optimal shadowing and noise reduction abstract the shadowing problem is that of finding a deterministic orbit as close as possible to a given noisy orbit we present an optimal solution to this problem in the sense of least mean squares which also provides an effective and convenient numerical method for noise reduction for data generated by a dynamical system given a noisy orbit y and a dynamical system we derive a set of nonlinear equations whose solution x is the deterministic orbit with the smallest possible euclidean distance to y we present a numerical method for solving these equations the quality of the solution depends on the initial noise level when is known exactly the noise can be reduced to machine precision over long trajectory segments with higher noise levels there are regions where the algorithm has difficulty but significant overall noise reductions are still achieved if must be learned from the data the noise reduction is limited by the accuracy of the learning algorithm and the number of available data points but large reductions are still possible in some cases

a generalized circular summation of theta function and its application in this paper we prove a generalized ramanujan s circular summation of theta function using the theory of elliptic and theta functions this identity also includes a result of m boon m l glasser j zar i j zucker and an addition formula of theta functions besides we can get some new trigonometric identities

a note on worst case analysis of approximation algorithms for a scheduling problem abstract worst case analyses of two approximation algorithms for the m machine permutation flow shop problem are presented worst case performane ratios m 2 o 1 m for the former and m 1 for the latter algorithm are found

flow shops with a dominant machine abstract flow shop problems with a dominant machine are introduced we show that for this kind of problems we can restrict our search for an optimal schedule to permutation schedules if the optimality criterion is regular furthermore we give an expression for the completion times with respect to a semi active permutation schedule and we give fast algorithms for the weighted completion times and the maximal lateness criterion

a noise reduction method for signals from nonlinear systems abstract a numerical algorithm is presented for the purpose of reducing noise from a discretely sampled input signal where the underlying signal of interest has a broadband spectrum it is designed to be useful even if the clean signal is contaminated with 100 or more noise signal to noise ratio less than or equal to zero the method is based on time delay embedding using coordinates generated by local low pass filtering which we call a low pass embedding the singular value decomposition is then used locally in embedding space to distinguish between the dynamics and the noise the algorithm is evaluated for chaotic signals generated by the lorenz and rossler systems to which gaussian white noise has been added

some results of the worst case analysis for flow shop scheduling abstract known approximation algorithms recommended for the permutation flow shop problem with the weighted sum of completion times have a worst case performance ratio which is unknown or known but unlimited we propose new algorithms with this ratio equal to m k k where k is the worst case performance ratio of an algorithm which solves an auxiliary k machine problem worst case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented

heuristics for scheduling in flowshop with multiple objectives abstract most of the heuristics for flowshop scheduling aim at minimizing makespan however scheduling with multiple objectives such as that of minimizing makespan total flowtime and machine idletime is more effective in reducing the total scheduling cost in this article we first address the problem of scheduling to minimize makespan and total flowtime and propose a new heuristic algorithm a heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to these two objectives the proposed as well as the existing heuristics are evaluated in a large number of randomly generated large sized problems the proposed heuristic algorithm is then extended to cover the problem of scheduling to minimize makespan total flowtime and machine idletime the results of the experimental investigation of the evaluation of this heuristic algorithm and the existing heuristic in meeting these objectives are also reported it is found that both the proposed heuristics are more effective than the existing one for scheduling with multiple objectives

a note on heuristics of flow shop scheduling we present an omn two group tg heuristic for the m machine n job permutation flow shop scheduling problem we show that heuristic tg has a worst case performance ratio of m 1 2 we also establish worst case bounds for several heuristics proposed in the past

a fast tabu search algorithm for the permutation flow shop problem abstract a fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented the algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion computational experiments up to 500 jobs and 20 machines show its excellent numerical properties

makespan minimization in machine dominated flowshop abstract in a flowshop scheduling problem a set of jobs is processed by a set of machines the jobs follow the same sequence in all machines we study the flowshop scheduling problem under a new case of machine dominance that is often found in the manufacturing of computers and electronic devices we provide a formula for makespan value for a given sequence show that the makespan value depends only on certain jobs in the sequence and present an algorithm that finds a sequence with minimum makespan numerical examples of the solution approaches are provided

flow shop scheduling problems with deteriorating jobs on no idle dominant machines abstract in this paper we study the permutation flow shop scheduling problems with deteriorating jobs on no idle dominant machines the objective is to minimize one of the two regular performance criteria namely makespan and total completion time for each objective the following dominant machines constraint idm ddm idm ddm and ddm idm are considered we present a polynomial time solution algorithm for each of the four cases

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

signals in chaos a method for the cancellation of deterministic noise from discrete signals abstract in this paper we describe a method for separating a combination of a chaotic time series and a discrete valued signal the method uses a feedback technique stabilised using knowledge of the chaotic system and the discrete nature of the signal it is not based on a linearization of the dynamics and therefore unlike previously proposed separation methods does not require that the signal be small nor does it make any assumptions about the relative timescales of the signal and the chaotic time series

ramanujan s circular summation t cores and twisted partition identities abstract in this paper we give new evaluations for ramanujan s circular summation function we also provide simpler proofs for known evaluations and give some generalizations we discover modular relations among circular summation function partition function and give uniform proof of ramanujan s partition congruences for the moduli 5 7 and 11 we also prove several interesting congruence relations

an efficient heuristic approach to the scheduling of jobs in a flowshop abstract three heuristic algorithms for flowshop scheduling with the objective of minimizing total flowtime are presented in this paper since the flowshop scheduling problem has been found to be an np complete problem the development of heuristic algorithms that guarantee fairly accurate solutions becomes necessary the proposed algorithms are found to give consistently near optimal solutions and fare better than the existing methods

minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem abstract this paper considers the following scheduling problem minimize the makespan in a single facility problem where the processing time of a job consists of a fixed and a variable part the variable part depends on the start time of the job the objective is to minimize makespan two optimizing algorithms based on dynamic programming and branch and bound techniques and five heuristic rules have been proposed the heuristic solutions have been compared with the optimal solution for upto 7 jobs to identify the best heuristic the detailed computational results for the branch and bound and the best heuristic rule are then obtained for problems with up to 15 jobs

noise reduction finding the simplest dynamical system consistent with the data abstract a novel method is described for noise reduction in chaotic experimental data whose dynamics are low dimensional in addition we show how the approach allows experimentalists to use many of the same techniques that have been essential for the analysis of nonlinear systems of ordinary differential equations and difference equations

cancelling deterministic noise by constructing nonlinear inverses to linear filters abstract in this paper we propose a method of noise cancellation where the noise is deterministic that is it is generated by some possibly chaotic dynamical system the method exploits the fact that a time series measured from a nonlinear dynamical system can be used to reconstruct the phase space of the system and that this is still true if the time series is first passed through a linear fir filter since both filtered and unfiltered versions reconstruct the same system there is an invertible nonlinear mapping from the filtered time series to the unfiltered one which undoes the effect of the filter to perform signal separation we use a filter which stops the signal we wish to recover so that the output is a filtered version of the noise alone using the nonlinear mapping the unfiltered noise time series can be recovered and subtracted from the original noisy signal two examples of the recovery of simple signals from chaotic time series are given and one in which one chaotic signal is separated from another

restricted neighborhood in the tabu search for the flowshop problem this paper deals with the minimizing weighted tardiness of jobs in a scheduling problem where the structure is that of the proportionate flowshop a modified version of the widmer hertz algorithm for the makespan problem is presented improving the computational performance by reducing the size of the neighborhoods the heuristic tests were applied to 720 flowshop problems from 10 to 50 jobs

permutation flow shop scheduling with dominant machines to minimize discounted total weighted completion time this paper deals with some special cases of general no wait and no idle permutation flow shop scheduling problems respectively special cases means that the machines form an increasing series of dominant machines a decreasing series of dominant machines an increasing decreasing series of dominant machines and a decreasing increasing series of dominant machines efficient polynomial time algorithms for finding the optimal schedules to minimize discounted total weighted completion time are developed

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

circular summation of theta functions in ramanujan s lost notebook in this paper we prove ramanujan s circular summation formulas previously studied by s s rangachari s h son k ono s ahlgren and k s chua using properties of elliptic and theta functions we also derive identities similar to ramanujan s summation formula and connect these identities to jacobi s and dixon s elliptic functions at the end of the paper we discuss the connection of our results with the recent thesis of e conrad

identification and prediction of low dimensional dynamics this contribution focuses upon extracting information from dynamic reconstructions of experimental time series data in addition to the problem of distinguishing between deterministic dynamics and stochastic dynamics applied questions such as the detection of parametric drift are addressed nonlinear prediction and dimension algorithms are applied to geophysical laboratory data and the significance of these results is established by comparison with results from similar surrogate series generated so as not to contain the property of interest a global nonlinear predictor is introduced which attempts to correct systematic bias due to the inhomogeneous distribution of data common in strange attractors variations in the quality of predictions with location in phase space are examined in order to estimate the uncertainty in a forecast at the time it is made finally the application of these methods to truly stochastic systems is discussed and the distinction between deterministic stochastic and low dimensional dynamics is considered

a note on flow shop scheduling problems with a learning effect on no idle dominant machines abstract this paper considers some permutation flow shop scheduling problems with a learning effect on no idle dominant machines the objective is to minimize maximum completion time this objective is considered under following dominant machines constraint idm ddm idm ddm and ddm idm we present a polynomial time solution algorithm for each of the above cases

a theta function identity and its implications in this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions this identity plays a central role for the cubic theta function identities we use this identity to re derive some important identities of hirschhorn garvan and borwein about cubic theta functions we also prove some other cubic theta function identities a new representation for n 1 1 q n 10 is given the proofs are self contained and elementary

sequencing games with controllable processing times in this paper we study a class of cooperative sequencing games that arise from sequencing situations in which the processing times are not fixed we obtain two core elements that depend only on the optimal schedule for the grand coalition furthermore we show that although these games are not convex in general many marginal vectors are core elements we also consider convexity for special instances of the sequencing situation