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

bounds on the rate of 2 d bit stuffing encoders a method for bounding the rate of bit stuffing encoders for 2 d constraints is presented instead of considering the original encoder we consider a related one which is quasi stationary we use the quasi stationary property in order to formulate linear requirements that must hold on the probabilities of the constrained arrays that are generated by the encoder these requirements are used as part of a linear program the minimum and maximum of the linear program bound the rate of the encoder from below and from above respectively a lower bound on the rate of an encoder is also a lower bound on the capacity of the corresponding constraint for some constraints our results lead to tighter lower bounds than what was previously known

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

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

study of coating flow by the finite element method abstract silliman s analysis of slot coating is extended to accommodate film flows with highly bent menisci as in slide and curtain coating by combining polar and cartesian coordinate parametrizations of meniscus shape the nonlinear algebraic equations from the subdomain galerkin weighted residual method and finite element basis functions are solved by newton s method which is perfected for the free boundary problem convergence behavior is examined slot coating results reveal slow flow zones and show that at high capillary number and low metering rate the downstream meniscus can no longer attach to the slot comparison of coyne and elrod s approximate solutions with the finite element solutions shows that their assumption of a parabolic velocity profile leads to reasonable approximations of meniscus shapes

new array codes for multiple phased burst correction an optimal family of array codes over gf q for correcting multiple phased burst errors and erasures where each phased burst corresponds to an erroneous or erased column in a code array is introduced as for erasures these array codes have an efficient decoding algorithm which avoids multiplications or divisions over extension fields replacing these operations with cyclic shifts of vectors over gf q the erasure decoding algorithm can be adapted easily to handle single column errors as well the codes are characterized geometrically by means of parity constraints along certain diagonal lines in each code array thus generalizing a previously known construction for the special case of two erasures algebraically they can be interpreted as reed solomon codes when q is primitive in gf q the resulting codes become conventional reed solomon codes of length p over gf q sup p 1 in which case the new erasure decoding technique can be incorporated into the berlekamp massey algorithm yielding a faster way to compute the values of any prescribed number of errors

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

approximation and geometric properties of complex favard szasz mirakjan operators in compact disks in this paper first we obtain quantitative estimates of the convergence and of the voronovskaja s theorem in compact disks for complex favard szasz mirakjan operators attached to analytic functions satisfying some suitable exponential type growth condition then we prove that beginning with an index these operators preserve the starlikeness convexity and spirallikeness in the unit disk

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

efficient numerical solution of steady free surface navier stokes flow numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics the usual method for solving steady viscous free surface flow subject to gravitation is alternating time integration of the kinematic condition and the navier stokes equations subject to the dynamic conditions until steady state is reached this paper shows that this time integration approach is often inefficient it proposes an efficient iterative method for solving the steady free surface flow problem the new method relies on a different but equivalent formulation of the free surface flow problem involving a so called quasi free surface condition the convergence behavior of the new method is shown to be asymptotically mesh width independent numerical results are presented for two dimensional flow over an obstacle in a channel the results confirm the mesh width independence of the convergence behavior and comparison of the numerical results with measurements shows good agreement

some approximation properties of baskakov durrmeyer stancu operators abstract in this paper we are dealing with a new type of baskakov durrmeyer stancu bds operators d n f x defined by 1 4 first we estimate moments of these operators and also obtain the recurrence relations for the moments we estimate some approximation properties and asymptotic formulae for these operators in the last section we give better error estimations for the operators 1 4 using king type approach

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

equilibria stability and bifurcations of rotating columns of fluid subjected to planar disturbances long gyrostatically rotating cylindrical drops held together by surface tension are amenable to conventional bifurcation analysis as well as newer computer aided methods of analysis and so are useful prototypes of three dimensional drops instability to rayleigh s axisymmetric mode is set aside and effects of translationally symmetric planar disturbances are investigated the shapes and stability of drops on and near the family of perfect cylinders are determined by means of the power series method of millman keller nonlinearly distorted shapes and their stability are calculated by galerkin or finite element analysis using either a a polar or b a composite polar and cartesian representation of drop shape the disadvantage of using single coordinate representation of drop shapes near break up is brought out the new results show that a family of symmetric two lobed shapes bifurcates from the main family of perfectly cylindrical shapes when the rotation rate attains a critical value in accord with the linearized hydrodynamic analysis of hocking moreover a new family of asymmetric two lobed shapes is uncovered that bifurcates from and rejoins the family of symmetric two lobed shapes using a polar representation of drop shape plainly the new shape family is the two dimensional analog of the family of three dimensional capillary peanuts discovered by brown scriven who used a spherical polar representation of drop shape by way of contrast the results obtained using a composite polar and cartesian representation of drop shape show that the gyrostatic family of symmetric two lobed shapes does not exchange stability with a family of asymmetric shapes and eventually breaks up by becoming a family of self intersecting shapes

the norm estimates of the q bernstein operators for varying q 1 the aim of this paper is to present norm estimates in c 0 1 for the q bernstein basic polynomials and the q bernstein operators b n q in the case q 1 while for 01 the norm b n q increases rather rapidly as q in this study it is proved that b n q c nq n n 1 2 q withc n 2n 1 1n n 1 moreover it is shown that b n q 2q n n 1 2ne as n q the results of the paper are illustrated by numerical examples

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

on the iterates of positive linear operators preserving the affine functions in this note we study the limit behavior of the iterates of a large class of positive linear operators preserving the affine functions and as a byproduct of our result we obtain the limit of the iterates of meyer konig and zeller operators

on multivariate baskakov operator abstract in this paper we study multivariate baskakov operator b n d f x we first show that the operator can retain some properties of the original function f such as monotony semi additivity and lipschitz condition etc secondly we discuss the monotony on the sequence of multivariate baskakov operator b n d f x for n when the function f is convex then we propose for estimating the rate of approximation a new modulus of smoothness and prove the modulus to be equivalent to certain k functional finally with the modulus of smoothness as metric we establish a strong direct theorem by using a decomposition technique for the operator

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

on the iterates of a class of summation type linear positive operators this note is focused upon positive linear operators which preserve the quadratic test function by using contraction principle we study the convergence of their iterates

interleaving schemes for multidimensional cluster errors we present two dimensional and three dimensional interleaving techniques for correcting two and three dimensional bursts or clusters of errors where a cluster of errors is characterized by its area or volume correction of multidimensional error clusters is required in holographic storage an emerging application of considerable importance our main contribution is the construction of efficient two dimensional and three dimensional interleaving schemes the proposed schemes are based on t interleaved arrays of integers defined by the property that every connected component of area or volume t consists of distinct integers in the two dimensional case our constructions are optimal they have the lowest possible interleaving degree that is the resulting t interleaved arrays contain the smallest possible number of distinct integers hence minimizing the number of codewords required in an interleaving scheme in general we observe that the interleaving problem can be interpreted as a graph coloring problem and introduce the useful special class of lattice interleavers we employ a result of minkowski dating back to 1904 to establish both upper and lower bounds on the interleaving degree of lattice interleavers in three dimensions for the case t spl equiv 0 mod 6 the upper and lower bounds coincide and the minkowski lattice directly yields an optimal lattice interleaver for t spl ne 0 mod 6 we construct efficient lattice interleavers using approximations of the minkowski lattice

on the regularity of flows with ladyzhenskaya shear dependent viscosity and slip or non slip boundary conditions navier stokes equations with shear dependent viscosity under the classical nonslip boundary condition were introduced and studied in the 1960s by o a ladyzhenskaya and in the case of gradient dependent viscosity by j l lions a particular case is the well known smagorinsky turbulence model this is nowadays a central subject of investigation on the other hand boundary conditions of slip type seems to be more realistic in some situations in particular in numerical applications they are a main research subject the existence of weak solutions u to the above problems with slip or nonslip type boundary conditions is well known in many cases however regularity up to the boundary still presents many open questions in what follows we present some regularity results in the stationary case for weak solutions to this kind of problem see theorem 3 1 and theorem 3 2 the evolution problem is studied in a forthcoming paper 6 a cornerstone in our proof is the classical nirenberg translation method see 38

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

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

on the spectrum of positive linear operators with a partition of unity property abstract we characterize the spectrum of positive linear operators between banach function spaces having finite rank and a partition of unity property our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle finally we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator

natural convection in steady solidification finite element analysis of a two phase rayleigh benard problem abstract galerkin finite element approximations and newton s method for solving free boundary problems are combined with computer implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt the newton method gives rapid convergence to steady state velocity temperature and pressure fields and melt solid interface shapes and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability the power of this combination is demonstrated for a two phase rayleigh benard problem composed of melt and and solid in a vertical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt solid interface is always a solution multiple cellular flows bifurcating from the static state are detected and followed as rayleigh number is varied changing the boundary conditions to approach those appropriate for the vertical bridgman solidification system causes imperfections that eliminate the static state the flow structure in the bridgman system is related to those for the rayleigh benard system by a continuous evolution of the boundary conditions

approximation properties of complex q szasz mirakjan operators in compact disks this paper deals with approximating properties of the newly defined q generalization of the szasz mirakjan operators in the case q 1 quantitative estimates of the convergence the voronovskaja s theorem and saturation of convergence for complex q szasz mirakjan operators attached to analytic functions in compact disks are given in particular it is proved that for functions analytic in email protected c z 2q the rate of approximation by the q szasz mirakjan operators q 1 is of order q n versus 1 n for the classical szasz mirakjan operators

nonlinear oscillations of inviscid free drops abstract inviscid oscillations of free liquid drops are analyzed by solving bernoulli s equation for the free surface shape and laplace s equation for the velocity potential field the means are a galerkin s weighted residual method which converts the governing equations into a large system of nonlinear time dependent ordinary differential equations b an implicit predictor corrector method for time integration which automatically adjusts time steps and c newton s method which solves the large system of nonlinear algebraic equations that results from time discretization results presented include sequences of drop shapes pressure distributions particle paths and evolution with time of kinetic and surface energies accuracy is attested by virtual constancy of drop volume and total energy and smallness of mass and momentum fluxes across drop surfaces dynamic response to small amplitude disturbances agrees with linear theory large amplitude oscillations are compared to the predictions by the marker and cell method and second order perturbation theory mode interactions and frequency shifts are analyzed by fourier power spectra and lend further insight into the nature of the oscillations

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

saturation of convergence for q bernstein polynomials in the case q 1 abstract in the note we discuss voronovskaya type theorem and saturation of convergence for q bernstein polynomials for a function analytic in the disc u r z z r r q for arbitrary fixed q 1 we give explicit formulas of voronovskaya type for the q bernstein polynomials for q 1 we show that the rate of convergence for the q bernstein polynomials is o q n q 1 for infinite number of points having an accumulation point on u r q if and only if f is linear

asymptotic properties of powers of linear positive operators which preserve e2 in this paper we prove korovkin type theorem for iterates of general positive linear operators t c 0 1 c 0 1 which preserve e 2 and derive quantitative estimates in terms of moduli of smoothness the results can be applied to several well known operators we present here the bernstein the q bernstein the genuine bernstein durrmeyer and the genuine q bernstein durrmeyer operators

numerical simulation of hydraulic jump hydraulic jump on a straight horizontal channel with supercritical froude numbers 2 0 and 4 0 is numerically simulated by solving the reynolds averaged navier stokes equations turbulence is modelled through the k closure equations and the mixed eulerian lagrangian description of flow is utilized to overcome the problem posed by moving free boundary time stepping is done via fractional step method and pressure is determined from poisson s equation galerkin finite element method with three noded triangular elements is used for spatial discretization a detailed study of the internal and external characteristics of hydraulic jump is done and compared with experimental values where possible surface roller and recirculation zone are found to play a dominant role in turbulence generation and dissipation

finite element analysis of wave motion to estimate wave motion the finite element method is presented based on the linear interpolation function and two step explicit numerical integration in time for the determination of free surface position the two step scheme based on the eulerian technique is usefully employed travel and run up of solitary wave have been analysed and compared with the analytical solution both results are reasonably well in agreement this method is applied to estimate the wave force on the practical breakwater to show the validity of the method

approximation in compact sets by q stancu faber polynomials q 1 we prove that the q stancu faber polynomials q 1 attached to a compact set email protected c and to an analytic function on g can represent good alternatives to the partial sums of the faber series attached to the same function and subset both giving the geometric progression order of approximation q n

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

variational formulation of a model free boundary problem the purpose of this work is to present an error analysis of the numerical approximation by a finite element method of a free surface problem the analysis has been done in an abstract model which has many of the features of a free surface problem for a viscous liquid we study in this paper how the numerical approximation of the free boundary affects the approximation of the other variables of the problem and vice versa we present the numerical analysis of a free boundary problem that is intended to incorporate many of the difficulties found in a class of models of fluid flow phenomena with free surfaces one such phenomenon which motivates the current work is the flow of a liquid constrained only partly by a container that is in which a part of the boundary of the domain filled by the liquid is an interface with another liquid of much smaller density and for which surface tension plays a significant role in determining the shape of the free surface one model for the behavior of such liquids is based on the assumption that the surface tension between the two liquids is proportional to the curvature of the free surface the constant of proportionality is a physical property of the two fluids this model has been studied extensively in recently years both experimentally cf jean and pritchard 15 and pritchard 19 theoretically cf allain 2 beale 4 bemelmans 5 jean 14 pukhnachov 20 and solonnikov 27 asymptotically keller and miksis 16 and computationally cf cuvelier 10 ryskin and leal 23 and saito and scriven 24 our purpose here is to establish a framework for the analysis of convergence properties of the computational techniques being used the only previous work that we are aware of in this direction is by nitsche 18 in the first section of the paper we define our model problem in classical terms in the second section we construct a variational formulation for the problem that has two new features one is that it allows the existence of a solution to be proved with weaker assumptions on the data than has been possible received february 26 1990 revised november 20 1990 1980 mathematics subject classification 1985 revision primary 65n30

convergence properties and iterations for q stancu polynomials in compact disks this paper deals with approximating properties and convergence results of the iterates for complex q stancu polynomials attached to analytic functions on compact disks in the case q 1 some estimates on the rate of convergence are given

approximation theorems for the iterated boolean sums of bernstein operators abstract for the iterated boolean sums of bernstein operators we prove global direct inverse and saturation results

an extension of the biharmonic boundary integral method to free surface flow in channels abstract the biharmonic boundary integral solution of two dimensional creeping flow of an incompressible newtonian fluid is extended to problems with free surfaces iterative construction of the free surface with the normal stress condition is achieved with a shooting method that is most appropriate for thin films and menisci of widely varying curvature a continuation scheme is also introduced to systematically construct the solution as a function of a given parameter these new techniques combined with the known storage and computational advantages of the biharmonic boundary integral method allow construction of difficult free surfaces we demonstrate this by solving the bretherton problem of a two dimensional air bubble traveling in a channel agreement with asymptotic theory and the finite difference method is shown other problems on formation and transport of bubbles in channels are also tackled

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

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

ifs on a metric space with a graph structure and extensions of the kelisky rivlin theorem abstract we develop the hutchinson barnsley theory for finite families of mappings on a metric space endowed with a directed graph in particular our results subsume a classical theorem of j e hutchinson j e hutchinson fractals and self similarity indiana univ math j 30 1981 713 747 on the existence of an invariant set for an iterated function system of banach contractions and a theorem of l mate l mate the hutchinson barnsley theory for certain non contraction mappings period math hungar 27 1993 21 33 concerning finite families of locally uniformly contractions introduced by edelstein also they generalize recent fixed point theorems of a c m ran and m c b reurings a c m ran m c b reurings a fixed point theorem in partially ordered sets and some applications to matrix equations proc amer math soc 132 2004 1435 1443 j j nieto and r rodriguez lopez j j nieto r rodriguez lopez contractive mapping theorems in partially ordered sets and applications to ordinary differential equations order 22 2005 223 239 j j nieto r rodriguez lopez existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations acta math sin engl ser 23 2007 2205 2212 and a petrusel and i a rus a petrusel i a rus fixed point theorems in ordered l spaces proc amer math soc 134 2006 411 418 for contractive mappings on an ordered metric space as an application we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary banach space this result yields new generalizations of the kelisky rivlin theorem on iterates of the bernstein operators on the space c 0 1 as well as its extensions given recently by h oruc and n tuncer h oruc n tuncer on the convergence and iterates of q bernstein polynomials j approx theory 117 2002 301 313 and h gonska and p pi ul h gonska p pi ul remarks on an article of j p king comment math univ carolin 46 2005 645 652

generalized szasz mirakjan type operators via q calculus and approximation properties abstract the aim of this paper is to construct q analogue of generalized szasz mirakjan type operators whose construction depend on a real valued function we prove that the new operators provide better weighted uniform approximation over 0 in terms of weighted moduli of smoothness we obtain degrees of approximation associated with the function also a voronovskaya type result is obtained finally we give some graphical examples for these operators and show that the new operators are more flexible in view of rate of convergence to the function f which depends on the selection of un q and vn q

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

penalty method with p1 p1 finite element approximation for the stokes equations under the slip boundary condition we consider the p1 p1 or p1b p1 finite element approximations to the stokes equations in a bounded smooth domain subject to the slip boundary condition a penalty method is applied to address the essential boundary condition u cdot n g on partial omega which avoids a variational crime and simultaneously facilitates the numerical implementation we give o h 1 2 epsilon 1 2 h epsilon 1 2 error estimate for velocity and pressure in the energy norm where h and epsilon denote the discretization parameter and the penalty parameter respectively in the two dimensional case it is improved to o h epsilon 1 2 h 2 epsilon 1 2 by applying reduced order numerical integration to the penalty term the theoretical results are confirmed by numerical experiments

on some convergence criteria for nets of positive operators on continuous function spaces we establish a simple criterion concerning the convergence of nets or generalized sequences of positive linear operators on c x x compact toward a positive linear operator as a consequence we discuss several criteria about the asymptotic behavior of the iterates of markov operators finally we present some applications concerning the asymptotic behavior of the iterates of bernstein schnabl operators on a convex compact subset not necessarily associated with a positive projection and the iterates of a special linear operator generalizing the so called cesaro operator on c 0 1

on the iterates of some bernstein type operators abstract in this paper we establish two basic functional type identities between the iterates of the bleimann butzer hahn operator and those of the bernstein operator on the one hand and the iterates of the modified meyer konig and zeller operator and those of the baskakov operator on the other these identities allow us to transfer the properties of these operators from one to another attention is focused on the limit behavior of the iterates and the linear combinations of iterates of fejer korovkin type

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

stationary markov random fields on a finite rectangular lattice this paper provides a complete characterization of stationary markov random fields on a finite rectangular non toroidal lattice in the basic case of a second order neighborhood system equivalently it characterizes stationary markov fields on z sup 2 whose restrictions to finite rectangular subsets are still markovian i e even on the boundaries until now pickard random fields formed the only known class of such fields first we derive a necessary and sufficient condition for markov random fields on a finite lattice to be stationary it is shown that their joint distribution factors in terms of the marginal distribution on a generic 2 spl times 2 cell which must fulfil some consistency constraints second we solve the consistency constraints and provide a complete characterization of such measures in three cases symmetric measures and gaussian measures are shown to necessarily belong to the pickard class whereas binary measures belong either to the pickard class or to a new nontrivial class which is further studied in particular the corresponding fields admit a simple parameterization and may be simulated in a simple although nonunilateral manner

discretization of the navier stokes equationswith slip boundary condition ii multilevel methods are a common tool for solving nonlinear systems arising from discretizations of elliptic boundary value problems see e g 1 2 multilevel methods consist of solving the nonlinear problem on a coarse mesh and then performing one or two newton correction steps on each subsequent mesh thus solving only one or two larger linear systems in a previous paper by the author 3 a two level method was proposed for the stationary navier stokes equations with slip boundary condition uniqueness of solution to the nonlinear problem step 1 of the two level method is guaranteed provided that the data of the problem i e the reynolds number and the forcing term is bounded in practice however the aforementioned bound on the data is rarely satisfied consequently a priori error estimates should not rely upon this bound such estimates will be established in this report for the two level method the scalings of the meshwidths that guarantee optimal accuracy in the h 1 norm are equally favorable to those in the uniqueness case

approximation by q durrmeyer type polynomials in compact disks in the case q 1 abstract recently agarwal and gupta 2012 1 studied some approximation properties of the complex q durrmeyer type operators in the case 0 q 1 in this paper this study is extended to the case q 1 more precisely approximation properties of the newly defined generalization of this operators in the case q 1 are studied quantitative estimates of the convergence the voronovskaja type theorem and saturation of convergence for complex q durrmeyer type polynomials attached to analytic functions in compact disks are given in particular it is proved that for functions analytic in z c z r r q the rate of approximation by the q durrmeyer type polynomials q 1 is of order q n versus 1 n for the classical q 1 durrmeyer type polynomials explicit formulas of voronovskaya type for the q durrmeyer type operators for q 1 are also given this paper represents an answer to the open problem initiated by gal 2013 6

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

finite element simulation of combined buoyancy and thermocapillary driven convection in open cavities thermocapillary induced and buoyancy driven convective flows that commonly occur in crystal growth are numerically simulated using galerkin finite element method the physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls the top gas melt interface is free to deform subject to 90 contact angle boundary conditions at the two vertical walls the unsteady two dimensional navier stokes equations are discretized in time using chorin type splitting scheme and pressure is determined from the poisson s equation the free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation the governing equations for heat and momentum are solved in the arbitrary lagrangian eulerian frame of reference to handle the moving boundary the influence of grashof number marangoni number bond number ohnesorge number and prandtl number on the flow field and heat transfer is investigated

a second order boundary fitted projection method for free surface flow computations this paper describes a new approach to the high fidelity simulation of axisymmetric free surface flows a boundary fitted grid is coupled with a new projection method for the solution of the navier stokes equations with second order accuracy in space and time two variants of this new method are developed by adapting two existing algorithms suitable for prescribed velocity boundary conditions to the case of prescribed normal and tangential stresses at the free boundary a normal mode analysis for a fixed boundary problem confirms the second order accuracy of the algorithms the approach is validated by comparison with a rayleigh plesset solution for an oscillating spherical bubble with an analysis of shape oscillations and with existing results for the buoyant rise of a deforming bubble for reynolds numbers up to 200 and weber numbers up to 12 in addition to the simulation of axisymmetric free surface flows of intrinsic interest the present approach is suitable for the validation of genuinely three dimensional calculations

finite element method for time dependent incompressible free surface flow we present a finite element method for time dependent incompressible free surface fluid flow problems described by the navier stokes equations the elements chosen have dimensions in both space and time and the resulting system of equations is block tridiagonal and lends itself to solution by standard techniques in the present article we restrict our attention to two dimensional problems although three dimensional problems may be solved by a straightforward generalization the method is essentially an implicit time stepping technique and therefore stable even for relatively large time steps with this choice of elements the method is completely adaptive to the changing nature of the solution an iterative procedure is used to find the position of the free surface this procedure is found to be rapidly convergent determining accurately the shape of the free surface within a few iterations numerical results are given for the problem of entrainment of fluid by a vertically moving plate which has applications to the chemical engineering problems of the free coating of metals we also consider the problem of circulation flow in a rectangular channel

regularity of solutions to a non homogeneous boundary value problem for general stokes systems in r n we give a simple and very complete proof of the existence of a strong h2 solution to the non homogeneous problem 1 1 under the non homogeneous boundary conditions 1 6 here we consider the half space case rn n 3 see theorem 1 2 this regularity result was previously obtained by solonnikov and scadilov in reference 33 for the classical stokes system 0 g x 0 in the 3 d homogenous case a 0 b 0 and a suitable open subset of r3

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

on the construction of bounded delay encodable codes for constrained systems we present a new technique to construct sliding block modulation codes with a small decoding window our method which involves both state splitting and look ahead encoding crucially depends on a new local construction method for bounded delay codes we apply our method to construct several new codes all with a smaller decoding window than previously known codes for the same constraints at the same rate

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

finite element approximation of incompressible navier stokes equations with slip boundary condition we consider mixed finite element approximations of the stationary incompressible navier stokes equations with slip boundary condition simultaneously approximating the velocity pressure and normal stress component the stability of the schemes is achieved by adding suitable consistent penalty terms corresponding to the normal stress component and to the pressure a new method of proving the stability of the discretizations allows us to obtain optimal error estimates for the velocity pressure and normal stress component in natural norms without using duality arguments and without imposing uniformity conditions on the finite element partition the schemes can easily be implemented into existing finite element codes for the navier stokes equations with standard dirichlet boundary conditions

sensitivity analysis of boundary value problems application to nonlinear reacti abstract a direct and very efficient approach for obtaining sensitivities of two point boundary value problems solved by newton s method is studied the link between the solution method and the sensitivity equations is investigated together with matters of numerical accuracy and efficiency this approach is employed in the analysis of a model three species unimolecular steady state premixed laminar flame the numerical accuracy of the sensitivities is verified and their values are utilized for interpretation of the model results it is found that parameters associated directly with the temperature play a dominant role the system s green s functions relating dependent variables are also controlled strongly by the temperature in addition flame speed sensitivities are calculated and shown to be a special class of derived sensitivity coefficients finally some suggestions for the physical interpretation of sensitivities in model analysis are given