ergodicity of markov channels a markov channel is a discrete information channel that includes as special cases the finite state channels and finite state codes of information theory kieffer and rahe proved that one sided and two sided markov channels have the following property if the input source to a markov channel is asymptotically mean stationary ams then so is the resulting input output process and hence the ergodic theorem and the shannon mcmillan breiman theorem hold for the input output process kieffer and rahe also provided a sufficient condition for any ams ergodic source to yield an ams ergodic input output process new conditions for a markov channel to have this ergodicity property are presented and discussed here several relations are developed among various classes of channels including weakly ergodic indecomposable and strongly mixing channels some connections between markov channels and the theory of nonhomogeneous markov chains are also discussed

analyticity of the stokes semigroup in spaces of bounded functions the analyticity of the stokes semigroup with the dirichlet boundary condition is established in spaces of bounded functions when the domain occupied with fluid is bounded or more generally admissible which admits a special estimate for the helmholtz decomposition the proof is based on a blow up argument this is the first proof of the analyticity in spaces of bounded functions which was left open more than thirty years

very weak generalized and strong solutions to the stokes system in the half space abstract in this paper we study the stokes system in the half space r n with n 2 we give existence and uniqueness results in weighted sobolev spaces after the central case of the generalized solutions we are interested in strong solutions and symmetrically in very weak solutions by means of a duality argument

spatial and temporal decay estimate of the stokes flow of weighted l1 initial data in the half space abstract in this paper we derive the spatial and temporal decay estimate of the stokes solution e t a a in the half space when the prescribed initial data is in a weighted l 1 space we obtained that x i r e t a a l c t n 2 1 2 x i r x n a l 1 c t n 2 r 1 2 x n a l 1 for 0 r n if i n and 0 r n 1 if i 1 n 1

an on line universal lossy data compression algorithm via continuous codebook refinement ii optimality for phi mixing source models for pt i see ibid vol 42 no 3 p 803 21 1996 two versions of the gold washing data compression algorithm one with codebook innovation interval and the other with finitely many codebook innovations are considered the version of the gold washing algorithm with codebook innovation interval k is a variant of the gold washing algorithm such that the codebook is innovated once every k 1 source words during the process of encoding the entire source it is demonstrated that when this version of the gold washing algorithm is applied to encode a stationary spl phi mixing source the expected distortion performance converges to the distortion rate function of the source as the codebook length goes to infinity furthermore if the source to be encoded is a markov source or a finite state source then the corresponding sample distortion performance converges almost surely to the distortion rate function the version of the gold washing algorithm with finitely many codebook innovations is a variant of the gold washing algorithm in which after finitely many codebook innovations the codebook is held fixed and reused to encode the forthcoming source sequence block by block similar results are shown for this version of the gold washing algorithm in addition the convergence speed of the algorithm is discussed

weighted lq l1 estimate of the stokes flow in the half space abstract in this paper we derive the weighted l q l 1 estimate of the stokes solution u in the half space when 1 q we obtained that x r u l q c t 1 2 n 2 1 1 q x r x n a l 1 c t r 1 2 n 2 1 1 q x n a l 1 for 0 r n 1 1 1 q and x n r u l q c t 1 2 n 2 1 1 q x n r 1 a l 1 c t r 1 2 n 2 1 1 q x n a l 1 for 0 r n 1 1 q

notes on the space time decay rate of the stokes flows in the half space in this paper a stokes equations in the half space r n n 2 has been considered we derive a rapid decay rate of the stokes flow in space and time when the initial data decreases fast enough and satisfies some additional condition initial data decreasing too slowly to be x h l1 r n are also considered

decay results of solutions to the incompressible navier stokes flows in a half space abstract in a half space we consider the asymptotic behavior of the strong solution for the non stationary navier stokes equations in particular the decay rates of the second order derivatives of the navier stokes flows in l r r n n 2 with 1 r are derived by using l q l r estimates and a clever analysis on the fractional powers of the stokes operator in addition we prove that the strong solution and its first and second derivatives decay in time more rapidly than observed in general if the initial datum lies in a suitable weighted space

on the navier stokes equations in the half space with initial and boundary rough data in morrey spaces abstract we consider the initial boundary value problem for the navier stokes equations in the half space with data in morrey spaces existence of small global solutions is proved in spaces with the right homogeneity to allow self similar solutions moreover we analyze the long time behavior of the solutions and obtain a class of asymptotically self similar ones

on l infty bmo estimates for derivatives of the stokes semigroup we consider the stokes equations in a class of domains that we will call admissible domains including bounded domains the half space and exterior domains we will prove new l infty estimates for derivatives of velocity and pressure the estimates will be given in terms of a bmo type norm of the initial data

asymptotic behavior for the stokes flow and navier stokes equations in half spaces abstract using the solution formula in ukai 1987 27 for the stokes equations we find asymptotic profiles of solutions in l 1 r n n 2 for the stokes flow and non stationary navier stokes equations since the projection operator p l 1 r n l 1 r n is unbounded we use a decomposition for p u u to overcome the difficulty and prove that the decay rate for the first derivatives of the strong solution u of the navier stokes system in l 1 r n is controlled by t 1 2 1 t n 2 2 for any t 0

time decay rates of non newtonian flows in rn abstract this paper is concerned with time decay rates of the weak solutions of an incompressible non newtonian fluid motion model in half spaces r n for n 3 with the use of the spectral decomposition of the stokes operator and l p l q estimates it is shown that the weak solutions decay in l 2 norm like t n 2 1 r 1 2 when the initial velocity u 0 l 2 l r for 1 r 2 the higher decay rates t n 2 1 r 1 2 1 2 are obtained if u 0 satisfies the additional moment condition r n x n u 0 x r d x 1 r 2 moreover the error estimates between the non newtonian flow and the navier stokes flow are discussed

temporal decays in l 1 and l for the stokes flow we estimate the time decay rates in l1 in the hardy space and in l of solutions for the stokes equations on the half spaces for the estimates in the hardy space we adopt the ideas in math z 231 1999 383 temporal and spatial decays for the stokes flows submitted for publication and also use the heat kernel and the solution formula for the stokes equations

weighted decay properties for the incompressible stokes flow and navier stokes equations in a half space abstract using the stokes solution formula and l q l r estimates of the stokes operator semigroup we establish the weighted decay properties for the stokes flow and navier stokes equations including their spatial derivatives in half spaces in addition the unboundedness of the projection operator p l r n l r n is overcome by employing a decomposition for the nonlinear term and l asymptotic behavior for the second derivatives of navier stokes flows in half spaces is given

on estimates for the stokes flow in a space of bounded functions in this paper we study regularizing effects of the composition operator s t p for the stokes semigroup s t and the helmholtz projection p in a space of bounded functions we establish new a priori l estimates of the operator s t p for a certain class of domains including bounded and exterior domains they imply unique existence of mild solutions of the navier stokes equations in a space of bounded functions

pointwise decay estimate of navier stokes flows in the half space with slowly decreasing initial value abstract in this paper we study the spatial and temporal decay estimate of the navier stokes flow in the half space corresponding to auniformly but slowly decreasing initial velocity we show the local in time solvability of the navier stokes equations with u x t c 0 1 x t and u x t c 0 t 1 2 1 x t when 1 x t e t a h l r n 0 and t 1 2 1 x t e t a h l r n 0 0 n asymptotically it holds that u x t e t a h x o t x 0 n as x the solution exists globally in time for 1 when the data is small enough and it holds that u x t e t a h x o x t 1 n as x t

space time asymptotics of the two dimensional navier stokes flow in the whole plane abstract we consider the space time behavior of the two dimensional navier stokes flow introducing some qualitative structure of initial data we succeed to derive the first order asymptotic expansion of the navier stokes flow without moment condition on initial data in l 1 r 2 l 2 r 2 moreover we characterize the necessary and sufficient condition for the rapid energy decay u t 2 o t 1 as t motivated by miyakawa schonbek 21 by weighted estimated in hardy spaces we discuss the possibility of the second order asymptotic expansion of the navier stokes flow assuming the first order moment condition on initial data moreover observing that the navier stokes flow u t lies in the hardy space h 1 r 2 for t 0 we consider the asymptotic expansions in terms of hardy norm finally we consider the rapid time decay u t 2 o t 3 2 as t with cyclic symmetry introduced by brandolese 2

a simple proof of the blowing up lemma corresp the blowing up lemma says that if the probability with respect to a product measure of a set a subseteq cal x n cal x finite n large is not exponentially small then its l n neighborhood has probability almost one for some l n o n here an information theoretic proof of the blowing up lemma generalizing it to continuous alphabets is given

simple universal lossy data compression schemes derived from the lempel ziv algorithm two universal lossy data compression schemes one with fixed rate and the other with fixed distortion are presented based on the well known lempel ziv algorithm in the case of fixed rate r the universal lossy data compression scheme works as follows first pick a codebook b sub n consisting of all reproduction sequences of length n whose lempel ziv codeword length is spl les nr and then use b sub n to encode the entire source sequence n block by n block this fixed rate data compression scheme is universal in the sense that for any stationary ergodic source or for any individual sequence the sample distortion performance as n spl rarr spl infin is given almost surely by the distortion rate function a similar result is shown in the context of fixed distortion lossy source coding

initial and boundary value problem of the unsteady navier stokes system in the half space with holder continuous boundary data abstract we study the initial boundary value problem of the navier stokes system in the half space we prove the unique solvability of the weak solution for some short time interval 0 t with the velocity in c 2 r n 0 t 0 1 when the given initial data in c r n and the given boundary data in c 2 r n 1 0 t satisfy the compatibility conditions our result generalizes the result in 29 considering nonhomogeneous dirichlet boundary data

a trade off between space and efficiency for routing tables two conflicting goals play a crucial role in the design of routing schemes for communication networks a routing scheme should use paths that are as short as possible for routing messages in the network while keeping the routing information stored in the processors local memory as succinct as possible the efficiency of a routing scheme is measured in terms of its stretch factor the maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices most previous work has concentrated on finding good routing schemes with a small fixed stretch factor for special classes of network topologies in this paper the problem for general networks is studied and the entire range of possible stretch factors is examined the results exhibit a trade off between the efficiency of a routing scheme and its space requirements almost tight upper and lower bounds for this trade off are presented specifically it is proved that any routing scheme for general n vertex networks that achieves a stretch factor k 1 must use a total of o n 1 1 2 k 4 bits of routing information in the networks this lower bound is complemented by a family k k of hierarchical routing schemes for every k l for unit cost general networks which guarantee a stretch factor of o k require storing a total of o k 3 n 1 1 h log n bits of routing information in the network name the vertices with o log 2 n bit names and use o log n bit headers

sample converses in source coding theory the rate and distortion performance of a sequence of codes along a sample sequence of symbols generated by a stationary ergodic information source are studied two results are obtained 1 the source sample sequence is encoded by an arbitrary sequence of block codes which operate at a fixed rate level r and a sample converse is obtained which states that with probability one the lower limit of the code sample distortions is lower bounded by d r the value of the distortion rate function at r 2 the source sample sequence is encoded by an arbitrary sequence of variable rate codes which operate at a fixed distortion level d and a sample converse is obtained which states that with probability one the lower limit of the code sample rates is lower bounded by r d the value of the rate distortion function at d a novel ergodic theorem is used to obtain both sample converses

long time behavior for the nonstationary navier stokes flows in l1 r n the large time decay for the navier stokes flows in l1 r n is a long standing unsolved question the main difficulties are that usual lq lr estimates for the stokes flow fail in this case and the projection operator p l1 r n l 1 r n becomes unbounded using the stokes solution formula we find a crucial and new estimate for the stokes flow in l1 r n which plays a fundamental role in studying the time l1 behavior for the navier stokes equations in addition we decompose the operator p into two parts and reduce its unboundedness to establish an l1 estimate for an elliptic problem with neumann boundary condition which is overcome by using the weighted estimates of the gaussian kernel s convolution the main results in this article are motivated by bae s works 2006 2008 1 2 and brandolese s work 2001 11

decentralized routing on spatial networks with stochastic edge weights we investigate algorithms to find short paths in spatial networks with stochastic edge weights our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual simplifying assumptions 1 we allow edge weights to be stochastic rather than deterministic and 2 we do not assume that global knowledge of a network is available we develop a decentralized routing algorithm that provides en route guidance for travelers on a spatial network with stochastic edge weights without the need to rely on global knowledge about the network to guide a traveler our algorithm uses an estimation function that evaluates cumulative arrival probability distributions based on distances between pairs of nodes the estimation function carries a notion of proximity between nodes and thereby enables routing without global knowledge in testing our decentralized algorithm we define a criterion that makes it possible to discriminate among arrival probability distributions and we test our algorithm and this criterion using both synthetic and real networks

pathlength scaling in graphs with incomplete navigational information the graph navigability problem concerns how one can find as short paths as possible between a pair of vertices given an incomplete picture of a graph we study the navigability of graphs where the vertices are tagged by a number between 1 and the total number of vertices in a way to aid navigation this information is too little to ensure errorfree navigation but enough as we will show for the agents to do significantly better than a random walk in our setup given a graph we first assign information to the vertices that agents can utilize for their navigation to evaluate the navigation we calculate the average distance traveled over random pairs of source and target and different graph realizations we show that this type of embedding can be made quite efficiently the more information is embedded the more efficient it gets we also investigate the embedded navigational information in a standard graph layout algorithm and find that although this information does not make algorithms as efficient as the above mentioned schemes it is significantly helpful

greedy connectivity of geographically embedded graphs we introduce a measure of greedy connectivity for geographical networks graphs embedded in space and where the search for connecting paths relies only on local information such as a node s location and that of its neighbors constraints of this type are common in everyday life applications greedy connectivity accounts also for imperfect transmission across established links and is larger the higher the proportion of nodes that can be reached from other nodes with a high probability greedy connectivity can be used as a criterion for optimal network design

the uniqueness of nondecaying solutions for the navier stokes equations the uniqueness of solutions of the navier stokes equations in the whole space is established when the velocity field is bounded and the pressure field is a bmo valued locally integrable in time function for bounded initial data here the velocity field may not decay at space infinity although there are a few results concerning uniqueness without the decay assumption our result is new and applicable for solutions constructed by solving the integral equations