a table of elliptic integrals cubic cases forty one integrands that are rational except for the square root of a cubic polynomial with known real zeros are integrated in terms of ital r functions for which fortran codes are available in cotrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand the table contains one elliptic integral of the first kind 26 of the second kind and 14 of the third kind only 10 of the integrals are treated in standard tables which list a large number of special cases that are unified here

a table of elliptic integrals of the second kind by evaluating elliptic integrals in terms of standard r functions instead of legendre s integrals many in one case 144 formulas in previous tables are unified the present table includes only integrals of the first and second kinds having integrands with real singular points the 216 integrals of this type listed in gradshteyn and ryzhik s table constitute a small fraction of the special cases of 13 integrals evaluated here the interval of integration is not required as it is in previous table to begin or end at a singular point of the integrand fortran codes for the standard r functions are included in a supplement

precise and fast computation of jacobian elliptic functions by conditional duplication we developed a new method to compute the cosine amplitude function c equiv mathrm cn u m by using its double argument formula the accumulation of round off errors is effectively suppressed by the introduction of a complementary variable b equiv 1 c and a conditional switch between the duplication of b and c the sine and delta amplitude functions s equiv mathrm sn u m and d equiv mathrm dn u m are evaluated from thus computed b or c by means of their identity relations the new method is sufficiently precise as its errors are less than a few machine epsilons also it is significantly faster than the existing procedures in case of single precision computation it runs more than 50 times faster than bulirsch s sncndn based on the gauss transformation and 2 7 times faster than our previous method based on the simultaneous duplication of s c and d the ratios change to 7 6 and 3 5 respectively in case of the double precision environment

limiting average criteria for nonstationary markov decision processes this paper deals with the so called limiting average criteria for nonstationary markov decision processes with possibly unbounded rewards and borel state space a new set of conditions is provided under which the existence of both a solution to the optimality equations and the limiting average epsilon geq 0 optimal markov policies is derived also a rolling horizon algorithm for computing limiting average epsilon 0 optimal markov policies is developed furthermore the results in this paper are illustrated by several examples such as the water regulation problem

remote state estimation with communication costs for first order lti systems consider a first order linear time invariant discrete time system driven by process noise a pre processor that accepts causal measurements of the state of the system and a state estimator the pre processor and the state estimator are not co located and at every time step the pre processor transmits either a real number or a free symbol to the estimator we seek the pre processor and the estimator that jointly minimize a cost that combines two terms the expected squared state estimation error and a communication cost in our formulation the transmission of a real number from the pre processor to the estimator incurs a positive cost while free symbols induce zero cost this paper proves analytically that a symmetric threshold policy at the pre processor and a kalman like filter at the estimator which updates its estimate linearly in the presence of free symbols are jointly optimal for our problem

simultaneous identification and adaptive control of unknown systems over finite parameter sets the problem considered is one of simultaneously identifying an unknown system while adequately controlling it the system can be any fairly general discrete time system and the cost criterion can be either of a discounted type or of a long term average type the chief restriction being that the unknown parameter lies in a finite parameter set for a previously introduced scheme of identification and control based on biased maximum likelihood estimates it is shown that 1 every cesaro limit point of the parameter estimates is closed loop equivalent to the unknown parameter 2 for both the discounted and long term average cost criteria the adaptive control law cesaro converges to the set of optimal control laws and 3 in the case of the long term average cost criterion the actual cost incurred by the use of the adaptive controller is optimal and cannot be bettered even if one knew the value of the unknown parameter at the start

controlled markov chains and stochastic networks controlled markov chains with average cost criterion and with special cost and transition structures are studied existence of optimal stationary strategies is established for the average cost criterion corresponding dynamic programming equations are derived a stochastic network problem that includes interconnected queues as a special case is described and studied within this framework

adaptive sampling for linear state estimation when a sensor has continuous measurements but sends occasional messages over a data network to a supervisor which estimates the state the available packet rate fixes the achievable quality of state estimation when such rate limits turn stringent the sensor s messaging policy should be designed anew what are good causal messaging policies what should message packets contain what is the lowest possible distortion in a causal estimate at the supervisor is delta sampling better than periodic sampling we answer these questions for a markov state process under an idealized model of the network and the assumption of perfect state measurements at the sensor if the state is a scalar or a vector of low dimension then we can ignore sample quantization if in addition we can ignore jitter in the transmission delays over the network then our search for efficient messaging policies simplifies first each message packet should contain the value of the state at that time thus a bound on the number of data packets becomes a bound on the number of state samples second the remaining choice in messaging is entirely about the times when samples are taken for a scalar linear diffusion process we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion we stick to finite horizons and impose a hard upper bound n on the number of allowed samples we cast the design as a problem of choosing an optimal sequence of stopping times we reduce this to a nested sequence of problems each asking for a single optimal stopping time under an unproven but natural assumption about the least square estimate at the supervisor each of these single stopping problems are of standard form the optimal stopping times are random times when the estimation error exceeds designed envelopes for the case where the state is a brownian motion we give analytically the shape of the optimal sampling envelopes the shape of the envelopes under optimal delta sampling and their performances surprisingly we find that delta sampling performs badly hence when the rate constraint is a hard limit on the number of samples over a finite horizon we should not use delta sampling

precise and fast computation of the general complete elliptic integral of the second kind we developed an efficient procedure to evaluate two auxiliary complete elliptic integrals of the second kind b m and d m by using their taylor series expansions the definition of jacobi s nome and legendre s relation the developed procedure is more precise than the existing ones in the sense that the maximum relative errors are 1 3 machine epsilons and it runs drastically faster around 5 times faster than bulirsch s cel2 and 16 times faster than carlson s rf and rd

fast computation of a general complete elliptic integral of third kind by half and double argument transformations we developed a novel method to calculate an associate complete elliptic integral of the third kind j n m p n m k m n the key idea is the double argument formula of j n m with respect to n we derived it from the not so popular addition theorem of jacobi s complete elliptic integral of the third kind p 1 a m with respect to a which is a real or pure imaginary argument connected with n and m as n msn 2 a m repeatedly using the half argument transformation fukushima 2010 28 of a new variable y n m or its complement x m n m we reduce y sufficiently small say less than 0 3 or so then we evaluate the integral for the reduced variable by its maclaurin series expansion the coefficients of the series expansion are recursively computed from two other associate complete elliptic integrals b m e m 1 m k m m and d m k m e m m the precise and fast computation of these two integrals is found in our previous work fukushima 2011 17 finally we recover the integral value for the original n by successively applying the double argument formula of j n m the new method is sufficiently precise in the sense that the maximum errors are less than around 10 machine epsilons for the sole computation of j n m the new method runs 1 2 1 5 and 4 7 5 5 times faster than bulirsch s cel and carlson s r j respectively in the simultaneous computation of three associate complete integrals the new method runs 1 6 1 7 and 5 3 8 0 times faster than cel and carlson s r d and r j respectively

long term values in markov decision processes and repeated games and a new distance for probability spaces we study long term markov decision processes mdps and gambling houses with applications to any partial observation mdps with finitely many states and zero sum repeated games with an informed controller we consider a decision maker who is maximizing the weighted sum t 1 x1d703 trt where rt is the expected reward of the t th stage we prove the existence of a very strong notion of long term value called general uniform value representing the fact that the decision maker can play well independently of the evaluations x1d703 t t 1 over stages provided the total variation or impatience t 1 x1d703 t 1 x1d703 t is small enough this result generalizes previous results of the literature that focus on arithmetic means and discounted evaluations moreover we give a variational characterization of the general uniform value via the introduction of appropriate invariant measures for the decision problems generalizing the fundamental theorem of gambling or the aumann maschler cav u formula for repeated games with incomple

average cost optimal policies for markov control processes with borel state space and unbounded costs abstract we show the existence of average cost optimal stationary policies for markov control processes with borel state space and unbounded costs per stage under a set of assumptions recently introduced by l i sennott 1989 for control processes with countable state space and finite control sets

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

efficient time symmetric simulation of torqued rigid bodies using jacobi elliptic functions if the three moments of inertia are distinct the solution to the euler equations for the free rigid body is given in terms of jacobi elliptic functions using the arithmetic geometric mean algorithm abramowitz and stegun 1992 handbook of mathematical functions with formulas graphs and mathematical tables new york dover these functions can be calculated efficiently and accurately compared to standard numerical ode and lie poisson solvers the overall approach yields a faster and more accurate numerical solution to the euler equations this approach is designed for mass asymmetric rigid bodies in the case of symmetric bodies the exact solution is available in terms of trigonometric functions see dullweber et al 1997 j chem phys 107 5840 51 reich 1996 fields inst commun 10 181 91 and benettin et al 2001 siam j sci comp 23 1189 203 for details in this paper we consider the case of asymmetric rigid bodies subject to external forces we consider a strategy similar to the symplectic splitting method proposed in reich 1996 fields inst commun 10 181 91 and dullweber et al 1997 j chem phys 107 5840 51 the method proposed here is time symmetric we decompose the vector field of our problem into a free rigid body frb problem and another completely integrable vector field the frb problem consists of the euler equations and a differential equation for the 3 3 orientation matrix the euler equations are integrated exactly while the matrix equation is approximated using a truncated magnus series in our experiments we observe that the overall numerical solution benefits greatly from the very accurate solution of the euler equations we apply the method to the heavy top and the simulation of artificial satellite attitude dynamics

optimal communication scheduling and remote estimation over an additive noise channel abstract this paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator the sensor makes sequential observations about the state of an underlying memoryless stochastic process and makes a decision as to whether or not to send this measurement to the estimator the sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process over a finite time horizon the sensor is either charged a cost for each transmission or constrained on transmission times as opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect noiseless in this work an additive noise channel with fixed power constraint is considered hence the sensor has to encode its message before transmission under some technical assumptions we obtain the optimal encoding and estimation policies within the piecewise affine class in conjunction with the optimal transmission schedule the impact of the presence of a noisy channel is analyzed numerically based on dynamic programming this analysis yields some rather surprising results such as a phase transition phenomenon in the number of used transmission opportunities which was not encountered in the noiseless communication setting

supplement to a table of elliptic integrals of the second kind c c double precision function rf x y z errtol ierr c c this function subroutine computes the incomplete elliptic c integral of the first kind c rf x y z integral from zero to infinity of c c 1 2 1 2 1 2 c 1 2 t x t y t z dt c c where x y and z are nonnegative and at most one of them c is zero if one of them is zero the integral is complete c the duplication theorem is iterated until the variables are c nearly equal and the function is then expanded in taylor c series to fifth order c references b c carlson and e m notis algorithms for c incomplete elliptic integrals acm transactions on mathemac tical software 7 1981 398 403 b c carlson computing c elliptic integrals by duplication numer math 33 1979 c 1 16 c authors b c carlson and elaine m notis ames laboratoryc doe iowa state university ames ia 50011 and r l pexton c lawrence livermore national laboratory livermore ca 94550 c aug 1 1979 revised jan 15 1987 c c check value rf 0 1 2 1 31102 87771 46059 90523 24198 c check by addition theorem rf xx z x w rf y y z y w c rf o z w where x y z w are positive and x y z w c integer ierr printr double precision c1 c2 c3 e2 e3 epslon errtol lamda double precision lolim mu s uplimx xn xndev xnroot double precision yyn yndev ynroot z zn zndev znroot c intrinsic functions used dabs dmax1 dmin1 dsqrt c c printr is the unit number of the printer data printr 6 c

on the non commutative factorization of wiener hopf kernels of khrapkov type there are a great many problems in mathematical physics and engineering which when modelled mathematically are reduced to wiener hopf functional equations defined in some region of a complex plane in simple models this equation is scalar but in more complicated situations inherent coupling etc can often give rise to coupled systems of equations and so the resulting wiener hopf kernels are of matrix form the crucial step in the solution of any wiener hopf equation is to decompose the kernel which can be a quite general function of the complex transform variable into a product of two factors which are regular in overlapping half planes this can be accomplished explicitly for scalar kernels and may be generalized to a particular class of matrix kernels namely those which permit a commutative decomposition although this class is wide and therefore contains some valuable physical problems it is found that many such kernels yield factorization elements with exponentially large behaviour at infinity in their half planes of analyticity this prevents a later step in the wiener hopf procedure being carried through and therefore introduces a serious limitation to the usefulness of khrapkov s approach previous researchers have offered schemes to eliminate the exponential behaviour of the khrapkov factors but for reasons discussed herein these have problems in their successful implementation this article offers a new procedure for quenching the exponential growth which is based on a method proposed recently by the author for fully coupled kernels which do not have commutative factors the approach is two step first a commutative factorization is obtained which is algebraic at infinity as required but which has spurious branch cuts in the regions of intended analyticity second an approximate procedure is used to eliminate the offending branch points by introduction of pade approximants for a certain scalar function and by inclusion of a regularizing meromorphic matrix for one particular example kernel in which an exact factorization happens to be known the explicit approximate kernel factors thus derived are shown to yield very close agreement to the exact factors the application of this work to problems in the area of fluid structural interaction is discussed

stochastic dominance constrained markov decision processes we are interested in risk constraints for infinite horizon discrete time markov decision processes mdps starting with average reward mdps we show that increasing concave stochastic dominance constraints on the empirical distribution of reward lead to linear constraints on occupation measures an optimal policy for the resulting class of dominance constrained mdps is obtained by solving a linear program we compute the dual of this linear program to obtain average dynamic programming optimality equations that reflect the dominance constraint in particular a new pricing term appears in the optimality equations corresponding to the dominance constraint we show that many types of stochastic orders can be used in place of the increasing concave stochastic order we also carry out a parallel development for discounted reward mdps with stochastic dominance constraints a portfolio optimization example is used to motivate the paper

on the optimality equation for average cost markov control processes with feller transition probabilities we consider markov control processes with borel state space and feller transition probabilities satisfying some generalized geometric ergodicity conditions we provide a new theorem on the existence of a solution to the average cost optimality equation

a recurrence principle for stochastic difference inclusions the invariance principle is extended to a recurrence principle and is developed for stochastic difference inclusions for these systems random solutions are not unique under appropriate lyapunov like conditions it is established for every random solution that almost every complete sample path converges to the largest weakly totally recurrent set contained in a level set of the lyapunov like function such a set is not larger and is sometimes smaller than the largest weakly invariant set contained in the level set the principle is useful for establishing robust uniform asymptotic stability in probability or robust uniform strong recurrence under weak lyapunov conditions for stochastic discrete time control systems that employ discontinuous feedback laws examples demonstrate the achieved results

the feedback capacity of the binary erasure channel with a no consecutive ones input constraint the input constrained erasure channel with feedback is considered where the binary input sequence contains no consecutive ones i e it satisfies the 1 infty rll constraint we derive the capacity for this setting which can be expressed as c epsilon max 0 leq p leq 0 5 frac 1 epsilon h b p 1 1 epsilon p where epsilon is the erasure probability and h b cdot is the binary entropy function moreover we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity the feedback capacity was calculated using an equivalent dynamic programming dp formulation with an optimal average reward that is equal to the capacity furthermore we obtained an optimal encoding procedure from the solution of the dp leading to a capacity achieving zero error coding scheme for our setting dp is thus shown to be a tool not only for solving optimization problems such as capacity calculation but also for constructing optimal coding schemes the derived capacity expression also serves as the only non trivial upper bound known on the capacity of the input constrained erasure channel without feedback a problem that is still open

the policy iteration algorithm for average reward markov decision processes with general state space the average cost optimal control problem is addressed for markov decision processes with unbounded cost it is found that the policy iteration algorithm generates a sequence of policies which are c regular where c is the cost function under consideration this result only requires the existence of an initial c regular policy and an irreducibility condition on the state space furthermore under these conditions the sequence of relative value functions generated by the algorithm is bounded from below and nearly decreasing from which it follows that the algorithm is always convergent under further conditions it is shown that the algorithm does compute a solution to the optimality equations and hence an optimal average cost policy these results provide elementary criteria for the existence of optimal policies for markov decision processes with unbounded cost and recover known results for the standard linear quadratic gaussian problem in particular in the control of multiclass queueing networks it is found that there is a close connection between optimization of the network and optimal control of a far simpler fluid network model

a table of elliptic integrals one quadratic factor integration in terms of real quantities is accomplished for 33 integrands that are rational except for the square root of a cubic or quartic polynomial with exactly one pair of conjugate complex zeros formulas are provided by which 45 more integrals of the same type can be expressed in terms of real quantities with the help of earlier papers neither limit of integration is assumed to be a singular point of the integrand all the integrals are reduced to r functions for which fortran programs are available most of the integrals are not listed in other tables

a certain class of incomplete elliptic integrals and associated definite integrals in many seemingly diverse physical contexts including for example certain radiation field problems studies of crystallographic minimal surfaces the theory of scattering of acoustic or electromagnetic waves by means of an elliptic disk studies of elliptical crack problems in fracture mechanics and so on a remarkably large number of general families of elliptic type integrals and indeed also many definite integrals of such families with respect to their modulus or complementary modulus are known to arise naturally motivated essentially by these and many other potential avenues of their applications we present here a systematic account of the theory of a certain family of incomplete elliptic integrals in a unified and generalized manner by means of the familiar riemann liouville fractional differintegral operators we obtain several explicit hypergeometric representations and apply these representations with a view to deriving various associated definite integrals not only with respect to the modulus or complementary modulus but also with respect to the amplitude of the incomplete elliptic integrals involved therein

numerical perturbative and chebyshev inversion of the incomplete elliptic integral of the second kind abstract the incomplete elliptic integral of the second kind e sin t m 0 t 1 m sin 2 t dt where m 0 1 is the elliptic modulus can be inverted with respect to angle t by solving the transcendental equation e sin t m z 0 we show that newton s iteration t n 1 t n e sin t m z 1 m sin 2 t always converges to t z m e 1 z m within a relative error of less than 10 10 in three iterations or less from the first guess t 0 z m 2 r 2 where defining 1 z e 1 m r 1 m 2 2 and atan 1 m we briefly discuss three alternative initialization strategies homotopy initialization t 0 z m 1 m z 0 mt z m m 1 perturbation series in powers of m and inversion of the chebyshev interpolant of the incomplete elliptic integral although all work well and are general strategies applicable to a very wide range of problems none of these three alternatives is as efficient as the empirical initialization which is completely problem specific this illustrates tai tsun wu s maxim usefulness is often inversely proportional to generality

phase transitions for controlled markov chains on infinite graphs this paper is concerned with some long run average cost problems for controlled markov chains with a denumerable state space the criterion to be optimized contains both reward and penalty functions as a trade off between reward and penalty we observe certain phase transition phenomena our results also provide a stochastic optimal control interpretation for phase transitions of discrete homopolymers with finite attracting potentials

precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations this is a continuation of our works to compute the incomplete elliptic integrals of the first and second kind fukushima 2010 2011 21 23 we developed a method to compute an associate incomplete elliptic integral of the third kind j f n m p f n m f f m n by the half argument formulas of the sine and cosine amplitude functions and the double argument transformation of the integral the relative errors of j f n m computed by the new method are sufficiently small as less than 20 machine epsilons meanwhile the simplicity of the adopted algorithm makes the new method run 1 5 to 3 7 times faster than carlson s duplication method the combination of the new method and that to compute simultaneously two other associate incomplete elliptic integrals of the second kind b f m e f m 1 m f f m m and d f m f f m e f m m which we established recently 23 enables a precise and fast computation of arbitrary linear combination of legendre s incomplete elliptic integrals of all three kinds f f m e f m and p f n m these new procedures share the same device the half argument transformations while the double argument transformation of j f n m includes those of b f m and d f m as its sub component as a result the simultaneous computation of the three associate integrals is significantly faster than computing them separately in fact our combined procedure is 2 7 to 5 9 times faster than the combination of carlson s duplication method to compute r d and r j

scattering by a semi infinite sandwich panel perforated on one side the scattering of sound waves by the edge of a sandwich panel which consists of two thin elastic plates containing a light interior cellular structure is analysed the wiener hopf method is used to examine the interaction effects of a semi infinite panel clamped to a semi infinite rigid screen one major difficulty is that the presence of two different velocity potentials on either side of the plane y 0 results in a matrix wiener hopf equation an approximate solution is given in the asymptotic limit of small values of a parameter tau which accounts for the perforations

symmetry in c d n of jacobian elliptic functions abstract the relation connecting the symmetric elliptic integral r f with the jacobian elliptic functions is symmetric in the first three of the four letters c d n and s that are used in ordered pairs to name the 12 functions a symbol p q ps 2 u k qs 2 u k p q c d n is independent of u and allows formulas for differentiation bisection duplication and addition to remain valid when c d and n are permuted the five transformations of first order which change the argument and modulus of the functions take a unified form in which they correspond to the five nontrivial permutations of c d and n there are 18 transformations of second order including landen s and gauss s transformations comprising three sets of six the sets are related by permutations of the original functions cs ds and ns and there are only three sets because each set is symmetric in two of these the six second order transformations in each set are related by first order transformations of the transformed functions and all 18 take a unified form all results are derived from properties of r f without invoking weierstrass functions or theta functions

necessary and sufficient conditions for a bounded solution to the optimality equation in average reward markov decision chains abstract we consider average reward markov decision processes with discrete time parameter and denumerable state space we are concerned with the following problem find necessary and sufficient conditions so that for arbitrary bounded reward function the corresponding average reward optimality equation has a bounded solution this problem is solved for a class of systems including the case in which under the action of any stationary policy the state space is an irreducible positive recurrent class

sampling of the wiener process for remote estimation over a channel with random delay in this paper we consider a problem of sampling a wiener process with samples forwarded to a remote estimator over a channel that is modeled as a queue the estimator reconstructs an estimate of the real time signal value from causally received samples we study the optimal online sampling strategy that minimizes the mean square estimation error subject to a sampling rate constraint we prove that the optimal sampling strategy is a threshold policy and find the optimal threshold this threshold is determined by how much the wiener process varies during the random service time and the maximum allowed sampling rate further if the sampling times are independent of the observed wiener process the above sampling problem for minimizing the estimation error is equivalent to a sampling problem for minimizing the age of information this reveals an interesting connection between the age of information and remote estimation error our comparisons show that the estimation error achieved by the optimal sampling policy can be much smaller than those of age optimal sampling zero wait sampling and periodic sampling

a note on the convergence of policy iteration in markov decision processes with compact action spaces the undiscounted unichain finite state markov decision process with compact action space is studied we provide a counterexample for a result in hordijk and puterman 1987 and give an alternate proof of the convergence of policy iteration under the condition that there exists a state that is recurrent under every stationary policy the analysis essentially uses a two term matrix representation for the relative value vectors generated by policy iteration procedure

markov decision processes with a borel measurable cost function the average case we consider a markov decision process with a borel measurable cost function we introduce a p step contraction property for the average cost case by use of this method the validity of the optimality equation and the existence of e optimal stationary policies are proved as some applications the sequential replacement model and the inventory model are considered

average cost markov decision processes optimality conditions we are concerned in this paper with discrete time markov decision processes mdps with borel state and action spaces x and a respectively and the long run expected average cost criterion when x is a denumerable set man y necessary and or sufficient conditions for the existence of optimal control policies are known however when x is a borel space i e a borel subset of a complete separable metric space most of the available results impose on the mdp very restrictive topological conditions e g compactness and or strong recurrence assumptions such as doeblin s condition see e g 4 9 12 and their references another related work is 7 where we have studied mdps from the viewpoint of the recurrence or ergodicity properties of the state process ln the present paper however we are concerned with the existence of average optimal policies by looking at static optimization problems see condition cs in section 4 related in sorne cases equivalent to the existence of a bounded solution to the so called optimality equation see c4 in section 4 these optimization problems are dual in the sense that under appropriate conditions the existence of an optimal solution to one of the problems implies existence of an optimal

the effective boundary conditions for a perforated elastic sandwich panel in a compressible fluid the transmission of sound through a sandwich panel consisting of a honeycomb cellular structure bounded by two thin elastic plates is considerably reduced at a certain frequency if one or both of the plates is perforated so as to link a significant number of the cells to the exterior fluid this effect occurs at or near the helmholtz resonance frequency for the cells with the acoustic wavelength large compared with the cell dimensions an analysis is given for the problem of plane waves incident upon a plane sandwich plate of infinite extent using matched expansions for the cases of acoustically hard or acoustically transparent cell walls the compound panel is shown to be acoustically equivalent to that of a hypothetical surface with different normal velocities on either side and effective boundary conditions are derived with generalizations to deal with more complicated structures finite plates and more general incident fields

a mixed value and policy iteration method for stochastic control with universally measurable policies we consider stochastic optimal control models with borel spaces and universally measurable policies for such models the standard policy iteration is known to have difficult measurability issues and cannot be carried out in general we present a mixed value and policy iteration method that circumvents this difficulty the method allows the use of stationary policies in computing the optimal cost function in a manner that resembles policy iteration it can also be used to address similar difficulties of policy iteration in the context of upper and lower semicontinuous models we analyze the convergence of the method in infinite horizon total cost problems for the discounted case where the one stage costs are bounded and for the undiscounted case where the one stage costs are nonpositive or nonnegative for undiscounted total cost problems with nonnegative one stage costs we also give a new convergence theorem for value iteration that shows that value iteration converges whenever it is initialized with a f

indexability of restless bandit problems and optimality of whittle index for dynamic multichannel access in this paper we consider a class of restless multiarmed bandit processes rmabs that arises in dynamic multichannel access user server scheduling and optimal activation in multiagent systems for this class of rmabs we establish the indexability and obtain whittle index in closed form for both discounted and average reward criteria these results lead to a direct implementation of whittle index policy with remarkably low complexity when arms are stochastically identical we show that whittle index policy is optimal under certain conditions furthermore it has a semiuniversal structure that obviates the need to know the markov transition probabilities the optimality and the semiuniversal structure result from the equivalence between whittle index policy and the myopic policy established in this work for nonidentical arms we develop efficient algorithms for computing a performance upper bound given by lagrangian relaxation the tightness of the upper bound and the near optimal performance of whittle index policy are illustrated with simulation examples

paging and registration in cellular networks jointly optimal policies and an iterative algorithm this paper explores optimization of paging and registration policies in cellular networks motion is modeled as a discrete time markov process and minimization of the discounted infinite horizon average cost is addressed the structure of jointly optimal paging and registration policies is investigated through the use of dynamic programming for partially observed markov processes it is shown that there exist policies with a certain simple form that are jointly optimal an iterative algorithm for policies with the simple form is proposed and investigated the algorithm alternates between paging policy optimization and registration policy optimization it finds a pair of individually optimal policies majorization theory and riesz s rearrangement inequality are used to show that jointly optimal paging and registration policies are given for symmetric or gaussian random walk models by the nearest location first paging policy and distance threshold registration policies

control of markov chains with long run average cost criterion the dynamic programming equations the long run average cost control problem for discrete time markov chains on a countable state space is studied in a very general framework necessary and sufficient conditions for optimality in terms of the dynamic programming equations are given when an optimal stable stationary strategy is known to exist e g for the situations studied in stochastic differential systems stochastic control theory and applications ima vol math app 10 springer verlag new york berlin 1988 pp 57 77 a characterization of the desired solution of the dynamic programming equations is given in a special case also included is a novel convex analytic argument for deducing the existence of an optimal stable stationary strategy when that of a randomized one is known

randomized and past dependent policies for markov decision processes with multiple constraints the markov decision problem of locating a policy to maximize the long run average reward subject to k long run average cost constraints is considered it is assumed that the state and action spaces are finite and the law of motion is unichain that is every pure policy gives rise to a markov chain with one recurrent class it is first proved that there exists an optimal stationary policy with a degree of randomization no greater than k consequently it is never necessary to randomize in more than k states a linear program produces the optimal policy with limited randomization for the special case of a single constraint we also address the problem of finding optimal nonrandomized but nonstationary policies we show that a round robin type policy is optimal and conjecture the same for a steering policy that depends on the entire past history of the process but whose implementation requires essentially no more storage than that of a pure policy

markov decision processes with sample path constraints the communicating case we consider time average markov decision processes mdps which accumulate a reward and cost at each decision epoch a policy meets the sample path constraint if the time average cost is below a specified value with probability one the optimization problem is to maximize the expected average reward over all policies that meet the sample path constraint the sample path constraint is compared with the more commonly studied constraint of requiring the average expected cost to be less than a specified value although the two criteria are equivalent for certain classes of mdps their feasible and optimal policies differ for many nontrivial problems in general there does not exist optimal or nearly optimal stationary policies when the expected average cost constraint is employed assuming that a policy exists that meets the sample path constraint we establish that there exist nearly optimal stationary policies for communicating mdps a parametric linear programming algorithm is given to construct nearly optimal stationary policies the discussion relies on well known results from the theory of stochastic processes and linear programming the techniques lead to simple proofs of the existence of optimal and nearly optimal stationary policies for unichain and deterministic mdps respectively

some monotonicity results for partially observed markov decision processes this paper provides sufficient conditions for the optimal value in a discrete time finite partially observed markov decision process to be monotone on the space of state probability vectors ordered by likelihood ratios the paper also presents sufficient conditions for the optimal policy to be monotone in a simple machine replacement problem and in the general case for the optimal policy to be bounded from below by an easily calculated monotone function

markov decision problems and state action frequencies consider a controlled markov chain with countable state and action spaces basic quantities that determine the values of average cost functionals are identified under some regularity conditions these turn out to be a collection of numbers one for each state action pair describing for each state the relative number of uses of each action these conditional frequencies which are defined pathwise are shown to determine the state action frequencies that in the finite case are known to determine the costs this is extended to the countable case allowing for unbounded costs the space of frequencies is shown to be compact and convex and the extreme points are identified with stationary deterministic policies conditions under which the search for optimality in several optimization problems may be restricted to stationary policies are given these problems include the standard markov decision process as well as constrained optimization both in terms of average cost functionals and variability sensitive optimization an application to a queueing problem is given where these results imply the existence and explicit computation of optimal policies in constrained optimization problems the pathwise definition of the conditional frequencies implies that their values can be controlled directly moreover they depend only on the limiting behavior of the control this has immediate application to adaptive control of markov chains including adaptive control under constraints

on optimal zero delay coding of vector markov sources optimal zero delay coding quantization of a vector valued markov source driven by a noise process is consid ered using a stochastic control problem formulation the exis tence and structure of optimal quantization policies are studied for a finite horizon problem with bounded per stage distortion measure the existence of an optimal zero delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells the bounded distortion assumption is relaxed to cover cases that include the linear quadratic gaussian problem for the infinite horizon problem and a stationary markov source the optimality of deterministic markov coding policies is shown the existence of optimal stationary markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed

periodic solutions of a derivative nonlinear schrodinger equation elliptic integrals of the third kind the nonlinear schrodinger equation nlse is an important model for wave packet dynamics in hydrodynamics optics plasma physics and many other physical disciplines the derivative nlse family usually arises when further nonlinear effects must be incorporated the periodic solutions of one such member the chen lee liu equation are studied more precisely the complex envelope is separated into the absolute value and the phase the absolute value is solved in terms of a polynomial in elliptic functions while the phase is expressed in terms of elliptic integrals of the third kind the exact periodicity condition will imply that only a countable set of elliptic function moduli is allowed this feature contrasts sharply with other periodic solutions of envelope equations where a continuous range of elliptic function moduli is permitted

a weighted markov decision process the two most commonly considered reward criteria for markov decision processes are the discounted reward and the long term average reward the first tends to neglect the future concentrating on the short term rewards while the second one tends to do the opposite we consider a new reward criterion consisting of the weighted combination of these two criteria thereby allowing the decision maker to place more or less emphasis on the short term versus the long term rewards by varying their weights the mathematical implications of the new criterion include the deterministic stationary policies can be outperformed by the randomized stationary policies which in turn can be outperformed by the nonstationary policies an optimal policy might not exist we present an iterative algorithm for computing an e optimal nonstationary policy with a very simple structure

technical communique maximizing the set of recurrent states of an mdp subject to convex constraints this paper focuses on the design of time homogeneous fully observed markov decision processes mdps with finite state and action spaces the main objective is to obtain policies that generate the maximal set of recurrent states subject to convex constraints on the set of invariant probability mass functions we propose a design method that relies on a finitely parametrized convex program inspired on principles of entropy maximization a numerical example is provided to illustrate these ideas

recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals presented are the recurrence formulas to compute the derivatives of a general elliptic function weierstrass s function the jacobian elliptic functions and the incomplete elliptic integrals in the forms of jacobi and legendre with respect to the argument or the amplitude the double precision computation by the formulas is correct with 15 digits or so for the first 10 orders of differentiation at least

a table of elliptic integrals of the third kind as many as 72 elliptic integrals of the third kind in previous tables are unified by evaluation in terms of r functions instead of legendre s integrals the present table includes only integrals having integrands with real singular points in addition to 31 integrals of the third kind most of them unavailable elsewhere 10 integrals of the first and second kinds from an earlier table are listed again in new notation in contrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand fortran codes for the standard r functions r sub c and r sub j revised to include their cauchy principal values are listed in a supplement

numerical inversion of a general incomplete elliptic integral we present a numerical method to invert a general incomplete elliptic integral with respect to its argument and or amplitude the method obtains a solution by bisection accelerated by half argument formulas and addition theorems to evaluate the incomplete elliptic integrals and jacobian elliptic functions required in the process if faster execution is desirable at the cost of complexity of the algorithm the sequence of bisection is switched to allow an improvement by using newton s method halley s method or higher order schroder methods in the improvement process the elliptic integrals and functions are computed by using maclaurin series expansion and addition theorems based on the values obtained at the end of the bisection also the derivatives of the elliptic integrals and functions are recursively evaluated from their values by adopting 0 2 as the critical value of the length of the solution interval to shift to the improvement process we suppress the expected number of bisections to be as low as four on average the typical number of applications of update formulas in the double precision environment is three for newton s method and two for halley s method or higher order schroder methods whether the improvement process is added or not our method requires none of the procedures to compute the incomplete elliptic integrals and jacobian elliptic functions but only those to evaluate the complete elliptic integrals once at the beginning as a result it runs fairly quickly in general for example when using the improvement process it is around 2 5 times faster than newton s method using boyd s starter boyd 2012 25 in inverting e f m legendre s incomplete elliptic integral of the second kind

optimal stationary policies in general state space markov decision chains with finite action sets the result of sennott 9 on the existence of optimal stationary policies in countable state markov decision chains with finite action sets is generalized to arbitrary state space markov decision chains the assumption of finite action sets occurring in a global countable action space allows a particularly simple theoretical structure for the general state space markov decision chain two examples illustrate the results example 1 is a system of parallel queues with stochastic work requirements a movable server with controllable service rate and a reject option example 2 is a system of parallel queues with stochastic controllable inputs a movable server with fixed service rates and a reject option

fast computation of incomplete elliptic integral of first kind by half argument transformation we developed a new method to calculate the incomplete elliptic integral of the first kind f varphi m by using the half argument formulas of jacobian elliptic functions the method reduces the magnitude of varphi by repeated usage of the formulas while fixing m the method is sufficiently precise in the sense that the maximum relative error is 3 5 machine epsilons at most thanks to the simplicity of the half argument formulas the new procedure is significantly faster than the existing procedures for example it runs 20 60 faster than bulirsch function el1 and 1 9 2 2 times faster than the method using carlson s function r f

on the convergence of policy iteration in finite state undiscounted markov decision processes the unichain case we study the convergence of policy iteration for the undiscounted finite state discrete time markov decision problem with compact action space and unichain transition structure using a newton method type representation for policy iteration we establish the existence of a solution to the optimality equation we show that to find an average optimal policy it is sufficient to solve the optimality equation on the recurrent set of the maximizing policy under the additional assumption of a unique maximizing policy at each stage of the policy iteration procedure we show that the iterates are convergent and the resulting policy is blackwell optimal

the distortion rate function of sampled wiener processes we consider the recovery of a continuous time wiener process from a quantized or a lossy compressed version of its uniform samples under limited bitrate and sampling rate we derive a closed form expression for the optimal tradeoff among sampling rate bitrate and quadratic distortion in this setting this expression is given in terms of a reverse waterfilling formula over the asymptotic spectral distribution of a sequence of finite rank operators associated with the optimal estimator of the wiener process from its samples we show that the ratio between this expression and the standard distortion rate function of the wiener process describing the optimal tradeoff between bitrate and distortion without a sampling constraint is only a function of the number of bits per sample we also consider a sub optimal lossy compression scheme in which the continuous time process is estimated from the output of an encoder that is optimal with respect to the discrete time samples we show that the latter is strictly greater than the distortion under optimal encoding but only by at most 3 we therefore conclude that near optimal performance is attained even if the encoder is unaware of the continuous time origin of the samples