Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain

In this paper, an inverse source problem for the Helium Production–Diffusion Equation on a columnar symmetric domain is investigated. Based on an a priori assumption, the optimal error bound analysis and a conditional stability result are given. This problem is ill-posed and Landweber iteration regularization method is used to deal with this problem. Convergence estimates are presented under the priori and the posteriori regularization choice rules. For the a priori and the a posteriori regularization parameters choice rules, the convergence error estimates are all order optimal. Numerical examples are given to show that the regularization method is effective and stable for dealing with this ill-posed problem.     

The Conjugacy Search Problem in Public Key Cryptography: Unnecessary and Insufficient

The conjugacy search problem in a group G is the problem of recovering an from given and h = x ⁻¹ gx. This problem is in the core of several recently suggested public key exchange protocols, most notably the one due to Anshel, Anshel, and Goldfeld, and the one due to Ko, Lee et al. In this note, we make two observations that seem to have eluded most people’s attention. The first observation is that solving the conjugacy search problem is not necessary for an adversary to get the common secret key in the Ko–Lee protocol. It is sufficient to solve an apparently easier problem of finding such that h = ygx for given . Another observation is that solving the conjugacy search problem is not sufficient for an adversary to get the common secret key in the Anshel–Anshel–Goldfeld protocol.     

Simulation of random vectors with given moments

We extend in this article the simulation method of scalar random variables with given moments, which was developed initially by Devroye, to n-dimensional random vectors. Using the conditional distribution approach, we show that the vector simulation problem can be reduced to simulate scalar random variables with given moments, which are solutions of given linear systems.     

The Extinction Problem for Three-dimensional Inward Solidification

The one-phase Stefan problem for the inward solidification of a three-dimensional body of liquid that is initially at its fusion temperature is considered. In particular, the shape and speed of the solid-melt interface is described at times just before complete freezing takes place, as is the temperature field in the vicinity of the extinction point. This is accomplished for general Stefan numbers by employing the Baiocchi transform. Other previous results for this problem are confirmed, for example the asymptotic analysis reveals the interface ultimately approaches an ellipsoid in shape, and furthermore, the accuracy of these results is improved. The results are arbitrary up to constants of integration that depend physically on both the Stefan number and the shape of the fixed boundary of the liquid region. In general it is not possible to determine this dependence analytically; however, the limiting case of large Stefan number provides an exception. For this limit a rather complete asymptotic picture is presented, and a recipe for the time it takes for complete freezing to occur is derived. The results presented here for fully three-dimensional domains complement and extend those given by McCue et al.[Proc. R. Soc. London A 459 (2003) 977], which are for two dimensions only, and for which a significantly different time dependence occurs.     

On a final value problem for the time-fractional diffusion equation with inhomogeneous source

In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method. We also proposed both parameter choice rule methods, the a-priori and the a-posteriori methods, to estimate the convergence rate of the regularized methods. In addition, the proposed regularized methods have been verified by numerical experiments, and a comparison of the convergence rate between the a-priori and the a-posteriori choice rule methods is also given.     

Logical inference for inverse problems

Estimating a deterministic single value for model parameters when reconstructing the system response has a limited meaning if one considers that the model used to predict its behaviour is just an idealization of reality, and furthermore, the existence of measurements errors. To provide a reliable answer, probabilistic instead of deterministic values should be provided, which carry information about the degree of uncertainty or plausibility of those model parameters providing one or more observations of the system response. This is widely-known as the Bayesian inverse problem, which has been covered in the literature from different perspectives, depending on the interpretation or the meaning assigned to the probability. In this paper, we revise two main approaches: the one that uses probability as logic, and an alternative one that interprets it as information content. The contribution of this paper is to provide an unifying formulation from which both approaches stem as interpretations, and which is more general in the sense of requiring fewer axioms, at the time the formulation and computation is simplified by dropping some constants. An extension to the problem of model class selection is derived, which is particularly simple under the proposed framework. A numerical example is finally given to illustrate the utility and effectiveness of the method.     

Adjoint‐weighted variational formulation for the direct solution of inverse problems of general linear elasticity with full interior data

We describe a novel variational formulation of inverse elasticity problems given interior data. The class of problems considered is rather general and includes, as special cases, plane deformations, compressibility and incompressiblity in isotropic materials, 3D deformations, and anisotropy. The strong form of this problem is governed by equations of pure advective transport. The variational formulation is based on a generalization of the adjoint‐weighted variational equation (AWE) formulation, originally developed for flow of a passive scalar. We describe how to apply AWE to various cases, and prove several properties. We prove that the Galerkin discretization of the AWE formulation leads to a stable, convergent numerical method, and prove optimal rates of convergence. The numerical examples demonstrate optimal convergence of the method with mesh refinement for multiple unknown material parameters, graceful performance in the presence of noise, and robust behavior of the method when the target solution is C^∞, C⁰, or discontinuous. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow-shop problems with intermediate buffers

In this paper the following extension of the classical flow-shop problem is considered: Between each two consecutive machines a buffer of limited capacity is given. After finishing processing on a machine, a job either directly has to be processed on the following machine or it has to be stored in the buffer between these machines. If the buffer is completely occupied the job may wait on its current machine but blocks this machine for other jobs. The objective is to determine a feasible schedule minimizing the makespan. To model such a problem setting, a variation of the classical disjunctive graph model for shop problems is extended. A tabu search procedure is described where neighborhoods based on an extension of the classical block approach theorem are used. Computational results for extended flow-shop benchmark instances are presented. Corespondence to: Silvia HeitmannThe authors are grateful to Tim Nieberg for implementing the tabu search procedure proposed in this paper.S. Heitmann     

广义欧几里德Steiner问题的研究与进展

广义欧几里德Steiner问题足指确定连接平面上一组给定点的满足特定连通性要求的最短网络的问题。本文主要介绍了比问题的研究与进展,在建立了求给定平面点集的最矩U-连通(或边连通)生成网络的整数规划模型的基础上,证明了文献[13]中所给的一个例子是错误的,并提出了一些关于广义Steiner问题的进一步研究的问题。     

Improved Identification Schemes Based on Error-Correcting Codes

As it is often the case in public-key cryptography, the first practical identification schemes were based on hard problems from number theory (factoring, discrete logarithms). The security of the proposed scheme depends on an NP-complete problem from the theory of error correcting codes:the syndrome decoding problem which relies on the hardness of decoding a binary word of given weight and given syndrome. Starting from Stern’s scheme [18], we define a dual version which, unlike the other schemes based on the SD problem, uses a generator matrix of a random linear binary code. This allows, among other things, an improvement of the transmission rate with regards to the other schemes. Finally, by using techniques of computation in a finite field, we show how it is possible to considerably reduce: — the complexity of the computations done by the prover (which is usually a portable device with a limited computing power), — the size of the data stored by the latter. Received March 10, 1995; revised version December 1, 1995     

Central limit theorem for the estimator of the value of an optimal stopping problem

We consider an optimal stopping problem defined on a finite Markov chain whose transition probabilities are unknown. We prove a central limit theorem for the maximum likelihood estimator and the stretch estimator of the optimal value of the optimal stopping problem. Also, we propose a perturbation technique to weaken the hypotheses of the central limit theorem. The author was supported by a grant from the SpanishScretaría de Estado de Educación y Universidades in cooperation with the European Social Funds.     

Pre‐college Electrical Engineering Instruction: The Impact of Abstract vs. Contextualized Representation and Practice on Learning

Background While engineering instructional materials and practice problems for pre‐college students are often presented in the context of real‐life situations, college‐level texts are typically written in abstract form. Purpose (Hypothesis ) The goal of this study was to jointly examine the impact of contextualizing engineering instruction and varying the number of practice opportunities on pre‐college students' learning and learning perceptions. Design/ Method Using a 3 × 2 factorial design, students were randomly assigned to learn about electrical circuit analysis with an instructional program that represented problems in abstract, contextualized, or both forms, either with two practice problems or four practice problems. The abstract problems were devoid of any real‐life context and represented with standard abstract electrical circuit diagrams. The contextualized problems were anchored around real‐life scenarios and represented with life‐like images. The combined contextualized‐abstract condition added abstract circuit diagrams to the contextualized representation. To measure learning, students were given a problem‐solving near‐transfer post‐test. Learning perceptions were measured using a program‐rating survey where students had to rate the instructional program's diagrams, helpfulness, and difficulty. Results Students in the combined contextualized‐abstract condition scored higher on the post‐test, produced better problem representations, and rated the program's diagrams and helpfulness higher than their counterparts. Students who were given two practice problems gave higher program diagram and helpfulness ratings than those given four practice problems. Conclusions These findings suggest that pre‐college engineering instruction should consider anchoring learning in real‐life contexts and providing students with abstract problem representations that can be transferred to a variety of problems.     

Cluster-level operations planning for the out-of-position robotic arc-welding

Recent advances in computer vision and arc-welding technology have motivated a rethinking of several postulates and conventions incorporated in the existing robot off-line programming methods. This paper addresses relaxing of the downhand-position assumption, which became a de facto standard in robotic welding and requires the weldline to be horizontal and the weld normal vector to be opposite to gravity. In contrast to the standard techniques, the developed method explicitly assumes that a weld may be processed in the out-of-position location, which differs from the downhand location within given tolerances. However, to ensure the prescribed quality, the downhand deviation is charged by a reduction in the welding speed. For such settings, a novel method is proposed for the cluster-level welding operations planning for a robotic cell with a positioning table. The objective is to minimize the overall manufacturing time by finding a reasonable trade-off between the positioner motion times and the cluster processing times. It is shown that the associated optimization problem may be presented as a specific case of the generalized travelling salesman problem, for which an efficient heuristic algorithm has been developed that produces both the optimal welding cluster sequence and corresponding optimal motions of the positioner. The algorithm effectiveness was verified for a number of randomly generated test problems, for which the results are reported and analysed in detail. An industrial case study is also presented, confirming the validity of the developed technique.     

An inverse solution for reconstruction of the heat transfer coefficient from the knowledge of two temperature values in a solid substrate

Reconstruction of the heat transfer coefficient from the knowledge of temperature distribution is an inverse problem. The main focus of this study was to develop an inverse model that could be used to determine the heat transfer coefficient associated with a fluid in contact with a solid surface from the knowledge of two measured temperature values (T₁ and T_M) in the solid substrate. The temperature distribution for the inverse problem was numerically generated, for a situation with a known heat transfer coefficient, using an implicit finite-differencing scheme. The solution domain was first discretized in to finite number of small regions and nodes. Conservation of energy was then applied to each of the control volume about the nodal regions. This approach resulted in a set of linear equations that was solved simultaneously. Two nodal temperatures in the substrate, from the direct solution, were then used in the inverse problem to reconstruct the heat transfer coefficient. To solve the inverse problem, the solution domain was divided into two distinct regions (Region I and Region II). Region I contained the solution domain between the two known temperatures (T₁ and T_M), and Region II included the region between T_M and the surface with the convective boundary condition. Again, a finite-differencing scheme was employed to generate a set of linear equations in each region. First, the set of linear equations in Region I was solved simultaneously and the results were then used to reconstruct the nodal temperatures in Region II. The convective surface temperature was then utilized to determine the heat transfer coefficient. A series of numerical experiments were conducted to test the validity of the inverse model. Comparison of the inverse solutions with the direct solutions confirms that the heat transfer coefficient can be reconstructed, with good accuracy, from the knowledge of two temperature points in the solid substrate.     

Numerical solution for multiple crack problem in an infinite plate under compression

This paper investigates a numerical solution for multiple crack problem in an infinite plate under remote compression. The influence of friction is taken into account. In the first step of the solution, we make a full contact assumption on the crack faces. The full contact assumption means that one component of the dislocation distribution vanishes, and the first mode stress intensity factors (K ₁) at the crack tips become zero. On the above-mentioned assumption, the problem can be solved by using integral equation method, and the second mode stress intensity factors (K ₂) at the crack tips can be evaluated. Meantime, after solving the integral equation the normal contact stress on the crack faces can be evaluated. The next step is to examine the full contact assumption. If the contact stresses on the crack faces are definitely negative, the solution is true. Otherwise, the obtained solution is not true. It is found from present study that in most cases the full contact condition is satisfied, and only in a few cases the full contact condition is violated. Numerical examples are given. It is found that the friction can lower the stress intensity factors at crack tips in general.     

Heuristic algorithms for visiting the customers in a rolling schedule environment

In this study, we consider a scheduling problem of a company providing certain kind of services for its customers. In each period, customers call the company to request for the services. In a call j, the customer specifies a date d _j and a time tolerance δ _j . A profit can be realized if the service can be made within the period window d _j ±δ _j . The problem is to construct a schedule for each period so that the average profit of serving a subset of the customer calls is maximized in the long run. We consider the problem in a rolling schedule environment and propose several heuristics based on iterative customer assignment and iterative center-of-gravity scheme for solving it. Extensive computational experiments for problems with various sizes are generated and solved by these heuristics. For the small problem instances, the solutions obtained are compared against the upper bound obtained by solving the LP relaxation of the problem by a column generation scheme. The computational results show that the proposed heuristics all perform very well. For large problem instances, the solutions obtained are compared among the heuristics. The factors affecting the performance of the various heuristics are analyzed and discussed.     

An inverse radiation problem of simultaneous estimation of heat transfer coefficient and absorption coefficient in participating media

An inverse radiation problem is investigated where the spatially varying heat transfer coefficient h(z) and the absorption coefficient κ in the radiant cooler are estimated simultaneously from temperature measurements. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using the conjugate gradient method. The gradient of the performance function is evaluated by means of the improved adjoint variable method that can take care of both the function estimation and the parameter estimation efficiently. The present method is found to estimate h(z) and κ with reasonable accuracy even with noisy temperature measurements. Copyright © 2002 John Wiley & Sons, Ltd.     

XFEM‐based crack detection scheme using a genetic algorithm

A new computational tool is developed for the accurate detection and identification of cracks in structures, to be used in conjunction with non‐destructive testing of specimens. It is based on the solution of an inverse problem. Based on some measurements, typically along part of the boundary of the structure, that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies, the goal is to estimate whether the structure contains a crack, and if so, to find the parameters (location, size, orientation and shape) of the crack that produces a response closest to the given measurement data in some chosen norm. The inverse problem is solved using a genetic algorithm (GA). The GA optimization process requires the solution of a very large amount of forward problems. The latter are solved via the extended finite element method (XFEM). This enables one to employ the same regular mesh for all the forward problems. Performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane. Various computational aspects of the method are discussed, including the a priori estimation of the ill‐posedness of the crack identification problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Prefix-Rewriting on Context-Free Groups

 A class of groups that has received much attention is the class of context-free groups. This class of groups can be characterized algebraically as well as through some language-theoretical properties as well as through certain combinatorial properties of presentations. Here we use the fact that a finitely generated group is context-free if and only if it admits a finite complete presentation of a certain form that we call a virtually free presentation. It is known that the generalized word problem for context-free groups is decidable. Here we show how prefix-rewriting systems can be used to solve this problem. In fact, we show that the Knuth-Bendix completion procedure always terminates when applied to prefix-rewriting systems on virtually free presentations of context-free groups. In addition, we present a specialized completion algorithm for prefix-rewriting systems on virtually free presentations which has polynomial-time complexity. Thus, the uniform generalized word problem for virtually free presentations of context-free groups is decidable in polynomial-time. Since finitely generated subgroups of context-free groups are again context-free, they admit presentations of the same form. We present a polynomial-time algorithm that, given a virtually free presentation of a context-free group G and a finite subset U of G as input, computes a virtually free presentation for the subgroup of G that is generated by U. Received: January 13, 1995; revised version: June 24, 1996