An inverse problem in estimating the strength of contaminant source for groundwater systems

A conjugate gradient method (CGM), (or called an iterative regularization method), based inverse algorithm is applied in this study in determining the unknown space and time-dependent contaminant source for groundwater systems based on the measurements of the concentrations. It is assumed that no prior information is available on the functional form of the unknown contaminant release function in the present study; thus, it is classified as the function estimation in the inverse calculations. The accuracy of this inverse mass transfer problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation on the space and time-dependent contaminant release function can be obtained with any arbitrary initial guesses on a Pentium IV 1.4 GHz personal computer.     

Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables

For multi-way tables with same categories, Bhapkar and Darroch [4] and Agresti [2], p. 440, considered the general order quasi-symmetry model and the ordinal quasi-symmetry model, respectively. Yamamoto, Iwashita and Tomizawa [16] considered the three kinds of linear ordinal quasi-symmetry models, which are special cases of the first and second order quasi-symmetry models. For multi-way tables with same ordinal categories, the present paper proposes the general linear ordinal quasi-symmetry models, which are special cases of the general order quasi-symmetry model, and gives new decomposition of the symmetry model. Moreover it is shown that the likelihood ratio statistic for testing goodness-of-fit of the symmetry model is asymptotically equivalent to the sum of those for testing goodness-of-fit of the decomposed models.     

Trajectory Planning for a Non-Flat Mechanical System Using Time-Reversal Symmetry

Some mechanical systems have a special discrete symmetry property associated with the inversion of the direction of the time flow. This "time-reversal symmetry" allows one to construct solutions of the equations of motion from other known solutions. In the present contribution we examine to which systems this property can be applied. Furthermore, we demonstrate how it can be used to determine an open loop control for equilibrium point transition by solving a stabilization problem in the negative time direction. As a non-flat mechanical example the popular pole-cart system is considered. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

裂缝-孔隙介质中地下水污染问题的Galerkin交替方向有限元方法

考虑裂缝 孔隙介质中地下水污染问题均匀化模型的数值模拟．对压力方程采用混合元方法,对浓度方程采用Ｇａｌｅｒｋｉｎ交替方向有限元方法,对吸附浓度方程采用标准Ｇａｌｅｒｋｉｎ方法,证明了交替方向有限元格式具有最优犔２ 和犎１ 模误差估计．     

Pitman closeness of current records for location-scale families

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. These statistics are referred to as current upper and lower records, respectively, in the statistical literature. We derive expressions for the Pitman closeness of current records to a common population parameter and then apply these results to location-scale families of distributions with a special emphasis on the estimation of quantiles. In the case of symmetric distributions, we show that this criterion possesses some symmetry properties. Exact expressions are derived for the Pitman closeness probabilities in the case of Uniform (?1, 1) and exponential distributions. Moreover, for the population median, we show that the Pitman closeness probability is distribution-free.     

F粗积分与它的度量(英文)

F-rough integrals is defined on the basis of the dual of function one direction S-rough sets,which has dynamic characteristics.Using F-rough integrals,the concepts of expansion measurement-expansion degree and expansion ratio are given.By expansion degree and expansion ratio the changing extent can be expressed with numbers,and the recognition principle of attribute effect on function equivalences is got.     

The fuzzy decision problem: An approach to the point estimation problem with fuzzy information

This paper is devoted to the extension of the Bayesian method for the point estimation, when the available information is ‘vague’.In the nonfuzzy case, the parametric estimation can be approached as a particularization in the statistical decision problem. This motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem (defined by Tanaka, Okuda and Asia).In this way, concepts in the fuzzy decision problem are first ‘expressed’ in the estimation terminology. Then, on the basis of these concepts, we shall introduce some notions and state some interesting results. Finally, several illustrative examples will be exposed.     

Bayesian point estimation and prediction

In the Bayesian viewpoint, point estimation and prediction are treated from a decision-making standpoint. If a loss function can be determined which associates a loss with every possible error of estimation or prediction, then the optimal estimator or predictor is that value which minimizes expected loss. In most applications, the loss function is assumed to be linear or quadratic in the error of estimation or prediction, although there are many practical situations in which these simple functions are quite inappropriate. In this paper, we investigate the properties of Bayesian point estimates under other loss functions; both the general case and two special cases (power and exponential loss functions) are considered. For the special cases, we also investigate the sensitivity of Bayesian point estimation and prediction to misspecification in the loss function and discuss the practical implications of the results.     

Asymptotic distribution of nonparametric estimates of distribution functions under a symmetry condition

We consider geometric concepts connected with infinite-dimensional families of probability measures. We give estimates for a symmetric distribution function both with known and unknown center of symmetry. The estimates considered are asymptotically optimal in the presence of information about the symmetry and in particular, they prove the ordinary empirical distribution function.Translated from Staticheskie Metody, pp. 39–58, 1978.The author thanks Yu. N. Tyurin for interest in the work.     

Flexible time-varying optimization methodology for the solution of groundwater management problems

An outer approximation based, time-varying optimization methodology to obtain a least-cost groundwater remediation design based upon a multi-period, pump-and-treat strategy is introduced. In this novel approach, the remediation design is modified, or updated, from time to time in order to obtain cost-effective removal of contaminants from the subsurface subject to the requirement of respecting upper-bound contaminant concentration constraints at target locations and times. Concentration constraints are defined at the end of each management period, the duration of which is calculated by the optimization algorithm in such a way as to ensure maximum mass removal and to prevent further off-site migration of the contaminant plume. At each stage, the pumping strategy is modified and constraints are relocated in response to the changes in the plume geometry. A penalty term is added to the objective function to assure the performance of the proposed remediation-pumping scheme at a pre-selected time beyond the end of the design period. The utilization of the suggested approach to a field application illustrates the effectiveness of the proposed strategy.     

Applications of Symmetry and Group Theory for the Investigation of Molecular Vibrations

The application of symmetry and mathematical group theory is a powerful tool for investigating the vibrations of molecules. In this paper, we present an overview of the methods utilized. First we briefly discuss the quantum mechanical nature of vibrations and the experimental methods used. We then present the principal concepts for applying group theory to molecules. The symmetry operations which are used to comprise groups are described and then used to determine the point groups of molecules. The properties of character tables are presented and the method for obtaining a reducible representation for all the motions of a molecule is detailed. This can then be broken down to obtain the irreducible representation which contains the symmetry species of the individual vibrations. The determination of symmetry adapted linear combinations is outlined and the basis for spectroscopic selection rules is presented. The paper concludes by examining how matrix algebra along with symmetry concepts simplifies calculations with molecular force constants.     

Large scale nonlinear deterministic and stochastic optimization: Formulations involving simulation of subsurface contamination

Once subsurface water supplies become contaminated, designing cost-effective and reliable remediation schemes becomes a difficult task. The combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water. Both deterministic and stochastic programming problems have been formulated and solved. These tend to be large scale problems, owing to the simulation component which serves as a portion of the constraint set. The overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems. Because the contaminant transport simulation models give highly uncertain results, quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems. The reliability problem is beginning to be addressed, and some strategies and formulations involving chance constraints and Monte Carlo methods are presented.     

Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones

In this paper we deal with several issues concerning variable-stepsize linear multistep methods. First, we prove their stability when their fixed-stepsize counterparts are stable and under mild conditions on the stepsizes and the variable coefficients. Then we prove asymptotic expansions on the considered tolerance for the global error committed. Using them, we study the growth of error with time when integrating periodic orbits. We consider strongly and weakly stable linear multistep methods for the integration of first-order differential systems as well as those designed to integrate special second-order ones. We place special emphasis on the latter which are also symmetric because of their suitability when integrating moderately eccentric orbits of reversible systems. For these types of methods, we give a characterization for symmetry of the coefficients, which allows their construction, and provide some numerical results for them.

     

Algebraic relationships between classical regression and total least-squares estimation

The total least-squares (TLS) technique, which is well known in numerical linear algebra and able to compute strongly consistent estimators of the parameters in a linear errors-in-variables model, is compared algebraically with the classical regression estimators. Using the singular-value decomposition and geometric concepts, algebraic equivalences and important relationships between the classical regression techniques and TLS estimation are established with special reference to problems of collinearity. The equivalence between principal-component and latent-root regression in collinearity problems is proven, and the difference between latent-root regression and TLS estimation is clarified.     

Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry

A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007.     

UMVU estimation of the ratio of powers of normal generalized variances under correlation

We consider estimation of the ratio of arbitrary powers of two normal generalized variances based on two correlated random samples. First, the result of Iliopoulos [Decision theoretic estimation of the ratio of variances in a bivariate normal distribution, Ann. Inst. Statist. Math. 53 (2001) 436-446] on UMVU estimation of the ratio of variances in a bivariate normal distribution is extended to the case of the ratio of any powers of the two variances. Motivated by these estimators’ forms we derive the UMVU estimator in the multivariate case. We show that it is proportional to the ratio of the corresponding powers of the two sample generalized variances multiplied by a function of the sample canonical correlations. The mean squared errors of the derived UMVU estimator and the maximum likelihood estimator are compared via simulation for some special cases.     

Symmetries in timed continuous Petri nets

The dynamics of timed continuous Petri nets under infinite server semantics can be expressed in terms of a piecewise linear system with polyhedral regions. In this article, Petri nets with symmetries are considered where symmetry is understood as a permutation symmetry of the nodes. We establish connections between the qualitative dynamical behavior of the continuous marking and the symmetries. In particular, it is shown that such a symmetry leads to a permutation of the regions and to equivariant dynamics. This allows us to identify special flow-invariant sets which can be used for reductions to systems of smaller dimension. For general piecewise linear systems with polyhedral regions, it is shown that equivariant dynamics always implies a permutation of the regions.     

Advection-Diffusion in Reversing and Oscillating Flows: 1. The Effect of a Single Reversal

Motivated by the need to understand effluent dispersion in shallowtidal waters, a two-dimensional analysis of advection and diffusionin a reversing flow has been carried out. The flow speed varieslinearly with time, passing through zero at time t=0. A pointsource discharges contaminant into this flow at a steady rate,so that water which is close to the source around the time offlow reversal will become highly contaminated. Thus a peak inthe contaminant concentration field will appear, moving downstreamafter the reversal at a speed close to that of the flow. Thisconcentration peak has certain characteristics similar to acloud of contaminant from an instantaneous discharge at t=0.The solution of the advection-diffusion equation is in the formof an integral of concentration fields due to instantaneousreleases of contaminant at all previous times. At large timesafter the flow reversal, asymptotic analysis yields good approximationsto this integral. The use of Laplace's method is equivalentto ignoring longitudinal diffusion (the boundary-layer approximation);however, the expansion obtained in this way is not uniformlyvalid near the concentration peak, indicating that longitudinaldiffusion plays an important role in the development of thispeak. Uniformly valid expansions are obtained for the concentrationaround the peak, and also around the source where the boundary-layerapproximation always breaks down. Numerical integration hasalso been carried out, the results being used to produce contourplots of concentration for various times either side of theflow reversal.     

On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

迭代的计算与估计

对高次多项式函数这类非线性映射给出了一般 n次迭代的一个计算结果 ,还讨论了一维欧氏空间中一些非多项式型映射的迭代 .在二维欧氏空间中 ,我们给出了几类特殊的非线性迭代的结果 .对于一些难以精确计算迭代表达式的映射 ,我们给出了其迭代的估计 .