenvalues and present a variational formulation by rayleigh s quotient this work provides a standard tool with the features of variational principles when numerically solving the governing equations in heterogeneous media with finite element methods treating the free vibrations and consistently deriving some onedimensional two dimensional equations of the poroelastic region

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

a rank metric approach to error control in random network coding the problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of rotter and kschischang a large class of constant dimension subspace codes is investigated it is shown that codes in this class can be easily constructed from rank metric codes while preserving their distance properties moreover it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank metric codes where partial information about the error is available this partial information may be in the form of erasures knowledge of an error location but not its value and deviations knowledge of an error value but not its location taking erasures and deviations into account when they occur strictly increases the error correction capability of a code if mu erasures and delta deviations occur then errors of rank t can always be corrected provided that 2t les d 1 mu delta where d is the minimum rank distance of the code for gabidulin codes an important family of maximum rank distance codes an efficient decoding algorithm is proposed that can properly exploit erasures and deviations in a network coding application where n packets of length m over f q are transmitted the complexity of the decoding algorithm is given by o dm operations in an extension field f qn

boundary conditions for the weak formulation of the mixed u p poroelasticity problem this paper presents the boundary conditions that apply to the weak integral formulation of the biot mixed u p poroelasticity equations these boundary conditions are derived from the classical boundary conditions of the biot displacement u u poroelasticity equations they are applied to the surface integrals of the associated weak form to account for exterior excitations supports and couplings with exterior elastic acoustic poroelastic media and a septum it will be shown that the derived boundary conditions for the u p formulation lead to simpler finite element equations compared to those obtained from the u u formulation finally two numerical examples are presented to validate the poroelastic septum coupling condition and to highlight the limitations of the free edge condition on a poroelastic medium

exact almost and optimal input decoupled delayed observers the core of this paper deals with the construction of input decoupled observers which seek asymptotic estimation of a desired output variable a linear combination of state and input of a time invariant either continuous or discrete time system driven by unknown inputs and disturbances exact almost optimal suboptimal and constrained optimal estimation or filtering problems are formulated and studied all the problems defined and studied here are inherently interconnected and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals they are interconnected from a variety of angles e g they are motivated by one another methods of obtaining the solvability conditions and their methods of solution rely on one another etc thus a hierarchy of problems and their solutions is built on top of one another some of the problems studied here are known in the literature but not in as general a form as is given here while a majority of the

linearized polynomial interpolation and its applications in this paper we first propose an interpolation algorithm in a well ordered free module of a linearized polynomial ring and then use this algorithm to decode several important families of codes gabidulin codes kotter and kschischang kk codes and mahdavifar and vardy mv codes our decoding algorithm for gabidulin codes is different from the polynomial reconstruction algorithm by loidreau when applied to decode kk codes our interpolation algorithm is equivalent to the sudan style list 1 decoding algorithm proposed by kotter and kschischang for kk codes the interpolation approach is also capable of solving the interpolation problem for the list decoding of mv codes proposed by mahdavifar and vardy and has a lower complexity than gaussian elimination an interpolator for list decoding of mv codes has also been implemented in hardware and the synthesis results show that it leads to better throughput and efficiency than gaussian elimination

time delayed state and unknown input observation the paper deals with the use of output anticipations to relax restrictions of the existing unknown input observer uio design methods the anticipation signals are treated as additional outputs of the original system and a modified existence condition is presented the modified condition is shown equal to the condition of system inversion a computer simulation shows that the proposed uio using the anticipation signals extends the applicability of uio to a larger class of dynamic systems

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

on the second relative greedy weight of 4 dimensional codes based on applications to the wire tap channel of type ii with the coset coding scheme we will define optimal codes which are described as the ones achieving upper bounds on e 2 m 2 where e 2 and m 2 are the second relative greedy weight and the second relative generalized hamming weight respectively by using the finite geometry method we will first classify all the 4 dimensional codes with respect to their k 1 dimensional subcodes for k 1 1 and k 1 2 and determine the upper bounds on e 2 m 2 for each class of codes and then obtain optimal codes by explicitly constructing the value assignments which achieve upper bounds on e 2 m 2

generalized rank weights of reducible codes optimal cases and related properties reducible codes for the rank metric were introduced for cryptographic purposes they have fast encoding and decoding algorithms include maximum rank distance mrd codes and can correct many rank errors beyond half of their minimum rank distance which makes them suitable for error correction in network coding in this paper we study their security behavior against information leakage on networks when applied as coset coding schemes giving the following main results 1 we give lower and upper bounds on their generalized rank weights grws which measure worst case information leakage to the wire tapper 2 we find new parameters for which these codes are mrd meaning that their first grw is optimal and use the previous bounds to estimate their higher grws 3 we show that all linear over the extension field codes whose grws are all optimal for fixed packet and code sizes but varying length are reducible codes up to rank equivalence and 4 we show that the information leaked to a wire tapper when using reducible codes is often much less than the worst case given by their optimal in some cases grws we conclude with some secondary related properties conditions to be rank equivalent to cartesian products of linear codes and conditions to be rank degenerate duality properties and mrd ranks

universal secure network coding via rank metric codes the problem of securing a network coding communication system against an eavesdropper is considered the network implements linear network coding to deliver n packets from source to each receiver and the adversary can eavesdrop on arbitrarily chosen links the objective is to provide reliable communication to all receivers while guaranteeing that the source information remains information theoretically secure from the adversary a coding scheme is proposed that can achieve the maximum possible rate of n packets the scheme which is based on rank metric codes has the distinctive property of being universal it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying linear network code the only requirement of the scheme is that the packet length be at least n which is shown to be strictly necessary for universal communication at the maximum rate a further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network and the network may suffer from a rank deficiency of at most in this case the proposed scheme can be extended to achieve the rate of n 2t packets this rate is shown to be optimal under the assumption of zero error communication

homogenization of the navier stokes equations with a slip boundary condition this paper deals with the homogenization of the stokes or navier stokes equations in a domain containing periodically distributed obstacles with a slip boundary condition i e the normal component of the velocity is equal to zero while the tangential velocity is proportional to the tangential component of the normal stress we generalize our previous results see 1 established in the case of a dirichlet boundary condition in particular for a so called critical size of the obstacles equal to e3 in the three dimensional case e being the inter hole distance we prove the convergence of the homogenization process to a brinkman type law

variational principles for perfect and dissipative fluid flows many versions of an extension of hamilton s principle to perfect fluid flows exist in the literature in this paper the most general form due to serrin is identified and the limitations of some of the others discussed an extension of the variational principle to viscous thermally conducting fluid flows is suggested this is compared with some other variational principles for viscous flows and the relative merits of the various approaches are discussed

subspace polynomials and cyclic subspace codes subspace codes have received an increasing interest recently due to their application in error correction for random network coding in particular cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms in this paper we consider such cyclic codes and provide constructions of optimal codes for which their codewords do not have full orbits we further introduce a new way to represent subspace codes by a class of polynomials called subspace polynomials we present some constructions of such codes which are cyclic and analyze their parameters