periodic schwarz christoffel mappings with multiple boundaries per period we present an extension to the theory of schwarzchristoffel sc mappings by permitting the target domain to be a single period window of a periodic configuration having multiple polygonal straigh

transient policies in discrete dynamic programming linear programming including suboptimality tests and additional constraints this paper investigates the computation of transient optimal policies in discrete dynamic programming the model is quite general it may contain transient as well as nontransient policies and the transition matrices are not necessarily substochastic a functional equation for the so called transient value vector is derived and the concept of superharmonicity is introduced this concept provides the linear program to compute the transientvalue vector and a transient optimal policy we also discuss the elimination of suboptimal actions the solution of problems with additional constraints and the computation of an efficient policy for a multiple objective dynamic programming problem

linear subspaces of matrices associated to a ferrers diagram and with a prescribed lower bound for their rank abstract fix a field k a subset p 1 k 1 m and an integer min k m let c m k p k be the vector space of all k m matrices with entries a i j 0 if i j p let k be the maximal dimension of a linear subspace v c m k p k such that all a v 0 have rank we show that known lower bounds for k for k one resp several resp almost all finite field give the same lower bounds for some resp many resp all number fields

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

coset construction for subspace codes one of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so called subspace codes in mathcal p q n i e the set of subspaces of mathbb f q n for a given minimal distance here we generalize a construction of etzion and silberstein to a wide range of parameters this construction named coset construction improves or attains several of the previously best known subspace code sizes and attains the maximum rank distance bound for an infinite family of parameters

contour surgery a topological reconnection scheme for extended integrations using contour dynamics abstract a numerical algorithm is described which it is believed can accurately model the dynamics of a two dimensional inviscid incompressible fluid with unparalled spatial resolution the fluid is assumed however to be divided into regions of uniform vorticity conservation of vorticity ensuring that this remains true for all time like contour dynamics the algorithm is concerned with following the evolution of the boundaries of vorticity discontinuity contours unlike contour dynamics the algorithm automatically removes vorticity features smaller than a predefined scale for example two contours enclosing the same uniform vorticity merge into one if they are close enough together also the curvature along a contour is not allowed to exceed the inverse of the cutoff scale at present calculations with contour surgery resolve fluid motions extending over four to five orders of magnitude of scales 13 to 20 octaves such high resolution pictures of two dimensional vortex dynamics have been facilitated by and indeed depend critically upon a nonlocal adaptive node adjustment scheme and a variety of tests quantify the accuracy of the technique

analytical formulae for the kirchhoff routh path function in multiply connected domains explicit formulae for the kirchhoff routh path functions or hamiltonians governing the motion of n point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero the method uses the schottky klein prime function to find representations of the hydrodynamic green s function in multiply connected circular domains the green s function is then used to construct the associated kirchhoff routh path function the path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains illustrative examples are presented for the case of single vortex motion in multiply connected domains

on the sparseness of certain linear mrd codes abstract we determine the proportion of linear 3 3 3 mrd codes over f q within the space of all 3 dimensional 3 3 rank metric codes over the same field this shows that for these parameters linear mrd codes are sparse in the sense that the proportion tends to 0 as q this is so far the only parameter case for which mrd codes are known to be sparse the computation is accomplished by reducing the space of all such rank metric codes to a space of specific bases and subsequently making use of a result by menichetti 1973 on 3 dimensional semifields

analytical solutions for an escape problem in a disc with an arbitrary distribution of exit holes along its boundary we analytically construct solutions for the mean first passage time and splitting probabilities for the escape problem of a particle moving with continuous brownian motion in a confining planar disc with an arbitrary distribution i e of any number size and spacing of exit holes absorbing sections along its boundary the governing equations for these quantities are poisson s equation with a non zero constant forcing term and laplace s equation respectively and both are subject to a mixture of homogeneous neumann and dirichlet boundary conditions our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map using special transcendental functions that are defined in terms of an associated schottky group they are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over no slip no shear surfaces as well as results from potential theory all of which were themselves derived using the same theory of schottky groups they are exact up to the determination of a finite set of mapping parameters which is performed numerically their evaluation also requires the numerical inversion of the parameterising conformal map computations for a series of illustrative examples are also presented

algebraic list decoding of subspace codes subspace codes are collections of subspaces of a certain ambient vector space over a finite field koetter and kschischang introduced subspace codes in order to correct errors and erasures in noncoherent random linear network coding they have also studied a remarkable family of subspace codes obtained by evaluating certain linearized polynomials the koetter kschischang subspace codes are widely regarded as the counterpart of reed solomon codes in the domain of network error correction koetter and kschischang have furthermore devised an algebraic decoding algorithm for these codes analogous to the berlekamp welch decoding algorithm for reed solomon codes in this paper we develop list decoding algorithms for subspace codes thereby providing for certain code parameters a better tradeoff between rate and error correction capability than that of the koetter kschischang codes in a sense we are able to achieve for these codes what sudan was able to achieve for reed solomon codes in order to do so we have to modify and generalize the original koetter kschischang construction in many important respects the end result is this for any integer our list l decoder guarantees successful recovery of the message subspace provided that the normalized dimension of the error satisfies l l l 1 2 r where r is the packet rate which is a new parameter introduced in this paper as in the case of sudan s list decoding algorithm this exceeds the previously best known error correction radius 1 r established by koetter and kschischang only for low rates r

calculating the lift on a finite stack of cylindrical aerofoils the classic exact solution due to lagally lagally m 1929 die reibungslose stromung im aussengebiet zweier kreise z angew math mech 9 299 305 for streaming flow past two cylindrical aerofoils or obstacles is generalized to the case of an arbitrary finite number of cylindrical aerofoils given the geometry of the aerofoils the speed and direction of the oncoming uniform flow and the individual round aerofoil circulations the complex potential associated with the flow is found in analytical form in a parametric pre image region that can be conformally mapped to the fluid region a complete determination of the flow then follows from knowledge of the conformal mapping between the two regions in the special case where the aerofoils are all circular the conformal mapping from the parametric pre image region to the fluid domain is a mobius mapping the solution for the complex potential in such a case can then be used in combination with the blasius theorem to compute the distribution of hydrodynamic forces on the multi aerofoil configuration

green s function for the laplace beltrami operator on a toroidal surface green s function for the laplacebeltrami operator on the surface of a three dimensional ring torus is constructed an integral ingredient of our approach is the stereographic projection of the toru

constrained undiscounted stochastic dynamic programming in this paper we investigate the computation of optimal policies in constrained discrete stochastic dynamic programming with the average reward as utility function the state space and action sets are assumed to be finite constraints which are linear functions of the state action frequencies are allowed in the general multichain case an optimal policy will be a randomized nonstationary policy an algorithm to compute such an optimal policy is presented furthermore sufficient conditions for optimal policies to be stationary are derived there are many applications for constrained undiscounted stochastic dynamic programming e g in multiple objective markovian decision models

equation of motion for point vortices in multiply connected circular domains the paper gives the equation of motion for n point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles called the circular domain the velocity field induced by the point vortices is described in terms of the schottky klein prime function associated with the circular domain the explicit representation of the equation enables us not only to solve the euler equations through the point vortex approximation numerically but also to investigate the interactions between localized vortex structures in the circular domain as an application of the equation we consider the motion of two point vortices with unit strength and of opposite signs when the multiply connected domain is symmetric with respect to the real axis the motion of the two point vortices is reduced to that of a single point vortex in a multiply connected semicircle which we investigate in detail

contour dynamics for the euler equations in two dimensions we present a contour dynamics algorithm for the euler equations of fluid dynamics in two dimensions this is applied to regions of piecewise constant vorticity withinfinite area vortexregions favrs essentially this reduces the dimensionality by one and we are treating the interaction of closed polygonal contours whose nodes are advected by the total fluid motion computed self consistently a leapfrog centered scheme is used for temporal advancement computer simulation results are given for two and four like signed interacting favrs in all cases wavelike surface deformations are observed if the distance between favrs is comparable to their extent diameter these surface deformations are large they play an essential role in the observed coalescence of favrs

constructions for optimal ferrers diagram rank metric codes optimal rank metric codes in ferrers diagrams can be used to construct good subspace codes such codes consist of matrices having zeros at certain fixed positions this paper generalizes the known constructions for ferrers diagram rank metric fdrm codes via a criterion for linear maximum rank distance mrd codes an explicit construction for a class of systematic mrd codes is presented which is used to produce new optimal fdrm codes by exploring the subcodes of gabidulin codes if each of the rightmost delta 1 columns in the ferrers diagram cal f has at least n r dots where r is taken in a range then the conditions that an fdrm code in cal f is optimal are established the known combining constructions for fdrm code are generalized by introducing the concept of proper combinations of ferrers diagrams

cyclic orbit codes a constant dimension code consists of a set of k dimensional subspaces of bbf qn orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group acting on the set of all subspaces of bbf qn if the acting group is cyclic the corresponding orbit codes are called cyclic orbit codes in this paper we show how orbit codes can be seen as an analog of linear codes in the block coding case we investigate how the structure of cyclic orbit codes can be utilized to compute the minimum distance and cardinality of a given code and propose different decoding procedures for a particular subclass of cyclic orbit codes

maximum stopping value policies in finite markov population decision chains this paper considers infinite horizon finite state and action markov population decision chains mpdcs in which the goal is to find a stationary stopping policy with maximum stopping value that is with maximum value over all deterministic markov stopping policies a policy is stopping if the resulting expected population size in a period diminishes to zero as the period converges to infinity the paper shows that the following are equivalent a there is a stationary maximum stopping value policy b the maximum stopping value is finite c there is a stopping policy and an excessive point of the optimal return operator and d the maximum stopping value is the least excessive resp fixed point of the optimal return operator the paper shows how to use linear programming policy improvement and successive approximations to solve the problem the problem arises in stopping a markov chain as in optimally eradicating a pest or disease the problem is one of two key subproblems used repeatedly to f

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

recurrence conditions for average and blackwell optimality in denumerable state markov decision chains in a previous paper dekker and hordijk 1988 presented an operator theoretical approach for multichain markov decision processes with a countable state space compact action sets and unbounded rewards conditions were presented guaranteeing the existence of a laurent series expansion for the discounted rewards the existence of average and blackwell optimal policies and the existence of solutions for the average and blackwell optimality equations while these assumptions were operator oriented and formulated as conditions for the deviation matrix we will show in this paper that the same approach can also be carried out under recurrence conditions these new conditions seem easier to check in general and are especially suited for applications in queueing models

parallel multilevel constructions for constant dimension codes constant dimension codes cdcs as special subspace codes have received a lot of attention due to their application in random network coding this paper introduces a family of new codes called rank metric codes with given ranks grmcs to generalize the parallel construction in xu and chen ieee trans inf theory 64 2018 6315 6319 and the classic multilevel construction a singleton like upper bound and a lower bound for grmcs derived from gabidulin codes are given via grmcs two effective constructions for cdcs are presented by combining the parallel construction and the multilevel construction many cdcs with larger size than the previously best known codes are given the ratio between the new lower bound and the known upper bound for 4 delta 2 delta 2 delta q cdcs is calculated it is greater than 0 99926 for any prime power q and any delta geq 3

maximal ferrers diagram codes constructions and genericity considerations this paper investigates the construction of rank metric codes with specified ferrers diagram shapes these codes play a role in the multilevel construction for subspace codes a conjecture from 2009 provides an upper bound for the dimension of a rank metric code with given specified ferrers diagram shape and rank distance while the conjecture in its generality is wide open several cases have been established in the literature this paper contributes further cases of ferrers diagrams and ranks for which the conjecture holds true in addition the proportion of maximal ferrers diagram codes within the space of all rank metric codes with the same shape and dimension is investigated special attention is being paid to mrd codes it is shown that for growing field size the limiting proportion depends highly on the ferrers diagram for instance for m times 2 mrd codes with rank 2 this limiting proportion is close to 1 e

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

the method of images and green s function for spherical domains motivated by problems in electrostatics and vortex dynamics we develop two general methods for constructing green s function for simply connected domains on the surface of the unit sphere we prove a riemann mapping theorem showing that such domains can be conformally mapped to the upper hemisphere we then categorize all domains on the sphere for which green s function can be constructed by an extension of the classical method of images we illustrate our methods by several examples such as the upper hemisphere geodesic triangles and latitudinal rectangles we describe the point vortex motion in these domains which is governed by a hamiltonian determined by the dirichlet green s function

linear programming for finite state multi armed bandit problems we consider the multi armed bandit problem we show that when the state space is finite the computation of the dynamic allocation indices can be handled by linear programming methods

vortex dynamics in complex domains on a spherical surface we consider the motion of both point vortices and uniform vortex patches in arbitrary possibly multiply connected regions bounded by impenetrable walls on the surface of a sphere by exploiting knowledge of the functional form of the relevant green s function in a pre image circular domain that is conformally equivalent to a stereographic projection of the fluid domain on the spherical surface we first generalize kirchhoff routh theory for point vortex motion in the plane to point vortex motion on a spherical shell next we study vortex patch motion and show that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected domain on a spherical shell bounded by impenetrable walls we describe a novel numerical scheme whereby this motion can be computed some illustrative calculations are shown

numerical conformal mapping of multiply connected regions by fornberg like methods we develop a new algorithm for computing conformal maps from regions exterior to non overlapping disks to unbounded multiply connected regions exterior to non overlapping smoothly bounded jordan regions the method is an extension of fornberg s original newton like method for mapping of the disk to simply connected regions a fortran program based on the algorithm has been developed and tested for the 2 and 3 disk case numerical examples are reported

vortex design problem in this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity the problem is formulated as a pde constrained optimization in which the solutions are found using a gradient based descent method recognizing such euler flows as free boundary problems the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients in explicit tracking of interfaces vortex boundaries this method offers an alternative to grid based techniques such as the level set methods and represents a natural optimization formulation for vortex problems computed using the contour dynamics technique we develop and validate this approach using the design of 2d equilibrium euler flows with finite area vortices as a model problem it is also discussed how the proposed methodology can be applied to euler flows featuring other vorticity distributions such as vortex sheets and to time dependent phenomena

a note on m n katehakis and y r chen s computation of the gittins index in a recent paper katehakis and chen propose a sequence of linear programs for the computation of the gittins indices if there are n projects and project v has kv states then v 1nkv linear programs have to be solved in this note it is shown that instead of the kv linear programs for project v also one parametric linear program with the same dimensions can be solved

the motion of point vortices on closed surfaces we develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere when the sum of the vortex circulations is non ze

force enhancing vortex equilibria for two parallel plates in uniform flow a two dimensional potential flow in an unbounded domain with two parallel plates is considered we examine whether two free point vortices can be trapped near the two plates in the presence of a uniform flow and observe whether these stationary point vortices enhance the force on the plates the present study is an extension of previously published work in which a free point vortex over a single plate is investigated the flow problem is motivated by an airfoil design problem for the double wings moreover it also contributes to a design problem for an efficient wind turbine with vertical blades in order to obtain the point vortex equilibria numerically we make use of a linear algebraic algorithm combined with a stochastic process called the brownian ratchet scheme the ratchet scheme allows us to capture a family of stationary point vortices in multiply connected domains with ease as a result we find that stationary point vortices exist around the two plates and they enhance the downward force and the counter clockwise rotational force acting on the two plates

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