on the singular values of weber modular functions the minimal polynomials of the singular values of the classical weber modular functions give far simpler defining polynomials for the class fields of imaginary quadratic fields than the minimal polynomials of singular moduli of level 1 we describe computations of these polynomials and give conjectural formulas describing the prime decomposition of their resultants and discriminants extending the formulas of gross zagier for the level 1 case

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

stabilization of infinte dimensional systems with periodic feedback gains and sampled output abstract a novel control technique periodic output feedback is investigated in the context of infinite dimensional linear dynamic systems with unbounded input and output operators this control scheme differs from classical control schemes in that the output of the system in question need not be monitored continuously but only monitored at sampling instants it is shown that for systems satisfying an analog of detectability and stabilizability periodic output feedback provides a stabilization scheme which is robust under perturbations of the sampling time sequence and is easily implementable

nonvanishing of hecke l functions and the bloch kato conjecture in this paper we study the central values of l functions associated to a large class of algebraic hecke characters of imaginary quadratic fields when these central values are nonzero the bloch kato conjecture predicts an exact formula for the algebraic parts of the central values in terms of periods and arithmetic data most notably the selmer groups corresponding to the hecke characters we investigate the nonvanishing of these central values and prove the p part of the bloch kato conjecture in these cases for primes p which split in k

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

a p adic algorithm to compute the hilbert class polynomial classically the hilbert class polynomial p z x of an imaginary quadratic discriminant a is computed using complex analytic techniques in 2002 couveignes and henocq suggested a p adic algorithm to compute p unlike the complex analytic method it does not suffer from problems caused by rounding errors in this paper we give a detailed description of the algorithm in the paper by couveignes and henocq and our careful study of the complexity shows that if the generalized riemann hypothesis holds true the expected runtime of the p adic algorithm is o log 8 e instead of o 1 e we illustrate the algorithm by computing the polynomial p 639 using a 643 adic algorithm

vibrational feedback control of time delay systems this paper applies vibrational feedback control to time lag systems averaging theory for differential delay systems is presented and then applied to aid in the design of periodic controllers both stabilization and transient issues are discussed an illustrative example is given which demonstrates that the proposed controller 1 provides superior robustness properties in comparison to time invariant controllers when applied correctly 2 is not robust with respect to unmodeled delays and 3 does not have zero placement capabilities in the sense defined in the paper

quantitative non vanishing of dirichlet l values modulo p let p be an odd prime and k a non negative integer let n be a positive integer such that p not mid n and lambda a dirichlet character modulo n we obtain quantitative lower bounds for the number of dirichlet character chi modulo f with the critical dirichlet l value l k lambda chi being p indivisible here f rightarrow infty with n f 1 and p not mid f phi f we explore the indivisibility via an algebraic and a homological approach the latter leads to a bound of the form f 1 2 the p indivisibility yields results on the distribution of the associated p selmer ranks we also consider an iwasawa variant it leads to an explicit upper bound on the lowest conductor of the characters factoring through the iwasawa mathbb z ell extension of mathbb q for an odd prime ell ne p with the corresponding critical l value twists being p indivisible

discrete time model reference adaptive control for continuous time systems using generalized sampled data hold functions the generalized sampled data hold functions approach of p t kabamba 1987 is extended to the control of linear time invariant systems with unknown parameters the idea of kabamba s approach is to periodically sample the plant output and define the control as the sampled output plus a discrete time reference each multiplied by an individual modulating function such a control makes it possible to assign an arbitrary discrete time transfer function for the sampled closed loop system and does not make assumptions on the plant other than controllability and observability the authors propose an indirect adaptive controller which is based on this approach and estimates the modulating functions online in particular the control is modified so that persistent excitation of the continuous time plant is ensured without making an assumption on the reference signal and discrete time asymptotic model following is nevertheless obtained the only assumptions on the plant are minimality for the continuous and sampled plant and known order

bayesian system identification in bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to describe mathematically the uncertain relation between the statistician and the external world the statistical inference is understood as a correction of prior subjective probability distribution by objective data the paper shows that on this bayesian basis it is possible to build a consistent theory of system identification the following problems are considered one shot and real time identification estimation and prediction in closed control loop redundant and unidentifiable parameters time varying parameters and adaptivity

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

hilbert class polynomials and traces of singular moduli where q e the values of j z at imaginary quadratic arguments in the upper half of the complex plane are known as singular moduli singular moduli are algebraic integers which play prominent roles in classical and modern number theory see c bcsh for example hilbert class fields of imaginary quadratic fields are generated by singular moduli furthermore isomorphism classes of elliptic curves with complex multiplication are distinguished by singular moduli throughout let d 0 3 mod 4 be a positive integer so that d is the discriminant of an order in an imaginary quadratic field and let h d be the hurwitz kronecker class number for the discriminant d let qd be the set of positive definite integral binary quadratic forms note including imprimitive forms if there are any

a nonsplit sum of coefficients of modular forms we introduce and study certain truncated sums of hecke eigenvalues of gl2 automorphic forms along quadratic polynomials a power saving estimate is established and new applications to moments of critical l values associated to quadratic fields are derived an application to the asymptotic behavior of the height of heegner points and singular moduli is discussed in detail

central values of hecke l functions of cm number fields 0 introduction it is well known that the zeta function of cm complex multiplication abelian varieties can be given in terms of l functions of associated hecke characters in this paper we prove a formula expressing the central special value of the l function of certain hecke characters in terms of theta functions the formula easily implies that the central value is nonnegative and yields a criterion for its positivity combining this criterion with the work of arthaud and rubin we show that certain cm elliptic curves have mordell weil rank zero over their field of definition let f be a totally real number field of degree t and let be a quadratic hecke character of f of conductor f such that 2f f 1 given a cm extension e of f we consider the twist can of by a canonical hecke character can of

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

a spectral proof of class number one we continue our previous work on the subject of re proving the heegner baker stark theorem giving another effective resolution of this conjecture of gauss namely there are exactly 9 imaginary quadratic fields mathbf q sqrt q with class number 1 specifically the list is q in 3 4 7 8 11 19 43 67 163 we again follow an ansatz of goldfeld considering a modular form l function of analytic rank 2 and reducing the situation to showing sufficient cancellation of the dirichlet series coefficients when restricted to the principal form previously we then chose a specific rank 2 elliptic curve with complex multiplication by mathbf q sqrt 1 and deduced the desired cancellation from an equi distribution result of hooley s for roots of a quadratic polynomial to varying moduli herein we instead use spectral techniques filling in details of work of templier and tsimerman to complete the proof relying on the duke iwaniec bound for fourier coefficients of half integral weight maass forms unlike the previous method we do not require complex multiplication and any analytic rank 2 modular form whose level has an even number of prime factors suffices

bayesian methods for prevalence estimation from incomplete administrative lists many studies aimed at estimating prevalence use several administrative lists from different sources in an attempt to enumerate all persons affected with the health condition of interest each list is incomplete in the sense that none of them enumerates all persons affected with the health condition further because the lists are drawn from different administrative sources the probability of enumeration varies from list to list the goal is to use information from the lists to estimate the total number of affected persons in the population but with some accounting for the different but unknown probabilities of enumeration on each list this paper presents a bayesian method to estimate prevalence when the probability of enumeration varies from list to list data from a survey of children with spina bifida illustrate the methodology

simultaneous pole assignment in linear periodic systems by constrained structure feedback the authors present methods for pole assignment by feedback with constrained structure in linear periodic systems using generalized sampled data hold functions gshf constrained structure is taken to mean that the input of each channel is restricted to depend only on the measurements of some specific output channels the basic idea of gshf control is to use sample and hold but to consider the hold function as a design parameter four strategies are proposed for closing a control loop using gshf the key to the results obtained is that when gshf control with constrained structure is applied to a periodic system a discrete time time invariant decentralized system is obtained for which control design methods are available

output feedback stabilization for heat equations with sampled data controls abstract in this paper we build up an output feedback law to stabilize a sampled data controlled heat equation with a potential in a bounded domain the feedback law abides the following rules first we divide equally the time interval 0 into infinitely many disjoint time periods and divide each time period into three disjoint subintervals second for each time period we observe a solution over an open subset of in the first subinterval take sample from outputs at one time point of the first subinterval add a time invariant output feedback control over another open subset of in the second subinterval let the equation evolve free in the last subinterval thus the corresponding feedback control is of sampled data our feedback law has the following advantages the sampling period which is the length of the above time period can be arbitrarily taken the feedback law has an explicit expression in terms of the sampling period the behaviors of the norm of the feedback law when the sampling period goes to zero or infinity are clear the construction of the feedback law is based on two kinds of approximate null controllability for heat equations one has time invariant controls while another has impulse controls the studies of the aforementioned controllability with time invariant controls need a new observability inequality for heat equations built up in the current work

stabilization of distributed parameter systems by piecewise polynomial control in this paper we consider the stabilization of continuous time distributed parameter systems by piecewise polynomial controls we obtain necessary and sufficient conditions for stabilization by piecewise polynomial controls

uniform distribution of heegner points let e be a modular elliptic curve over q of conductor n let k denote an imaginary quadratic field of discriminant d with n d 1 if p is a prime then there exists a unique zp extension k k such that gal k q acts nontrivially on gal k k the field k is called the anticyclotomic zp extension of k let e k denote the mordell weil group of e over k then a fundamental conjecture of mazur maz predicts that the size of e k is controlled by the prime factorization of n in k equivalently mazur s conjecture relates the size of the mordell weil group to the sign in the functional equation of certain l series the conjecture was verified by greenberg rohrlich and rubin in what mazur calls the exceptional case when e has complex multiplication by k more generally they settled the conjecture for certain abelian varieties with complex multiplication for a discussion of this cm case we refer the reader to gre roh and rub our goal in this paper is to treat the generic case which occurs either when e has no cm or when the field of complexmultiplications is distinct from k under certain conditions on e and k mazur s conjecture predicts that the group e k is finitely generated our main result asserts that this is in fact the case at least when p is an ordinary prime for e or when the class number of k is prime to p the main new ingredient we introduce is that of equidistribution following ideas used by ferrero andwashington to study the cyclotomic invariant more precisely we show that theheegner points associated to definite quaternion algebras are uniformly distributed on the components of a certain curve x and that the elements of a certain galois group act independently in a suitable sense this combined with a special value formula due to gross allows us to conclude that the special values of anticyclotomic l functions are almost always nonzero so that the statement about the mordell weil groups follows from the machinery of euler systems as developed by bertolini and darmon bd

trilinear forms and the central values of triple product l functions we give an explicit formula for certain global trilinear forms that appear in jacquet s conjecture in terms of local trilinear forms and the central values of triple product l functions

generalized sampled data feedback control of distributed parameter systems abstract in the sampled data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled data control for finite dimensional systems the necessary conditions are also known to be sufficient we show that this equivalence extends to the infinite dimensional case if the underlying semigroup is analytic however for general systems the necessary conditions are not sufficient nor are the sufficient conditions necessary we prove this by a single example with a free parameter one choice of parameter shows that the necessary conditions are too weak and another choice shows that the sufficient conditions are too strong

descent algorithms for optimal periodic output feedback control periodic output feedback is investigated in the context of linear quadratic regulation for finite dimensional time invariant linear systems discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control the optimal solution is obtained in two steps by separating the continuous time from the discrete time structure first the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix g then the minimum value which depends on g is substituted into the overall objective this results in a finite dimensional nonlinear programming problem over all admissible gain matrices g the solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem a steepest descent and a direct iterative method for solving this problem are formulated and compared numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous state feedback

faltings heights of cm cycles and derivatives of l functions we study the faltings height pairing of arithmetic special divisors and cm cycles on shimura varieties associated to orthogonal groups we compute the archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a rankin l function we prove the conjecture in certain cases where the shimura variety has dimension 0 1 or 2 in particular we obtain a new proof of the gross zagier formula

ripple free robust output regulation and tracking for multirate sampled data control the problem of the robust continuous time asymptotic tracking and disturbance rejection for a multivariable multirate sampled data system is studied the necessity of a continuous time internal model of the exogenous signals except for the constant ones if any for obtaining a ripple free zero error response is proven the conditions are given for the existence of a hybrid control system including possibly a continuous time subcompensator for which the exponential stability and a continuous time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters this in particular both for when the dead beat convergence of the state free response and the continuous time error response is required at the nominal parameters and for when an exponential convergence with a prescribed rate of decay is required including design procedures of the continuous time and the discrete time subcompensators both for when the available description of the plant has a

stabilizing binomial n estimators abstract the maximum likelihood estimator of the binomial parameter n can be highly unstable resulting in huge fluctuations in the estimate when the data are only slightly perturbed a method of assessing this sensitivity based on perturbing the log likelihood function is proposed and examined

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points ii we prove a general subconvex bound in the level aspect for rankin selberg l functions associated with two primitive holomorphic or maass cusp forms over q we use this bound to establish the equidistribution of incomplete galois orbits of heegner points on shimura curves associated with indefinite quaternion algebras over q

optimal hold functions for sampled data regulation abstract this paper investigates the use of generalized sampled data hold function control gshf to optimize quadratic measures of performance in sampled data control loops the idea of gshf control is to use sampled data feedback but consider the hold function as a design parameter explicit solutions are given for the gshf versions of the optimal lq and lqg regulators the questions of existence uniqueness and computation of optimal hold functions are treated an example is presented

a bayesian analysis of multiple recapture sampling for a closed population summary this paper considers from a bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple recapture sampling scheme the method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods several ways of expressing such prior information are explored and a practical example of the uses of these ways is given the main result of the paper is an approximation to the posterior distribution of sample size that exhibits the contributions made by the likelihood and the prior ideas the multiple recapture sampling scheme involves taking samples from a population of animals at each stage counting the number of marked animals in the sample marking the previously unmarked animals and returning the sample to the population the literature is reviewed by cormack 1968 and the papers most relevant to our problem are those of chapman 1952 and darroch 1958 in these papers maximum likelihood estimates for the population parameters and variances for these estimates are given our approach differs from previous ones by introducing prior information about the population size and about the propensities of the animals to be captured called catch probabilities by some previous authors the incorporation of these propensities is a feature not shared by many previous approaches darroch 1958 found their introduction into his model does not change the maximum likelihood estimates of the population size our approach will show that strong prior knowledge about the catch probabilities can greatly affect inference about the population size and it is in this respect that the greatest difference from previous approaches lies although it is recognized that models of an open population incorporating death and immigration such as those of jolly 1965 and seber 1965 are more practically realistic we feel that our method which deals only with a closed population is worth investigating as a step towards providing a bayesian treatment of the open population problem

stability of infinite dimensional sampled data systems suppose that a static state feedback stabilizes a continuous time linear infinite dimensional control system we consider the following question if we construct a sampled data controller by applying an idealized sample and hold process to a continuous time stabilizing feedback will this sampled data controller stabilize the system for all sufficiently small sampling times here the state space x and the control space u are hilbert spaces the system is of the form x t ax t bu t where a is the generator of a strongly continuous semigroup on x and the continuous time feedback is u t fx t the answer to the above question is known to be yes if x and u are finite dimensional spaces in the infinite dimensional case if f is not compact then it is easy to find counterexamples therefore we restrict attention to compact feedback we show that the answer to the above question is yes if b is a bounded operator from u into x moreover if b is unbounded we show that the answer yes remains correct provided that the semigroup generated by a is analytic we use the theory developed for static state feedback to obtain analogous results for dynamic output feedback control

generalized sampled data stabilization of well posed linear infinite dimensional systems we consider well posed linear infinite dimensional systems the outputs of which are sampled in a generalized sense using a suitable weighting function under certain natural assump tions on the system the weighting function and the sampling period we show that there exists a generalized hold function such that unity sampled data feedback renders the closed loop system exponentially stable in the state space sense as well as l 2 stable in the input output sense to illustrate our main result we describe an application to a structurally damped euler bernoulli beam

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

exact and asymptotic inference for the size of a population on montre que la vraisemblance a un maximum local unique et que l algorithme iteratif propose converge vers celui ci

an indirect adaptive controller with a self excitation capability an indirect adaptive pole placement controller is presented which stabilizes and asymptotically regulates any discrete time single input single output linear time invariant plant which is of known order n is controllable and observable and has unknown parameters to avoid singular points in the algorithm the adaptive controller solves the pole placement design equation asymptotically with time rather than trying to solve it exactly at each time instant the stability of the adaptive control system and the asymptotic regulation of the plant output to zero are ensured by an additional self excitation generated by the adaptive controller a novel kind of an error signal to control the magnitude of the self excitation is obtained by suitably filtering the self exciting signal and monitoring changes of the controller parameters as they are generated by the adaptive algorithm

bayesian methods for estimation of the size of a closed population summary a bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed the approach allows for a variety of dependence structures between the lists can make use of covariates and explicitly accounts for model uncertainty interval estimates from this approach are compared to frequentist and previously published bayesian approaches several examples are considered

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points keywords rankin selberg l function subconvexity heegner points reference tan article 2004 002doi 10 4007 annals 2004 160 185 record created on 2008 11 14 modified on 2017 05 12

horizontal non vanishing of heegner points and toric periods abstract let f be a totally real number field and a a modular gl 2 type abelian variety over f let k f be a cm quadratic extension let be a class group character over k such that the rankin selberg convolution l s a is self dual with root number 1 we show that the number of class group characters with bounded ramification such that l 1 a 0 increases with the absolute value of the discriminant of k we also consider a rather general rank zero situation let be a cuspidal cohomological automorphic representation over gl 2 a f let be a hecke character over k such that the rankin selberg convolution l s is self dual with root number 1 we show that the number of hecke characters with fixed type and bounded ramification such that l 1 2 0 increases with the absolute value of the discriminant of k the gross zagier formula and the waldspurger formula relate the question to horizontal non vanishing of heegner points and toric periods respectively for both situations the strategy is geometric relying on the zariski density of cm points on self products of a quaternionic shimura variety the recent result 26 31 1 on the andre oort conjecture is accordingly fundamental to the approach