heights of heegner cycles and derivatives of l series 0 introduction 99 1 intersections and heights 103 2 kuga sato varieties and cm cycles 117 3 heights of cm cycles 124 4 heights of heegner cycles 137 5 proof of the main identity and the consequences 147 references 151

on the solution of block tridiagonal systems of linear algebraic equations having a special structure recently the present author has developed some high order finite difference formulae for the approximate numerical integration of general two point boundary value problems for ordinary differential equations the algebraic equations arising from using these formulae in conjunction with a modified newton iteration scheme are block tridiagonal with an additional special structure efficient algorithms for solving these equations are given and these appear to make high order finite difference schemes particularly attractive for the numerical solution of general two point boundary value problems

closed form discrete fractional and affine fourier transforms the discrete fractional fourier transform dfrft is the generalization of discrete fourier transform many types of dfrft have been derived and are useful for signal processing applications we introduce a new type of dfrft which are unitary reversible and flexible in addition the closed form analytic expression can be obtained it works in performance similar to the continuous fractional fourier transform frft and can be efficiently calculated by the fft since the continuous frft can be generalized into the continuous affine fourier transform aft the so called canonical transform we also extend the dfrft into the discrete affine fourier transform daft we derive two types of the dfrft and daft type 1 is similar to the continuous frft and aft and can be used for computing the continuous frft and aft type 2 is the improved form of type 1 and can be used for other applications of digital signal processing meanwhile many important properties continuous frft and aft are kept in the closed form dfrft and daft and some applications such as filter design and pattern recognition are also discussed the closed form dfrft we introduce has the lowest complexity among all current dfrfts that is still similar to the continuous frft

big line bundles over arithmetic varieties 5 equidistribution theory 26 5 1 a generic equidistribution theorem 27 5 2 equidistribution at infinite places 30 5 3 equidistribution at finite places 32 5 4 equidistribution of small subvarieties 35 5 5 equidistribution over algebraic dynamical systems 37 5 6 equidistribution over multiplicative groups 39 5 7 equidistribution theory 41

invariant imbedding the box scheme and an equivalence between them we show for general linear two point boundary value problems that the box scheme and invariant imbedding are equivalent in the sense that a specific algorithm for solving the difference equations is valid if and only if an appropriate imbedding is valid a key element in the equivalence is the role played by pivoting to solve the linear equations and switching to get a finite imbedding part of the equivalence proof shows that imbedding is the completion of the box scheme multiple imbeddings are introduced and a lower bound for the critical length problem is obtained

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

concernant la relation de distribution satisfaite par la fonction φ associee a un reseau complexe for any pair of latticesl andl satisfying i l l and ii the indexn ofl intol is prime to 6 we construct from the usual function ofl cf no 1 some elliptic function psi psi z l underset raise0 3em hbox smash scriptscriptstyle l of the variablez with period latticel and divisor n 0 l sum limits i 1 n t i l over the torus l where the complex numberst i 1 i n describe a complete set of representatives of the quotientl l

a new time delay estimator based on etde in this paper we address the problem of online subsample time delay estimation of narrowband signals of known center frequency we propose a new so called mixed modulated lagrange explicit time delay estimation mmletde algorithm and study its performance through computer simulations the mmletde is a modulated lagrange etde but the delay estimate adaptation process is based on the truncated sinc fractional delay filter algorithm we provide theoretical derivations for our proposed estimator a proof of its convergence performance learning characteristics of its error performance surface and an expression for its delay variance using simulations we show that mmletde requires only a small filter order and has no noticeable estimation bias over a wide frequency range

spectral analysis and reconstruction for periodic nonuniformly sampled signals in fractional fourier domain nonuniform sampling occurs in many applications due to imperfect timebase or random events periodic nonuniform sampling is a special type of nonuniform sampling the properties and applications of periodic nonuniform sampling signals in traditional fourier domain have been extensively studied but so far none of the research papers covering the spectral analysis and reconstruction of periodic nonuniformly sampled signals in fractional fourier domain have been published this correspondence is to explore the spectral properties of periodic nonuniformly sampled signals associated with the fractional fourier transform first based on the uniform fractional fourier transform kernel the general spectral representation of periodic nonuniformly sampled signals has been derived second detailed analysis of periodic nonuniformly sampled chirp signals in the fractional fourier domain have been performed the results can be used to estimate the chirp rate and the sampling offsets finally a more simple relationship between the discrete fractional spectrum of periodic nonuniformly sampled signals and the continuous spectrum has been obtained based on this relationship the original continuous spectrum can be reconstructed from periodic nonuniformly sampled signals in fractional fourier domain in addition the simulations are carried out to verify the correctness of the results

un lemme matriciel effectif we show an almost optimal effective version of masser s matrix lemma lecture notes math 1290 109 148 1987 giving a lower bound of the height of an abelian variety in terms of its period lattices

multiloop calculations in p adic string theory and bruhat tits trees we treat the openp adic string world sheet as a coset spacef t wheret is the bruhat tits tree for thep adic linear groupgl 2 p and pgl 2 p is some schottky group the boundary of this world sheet corresponds to ap adic mumford curve of finite genus the string dynamics is governed by the local gaussian action on the coset spacef the tachyon amplitudes expressed in terms ofp adic functions are proposed for the mumford curve of arbitrary genus we compare them with the corresponding usual archimedean amplitudes the sum over moduli space of the algebraic curves is conjectured to be expressed in the arithmetic surface terms we also give the necessary mathematical background including the mumford approach top adic algebraic curves the connection of the problem of closedp adic strings with the considered topics is discussed

second variation of zhang s λ invariant on the moduli space of curves we compute the second variation of the invariant recently introduced by s zhang on the complex moduli space mg of curves of genus g 2 using work of n kawazumi as a result we prove that 8g 4 is equal up to a constant to the invariant introduced some time ago by r hain and d reed we deduce some consequences for example we calculate the invariant for each hyperelliptic curve expressing it in terms of the petersson norm of the discriminant modular form 1 introduction recently independently s zhang 27 and n kawazumi 16 introduced a new interesting real valued function on the moduli space mg of complex curves of genus g 2 its value at a curve x m g is given as follows let h 0 x x be the space of holomorphic differentials on x equipped with the

multipath time delay estimation using regression stepwise procedure consider a multipath signal whose individual signals are deterministic known pulses our problem is to estimate the amplitudes and delay times of individual signals our main idea is to consider the multipath signal as a multiple regression model where each time sample is considered to be a possible arrival time of a pulse that may not be real we use the regression stepwise procedure to select true pulses and eliminate the false pulses by using this procedure the number of pulses in a multipath signal does not need to be known the results of a monte carlo simulation study with sinusoidal and trapezoidal pulses are presented to demonstrate the accurate estimation of arrival times and amplitudes by the regression stepwise procedure

symmetric roots and admissible pairing using the discriminant modular form and the noether formula it is possible to write the admissible self intersection of the relative dualising sheaf of a semistable hyperelliptic curve over a number field or function field as a sum over all places of a certain adelic invariant we provide a simple geometric interpretation for this invariant based on the arithmetic of symmetric roots we propose the conjecture that the invariant coincides with the invariant introduced in a recent paper by s w zhang this conjecture is true in the genus 2 case and we obtain a new proof of the bogomolov conjecture for curves of genus 2 over number fields

fractional power spectrum in this paper by investigating the definitions of the fractional power spectrum and the fractional correlation for the deterministic process we consider the case associated with the random process in an explicit manner the fractional power spectral relations for the fractional fourier domain filter are derived and the expression for the fractional power spectrum in terms of the fractional correlation is obtained in addition the definitions and the properties of the fractional white noise and the chirp stationary process are presented simulation results verify the theoretical derivations and demonstrate the potential applications such as detection and parameter estimation of chirp signals fractional power spectral estimation and system identification in the fractional fourier domain

partiallyu 1 compactified scalar massless field on the compact riemann surface and the bosonic string amplitudes the theory of the partiallyu 1 compactified scalar massless field on the compact riemann surface with nambu goto action is defined the partition function is determined completely by a choice of the finite dimensional approximations the correlation functions are the only correctly defined objects of the theory the averages of the correlation function asymptotic values provide the amplitudes for the compact riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes

arakelov self intersection numbers of minimal regular models of modular curves x_0 p 2 x0 p2 we compute an asymptotic expression for the arakelov self intersection number of the relative dualizing sheaf of edixhoven s minimal regular model for the modular curve x 0 p 2 over mathbb q the computation of the self intersection numbers are used to prove an effective version of the bogolomov conjecture for the semi stable models of modular curves x 0 p 2 and obtain a bound on the stable faltings height for those curves in a companion article banerjee and chaudhuri in isr j math 2020

a sparsity exploiting variant of the bartels golub decomposition for linear programming bases we describe a sparsity exploiting variant of the bartels golub decomposition for linear programming bases it includes interchanges that whenever this is possible avoid the use of any eliminations with consequent fill ins when revising the factorization at an iteration test results on some medium scale problems are presented and comparisons made with the algorithm of forrest and tomlin

solving staircase linear programs by the simplex method 2 pricing this and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged or staircase structure the preceding paper considered inversion routines that factorize the basis and solve linear systems the present paper examines pricing routines that compute reduced costs for nonbasic variables and that select a variable to enter the basis at each iteration both papers describe extensive although preliminary computer experiments and can point to some quite promising results for pricing in particular staircase computation strategies appear to offer modest but consistent savings staircase selection strategies properly chosen may offer substantial savings in number of iterations time per iteration or both

explicit arithmetic intersection theory and computation of neron tate heights we describe a general algorithm for computing intersection pairings on arithmetic surfaces we have implemented our algorithm for curves over q and we show how to use it to compute regulators for a number of jacobians of smooth plane quartics and to numerically verify the conjecture of birch and swinnerton dyer for the jacobian of the split cartan curve of level 13 up to squares

a computational study of finite element methods for second order linear two point boundary value problems a computational study of five finite element methods for the solution of a single second order linear ordinary differential equation subject to general linear separated boundary conditions is described in each method the approximate solution is a piecewise polynomial expressed in terms of a b spline basis and is determined by solving a system of linear algebraic equations with an almost block diagonal structure the aim of the investigation is twofold to determine if the theoretical orders of convergence of the methods are realized in practice and to compare the methods on the basis of cost for a given accuracy in this study three parametrized families of test problems containing problems of varying degrees of difficulty are used the conclusions drawn are rather straightforward collocation is the cheapest method for a given accuracy and the easiest to implement also for solving the linear algebraic equations the use of a special purpose solver which takes advantage of the structure of the equations is advisable 1 introduction finite element methods for two point boundary value problems for a single ordinary differential equation may take many forms the simplest type of method is probably collocation 3 where an approximate solution is sought in some finite space subject to the constraint that it satisfy the differential equation at certain specified points this type of method has been applied very successfully in the case of mixed order systems of boundary value problems see for example 1 other methods can be described based on the standard l2 galerkin approximation 9 or on a combination of this and the collocation approach 7 13 25 in addition different weak formulations of the boundary value problem lead to two other techniques the hx and galerkin methods 12 14 15 17 how one would apply these methods to a system of differential equations with the exception of the collocation case is not immediately clear in addition it is not apparent what the relative advantages are of these various methods even when applied to a single equation in this paper we restrict our attention to the case of a single linear differential equation our aim is to investigate numerically five finite element techniques for a second order linear two point boundary value problem with separated boundary conditions of a general nature in particular we consider i the organization of the methods ii the treatment of the boundary conditions

hauteur de faltings de quotients de j 0 n discriminants d algebres de hecke et congruences entre formes modulaires in this paper we compute the faltings height of the jacobian of the modular curve j 0 n we explain how it is related to the discriminant of the hecke algebra this discriminant measures congruences between modular forms as a corollary we obtain a lower bound for this discriminant the faltings height of a quotient a of j 0 n is also computed

error analysis and bounds in time delay estimation we have analyzed the error propagation in the classical delay estimation based on the identification of the maximum of the cross correlation between the input signals the resulting error propagation model has the form of a linear combination of the errors additional to the signal samples these errors are weighted by the derivative of the input signals at the sampling instants based on the error propagation model we have further found an upper bound to the square of the estimation error the use of the model is demonstrated by two simple examples

summations over equilaterally triangulated surfaces and the critical string measure we propose a new approach to the summation over dynamically triangulated riemann surfaces which does not rely on properties of the potential in a matrix model instead we formulate a purely algebraic discretization of critical string path integral this is combined with a technique which assigns to each equilateral triangulation of a two dimensional surface a riemann surface defined over a certain finite extension of the field of rational numbers i e an arthmetic surface thus we establish a new formulation in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces it is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory i e liouville theory or critical string theory in low genus this subtlety does not exist in the case of critical string theory we explicity compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure we also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

the asymptotics of the arakelov geen s function and faltings delta invariant we study the behavior of the arakelov green s function and faltings delta invariant on degenerating riemann surfaces

closed form formulae for time difference of arrival estimation for a positioning system with l sensors a maximum of l l 1 2 distinct time difference of arrival tdoa measurements which are referred to as the full tdoa set can be obtained in this paper closed form expressions regarding optimum conversion of the full tdoa set to the nonredundant tdoa set which corresponds to l 1 tdoa measurements with respect to a common reference receiver in the case of white signal source and noise are derived the most interesting finding is that optimum conversion can be achieved via the standard least squares estimation procedure furthermore the cramer rao lower bound for tdoa based positioning is produced in closed form which will be useful for optimum sensor array design

special values of canonical green s functions we give a precise formula for the value of the canonical green s function at a pair of weierstrass points on a hyperelliptic riemann surface further we express the energy of the weierstrass points in terms of a spectral invariant recently introduced by n kawazumi and s zhang it follows that the energy is strictly larger than log 2 our results generalize known formulas for elliptic curves

higher picard varieties and the height pairing let x be a smooth projective variety which is defined over a number field beilinson and bloch have defined under suitable asssumptions height pairings between chow groups of homologically trivial cycles on x beilinson has also formulated a hard lefschetz and a hodge index conjecture for these chow groups we show that the restriction of the height pairing to cycles algebraically equivalent to zero can be computed via abel jacobi maps in terms of the neron tate height pairing on the higher picard varieties of x this description is used in the case where x is an abelian variety to prove a consequence of beilinson conjectures namely we prove a hard lefschetz and a hodge index theorem for the groups of cycles algebraically equivalent to zero modulo incidence equivalence

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

solving staircase linear programs by the simplex method 1 inversion this and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged or staircase structure the present paper looks at inversion routines within the simplex method particularly those for sparse triangular factorization of a basis by gaussian elimination and for solution of triangular linear systems the succeeding paper examines pricing routines both papers describe extensive though preliminary computational experience and can point to some quite promising results

theta functions modular invariance and strings we use quillen s theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory in particular we show that the spin structure dependence of the chiral dirac determinant on a riemann surface is given by riemann s theta function we use this result to investigate the modular invariance of multiloop heterotic string amplitudes

parallel treatment of block bidiagonal matrices in the solution of ordinary differential boundary value problems abstract ignoring boundary conditions a number of schemes such as multiple shooting give rise to systems of equations in block bidiagonal form with some preliminary transformation others such as collocation can be reduced to this form an algorithm which reduces a block bidiagonal system of size n n 1 to a system of size 1 2 blocks will be described these equations can then be combined with the boundary conditions and the solution completed the reduction uses ideas similar to recursive doubling and block cyclic reduction but full row interchanges are included the alrogithm is designed to facilitate the use of parallel processes the algorithm has been implemented on the 14 processor encore multimax shared memory multiprocessor in newcastle results will be described for different numbers of processors and the algorithm compared with other possibilities

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

a class of fractional integral transforms a generalization of the fractional fourier transform the paper presents a systematic and unified approach to fractional integral transforms we introduce a new class of fractional integral transforms that includes the fractional fourier and hankel transforms and the fractional integration and differentiation operators as special cases these fractional transforms may also be viewed as angular transforms indexed by an angular parameter spl alpha since their kernels are obtained by taking the limits of analytic functions in the unit disc along a radius making an angle spl alpha with the x axis

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

heights and arakelov s intersection theory introduction this paper relates the neron tate height on jacobian varieties to an intersection theory on arithmetic surfaces constructed by s arakelov a1 here i extend and prove a statement of arakelov to the effect that his intersection pairing is a neron pairing a2i i use this to prove an analogue of the hodge index theorem for arithmetic surfaces a result due independently to g faltings the results of this paper have been extracted from my thesis written under the direction of michael artin it differs from the thesis in three ways firstly it employs the language of local height functions as defined by a neron and j tate and expounded by s lang li in the thesis i used neron s language of local intersection pairings n1 the second major difference is in the proof of theorem 1 3 in my thesis i proved this result by using work of raynaud and picard functors r 1 this method was suggested by m artin in this paper i provide a simpler proof observed by s lang and independently by b gross finally the development of arakalov s theory in the context of neron functions in section 2 is due to s lang who has kindly given me leave to publish it this exposition of my results is due in considerable part to s lang it is essentially an edited transcript of a series of conversations between us which he provided it is my great pleasure to thank both him and michael artin for their help and encouragement 1 the neron pairing neron ne has given a pairing between divisors and points on abelian varieties and also on arbitrary varieties under suitable conditions we shall give a complement to the neron theory on curves let c be a curve by which we mean a complete regular curve geometrically irreducible over a field k with an absolute value v let

modeling of time delay and its application to estimation of nonstationary delays a method to model a time delay by a finite impulse response filter is presented it is useful in simulation work that involves time delays and transforms the time delay estimation problem into one of parameter estimation the benefits of this approach are the elimination of spectral estimation a choice of many parameter estimation algorithms and the capability to track time varying delays two examples of estimating nonstationary time delays are also given

bosonization on higher genus riemann surfaces we prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions the theories have fields of arbitrary spin on compact surfaces with any number of handles global considerations require that we add new topological terms to the bosonic action the proof that our prescription is correct relies on methods of complex algebraic geometry

parallel interior point solver for structured linear programs issues of implementation of an object oriented library for parallel interior point methods are addressed the solver can easily exploit any special structure of the underlying optimization problem in particular it allows a nested embedding of structures and by this means very complicated real life optimization problems can be modelled the efficiency of the solver is illustrated on several problems arising in the optimization of networks the sequential implementation outperforms the state of the art commercial optimization software the parallel implementation achieves speed ups of about 3 1 3 9 on 4 processors parallel systems and speed ups of about 10 12 on 16 processors parallel systems

staircase matrices and systems difference equations spline approximations and multiperiod linear programs all give rise to linear equation systems that have a characteristic staircase structure a staircase system s variables can be partitioned into a natural sequence of periods in such a way that every equation involves at most the variables of two adjacent periods this paper surveys the numerous properties of staircase systems and of the staircase matrices that comprise their coefficients particular attention is given to reduced and sparse staircase forms and to the varieties of gaussian elimination for solving staircase systems

frequency selective adaptive time delay estimation a frequency selective algorithm for time delay estimation between two channel data is proposed and its performance is studied the adaptive stochastic gradient scheme provides a direct estimate of the time delay it has a low numerical complexity and it is an alternative to data prefiltering and time delay estimation when the source and noise components have different spectral characteristics

a dynamical pairing between two rational maps this is the publisher s final pdf the published article is copyrighted by american mathematical society and can be found at http www ams org home page

sparse discrete fractional fourier transform and its applications the discrete fractional fourier transform is a powerful signal processing tool with broad applications for nonstationary signals in this paper we propose a sparse discrete fractional fourier transform sdfrft algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional fourier domain the proposed technique achieves multicomponent resolution in addition to its low computational complexity and robustness against noise in addition we apply the sdfrft to the synchronization of high dynamic direct sequence spread spectrum signals furthermore a sparse fractional cross ambiguity function sfrcaf is developed and the application of sfrcaf to a passive coherent location system is presented the experiment results confirm that the proposed approach can substantially reduce the computation complexity without degrading the precision

hilbert transformer and time delay statistical comparison in the presence of gaussian noise we have shown that in the presence of independent and identically distributed i i d additive gaussian noise the performance of a time delay as a phase shifter which produces a signal dependent phase shift is comparable with the performance of a hilbert transformer which produces a signal independent 90 spl deg phase shift especially for high signal to noise ratios snrs and the proper choice of the delay sinusoidal signals are considered it is shown that the time delay phase process in gaussian noise can be approximated by the noise free phase plus a non gaussian phase noise as the snr increases the expected value of the time delay phase estimator approaches the true value of the phase and its variance substantially decreases and converges to the cramer rao bound for all ranges of the effective parameters the phase shift the deterministic phase and snr a symmetric transformation of the phase probability density function pdf that improves the performance of the time delay in gaussian noise is also proposed

discriminants and artin conductors we study questions of multiplicities of discriminants for degenerations coming from projective duality over discrete valuation rings the main observation is a type of discriminant different formula in the sense of classical algebraic number theory and we relate it to artin conductors via bloch s conjecture in the case of discriminants of planar curves we can calculate the different precisely in general these multiplicities encode topological invariants of the singular fibers and in the case of characteristic p also wild ramification data in the form of swan conductors this builds upon results of t saito

computing block angular karmarkar projections with applications to stochastic programming we present a variant of karmarkar s algorithm for block angular structured linear programs such as stochastic linear programs by computing the projection efficiently we give a worst case bound on the order of the running time that can be an order of magnitude better than that of karmarkar s standard algorithm further implications for approximations and very large scale problems are given

time delay estimation of chirp signals in the fractional fourier domain a new time delay estimator is presented in this paper it is evaluated based on the delay property of the fractional fourier transform with less computation and is suitable for chirp signals the statistical analysis in terms of signal to noise ratio snr and estimation accuracy for this estimation is also studied the proposed method for the time delay yields a variance which is theoretically equal to the cramer rao lower bound the validity of this estimation method is demonstrated via simulations

discrete fractional fourier transform based on orthogonal projections the continuous fractional fourier transform frft performs a spectrum rotation of signal in the time frequency plane and it becomes an important tool for time varying signal analysis a discrete fractional fourier transform has been developed by santhanam and mcclellan see ibid vol 42 p 994 98 1996 but its results do not match those of the corresponding continuous fractional fourier transforms we propose a new discrete fractional fourier transform dfrft the new dfrft has dft hermite eigenvectors and retains the eigenvalue eigenfunction relation as a continous frft to obtain dft hermite eigenvectors two orthogonal projection methods are introduced thus the new dfrft will provide similar transform and rotational properties as those of continuous fractional fourier transforms moreover the relationship between frft and the proposed dfrft has been established in the same way as the conventional dft to continuous fourier transform

computing canonical heights using arithmetic intersection theory the canonical height on an abelian variety a defined over a global field k is an object of fundamental importance in the study of the arithmetic of a for many applications it is required to compute p for a given point p a k for instance given generators of a subgroup of the mordell weil group a k of finite index this is necessary for most known approaches to the computation of generators of the mordell weil group a k furthermore the regulator of a k which appears in the statement of the conjecture of birch and swinnerton dyer is defined in terms of the canonical height and thus we need the ability to compute canonical heights in order to gather numerical evidence for the conjecture in the case of positive rank

a new algorithm for explicit adaptation of time delay by using an adaptive technique similar to the one developed by etter and stearns 1981 a novel constrained algorithm for explicit time delay estimation tde is derived the adaptive process provides an unbiased delay estimate and its respective performance surface learning characteristics and delay variance will be given the mean square error surface though a function of the estimated delay only is multimodal and proper initialization is required to guarantee global convergence simulation results are included to validate the convergence behavior of the tde system

asymptotics of determinants from functional integration the expression for the determinant of the laplace operator is used in terms of functional integration to compute the asymptotic behavior on degenerating riemann surfaces in the case of the arakelov metric the information is sufficiently precise to give a value for the absolute constants appearing in bosonization formulas

decoupling and stability of algorithms for boundary value problems the ordinary differential equations occurring in linear boundary value problems characteristically have both stable and unstable solution modes therefore a stable numerical algorithm should avoid both forward and backward integration of solutions on large intervals it is shown that most methods like multiple shooting collocation invariant imbedding and difference methods derive their stability from the fact that they all decouple the continuous or the discrete problem sooner or later for instance when solving a linear system this decoupling is related to the dichotomy of the ordinary differential equations in fact it turns out that the inherent initial value instability is an important prerequisite for a stable utilization of the decoupled representations from which the solutions are computed how this stability is related to the use of the boundary conditions is also investigated

adaptive time delay estimation with constraints the time shift delay parameter between two signals is modeled as a finite impulse response filter whose coefficients are samples of a sinc function the time domain lms least mean squares adaptive algorithm is used but only the weight with the largest magnitude is updated which involves less computation the result is a faster adaptation and the elimination of interpolation needed in previous approaches to obtain nonintegral multiples of sampling period time delay estimates