maximal theorems for the directional hilbert transform on the plane for a schwartz function f on the plane and a non zero v r 2 define the hilbert transform of f in the direction v to be h v f x p v r f x vy dy y let be a schwartz function with frequency support in the annulus 1 2 the l 2 estimate is sharp the method of proof is based upon techniques related to the pointwise convergence of fourier series indeed our main theorem implies this result on fourier series

on average reward semi markov decision processes with a general multichain structure in this paper we investigate average reward semi markov decision processes with a general multichain structure using a data transformation method by solving the transformed discrete time average markov decision processes we can obtain significant and interesting information on the original average semi markov decision processes if the original semi markov decision processes satisfy some appropriate conditions then stationary optimal policies in the transformed discrete time models are also optimal in the original semi markov decision processes

multi parameter singular radon transforms iii real analytic surfaces abstract the goal of this paper is to study operators of the form t f x x f t x k t d t where is a real analytic function defined on a neighborhood of the origin in t x r n r n satisfying 0 x x is a cutoff function supported near 0 r n and k is a multi parameter singular kernel supported near 0 r n a main example is when k is a product kernel we also study maximal operators of the form m f x x sup 0 1 n 1 t 1 f 1 t 1 n t n x d t we show that m is bounded on l p 1 p we give conditions on under which t is bounded on l p 1 p these conditions hold automatically when k is a calderon zygmund kernel this is the final paper in a three part series the first two papers consider the more general case when is c

square functions for bi lipschitz maps and directional operators abstract first we prove a littlewood paley diagonalization result for bi lipschitz perturbations of the identity map on the real line this result entails a number of corollaries for the hilbert transform along lines and monomial curves in the plane second we prove a square function bound for a single scale directional operator as a corollary we give a new proof of part of a theorem of katz on direction fields with finitely many directions

optimality of quasi open loop policies for discounted semi markov decision processes quasi open loop policies consist of sequences of markovian decision rules that are insensitive to one component of the state space given a semi markov decision process smdp we distinguish between exogenous and endogenous state components as follows i the decision maker s actions do not impact the evolution of an exogenous state component and ii between consecutive decision epochs the exogenous and endogenous state components are conditionally independent given the decision maker s latest action for simplicity we consider an smdp with one exogenous and one endogenous state component when transition times between epochs are conditionally independent of the exogenous state given the most recent action and the exogenous component is a multiplicative compound poisson process we provide an almost everywhere condition on the reward function sufficient for the optimality of a quasi open loop policy after adjusting the discount factor to account for the statistical properties of the exogenous state process obtaining this policy amounts to solving a reduced smdp in which the exogenous state is static depending on the relationship between the structure of the exogenous state process and the shape of the reward function we can replace the almost everywhere condition with one that applies only in expectation quasi open loop optimality holds even if the times between decision epochs depend on the poisson process underlying the exogenous state component and or the poisson process is replaced with a generic counting process

on the existence of average optimal policies in semiregenerative decision models this paper gives sufficient conditions for the existence of average optimal policies in a decision model which is a generalization of a denumerable state space semi markov decision model the conditions extend most of those previously known especially neither uni chainedness nor communicatingness is assumed an average optimal policy can be obtained as a limit of discount optimal policies if structured policies are discount optimal there exists a structured average optimal policy the results are applicable to more general continuous time models such as the one by yushkevich and fainberg yushkevich a a e a fainberg 1979 on homogeneous markov models with continuous time and finite or countable state space theory probab appl 24 156 161

singular and maximal radon transforms analysis and geometry part 2 geometric theory 8 curvature introduction 8 1 three notions of curvature 8 2 theorems 8 3 examples 9 curvature some details 9 1 the exponential representation 9 2 diffeomorphism invariance 9 3 curvature condition cy 9 4 two lemmas 9 5 double fibration formulation 10 equivalence of curvature conditions 10 1 invariant submanifolds and deficient lie algebras 10 2 vanishing jacobians 10 3 construction of invariant submanifolds

lossless compression of map contours by context tree modeling of chain codes we consider lossless compression of digital contours in map images the problem is attacked by the use of context based statistical modeling and entropy coding of the chain codes we propose to generate an optimal n ary incomplete context tree by first constructing a complete tree up to a predefined depth and creating the optimal tree by pruning out nodes that do not provide improvement in compression we apply this method for both vector and raster maps experiments show that the proposed method gives lower bit rates than the existing methods of chain codes compression for the set of test data

a new chain code abstract a new chain code for shapes composed of regular cells is defined this boundary chain code is based on the numbers of cell vertices which are in touch with the bounding contour of the shape this boundary chain code is termed vertex chain code vcc the vcc is invariant under translation and rotation also it may be starting point normalized and invariant under mirroring transformation using this concept of chain code it is possible to relate the chain length to the contact perimeter which corresponds to the sum of the boundaries of neighboring cells of the shape bribiesca e comp math appl 33 11 1997 1 9 also to relate the chain nodes to the contact vertices which correspond to the vertices of neighboring cells so in this way these relations among the chain and the characteristics of interior of the shape allow us to obtain interesting properties this work is motivated by the idea of obtaining various shape features computed directly from the vcc without going to cartesian coordinate representation finally in order to illustrate the capabilities of the vcc we present some results using real shapes

convergence of dynamic programming models weak conditions are presented for approximating dynamic programming models for a sequence of these models continuous convergence of the sequence of associated optimal value functions is obtained under the condition that state and action space converge in the sense of kuratowski and that the mappings of admissible actions as well as the transition law the discount factors and the reward functions converge continuously further a relation for the associated sets of optimal actions is given the analysis is based on results about convergence preserving properties of supremum value functions and integrals the approximation results are extended to so called upper semi continuous convergent sequences and are related to discretization procedures by using projections

conditions for existence of average and blackwell optimal stationary policies in denumerable markov decision processes abstract sufficiency conditions are given for the existence of stationary blackwell optimal policies these conditions concern only the one step transition probability matrices and their resolvents and therefore appear to be more natural than those recently introduced by dekker and hordijk we use the same operator theoretic approach and standard results about spectral theory of bounded linear operators

on the second optimality equation for semi markov decision models for a semi markov decision model with average return the validity of the second optimality equation is shown in the nonmodified form where the actions run through the set of all admissible actions rather than through the set of maximum points conserving actions for the first optimal equation as a consequence the existence of a strongly optimal stationary policy is shown the results seem to be known only for finite state finite action models whereas here countable state compact action models with unbounded rewards are considered

average sensitive and blackwell optimal policies in denumerable markov decisionchains with unbounded rewards in this paper we consider a discrete time markov decision chain with a denumerable state space and compact action sets and we assume that for all states the rewards and transition probabilities depend continuously on the actions the first objective of this paper is to develop an analysis for average optimality without assuming a special markov chain structure in doing so we present a set of conditions guaranteeing average optimality which are automatically fulfilled in the finite state and action model the second objective is to study simultaneously average and discount optimality as veinott veinott a f jr 1969 on discrete dynamic programming with sensitive discount optimality criteria ann math statist 40 1635 1660 did for the finite state and action model we investigate the concepts of n discount and blackwell optimality in the denumerable state space using a laurent series expansion for the discounted rewards under the same condition as for average optimality we establish solutions to the n discount optimality equations for every n

on calderon s conjecture for the bilinear hilbert transform abstract we show that the bilinear hilbert transform defined by maps lp lq into lr for 1 p q 1 p 1 q 1 r and 2 3 r

a one pass algorithm for local symmetry of contours from chain codes this paper presents a one pass algorithm for computing the local symmetry of contours from their chain code representation this algorithm embeds the local symmetry deficiency lsd computation into our chain codes extraction process the existing algorithms need to extract chain codes first and use them as input to compute lsd the new algorithm uses a binary image as input and can complete the code extraction and the lsd computation in one pass it can also extract multiple contours in an image in one pass the algorithm is suitable for parallel implementation

kakeya sets and directional maximal operators in the plane we completely characterize the boundedness of planar directional maximal operators on lp more precisely if is a set of directions we show that m the maximal operator associated to line segments in the directions is unbounded on lp for all p 1

symmetry detection in 3d chain coded discrete curves and trees symmetry detection in 2d and 3d shapes has been a classical problem in computer vision computational geometry and pattern recognition one of the reasons of this interest is because symmetry is related to the balance and harmony and in most cases it is considered like a beautiful proportion in this paper we present different methods to detect mirror and rotational symmetries in 2d and 3d open and closed curves and in trees represented by means of the orthogonal direction change chain code these methods detect both global and local symmetries they can also detect the number and position of the axes of symmetry they are simple easy to implement and fast to execute highlightssymmetry detection for 3d curves and tree objects via chain coding is presented symmetry is related to the balance and harmony the symmetry of plane and space filling curves is shown the symmetry detection on plane and space filling trees is computed

continuity of mean recurrence times in denumerable semi markov processes for a family of semi markov processes where the transition matrices for the embedded markov chains and the mean sojourn times depend continuously on a parameter we give equivalent as well as sufficient conditions for the continuity of the mean recurrence times the results will be used in a subsequent paper on average costs in a dynamic programming model

lp estimates for the bilinear hilbert transform for the bilinear hilbert transform given by we announce the inequality h fg p3 kp1 p2 f p1 g p2 provided 2 p1 p2 1 p3 1 p1 1 p2 and 1 p3 2