conservative arrays multidimensional modulation codes for holographic recording in holographic storage two dimensional arrays of binary data is optically recorded in a medium via an interference process to ensure optimum operation of a holographic recording system it is desirable that the patterns of 1s light and 0s no light in the recorded array satisfy the following modulation constraint in each row and column of the array there are at least t transitions of the type 1 spl rarr 0 or 0 spl rarr 1 for a prescribed integer t a two dimensional array with this property is said to be a conservative array of strength t in general an n dimensional conservative array of strength t is a binary array having at least t transitions in each column extending in any of the n dimensions of the array we present an algorithm for encoding unconstrained binary data into an n dimensional conservative array of strength t the algorithm employs differential coding and error correcting codes using n binary codes one per dimension with minimum hamming distance d spl ges 2t 3 we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code

the 1 vertex transfer matrix and accurate estimation of channel capacity the notion of a 1 vertex transfer matrix for multidimensional codes is introduced it is shown that the capacity of such codes or the topological entropy can be expressed as the limit of the logarithm of spectral radii of 1 vertex transfer matrices storage and computations using the 1 vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix the method is applied to estimate the first 15 digits of the entropy of the 2 d 0 1 run length limited channel a large scale computation of eigenvalues for the 0 1 run length limited channel in 2 d and 3 d have been carried out this was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with this in turn leads to improvements on the best previous lower and upper bounds for these channels

finite element approximations of a ladyzhenskaya model for stationary incompressible viscous flow some finite element approximation procedures are presented for a model proposed by ladyzhenskaya for stationary incompressible viscous flow the approximate problems are proved to be well posed and stable under standard assumptions on the finite element families the solutions of the approximate problems converge to the solution of the original problem under minimum regularity assumptions some error estimates are derived the optimal order of accuracy is assured with or even without using exact integration rules in the approximation procedure iterative methods for solving the discrete nonlinear problems and comments on some computational experiments are provided special attention is also paid to the common properties as well as differences between the approximation procedure presented here and the approximation for the stationary navier stokes equations

the stability in _ and _ of the projection onto finite element function spaces on etablit la stabilite de la l 2 projection sur quelques espaces a elements finis v h consideree comme une application dans l p et w p 1 1 p sous des hypotheses de regularite faibles

a parameter free dynamic diffusion method for advection diffusion reaction problems abstract in this paper we present a two scale finite element formulation named dynamic diffusion dd for advection diffusion reaction problems by decomposing the velocity field in coarse and subgrid scales the latter is used to determine the smallest amount of artificial diffusion to minimize the coarse scale kinetic energy this is done locally and dynamically by imposing some constraints on the resolved scale solution yielding a parameter free consistent method the subgrid scale space is defined by using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales convergence tests on a two dimensional example are reported yielding optimal rates in addition numerical experiments show that dd method is robust for a wide scope of application problems

generalized belief propagation for the noiseless capacity and information rates of run length limited constraints the performance of the generalized belief propagation algorithm to compute the noiseless capacity and mutual information rates of finite size two dimensional and three dimensional run length limited constraints is investigated in both cases the problem is reduced to estimating the partition function of graphical models with cycles the partition function is then estimated using the region based free energy approximation technique for each constraint a method is proposed to choose the basic regions and to construct the region graph which provides the graphical framework to run the generalized belief propagation algorithm simulation results for the noiseless capacity of different constraints as a function of the size of the channel are reported in the cases that tight lower and upper bounds on the shannon capacity exist convergence to the shannon capacity is discussed for noisy constrained channels simulation results are reported for mutual information rates as a function of signal to noise ratio

block pickard models for two dimensional constraints in pickard random fields prf the probabilities of finite configurations and the entropy of the field can be calculated explicitly but only very simple structures can be incorporated into such a field given two markov chains describing a boundary an algorithm is presented which determines whether a prf consistent with the distribution on the boundary and a 2 d constraint exists iterative scaling is used as part of the algorithm which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists a prf is defined for the domino tiling constraint represented by a quaternary alphabet prf models are also presented for higher order constraints including the no isolated bits n i b constraint and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

capacity bounds for two dimensional asymmetric m ary 0 κ and d α runlength limited channels we present bounds on the two dimensional capacity for two sets of symmetric and asymmetric m ary runlength limited constraints based on simple constructions the bounds extend and generalize previous work on binary constraints

two dimensional runlength constrained arrays with equal horizontal and vertical constraints a binary array is a d1 k1 d2 k 2 runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 and the runs of ones in every row and column have length at least d2 and at most k2 such arrays arise in the context of digital storage devices writing n m n d1 k1 d2 k2 for the number of d1 k 1 d2 k2 runlength constrained arrays of size mtimesn the capacity c d1 k1 d2 k2 is defined to be limm nrarrinfin 1 mn log2n m n d1 k 1 d2 k2 let d2 be an integer such that d2 ges 1 the paper shows that c 1 d2 delta d2 d2 is positive when delta ges 2 but is zero when delta les 1

partial characterization of the positive capacity region of two dimensional asymmetric run length constrained channels a binary sequence satisfies a one dimensional d k run length constraint if every run of zeros has length at least d and at most k a two dimensional binary pattern is d sub 1 k sub 1 d sub 2 k sub 2 constrained if it satisfies the one dimensional d sub 1 k sub 1 run length constraint horizontally and the one dimensional d sub 2 k sub 2 run length constraint vertically for given d sub 1 k sub 1 d sub 2 and k sub 2 the asymmetric two dimensional capacity is defined as c sub d1 k1 d2 k2 lim sub m n spl rarr spl infin 1 mn log sub 2 n sub m n sup d1 k1 d2 k2 where n sub m n sup d1 k1 d2 k2 denotes the number of d sub 1 k sub 1 d sub 2 k sub 2 constrained m spl times n binary patterns we determine whether the capacity is positive or is zero for many choices of d sub 1 k sub 1 d sub 2 k sub 2

a nonlinear subgridscale model for incompressible viscous flow problems we consider a nonlinear subgridscale model of the navier stokes equations resulting in a ladyzhenskaya type system the difference is that the power p and scaling coefficient mu h doteq o h sigma do not arise from macroscopic fluid properties and can be picked to ensure both l infty stability and yet be of the order of the basic discretization error in smooth regions with a properly scaled p laplacian type artificial viscosity one can construct a higher order method which is just as stable as first order upwind methods

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

nonconforming streamline diffusion finite element methods for convection diffusion problems we analyze nonconforming finite element approximations of streamline diffusion type for solving convection diffusion problems both the theoretical and numerical investigations show that additional jump terms have to be added in the nonconforming case in order to get the same o h k 1 2 order of convergence in l 2 as in the conforming case for convection dominated problems a rigorous error analysis supported by numerical experiments is given

block codes for the hard square model the hard square model is a two dimensional 2 d constrained system consisting of all binary arrays on a rectangular grid in which 1 s are isolated both horizontally and vertically this paper proposes algorithms to search for single state and finite state block codes with rectangular codewords that satisfy the hard square constraint although the codeword size is small single state block codes with coding rates larger than 0 5 can be designed letting the 2 d constrained sequences have finite memory increases the achievable coding rate a method for designing low complexity encoders and decoders is also presented when the codeword size increases the coding rate asymptotically approaches the capacity but with rapidly increasing complexity of the encoder and decoder

reliable communications across parallel asynchronous channels with arbitrary skews transmissions across asynchronous communication channels are subject to delay injection attacks which can cause an arbitrary number of skews that is such attacks can cause an arbitrary number of transmitted signals to arrive after the first signal of the next transmission has arrived the common assumption that despite the delays all signals from the i th transmission arrive at the decoder before any signal from the i 2 text nd transmission arrives is called a no switch assumption this paper presents a self synchronizing zero latency zero error coding scheme that requires no acknowledge and can decode transmissions distorted by an arbitrary number of skews that obey this no switch assumption the rate associated with the coding scheme provides a lower bound of 0 6942 for the zero error capacity of such a channel it is further shown that zero error channel capacity of the channel is upper bounded by 0 7248 finally this paper presents bounds on the zero error capacity of a channel for which the number of transmissions that can mix with one another is large

partially hidden markov models partially hidden markov models phmm are introduced they differ from the ordinary hmms in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations as an illustration they are applied to black and white image compression where the hidden variables may be interpreted as representing noncausal pixels

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

adaptive partially hidden markov models with application to bilevel image coding partially hidden markov models phmms have previously been introduced the transition and emission output probabilities from hidden states as known from the hmms are conditioned on the past this way the hmm may be applied to images introducing the dependencies of the second dimension by conditioning in this paper the phmm is extended to multiple sequences with a multiple token version and adaptive versions of phmm coding are presented the different versions of the phmm are applied to lossless bilevel image coding to reduce and optimize the model cost and size the contexts are organized in trees and effective quantization of the parameters is introduced the new coding methods achieve results that are better than the jbig standard on selected test images although at the cost of increased complexity by the minimum description length principle the methods presented for optimizing the code length may apply as guidance for training p hmms for e g segmentation or recognition purposes thereby the phmm models provide a new approach to image modeling

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

two dimensional constrained coding based on tiling a new variable rate coding technique is presented for two dimensional 2 d constraints for certain constraints such as the 0 2 runlength limited rll and 3 rll constraints the technique is shown to improve on previously published lower bounds on the capacity of the constraint

the construction of m ary d spl infin codes that achieve capacity and have the fewest number of encoder states the existence of 100 efficient i e capacity achieving fixed rate codes for input constrained noiseless channels is guaranteed provided the channel has rational capacity a class of m ary runlength limited m d spl infin constraints was shown in previous work to have rational capacity in this correspondence we present a code construction procedure for obtaining 100 efficient codes with the fewest number of encoder states for all m d spl infin constraints with rational capacity the decoders are sliding block decoders with sliding window size d 1

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

genuinely nonlinear models for convection dominated problems this paper introduces a general nonlinear subgrid scale sgs model having boundedartificial viscosity for the numerical simulation of convection dominated problems we also present a numerical comparison error analysis and numerical experiments between this model and the most common sgs model of smagorinsky which uses a p laplacian regularization the numerical experiments for the 2 d convection dominated convection diffusion test problem show a clear improvement in solution quality for the new sgs model this improvement is consistent with the bounded amount of artificial viscosity introduced by the new sgs model in the sharp transition regions

a nonlinear subgrid method for advection diffusion problems abstract this work presents a general framework for approximating advection diffusion equations based on principles of scale separation a two level decomposition of the discrete approximation space is performed and the local problem is modified to capture both local and nonlocal discontinuities the new feature is the local control resulting from decomposing the velocity field into the resolved and unresolved scales and requiring the satisfaction of the discrete model problem at the element level for a minimum kinetic energy associated to the unresolved scales this procedure leads to a nonlinear subgrid model that acts only on the unresolved scales but does not require any tuned up parameter it can be considered a self adaptive method such that the amount of the subgrid viscosity is automatically introduced according to the residual of the resolved scale at element level

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

fields from markov chains a simple construction of two dimensional 2 d fields is presented rows and columns are outcomes of the same markov chain the entropy can be calculated explicitly

analysis of a ladyzhenskaya model for incompressible viscous flow abstract in this paper we analyze a model for the motion of incompressible viscous flows proposed by ladyzhenskaya we establish a new a priori estimate for the nonstationary model and then obtain more general existence and uniqueness results we also present some uniqueness results for the stationary model the relationship between fluid motion governed by the ladyzhenskaya model and that governed by the navier stokes equations is addressed

a bounded artificial viscosity large eddy simulation model in this paper we present a rigorous numerical analysis for a bounded artificial viscosity model tau mu delta sigma a delta nabla s bm u f nabla s bm u for the numerical simulation of turbulent flows in practice the commonly used smagorinsky model tau c s delta 2 nabla s bm u f nabla s bm u is overly dissipative and yields unphysical results to date several methods for clipping the smagorinsky viscosity have proven useful in improving the physical characteristics of the simulated flow however such heuristic strategies strongly rely upon a priori knowledge of the flow regime the bounded artificial viscosity model relies on a highly nonlinear but monotone and smooth semilinear elliptic form for the artificial viscosity for this model we have introduced a variational computational strategy provided finite element error convergence estimates and included several computational examples indicating its improvement on the overly diffusive smagorinsky model

on the entropy of zd subshifts of finite type abstract in this paper we study the combinatorial the topological and the periodic entropies of z d subshifts of finite type we show that the combinatorical and the topological entropies are equal we give sufficient conditions for the periodic entropy to be equal to the topological entropy

bifurcation points and eigenvalues of inequalities of reaction diffusion type on demontre certaines assertions concernant les points de bifurcation et les valeurs propres de systemes de reaction diffusion avec des conditions unilaterales

bounds on the capacity of constrained two dimensional codes bounds on the capacity of constrained two dimensional 2 d codes are presented the bounds of calkin and wilf see siam j discr math vol 11 no 1 p 54 60 1998 apply to first order symmetric constraints the bounds are generalized in a weaker form to higher order and nonsymmetric constraints results are given for constraints specified by run length limits or a minimum distance between pixels of a given value

convex programming upper bounds on the capacity of 2 d constraints the capacity of 1 d constraints is given by the entropy of a corresponding stationary maxentropic markov chain namely the entropy is maximized over a set of probability distributions which is defined by some linear equalities and inequalities in this paper certain aspects of this characterization are extended to 2 d constraints the result is a method for calculating an upper bound on the capacity of 2 d constraints the key steps are as follows the maxentropic stationary probability distribution on square configurations is considered set of linear equalities and inequalities is derived from this stationarity the result is then a convex program which can be easily solved numerically our method improves upon previous upper bounds for the capacity of the 2 d no isolated bits constraint as well as certain 2 d rll constraints

constrained codes as networks of relations we address the well known problem of determining the capacity of constrained coding systems while the one dimensional case is well understood to the extent that there are techniques for rigorously deriving the exact capacity in contrast computing the exact capacity of a two dimensional constrained coding system is still an elusive research challenge the only known exception in the two dimensional case is an exact however not rigorous solution to the run length limited rll system on the hexagonal lattice furthermore only exponential time algorithms are known for the related problem of counting the exact number of constrained two dimensional information arrays we present the first known rigorous technique that yields an exact capacity of a two dimensional constrained coding system in addition we devise an efficient polynomial time algorithm for counting the exact number of constrained arrays of any given size our approach is a composition of a number of ideas and techniques describing the capacity problem as a solution to a counting problem in networks of relations graph theoretic tools originally developed in the field of statistical mechanics techniques for efficiently simulating quantum circuits as well as ideas from the theory related to the spectral distribution of toeplitz matrices using our technique we derive a closed form solution to the capacity related to the path cover constraint in a two dimensional triangular array the resulting calculated capacity is path cover is a generalization of the well known one dimensional rll constraint for which the capacity is known to be

shannon capacity of m ary redundant multitrack runlength limited codes we consider multiamplitude multitrack runlength limited d k constrained channels with and without clock redundancy we calculate the shannon capacities of these channels and present some simple 100 efficient codes to compute capacity a constraint graph equivalent to the usual runlength limited constraint graph is used the introduced graph model has the vertex labeling independent of number of tracks to be written on in parallel which provides computational savings when the number of tracks is large we show that increasing the number of tracks written on in parallel provides significant increase of per track capacity for the more restrictive clocking constraint case i e when k d but it does not have much influence on the channel capacity when k spl ges d

entropy of bit stuffing induced measures for two dimensional checkerboard constraints a modified bit stuffing scheme for two dimensional 2 d checkerboard constraints is introduced the entropy of the scheme is determined based on a probability measure defined by the modified bit stuffing entropy results of the scheme are given for 2 d constraints on a binary alphabet the constraints considered are 2 d rll d infin for d 2 3 and 4 as well as for the constraint with a minimum 1 norm distance of 3 between 1s for these results the entropy is within 1 2 of an upper bound on the capacity for the constraint as a variation of the scheme periodic merging arrays are also considered

bit stuffing algorithms and analysis for run length constrained channels in two and three dimensions a rigorous derivation is given of the coding rate of a variable to variable length bit stuffing coder for a two dimensional 1 spl infin constrained channel the coder studied is nearly a fixed to fixed length algorithm then an analogous variable to variable length bit stuffing algorithm for the three dimensional 1 spl infin constrained channel is presented and its coding rate is analyzed using the two dimensional method the three dimensional coding rate is demonstrated to be at least 0 502 which is proven to be within 4 of the capacity

runlength limited codes for single error detection in the magnetic recording channel an arithmetic function that assigns the value 0 1 or 2 to each binary sequence is introduced the authors call this function the error check value two sequences that differ by a single symmetric error or a single shift error are shown to have different error check values runlength limited codes for detecting single errors are designed by taking a set of the constrained sequences such that each code sequence has the same error check value systematic runlength limited codes that detect single errors are constructed based on the error check value it is shown that these systematic runlength limited codes have the shortest parity length possible for a single error detecting code

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

on row by row coding for 2 d constraints a constant rate encoder decoder pair is presented for a fairly large family of two dimensional 2 d constraints encoding and decoding is done in a row by row manner and is sliding block decodable essentially the 2 d constraint is turned into a set of independent and relatively simple one dimensional 1 d constraints this is done by dividing the array into fixed width vertical strips each row in the strip is seen as a symbol and a graph presentation of the respective 1 d constraint is constructed the maxentropic stationary markov chain on this graph is next considered a perturbed version of the corresponding probability distribution on the edges of the graph is used in order to build an encoder which operates in parallel on the strips this perturbation is found by means of a network flow with upper and lower bounds on the flow through the edges a key part of the encoder is an enumerative coder for constant weight binary words a fast realization of this coder is shown using floating point arithmetic

two dimensional low pass filtering codes we describe a framework for designing encoders that transform arbitrary data sequences into two dimensional arrays satisfying certain constraints in particular constraints that guarantee arrays with limited high spatial frequency content we also exhibit specific codes that produce such arrays such codes are useful for holographic recording systems

reaction diffusion systems destabilizing effect of unilateral conditions on considere un systeme de reaction diffusion dans un domaine r n soit v une solution stationnaire et spatialement homogene avec les conditions aux limites de neumann on etudie la stabilite linearisee de v

a note on the shannon capacity of run length limited codes corresp it is proven that 100 percent efficient fixed rate codes for run length limited rll d k and rll charge constrained d k c channels are possible in only two eases namely d k c 0 1 1 and 1 3 3 specifically the binary shannon capacity of rll d k constrained systems is shown to be irrational for all values of d k 0 leq d for rll charge constrained systems with parameters d k c the binary capacity is irrational for all values of d k c 0 leq d except 0 1 1 and 1 3 3 which both have binary capacity 1 2

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

new bounds on the capacity of multidimensional run length constraints we examine the well known problem of determining the capacity of multidimensional run length limited constrained systems by recasting the problem which is essentially a combinatorial counting problem into a probabilistic setting we are able to derive new lower and upper bounds on the capacity of 0 k rll systems these bounds are better than all previously known analytical bounds for k 2 and are tight asymptotically thus we settle the open question what is the rate at which the capacity of 0 k rll systems converges to 1 as k we also provide the first nontrivial upper bound on the capacity of general d k rll systems

adaptive defect correction methods for convection dominated convection diffusion problems abstract we present a posteriori error estimates for a defect correction method for approximating solutions of convection diffusion problems the algorithms and estimators include the possibility of using in the discretization a nonlinear selection mechanism which we find improves solution quality in and near layers energy norm and l2 a posteriori error estimates are proven for the full algorithm two examples of fully adaptive finite element defect correction calculations are presented these examples illustrate the scheme and demonstrate the effectiveness of the method

improved lower bounds on capacities of symmetric 2d constraints using rayleigh quotients a method for computing lower bounds on capacities of two dimensional 2d constraints having a symmetric presentation in either the horizontal or the vertical direction is presented the method is a generalization of the method of calkin and wilf siam j discrete math 1998 previous best lower bounds on capacities of certain constraints are improved using the method it is also shown how this method as well as their method for computing upper bounds on the capacity can be applied to constraints which are not of finite type additionally capacities of two families of multidimensional constraints are given exactly

a characterization of the entropies of multidimensional shifts of finite type we show that the values of entropies of multidimensional shifts of finite type sfts are characterized by a certain computation theoretic property a real number h 0 is the entropy of such an sft if and only if it is right recursively enumerable i e there is a computable sequence of rational numbers converging to h from above the same characterization holds for the entropies of sofic shifts on the other hand the entropy of strongly irreducible sfts is computable

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100