Decision-Making for Long Memory Data in Technical-Economic Design, Fractals and Decision Area Bubbles

Economic and management theories are very often based in their applications on the perception of homogeneity of the application space. The purpose of this article is to query such a conviction and indicate new possible directions of discipline development. The article deals with symbiosis of process and his steering model as a process of management. It is possible that in relative near future it will be necessary to accept approaches and changes in interpretations of decision-making. Applications of fractals can be one of the interesting stimulations.     

A quantum chemical study of the influence of an electrostatic field on the reactivity of methanol over zeolites

The INDO method with an electrostatic potential term in its Hamiltonian has been used to estimate the changes in the electronic structure of methanol and methanol dimer due to the electrostatic field of zeolites. It has been shown that fields of the strength F=2–8×10¹⁰V/m change significantly the electronic structure as well as the geometry of both molecules and can cause their decomposition leading to the species H₂O, CH₃, CH₃O, CH₂O, and CH₂.

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INDO . , F=2÷8·10¹⁰ / , , H₂O, CH₃, CH₃O, CH₂O CH₂.

     

Sequential Injection Analysis for Automation and Evaluation of Drug Liberation Profiles: Clotrimazole Liberation Monitoring

A fully automated sequential injection system was tested in terms of its application in liberation testing, and capabilities and limitations were discussed for clotrimazole liberation from three semisolid formulations. An evaluation based on kinetic profiles obtained in short and longer sampling intervals and steady-state flux values were applied as traditional methods. The obtained clotrimazole liberation profile was faster in the case of Delcore and slower for Clotrimazol AL and Canesten cream commercial formulations. The steady-state flux values for the tested formulations were 52 µg cm⁻² h⁻¹ for Canesten, 35 µg cm⁻² h⁻¹ for Clotrimazol AL, and 7.2 µg cm⁻² h⁻¹ for Delcore measured in 4 min sampling intervals. A simplified approach for the evaluation of the initial rate based on the gradient between the second and third sampling points was used for the first time and was found to correspond well with the results of the conventional methods. A comparison based on the ratio of the steady-state flux and the initial rate values for Canesten and Clotrimazol AL proved the similarity of the obtained results. The proposed alternative was successfully implemented for the comparison of short-term kinetic profiles. Consequently, a faster and simpler approach for dissolution/liberation testing can be used.     

A Reduced Order Cyclic Method for Computation of Limit Cycles

A reduced order cyclic method was developed to compute limit-cycle oscillations for large, nonlinear, multidisciplinary systems of equations. Method efficacy was demonstrated for two simplified models: a typical-section airfoil with nonlinear structural coupling and a nonlinear panel in high-speed flow. The cyclic method was verified to maintain second-order temporal accuracy, yield converged limit cycles in about 10 Newton iterates, and provide precise estimates of cycle frequency. This method was projected onto a low-order space using a set of variables governing the amplitudes of empirically derived modes, which were computed with the proper orthogonal decomposition. In this reduced order form, the cyclic Jacobian was greatly compressed, allowing accurate limit cycle solutions to be very efficiently computed.The U.S. Governments right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.     

On estimation of mean and covariance functions in repeated time series with long-memory errors*

We consider kernel estimation of trend and covariance functions in models typically encountered in functional data analysis (FDA), with the modification that the random curves are perturbed by error processes that exhibit short- or long-range dependence. Uniform convergence of standardized maximal differences between estimated and true (trend and covariance) functions is established. For the covariance function, a transformation based on contrasts is proposed that does not require explicit trend estimation. Improved estimators can be obtained by using higher-order kernels.     

Energetic stability and electronic properties of exohedral derivatives of C20: C20Xn (X = H,F, Cl; n = 1–4)

Exohedral derivatives of the smallest fullerene, C₂₀, with the general formula of C₂₀X_n (X = H, F, Cl; n = 1–4) have been systematically investigated to evaluate the energetic stability of these molecular structures and determine their respective electronic properties. Analysis of the theoretical results indicate that the addition of exohedral atoms increase the stability of the caged‐structure to varying degrees according to the predicted HOMO‐LUMO gaps, ionization energies, and electron affinities. Further support for increasing stability is deduced from the calculated reaction and binding energies of the exohedral atoms. © 2012 Wiley Periodicals, Inc.     

Improving Penalized Least Squares through Adaptive Selection of Penalty and Shrinkage

Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk.     

ASP fits to multi-way layouts

The balanced complete multi-way layout with ordinal or nominal factors is a fundamental data-type that arises in medical imaging, agricultural field trials, DNA microassays, and other settings where analysis of variance (ANOVA) is an established tool. ASP algorithms weigh competing biased fits in order to reduce risk through variance-bias tradeoff. The acronym ASP stands for Adaptive Shrinkage of Penalty bases. Motivating ASP is a penalized least squares criterion that associates a separate quadratic penalty term with each main effect and each interaction in the general ANOVA decomposition of means. The penalty terms express plausible conjecture about the mean function, respecting the difference between ordinal and nominal factors. Multiparametric asymptotics under a probability model and experiments on data elucidate how ASP dominates least squares, sometimes very substantially. ASP estimators for nominal factors recover Stein's superior shrinkage estimators for one- and two-way layouts. ASP estimators for ordinal factors bring out the merits of smoothed fits to multi-way layouts, a topic broached algorithmically in work by Tukey. This research was supported in part by National Science Foundation Grants DMS 0300806 and 0404547.     

Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors

Local polynomial smoothing for the trend function and its derivatives in nonparametric regression with long-memory, short-memory and antipersistent errors is considered. We show that in the case of antipersistence, the convergence rate of a nonparametric regression estimator is faster than for uncorrelated or short-range dependent errors. Moreover, it is shown that unified asymptotic formulas for the optimal bandwidth and the MSE hold for all of the three dependence structures. Also, results on estimation at the boundary are included. A bandwidth selector for nonparametric regression with different types of dependent errors is proposed. Its asymptotic property is investigated. The practical performance of the proposal is illustrated by simulated and real data examples.     

Transverse spectra of waves in random media

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.