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In this study, we theoretically scrutinize the effect of the inverse-square interaction on the thermal properties of two electrons trapped in a parabolic GaAs quantum dot. The analytical energy spectrum was used to calculate the thermal properties of the system using the canonical ensemble formalism. It was found that the thermal energy increased with the increase in temperature, while it remained almost constant for sufficiently low temperatures; it was also demonstrated that the inverse-square interaction increased the thermal mean energy. Moreover, the heat capacity increased sharply within a low-temperature window and saturated to the value of 2 [k.sub.B] in the high-temperature limit. As expected, entropy increased linearly with increasing temperature. It was also shown that both entropy and heat capacity decreased rapidly when the confinement strength increased (or the dot size decreased) in the low-temperature limit, regardless of the influence of the interaction between the electrons. We also show that the number of allowed states of the system decreased as the interaction strength increased (Z([lambda] = 0) > Z([lambda] [not equal to] 0)). Finally, the stability of the system was investigated through F-T curves. The three-dimensional surface for the temperature-dependent mean energy and heat capacity was also plotted. It should be noted that, for the thermal mean energy, partition function, and Helmholtz free energy, the normal physical behavior of the two-oscillator system with Fermi statistics is recovered for [lambda] [right arrow] 0. However, heat capacity and entropy show exact two-fermion oscillator system behavior. The most impressive result found in this work is that the inverse-square interaction does not affect the heat capacity and entropy at all despite its noticeable effects on the thermal mean energy. This, in turn, facilitates theoretical studies related to finding the distinctive parameters of quantum dots without going into the heavy calculations resulting from the effects of interactions. Key words: quantum dot, inverse-square interaction, heat capacity, Helmholtz free energy, entropy. Nous completons une etude theorique de l'effet de l'interaction en carre inverse sur les proprietes thermiques de deux electrons captifs dans un point quantique parabolique GaAs. Le spectre analytique en energie est utilise pour calculer les proprietes thermiques de ce systeme en utilisant le formalisme de l'ensemble canonique. Nous trouvons que l'energie thermique augmente avec la temperature, mais demeure pratiquement constante aux temperatures suffisamment basses. Nous demontrons aussi que l'interaction en carre inverse augmente l'energie thermique moyenne. De plus, la capacite calorifique augmente rapidement a l'interieur d'une fenetre a basse temperature et elle sature a la valeur 2[k.sub.B] dans la limite des hautes temperatures. Comme attendu, l'entropie augmente lineairement avec la temperature. Nous montrons egalement que l'entropie et la capacite calorifique diminuent rapidement lorsque la force de confinement augmente (le point quantique se contracte) dans la limite des basses temperatures et ce, sans regard a l'influence de l'interaction entre les electrons. Nous montrons aussi que le nombre des etats permis du systeme diminue lorsque la force d'interaction augmente (Z([lambda] = 0) > Z([lambda] [not equal to] 0)). Finalement, nous etudions la stabilite du systeme a l'aide des courbes F-T. Nous tracons des courbes de la surface tridimensionnelle pour la dependance en temperature de l'energie moyenne et de la capacite calorifique. Il faut souligner que, pour l'energie thermique moyenne, la fonction de partition et l'energie libre de Helmholtz, nous recouvrons le comportement physique normal d'un systeme a deux oscillateurs obeissant a la statistique de Fermi dans la limite ou [lambda] [right arrow] 0. Cependant, pour la capacite calorifique et l'entropie, le comportement est alors celui d'un oscillateur a deux fermions. Le resultat le plus impressionnant ici, c'est que l'interaction en carre inverse n'affecte en aucune facon la capacite calorifique ni l'entropie, malgre un effet tres notable sur l'energie thermique moyenne. En retour, ceci facilite les etudes theoriques reliees a la decouverte de parametres distinctifs de points quantiques, sans aller dans des calculs lourds resultant des effets de l'interaction. [Traduit par la Redaction] Mots-cles: point quantique, interaction en carre inverse, capacite calorifique, energie libre d'Helmholtz, entropie., 1. Introduction In the last decade, researchers have been extensively interested in nanotechnology in all its theoretical and experimental branches because of its ability to create a wide range of [...]

Automatic optimization techniques have been used in recent years for the aerodynamic and mechanical design of turbomachine components. Despite the many advantages, their use is usually limited to simple applications in industrial practice, because of their high computational cost. In this paper, an optimization strategy is presented, which enables the three-dimensional multipoint, multiobjective aerodynamic optimization of turbomachinery blades in a time frame compatible with industrial standards. The design strategy is based on the coupling of three-dimensional inverse design, response surface method, multiobjective evolutionary algorithms, and computational fluid dynamics analyses. The blade parametrization is performed by means of a three-dimensional inverse design method, where aerodynamic parameters, such as the blade loading, are used to describe the blade shape. Such a parametrization allows for a direct control of the aerodynamic flow field and performance, leading to a major advantage in the optimization process. The design method was applied to the redesign of a centrifugal and of an axial compressor stage. The two examples confirmed the validity of the design strategy to perform the three-dimensional optimization of turbomachine components, accounting for both design and off-design performance, in a time-efficient manner. The coupling of response functions and inverse design parametrization also allowed for an easy sensitivity analysis of the impact of the design parameters on the performance ones, contributing to the development of design guidelines that can be exploited for similar design applications. [DOI: 10.1115/1.2950065]

By means of a numerical study we show particle-size distributions retrieved with the Chin-Shifrin, Phillips-Twomey, and singular value decomposition methods. Synthesized intensity data are generated using Mie theory, corresponding to unimodal normal, gamma, and lognormal distributions of spherical particles, covering the size parameter range from 1 to 250. Our results show the advantages and disadvantages of each method, as well as the range of applicability for the Fraunhofer approximation as compared to rigorous Mie theory. OCIS codes: 290.0290, 290.3200, 290.4020, 290.5850.

Electrical impedance tomography (EIT) is a badly posed inverse problem, but can be stabilized if one assumes that the conductivity is piecewise constant, with a relatively small number of distinct regions, and that the region boundaries are known, for example from prior anatomical imaging. With this assumption, we introduce a three-dimensional (3-D) boundary element method (BEM) model for the forward EIT map from injected currents to measured voltages, and 3-D inverse solutions for both BEM and the finite element method (FEM) which explicitly take into account the parameterization implied by the known boundary locations. We develop expressions for the Jacobians for both methods, since they are nonlinear, to more rapidly solve the inverse problem. We show simulation results in a torso geometry with the heart and lungs as inhomogeneities. In a simulation study, we could reconstruct the conductive values of some internal organs of a human torso with more than 92% accuracy even with inaccurate internal boundary locations, a randomized rather than constant conductivity profile (with the standard deviation of the Gaussian-distributed conductivities set to 20% of their mean values), signal to measurement noise of 50 dB, and with different meshes used for the forward and inverse problems. BEM and FEM perform similarly, leading to the conclusion that the choice between them should be based on secondary considerations such as computational efficiency or the need to model conductivity anisotropies. Index Terms--Boundary element methods, electrical impedance tomography, finite element methods, forward model, inverse problem.

The notion of nonlocal Riemann problem was introduced by S. V. Manakov in connection with the application of the inverse scattering method to the KP-1 equation in [146]. In this [...]

Using modern EHL programs it is relatively simple to determine the pressures and clearances in rough EHL contacts. The pressures may then be used to calculate the subsurface stresses in the two contacting components. However, the results depend on the assumptions made about the fluid's rheology. While it is possible to measure the clearances using interferometric techniques, measurement of either the pressures or stresses is extremely difficult. However it is these, rather than the clearances, that determine the life of the contact. In previous papers the authors have described how the inverse method may be used to validate the stress predictions for contacts with transverse roughness. This type of contact has fluid flow in only one plane and it remained necessary to check the results for more general rough surfaces where the flow is three-dimensional. Accordingly, the inverse method is extended, in this paper, to a situation where out-of-plane flow is significant. The paper describes the approach and presents some preliminary results for rolling contacts. [DOI: 10.1115/1.2345396] Keywords: EHL, roughness, stresses, inverse method

Magnetoencephalography (MEG) provides unique insights into the spatio-temporal dynamics of neural activation in the human brain. Unfortunately, the accuracy with which neural sources can be localized is limited by the highly illposed nature of the inverse problem. A large number of inverse methods have been proposed that deal with this illposedness using a range of different modeling and regularization procedures. Here we describe an objective task-based framework for comparing different inverse methods. Using the free-response receiver operating characteristic (FROC) we compare the performance of matched filters, cortically constrained dipole scanning, and minimum norm imaging methods for the task of detecting focal cortical activation. Our results indicate that the scanning methods outperform matched filters and minimum norm imaging for the case of one and two 2 [cm.sup.2] patches of cortical activity when the dynamics of the two patches are both strongly and weakly correlated and irrespective of the spacing of the two activated regions. Index Terms--Comparison of MEG inverse methods, FROC, LCMV beamformer, matched filter, MUSIC, ROC, Tikhonov regularization.

It is well known that the presence of myocardial ischemia can be observed as a shift in the ST segment of an electrocardiogram (ECG) recording. The question we address in this paper is whether or not ST shift can be used to compute approximations of the size and location of the ischemic region. We begin by investigating a cost functional (measuring the difference between synthetic recorded data and simulated values of ST shift) for a parameter identification problem to locate the ischemic region. We then formulate a more flexible representation of the ischemia using a level set framework and solve the associated minimization problem for the size and position of the ischemia. We apply this framework to a set of ECG data generated by the Bidomain model using the cell model of Winslow et al.. Based on this data, we show that values of ST shift recorded at the body surface are capable of identifying the position and (roughly) the size of the ischemia. Index Terms--Inverse problem, level set method, myocardial ischemia, ST-segment shift.

The present paper addresses the problem of spin recovery of an aircraft as a nonlinear inverse dynamics problem of determining the control inputs that need to be applied to transfer the aircraft from a spin state to a level trim flight condition. A stable, oscillatory, flat, left spin state is first identified from a standard bifurcation analysis of the aircraft model considered, and this is chosen as the starting point for all recovery attempts. Three different symmetric, level-flight trim states, representative of high, moderate, and low-angle-of-attack trims for the chosen aircraft model, are computed by using an extended-bifurcation-analysis procedure. A standard form of the nonlinear dynamic inversion algorithm is implemented to recover the aircraft from the oscillatory spin state to each of the selected level trims. The required control inputs in each case, obtained by solving the inverse problem, are compared against each other and with the standard recovery procedure for a modern, low-aspect-ratio, fuselage heavy configuration. The spin recovery procedure is seen to be restricted because of limitations in control surface deflections and rates and because of loss of control effectiveness at high angles of attack. In particular, these restrictions adversely affect attempts at recovery directly from high-angle-of-attack oscillatory spins to low-angleof-attack trims using only aerodynamic controls. Further, two different control strategies are examined in an effort to overcome difficulties in spin recovery because of these restrictions. The first strategy uses an indirect, two-step recovery procedure in which the airplane is first recovered to a high- or moderate-angle-of-attack level-flight trim condition, followed by a second step where the airplane is then transitioned to the desired low-angle-of-attack trim. The second strategy involves the use of thrust-vectoring controls in addition to the standard aerodynamic control surfaces to directly recover the aircraft from high-angle-of-attack oscillatory spin to a low-angle-of-attack level-flight trim state. Our studies reveal that both strategies are successful, highlighting the importance of effective thrust management in conjunction with suitable use of all of the aerodynamic control surfaces for spin recovery strategies.

ABSTRACT--We propose an inverse method, using a circular disk in diametrical compression, for the simultaneous determination of two elastic constants, E and v, from a single displacement map. Moire interferometry [...]

This paper describes a methodology to assess the severity of a tsunami in progress based on real-time water-level data near the source. The inverse method, which uses tsunami signals in water-level data to infer seismic source parameters, is extended to predict the tsunami waveforms away from the source. This study focuses on the Alaska-Aleutian source region and its potential threat to Hawaii. The algorithm divides the source region into 41 subfaults based on previous analyses of major tsunamigenic earthquakes from 1938 to 1986. For unit slip of the subfaults, a linear long-wave model generates a database of synthetic mareograms at 13 water-level stations near the source and at six strategic locations in the Pacific. Regression of recorded tsunami signals using the mareograms provides the slip distribution at the source and the expected waveforms near Hawaii. A jackknife resampling scheme provides the confidence interval bounds of the predictions. The algorithm along with the database is tested and verified using numerically simulated and actual water-level data of past tsunami events. CE Database keywords: Floods; Least square method; Tsunamis; Forecasting; Hawaii.

In this paper, the reconstruction of crack shapes from the magnetic flux leakage testing (MFLT) signals is realized by introducing a rapid forward simulator and applying a deterministic optimization approach. The MFLT signals due to cracks of different shape are calculated with an FEM-BEM code employing A method and polarization algorithm, which is accelerated by the new rapid forward scheme. For reconstructing the crack shape, the conjugate gradient method is applied with the gradients predicted by using the difference technique. Both inner and outer crack are successfully reconstructed from simulated MFLT signals that verified both the efficiency of the fast-forward scheme and the feasibility of the deterministic inverse approach. Index Terms--Deterministic methods, fast-forward scheme, inverse problems, nondestructive testing.

This paper presents an intelligent-based control strategy for tip position tracking control of a single-link flexible manipulator. Motivated by the well-known inverse dynamics control strategy for rigid-link manipulators, two feedforward neural networks (NNs) are proposed to learn the nonlinearities of the flexible arm associated with the inverse dynamics controller. The redefined output approach is used by feeding back this output to guarantee the minimum phase behavior of the resulting closed-loop system. No a priori knowledge about the nonlinearities of the system is needed and the payload mass is also assumed to be unknown. The network weights are adjusted using a modified online error backpropagation algorithm that is based on the propagation of output tracking error, derivative of that error and the tip deflection of the manipulator. The real-time controller is implemented on an experimental test bed. The results achieved by the proposed NN-based controller are compared experimentally with conventional proportional-plus-derivative-type and standard inverse dynamics controls to substantiate and verify the advantages of our proposed scheme and its promising potential in identification and control of nonlinear systems. Index Terms--Flexible-link manipulators, inverse control, neural networks, nonlinear control, online training.

Byline: Jozsef Garay (1), M. Barnabas Garay (2) Keywords: Key words:aGenotype; Phenotype; Hereditary system Abstract: aConsider a panmictic, sexual (diploid or polyploid) population where the genotype of an individual is determined by n alleles at a single autosomal locus. Assume that the number of the different phenotypes is also n and that genotype determines phenotype uniquely. It is shown that this population can realize all possible phenotypic states if and only if the hereditary system is either dominant-recessive or maternal or the combination of these. The proof is based on topological degree arguments. Connections to global inverse function techniques are also discussed. Author Affiliation: (1) Ecological Modelling Research Group of the Hungarian Academy of Science and Department of Taxonomy and Ecology, L. Eotvos University, Ludorika ter 2, H-1083 Budapest, Hungary e-mail: garayj@ludens.elte.hu, HU (2) Department of Mathematics, University of Technology, H-1521 Budapest, Hungary e-mail: garay@math.bme.hu, HU Article note: Received: 29 July 1997/Revised version: 26 November 1997

This paper explores the possibilities of using linear inverse solutions to reconstruct arbitrary current distributions within the human brain. We formally prove that due to the underdetermined character of the problem, the only class of measurable current distributions that can be totally retrieved are those of minimal norm. The reconstruction of smooth or averaged versions of the currents is also explored. A solution that explicitly attempts to reconstruct averages of the current is proposed and compared with the minimum norm and the minimum Laplacian solution. In contrast to the majority of previous analysis carried out in the field, in the comparisons, we avoid the use of measures designed for the case of dipolar sources. To allow for the evaluation of distributed solutions in the case of arbitrary current distributions we use the concept of resolution kernels. Two summarizing measures, source identifiability and source visibility, are proposed and applied to the comparison. From this study can be concluded: 1) linear inverse solutions are unable to produce adequate estimates of arbitrary current distributions at many brain sites and 2) averages or smooth solutions are better than the minimum norm solution estimating the position of single point sources. However, they systematically underestimate their amplitude or strength especially for the deeper brain areas. based on these result, it appears unlikely that a three-dimensional (3-D) tomography of the brain electromagnetic activity can be based on linear reconstruction methods without the use of a significant amount of a priori information. Index Terms - Electromagnetic tomography, linear inverse solutions, neuroelectromagnetic inverse problem, source localization.

Fractiles are tiles bounded by fractal curves. They may be generated using an iterative procedure, whereby at least two functions are repeatedly composed. The functions are formed from translates of the inverse of a linear transformation of the form g(z) = Mz, in which M is an invertible 2x2 matrix having integer entries. The inverse transformation g-1(z) is then responsible for mapping the whole fractal tiling onto a fractile.

Six coincident contaminant distributions or plumes are applied with inverse analytical techniques at Otis Air Force Base near Cape Cod, MA. These plumes contain chloride, boron, biodegradable and non-biodegradable detergents, trichloroethene and tetrachloroethene. Chemical and physical processes are assumed to be operative in them. Unique values for several unknowns which control the behaviour of contaminant plumes are provided by this inverse method. Only limited amounts of variations in the parameters were found in the results.

Modern advances in computing power have greatly widened scientists' scope in gathering and investigating information from many variables, information which might have been ignored in the past. Yet to effectively scan a large pool of variables is not an easy task, although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics. In this article, we propose a novel data-analytic tool, sliced inverse regression (SIR), for reducing the dimension of the input variable x without going through any parametric or nonparametric model-fitting process. This method explores the simplicity of the inverse view of regression; that is, instead of regressing the univariate output variable y against the multivariate x, we regress x against y. Forward regression and inverse regression are connected by a theorem that motivates this method. The theoretical properties of SIR are investigated under a model of the form, y = f([[beta].sub.1]x, ..., /[[beta].sub.k]x, [member of]), where the [[beta].sub.k]'s are the unknown row vectors. This model looks like a nonlinear regression, except for the crucial difference that the functional form of f is completely unknown. For effectively reducing the dimension, we need only to estimate the space [effective dimension reduction (e.d.r.) space] generated by the [[beta].sub.k]'s. This makes our goal different from the usual one in regression analysis, the estimation of all the regression coefficients. In fact, the [[beta].sub.k]'s themselves are not identifiable without a specific structural form on f. Our main theorem shows that under a suitable condition, if the distribution of x has been standardized to have the zero mean and the identity covariance, the inverse regression curve, E(x | y), will fall into the e.d.r. space. Hence a principal component analysis on the covariance matrix for the estimated inverse regression curve can be conducted to locate its main orientation, yielding our estimates for e.d.r. directions. Furthermore, we use a simple step function to estimate the inverse regression curve. No complicated smoothing is needed. SIR can be easily implemented on personal computers. By simulation, we demonstrate how SIR can effectively reduce the dimension of the input variable from, say, 10 to K = 2 for a data set with 400 observations. The spin-plot of y against the two projected variables obtained by SIR is found to mimic the spin-plot of y against the true directions very well. A chi-squared statistic is proposed to address the issue of whether or not a direction found by SIR is spurious. KEY WORDS: Dynamic graphics; Principal component analysis; Projection pursuit., 1 INTRODUCTION Regression analysis is a popular way of studying the relationship between a response variable y and its explanatory variable x, a p-dimensional column vector. Quite often, a parametric [...]

Moore-Penrose generalized inverses of matrices, defined by four conditions, are useful tools in statistical analysis. In this article a three-condition characterization of the inverses is derived. This characterization is then applied to establish a result on the Moore-Penrose generalized inverse of a matrix product. KEY WORDS: Orthogonal projection matrix; Singular value decomposition.

Whole domain function specification method is used to obtain estimates of the time-varying inlet temperature and outer-wall heat flux in laminar pipe flow using temperature measurements taken inside the pipe flow. The results showed that when fewer future-time measurements are used for estimating the heat flux, the estimated solution is found to be unstable and the stability increases with increase in the number of future measurements.

The remarkable inverse provided by the banded invertible matrix 'T' is discussed. This helps to know the exact rank condition and it allows fast multiplication by full matrices that arises in the boundary element method.

The logit Wald and Wilson score intervals for the binomial proportion are both symmetrical on the logit scale. They are closely related: the widths of the two intervals on the [...]

In this paper, artificial neural networks (ANNs) have been employed for the inversion of the geometrical parameters of a magma-filled dike, which causes observable changes in various geophysical fields. The inversion approach, which is based on the function approximation capabilities of multilayer perceptrons (MLPs), is also carried out by a systematic search technique based on the simulated annealing (SA) optimization algorithm in order to emphasize the merits of the proposed strategy. It is shown that even if the SA approach guarantees a high degree of accuracy, it requires a considerable amount of time, incompatible with on-line applications. On the other hand, it is shown that MLPs, once correctly trained, can solve the inversion problem very fast and with an appreciable degree of accuracy. It is also demonstrated that an integrated approach involving geophysical data of different kinds allows for a more accurate solution than when ground deformation data alone is considered. The results given in the paper are supported by experiments carried out using an interactive software tool developed ad hoc, which allows both direct and inverse modeling of data related to the opening of a crack at the beginning and throughout a volcanic activity episode. Index Terms--Artificial neural networks (ANNs), inverse problems, multilayer perceptron, simulated annealing, source location.

This paper presents a technique for solving the inverse problem using multiresolution analysis. For any real problem in modeling, the quality and quantity of available data are very limited. It is impossible to identify a distributed parameter with infinite or very large freedom. So, multiresolution analysis is proposed in order to obtain a good estimation of the permeability profile with a limited number of unknown parameters. The permeability variations are supposed to be localized spatially and spanned with wavelet bases. Some simulation results show the feasibility of this method. Index Terms--Inverse problem, multiresolution, wavelet

A study has been conducted to develop a synthesis method for the design of complex fiber Bragg gratings based on differential inverse scattering algorithms. This method has never been attempted before. In order to achieve this, a layer-peeling algorithm was developed for the case of fiber gratings and its efficiency and accuracy was compared with known linear integral approaches. This novel method produced accurate designs that matched the desire spectral response and has been proven to be suitable for fabrication with existing technologies.