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In the Russian school, the total normalized gradient method belongs to the most wide‐spread of direct interpretation methods for potential field data. This method was also used and partly developed by many experts from abroad. The main advantage of the total normalized gradient method is its relative independence of parameters such as the expected differential density of interpreted structures. The method is built from a construction of a specially transformed field (total normalized gradient) on a section crossing the potential field sources. The special properties of this transformed field allow it to be used to detect the source positions. From the 1960s, the mathematical basis of the method underwent enormous development and several modifications of the method have been elaborated. The total normalized gradient operator itself represents a relatively complicated, non‐linear band‐pass filter in the spectral domain. The properties of this operator can be handled by means of several parameters that act to separate the information about field sources at different depth levels. In this contribution, we describe the development of the method from its very beginning (based mostly on qualitative interpretation of simple total normalized gradient sections) through to more recent numerical improvements to the method. These improvements include the quasi‐singular points method, which refines the filter properties of the total normalized gradient operator and defines an objective criteria (so called criterion 'α' and 'Г') for the definition of source depths in the section. We end by describing possibilities for further development of the method in the future. [ABSTRACT FROM AUTHOR]

Though it is said that the paperless age arrived with the spread of personal computers, the amount of office paper used shows no tendency to decrease. In general, used paper is recovered and recycled in order to preserve the environment. But labor and expense are required for the recovery of used paper and the recycled paper is lower in quality. If we could reuse used paper repeatedly without these disadvantages, for example, by using copying machines that could print again by removing the toner on used paper, it would be very convenient and ecological. We therefore studied the removal of toner from used paper by the laser ablation technique. As an optical source, an SHG-YAG laser was chosen. The energy density of irradiation with an SHG-YAG laser for the removal of toner from used paper was examined. At an energy density of approximately 12 mJ/mm2, which was the average value, the toner was removed sufficiently to allow reuse of the paper. The conditions of the laser irradiation, specifically the laser scanning speed and the number of irradiations, were studied. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 179(1): 8-14, 2012; Published online in Wiley Online Library (). DOI 10.1002/eej.21214 [ABSTRACT FROM AUTHOR]

We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of [ABSTRACT FROM AUTHOR]

Presents comments on the study "Comparison of Continuous and Cyclic Pumping From a Well," by M.W. Kawecki. Use of exact well function values in the study; Error in the results of the study; Ratio of pumping rates obtained by using the logarithmic approximation.

In the design of antenna arrays which require fast and robust flat‐top beam synthesis, computationally efficient methods are preferred. This feature is usually met by analytical techniques or simple optimisation procedures. On the other hand, in the flat‐top beam synthesis, a common requirement is the ability to control beamwidth or sidelobe level. However, this can result in a high dynamic range ratio (DRR) of array's excitation coefficients. In this paper, a straightforward method for the design of symmetrical flat‐top arrays with controllable sidelobe level or DRR is proposed. The method is based on quadratic and cubic transforms of Gaussian excitations. In addition, the method utilises zero coefficients whose positions are used to control the DRR, including the ability to achieve its minimum. Compared to other flat‐top arrays with analytically shaped beams, the proposed arrays have lower DRRs for the same sidelobe level. [ABSTRACT FROM AUTHOR]

In approximation theory, classical discrete operators, like generalized sampling, Szász‐Mirak'jan, Baskakov, and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of curves by a class of discrete operators, and we exhibit graphical examples concerning several cases. The topic has useful implications about the computer graphics and the image processing: We discuss applications on the approximation and the reconstruction of curves in images. [ABSTRACT FROM AUTHOR]

In order to study the fast calculation method of a surface electric field of the arbitrary-quantity bundled conductor and a ground nominal electric field of the HVDC transmission line on slope terrain. Based on the basic principles of the image method, this paper deduces the calculation formula of the surface maximum electric field of the arbitrary-quantity bundled conductor and the ground nominal electric field of the HVDC transmission line with single bipolar horizontal arrangement over the slope terrain by making the reasonable approximation and equivalence to the actual situation. Compared with the finite element method, the results got from the formula proposed in this paper verify that these formulas are accurate and valid. The effects of slope inclination, pole–pole spacing of the conductor on the electric field of the conductor surface and the ground nominal electric field of the HVDC transmission line are analyzed and obtained. The results of research indicate that the inclination of the slope and the pole–pole spacing of the conductor have a great influence on the conductor surface electric field and the ground nominal electric field. When the HVDC transmission line is erected on the slope terrain, the formula proposed in this paper can provide references for circuit design and electromagnetic environment analysis. [ABSTRACT FROM AUTHOR]

This paper considers the verification of integrity monitors used commonly in safety‐of‐life navigation systems. The paper compares three conservative bounds (also known as overbounds) that can be used to compute missed‐detection performance for nominally chi‐square integrity monitors subject to random noise with non‐Gaussian heavy tails. The three overbounds rely on simple geometric shapes – cones, cylinders, and spheres – to ensure that missed‐detection probability can be computed conservatively, reliably, and efficiently. The overbounds provide conservative estimates of missed‐detection performance even when the exact form of the noise distribution is not known, so long as the noise CDF is spherically symmetric. Monte Carlo simulations suggest that, for moderate and large faults, the spherical overbound performs best, but for small faults, the cylindrical overbound performs best, at least in the case of a two‐dimensional vector space. © 2018 Institute of Navigation [ABSTRACT FROM AUTHOR]

Summary: The marginalized particle filtering (MPF) is a powerful technique reducing the number of particles necessary to effectively estimate hidden states of state‐space models. This paper alleviates the assumption of a fully known and computationally tractable observation model. Exploiting the recent developments in the theory of approximate Bayesian computation (ABC) filtration, an ABC counterpart of MPF is proposed, applicable when the observation model is too complex to be evaluated analytically or even numerically, but it is still possible to sample from it by plugging in the state. The novelty is 2‐fold. First, ABC methods have not been used in marginalized filtering yet. Second, a new multivariate robust method for evaluation of particle weights is proposed. The goal of this paper is to demonstrate the idea on the background of the MPF with a particular accent on exposition. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the command filter‐based adaptive neural network tracking control problem for uncertain nonsmooth nonlinear systems. First, an integral barrier Lyapunov function is introduced to deal with the symmetric output constraint and make the output comply with prescribed restrictions. Second, by the Filippov's differential inclusion theory and approximation theorem, the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system. Third, the Levant's differentiator is used to deal with the "explosion of complexity" problem. An error compensation mechanism is established to attenuate the effect of the filtering error on control performance. Then, an adaptive neural network controller is set up by resorting to the backstepping technique. It is strictly mathematically proved that the tracking error can converge to an arbitrarily small neighborhood of the origin and all the signals in the closed‐loop system are semi‐globally uniformly ultimately bounded. Finally, a numerical example and an application example of the robotic manipulator system are provided to demonstrate the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: We consider the B‐spline isogeometric analysis approximation of the Laplacian eigenvalue problem −Δu = λu over the d‐dimensional hypercube (0,1)d. By using tensor‐product arguments, we show that the eigenvalue–eigenvector structure of the resulting discretization matrix is completely determined by the eigenvalue–eigenvector structure of the matrix L n [ p ] arising from the isogeometric analysis approximation based on B‐splines of degree p of the unidimensional problem − u ′ ′ = λ u. Here, n is the mesh fineness parameter, and the size of L n [ p ] is N(n,p) = n + p − 2. In previous works, it was established that the normalized sequence { n − 2 L n [ p ] } n enjoys an asymptotic spectral distribution described by a function ep(θ), the so‐called spectral symbol. The contributions of this paper can be summarized as follows: We prove several important analytic properties of the spectral symbol ep(θ). In particular, we show that ep(θ) is monotone increasing on [0,π] for all p ≥ 1 and that ep(θ)→θ2 uniformly on [0,π] as p→∞. For p = 1 and p = 2, we show that L n [ p ] belongs to a matrix algebra associated with a fast unitary sine transform, and we compute eigenvalues and eigenvectors of L n [ p ]. In both cases, the eigenvalues are given by ep(θj,n), j = 1,…,n + p − 2, where θj,n = jπ/n. For p ≥ 3, we provide numerical evidence of a precise asymptotic expansion for the eigenvalues of n − 2 L n [ p ], excluding the largest n p out = p − 2 + mod (  p , 2 ) eigenvalues (the so‐called outliers). More precisely, we numerically show that for every p ≥ 3, every integer α ≥ 0, every n, and every j = 1 , … , N ( n , p ) − n p out, λ j n − 2 L n [ p ] = e p ( θ j , n ) + ∑ k = 1 α c k [ p ] ( θ j , n ) h k + E j , n , α [ p ] , where the eigenvalues of n − 2 L n [ p ] are arranged in ascending order, λ 1 ( n − 2 L n [ p ] ) ≤ … ≤ λ n + p − 2 ( n − 2 L n [ p ] ); { c k [ p ] } k = 1 , 2 , … is a sequence of functions from [0,π] to R, which depends only on p; h = 1/n and θj,n = jπh for j = 1,…,n; and E j , n , α [ p ] = O ( h α + 1 ) is the remainder, which satisfies | E j , n , α [ p ] | ≤ C α [ p ] h α + 1 for some constant C α [ p ] depending only on α and p. We also provide a proof of this expansion for α = 0 and j = 1,…,N(n,p) −(4p − 2), where 4p − 2 represents a theoretical estimate of the number of outliers n p out. We show through numerical experiments that, for p ≥ 3 and k ≥ 1, there exists a point θ( p,k) ∈ (0,π) such that c k [ p ] ( θ ) vanishes on [0,θ( p,k)]. Moreover, as it is suggested by the numerics of this paper, the infimum of θ(p,k) over all k ≥ 1, say yp, is strictly positive, and the equation λ j ( n − 2 L n [ p ] ) = e p ( θ j , n ) holds numerically whenever θj,n < θ( p), where θ( p) is a point in (0,yp] which grows with p. For p ≥ 3, based on the asymptotic expansion in the above item 3, we propose a parallel interpolation–extrapolation algorithm for computing the eigenvalues of L n [ p ], excluding the n p out outliers. The performance of the algorithm is illustrated through numerical experiments. Note that, by the previous item 4, the algorithm is actually not necessary for computing the eigenvalues corresponding to points θj,n < θ( p). [ABSTRACT FROM AUTHOR]

The Arbitrage Pricing Theory (APT) has been proposed as an alternative to the mean-variance Capital Asset Pricing Model (CAPM). This paper considers the testability of the APT and points out the irrelevance for testing of the approximation error. We refute Shanken's objections, including his assertion that Roll's critique of the CAPM is applicable to the APT. We also explain the testability of the APT on subsets, and we explore the relationship between the APT and the CAPM. [ABSTRACT FROM AUTHOR]

Earlier, the authors attempted an explicit evaluation of the total variation of best piecewise polynomial approximations and obtained a result [9]. However, there, the discussion was on polynomials and cannot be applied to other families of functions. Thus, the present paper considers a similar discussion with respect to the trigonometric functions, that is, the Fourier series expansion. Specifically, the total variation of Fourier series approximations is investigated, and, in addition, the norms of Fourier coefficients are evaluated. For the norms of Fourier coefficients, we confirm that they converge to zero when the degree m → ∞ and its rate is O(m-1) (Riemann-Lebesgue lemma). Conventionally, the norm of Fourier coefficients had been evaluated mostly by assuming the periodicity of functions to be approximated. However, in this paper, we evaluate the norm without using the periodicity condition of the approximated functions. Moreover, it is shown that the upper bound of the ratio between the total variations of K-th partial sum of Fourier series and that of the function to be approximated, is proportional to K. This implies that compared to the evaluation of total variation of the best piecewise polynomial approximations obtained in the authors' previous paper, this evaluation excels it by far. [ABSTRACT FROM AUTHOR]

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m≳Θ2s×logfactors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s‐sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. In this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s‐sparse Legendre expansions, m≳s2×logfactors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average. [ABSTRACT FROM AUTHOR]

We studied the impact of magnetic field and chemical reaction on the peristaltic motion of nanofluid in the horizontal asymmetric channel with heat and mass transfer in this paper. The unsteady governing equations of the present problem were formulated. After the unsteady equations are transformed to steady and then the implementation of lubrication theory approximation, the lengthy equations are shortened. The coupled nonlinear differential equations (temperature and concentration equations) are analytically solved using the perturbation method. The exact analytical solution of the stream function was also calculated. The results of the velocity profile, pressure rise, temperature, and concentration are plotted through the MATLAB software and the streamlines are drawn through the MATHEMATICA software. The impact of key fluid parameters is discussed using graphical results. One observes that, for large values of the thermophoresis parameter, the temperature of the fluid increases, and more energy is produced. [ABSTRACT FROM AUTHOR]

A large high‐quality crystal is required to specify the positions of H atoms in neutron structural analysis. Consequently, several methods have been proposed for obtaining such large crystals, and theoretical considerations for growing them have been presented. However, further investigation is required to obtain a numerical model that can provide quantitative experimental conditions for obtaining a single large crystal. In the case of protein crystallization experiments, the amount of sample is often limited. Therefore, it is more realistic to make a rough estimation from a small number of experiments. This paper proposes a method of estimating the optimum experimental conditions for the growth of large protein crystals by performing a small number of experiments using a micro‐batch method and reporting a numerical model based on nucleation theory and a linear approximation of the crystal‐growth rate. Specifically, micro‐batch experiments are performed to provide the empirical parameters for the model and to help to estimate the conditions for the growth of a crystal of a predetermined size using a certain sample concentration and volume. This method is offered as a step on the path towards efficiently and rationally producing large crystals that can be subjected to neutron diffraction without depending on luck or on performing many experiments. It is expected to contribute to drug design and the elucidation of protein molecular functions and mechanisms by obtaining positional information on H atoms in the protein molecule, which is an advantage of neutron diffraction. [ABSTRACT FROM AUTHOR]

Abstract: The paper is focused on the application of a surrogate model to reliability analysis. Despite recent advances in this field, the reliability analysis of complex non‐linear finite element models is still highly time‐consuming. Thus, the approximation of the non‐linear finite element model by a surrogate meta‐model is often the only choice if one wishes to perform a sufficient amount of simulations to enable reliability analysis. First, the basic theory of polynomial chaos expansion (PCE) is described, including the transformation of correlated random variables. The usage of the PCE for the estimation of statistical moments and sensitivity analysis is then presented. It can be done efficiently via the post‐processing of the employed surrogate model in explicit form without any additional computational demands. The possibility of utilizing the adaptive algorithm Least Angle Regression is also discussed. The implementation of the discussed theory into a software tool, and its application, are presented in the last part of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual‐phase‐lag and 3‐phase‐lag theories, reflecting Saint‐Venant's principle. In a recent paper, 2 families of cases for high‐order partial differential equations were studied. Here, we investigate a third family of cases, which corresponds to the fact that a certain condition on the time derivative must be satisfied. We also study the spatial behavior of a thermoelastic problem. We obtain a Phragmén‐Lindelöf alternative for the solutions in both cases. The main tool to handle these problems is the use of an exponentially weighted Poincaré inequality. [ABSTRACT FROM AUTHOR]

Summary: The goal of this paper is to find a low‐rank approximation for a given nth tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP‐hard problem. In this paper, we formulate a sparse optimization problem via an l1‐regularization to find a low‐rank approximation of tensors. To solve this sparse optimization problem, we propose a rescaling algorithm of the proximal alternating minimization and study the theoretical convergence of this algorithm. Furthermore, we discuss the probabilistic consistency of the sparsity result and suggest a way to choose the regularization parameter for practical computation. In the simulation experiments, the performance of our algorithm supports that our method provides an efficient estimate on the number of rank‐one tensor components in a given tensor. Moreover, this algorithm is also applied to surveillance videos for low‐rank approximation. [ABSTRACT FROM AUTHOR]

Summary: In this paper, generalized model based on the multiplicative least square method presented and showed that it is convenient to approximate observation in the electrical system analysis. The introduced model is exponential based and relies on parametric values. The advantage of the method is due to exponential derivation process within multiplicative calculus and has the flexibility to represent widely used functions such as Gaussian and exponentials. In spite of numerous results on the best fitting model, we study the robustness of the method by making direct comparisons with Matlab built‐in functions. The presented model is challenging because modern electrical circuits and systems are faced with different types of inputs that require near exact representation for accurate processing. Some real applications of exponential‐based data were selected to demonstrate the applicability and efficiency of the proposed representation. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a unified and exact nonaveraged approach to derive a frequency‐domain control‐oriented model for accurate prediction of the fast timescale dynamics and performances of switching converters with fixed frequency naturally sampled pulse width modulation and integrating feedback loop. Because the approach avoids averaging and approximations related to this process, a very good accuracy of the derived model is obtained. The main difference between the presented approach and the existing methodology for accurately predicting the behavior of switching converters is that, here, we break the feedback loop and we focus on analyzing the open‐loop gain and the effect of the system parameters on relative stability. This results in an approach much similar to control systems techniques rather than nonlinear dynamical system approaches. Consequently, the relative stability is tackled easily in the frequency domain. In particular, by treating the modulator as a gain depending on the operating point, the new model is formulated in such a way that standard control‐oriented tools such as Bode diagrams and root‐loci can be easily used. Therefore, the proposed approach gives some important issues like gain and phase margins that are highly useful in controller design. It is noticed that the crossover frequency, gain, and phase margins predicted by using the averaged model may deviate significantly from the actual values given by the proposed approach. The paper points out the sources of discrepancies and the theoretical results are validated by simulations using a circuit‐level switched model. [ABSTRACT FROM AUTHOR]

Orthogonal least squares (OLS) algorithm, as a popular greedy algorithm for sparse signal recovery, has attracted much attention in recent years. In this paper, the completely perturbed model is considered, y∼=Ax+b,A∼=A+E, $\tilde{\mathbf{y}}=\mathbf{A}\mathbf{x}+\mathbf{b},\tilde{\mathbf{A}}=\mathbf{A}+\mathbf{E},$ where x is K‐sparse. Assume that the matrix A∼ $\tilde{\mathbf{A}}$ has unit ℓ2‐norm columns and satisfies the restricted isometry property of order K + 1. Given stopping criterion ‖r∼k‖≤ε0 ${\Vert}{\tilde{\mathbf{r}}}^{k}{\Vert}\le {\varepsilon }_{0}$, then the authors prove that the OLS algorithm precisely recovers the support of the K‐sparse signal x in at most K iterations under the suitable constraint condition on x. In addition, the authors also show that the authors' conclusion is superior to the current results. [ABSTRACT FROM AUTHOR]

Load forecasting (LF), particularly short‐term load forecasting (STLF), plays a vital role throughout the operation of the conventional power system. The precise modelling and complex analyses of STLF have become more significant in advanced microgrid (MG) applications. Several models are proposed for STLF and tested successfully in the literature. The selection of a forecasting method is mostly based on data availability and its objectives. This article presents a survey of the latest analytical and approximation techniques reported in the literature to model STLF in an MG environment. This article mainly focusses on the review on important methods applied to forecast renewable energy availability, energy demand, and price and load demand. Different models, their main objectives, methodology, error percentage, and so forth, are critically reviewed and analysed. For quick reference, we have highlighted the important points in the form tables. The researchers can quickly identify and frame their research problem related to the LF area by reading this review paper. [ABSTRACT FROM AUTHOR]

This paper presents a completely new method for the calculation of expectations (and thus joint probability distributions) of structure factors or phase invariants. As an example, a first approximation of the expectation of the triplet invariant (up to a constant) is given and a complex number is obtained. Instead of considering the atomic vector positions or reciprocal vectors as the fundamental random variables, the method samples over all functions (distributions) with a given number of atoms and given Patterson function. The aim of this paper was to explore the feasibility of the method, so the easiest problem was chosen: the calculation of the expectation value of the triplet invariant in P1. Calculation of the joint probability distribution of the triplet is not performed here but will be done in the future. [ABSTRACT FROM AUTHOR]

Power system automation is an effective tool from both economical and technical aspects to improve the optimal operation of power generators. In this regard, Security Constrained Unit Commitment (SCUC) incorporating Dynamic Thermal Line Rating (DTLR) of overhead transmission lines can boost the system security effectively. Using Transmission Switching (TS) tool in SCUC problems leads to cost reduction. Still, one of the main challenges arisen in TS problems is the excessive number of switching in lines, which decreases the lifespan of power switches. In this paper, an Improved Linear AC Optimal Power Flow (ILACOPF) is proposed by using TS and considering Heat Balance Equation (HBE) as a security constraint. Merging dynamic thermal line rating (considering the weather conditions) in SCUC with TS, besides decreasing the number of switching and increasing the lifespan of power switches, causes a remarkable reduction in operating costs. In this power flow, system losses are modeled by linear formulations. Moreover, a linear approximation of the heat losses due to power flow through lines is proposed. To solve the proposed model, Benders' decomposition approach is applied. The performance of the proposed framework has been evaluated on 6‐bus and 118‐bus IEEE test systems. [ABSTRACT FROM AUTHOR]

In this paper some properties of the generalized Szasz operators by multiple Appell polynomials are given, using into consideration the power summability method. In the first section are given some direct estimation related to the generalized Szasz operators by multiple Appell polynomials, including Korovkin type theorem. In the second section, we give some results related to the weighted spaces of continuous functions and Voronovskaya type theorem. In the third section, we have proved some results related to the statistical convergence of the generalized Szasz operators by multiple Appell polynomials, using into consideration the A− transformation. At the end of the paper are given some illustrative computational examples which make such summability methods (for example, power series method) more useful and fruitful for applications of functional analysis in approximation theory. [ABSTRACT FROM AUTHOR]

Inertial and droop control are common methods for improving grid frequency control. Using the first‐order derivative of the frequency in the inertial control loop only investigates the rate of frequency variation, while other useful information is not taken into consideration. Accordingly, in this study, the application of a fractional‐order derivative (between 1 and 2) in the inertial control loop is proposed to have more useful frequency‐based information. To achieve this goal, firstly continued fraction approximations and secondly, the discretization is adopted by using the Tustin Method with Prewarping. Inertia loop and droop loop gain have a significant impact on the operation of the wind turbines and the power system frequency control. Therefore, in this paper, a novel method for the adaptive adjusting of droop and inertia control loops gains in DFIG is proposed. To utilize more frequency error information, fractional‐order adaptive law is proposed to update the loop gains and the inertia control loop. In order to have a robust system, which is permanently stable for every fractional order (FO), is used parameter space method. Simulation results demonstrate the proper performance of the FO‐based adaptive approach to increase the frequency nadir (FN) and decrease the frequency variations. [ABSTRACT FROM AUTHOR]

Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra A, which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper, we do the same but now A is an algebra of operators on a Hilbert space. We briefly survey this noncommutative peak interpolation, which we have studied with coauthors in a long series of papers, and whose basic theory now appears to be approaching its culmination. This programme developed from, and is based partly on, theorems of Hay and Read whose proofs were spectacular, but therefore inaccessible to an uncommitted reader. We give short proofs of these results, using recent progress in noncommutative peak interpolation, and conversely give examples of the use of these theorems in peak interpolation. For example, we prove a useful new noncommutative peak interpolation theorem. [ABSTRACT FROM AUTHOR]

This paper deals with Lasota-Wazewska red blood cell model with perturbation on time scales. By applying the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by means of Gronwall inequality. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we mainly focus on similarity joins on massive high-dimensional vectors, it is a costly operation because of curse of dimensionality. The main idea of our proposed solution is to design a novel filtering method that can filter out as many vector pairs as possible at relative low cost. By using the good dimension reduction ability of piecewise aggregate approximation and symbolic aggregate approximation techniques, we proposed three novel approaches to deal with high dimensional-vector similarity join query: single-PAA-based vector similarity join query, multi-PAA-based vector similarity join query and SAX-based vector similarity join query. We conducted comprehensive experiments to test the performance of the above approaches, we also test the speedup ratio compared with the naive method: block nested loop join. The experimental results show that our approaches have much better performance than that of block nested loop join and also have good scalability. To the best of our knowledge, this is the first work to try to deal with high-dimensional vector similarity joins using piecewise aggregate approximation and symbolic aggregate approximation techniques, and the approaches proposed in this paper provide a new way to process the massive high-dimensional vector data set. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of stabilizing a time-varying nonlinear sampled-data system based on its approximate models. Given a time-varying nonlinear sampled-data system, we make use of the approximate models of the system at each sampling instant to build a time-varying approximate model with which an appropriate controller is designed. This paper provides some sufficient conditions under which a controller stabilizing the approximate models can also stabilize the exact sampled-data system under any sufficiently small sampling period. With this method, we do not need to compute the complicated exact discrete-time model of the concerned system and significantly simplify the controller design. The major contribution of this method lies in extending the available results regarding the time-invariant sampled-data systems to the time-varying case. Moreover, this method enables us to analyze the influence of the precision of approximate models on the system performance. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of output waves obtained by impressing simultaneously an n-dimensional input wave f(X) to the finite number of time-Invariant linear net- works. A problem is considered, where the original wave f(X) is to be approximated using the sampled values of the forementioned output waves. A unified theory is presented with respect to the convergence of the approximate wave to the original wave f(X). The discussion given in this paper may be considered as a basis for the future theory of subband coding and multiplexing of the multidimensional signals, in the sense that we use the sampled values of the multidimensional waves transferred through the linear networks. The approximate wave h(X) for f(X) is a sum of the forementioned sample values of these output waves, being multiplied by certain n-dimensional waves called interpolation functions. The set of sampling points considered in this paper includes most of the practically import- ant arrangements of sapling points, such as hexagonal and octagonal lattices on the two- dimensional plane. The set of f(X) in this paper is defined as the set of n-dimensional waves such that the corresponding Fourier spectrum has the weighted powereofap norm (p > 1) which is less than a given positive value. Under several assumptions, sufficient, necessary, and necessary and sufficient conditions are derived for the wave h(X) always to converge to f(X). These convergence conditions are presented which are imposed on the transfer functions of the time-invariant linear networks through which f(X) propagates as well as the arrangement of the sampling points and the interpolation functions. They are closely related to the rank of the system of linear equations determined by those parameters. [ABSTRACT FROM AUTHOR]

The signal space composed of spline functions, which are smooth piecewise polynomials and almost free from oscillation, has attracted attention in the problems of interpolation and signal approximation. To make full use of such a signal space, there must be available a clear description of its properties. As a general approach to this problem, it is effective to derive the sampling basis in the signal space. Previously, the authors discussed the signal space composed of spline functions, and derived the sampling basis for the case where the degree is restricted to two. This paper extends the result to the arbitrary degree. Examples of sampling bases are shown for the practical cases of the second and the third degrees. The sampling basis derived in this paper provides the basic characterization of the signal space composed of spline functions of arbitrary degree. [ABSTRACT FROM AUTHOR]

Restoring the controllability of networked control systems is a fundamental issue that needs to be settled, especially when malicious attacks or malfunctions occur. Previous studies tried to address such an issue by adding extra driver nodes or rewiring edges, which will inevitably change the original network structure. In this paper, an algorithm to restore the controllability of networked systems while preserving the integrity of the original network structure is proposed. Specifically, a static uncontrollable network will be transformed into a controllable temporal network by means of the cactus‐based segmentation method. The original problem will be equivalent to the classical set cover problem, which is known to be NP‐Hard, if the least number of segmentations is considered. An approximation algorithm with polynomial time complexity is proposed and it is proved that the solution to the problem is two‐optimal. Finally, simulations are carried out to verify the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper considers Bayesian identification of macroscopic bone material characteristics given digital image correlation (DIC) data. As the evaluation of the full Bayesian posterior distribution is known to be computationally intense, here we consider the approximate estimation in a Newton‐like manner by using the theory of conditional expectation. The approach is extended to include the epistemic uncertainties in the process of modelling the prior. [ABSTRACT FROM AUTHOR]

In the linear source of a thermal evaporation system, the thickness of the deposited molecules depends on the angular distribution of the emitted molecular flux from the nozzle. According to Knudsen in 1907, for a cylindrical nozzle, the angular distribution of the emitted molecular flux can be expressed in the form of cosn(θ). The actual angular distribution, however, does not precisely match the form of cosn(θ) by Knudsen. Therefore, various theoretical methods have been studied in an effort to express the angular distribution of the emitted molecular flux mathematically. Using these conventional methods can allow one to determine the accurate angular distribution of the emitted molecular flux, but the same calculation should be repeated whenever the shape of the nozzle changes, as the angular distribution acquired by these methods is not an "analytical solution" but a "numerical solution." In this paper, an analytical model of the accurate angular distribution determined via an approximation method is proposed to make the nozzle array optimization processes of linear sources faster and more accurate for a cylindrical nozzle. The model is verified through a comparison involving the direct simulation Monte Carlo method and an experiment with a point evaporation source. The molecules emitted from the nozzle outlet can be divided into two main types. The first type consists of reflected molecules emitted after a collision. The second type includes the molecules directly emitted without collisions with the inner wall of the nozzle. [ABSTRACT FROM AUTHOR]

In this paper, numerical solution of the generalized Burgers‐Fisher (BF) equation is presented on the basis of the nonstandard finite‐difference (NSFD) scheme. At first, two exact finite‐difference schemes for the BF equation are obtained. Afterwards, an NSFD scheme is presented for this equation. The positivity, consistency, and boundedness of the scheme are discussed. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods to verify the accuracy and efficiency of the NSFD scheme. [ABSTRACT FROM AUTHOR]

Summary: To improve the stability and efficiency of explicit technique, one proposed method is to use an unconditionally stable alternating direction explicit (ADE) scheme. However, the standard ADE scheme is only moderately accurate and restricted to uniform grids. This paper derives a novel high‐order ADE scheme capable of solving the fluid diffusion equation in non‐uniform grids. The new scheme is derived by performing a fourth‐order finite difference approximation to the spatial derivatives of the diffusion equation in non‐uniform grid. The implicit Crank‐Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new high‐order ADE scheme. Because the new scheme can be potentially applied in coupled hydro‐mechanical (H‐M) simulation, the pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer program Fast Lagrangian Analysis of Continua. This coupling procedure is called the sequentially explicit coupling technique based on the fourth‐order ADE scheme (SEA‐4). Verifications of well‐known consolidation problems showed that the new ADE scheme and SEA‐4 can reduce computer runtime by 46% to 75% to that of Fast Lagrangian Analysis of Continua's basic scheme. At the same time, the techniques still maintained average percentage error of 1.6% to 3.5% for pore pressure and 0.2% to 1.5% for displacement solutions and were still accurate under typical grid non‐uniformities. This result suggests that the new high‐order ADE scheme can provide an efficient explicit technique for solving the flow equation of a coupled H‐M problem, which will be beneficial for large‐scale and long‐term H‐M problems in geoengineering. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we analyze the convergence of a projected fixed‐point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method, we use the projector splitting scheme. We prove that the convergence rate of the projector splitting scheme is bounded by the convergence rate of standard fixed‐point iteration without rank constraints multiplied by the function of initial approximation. We also provide counterexample to the case when conditions of the theorem do not hold. Finally, we support our theoretical results with numerical experiments. [ABSTRACT FROM AUTHOR]

Levy and Markowitz showed, for various utility functions and empirical returns distributions, that the expected utility maximizer could typically do very well if he acted knowing only the mean and variance of each distribution. Levy and Markowitz considered only situations in which the expected utility maximizer chose among a finite number of alternate probability distributions. The present paper examines the same questions for a case with an infinite number of alternate distributions, namely those available from the standard portfolio constraint set. [ABSTRACT FROM AUTHOR]

This paper traces the historical developments of the efforts to find simple and accurate methods of approximating an annuity's implicit yield and a bond's yield to maturity. It is shown that the little known history of yield approximations is nevertheless very rich, with contributions dating as far back as the late seventeenth century. It is also shown that the standard textbook approximation formula for the bond's yield to maturity is the least accurate of a large family of formulas, some of which were suggested as early as 1855. [ABSTRACT FROM AUTHOR]

The initial simulation study of the neoclassical perpendicular self-diffusion transport in the SOL/Divertor regions for a realistic tokamak geometry with the IMPGYRO code has been performed in this paper. One of the most unique features of the IMPGYRO code is calculating exact Larmor orbit of the test particle instead of assuming guiding center approximation. Therefore, effects of the magnetic drifts in realistic tokamaks are naturally taken into account in the IMPGYRO code. This feature makes it possible to calculate neoclassical transport processes, which possibly become large in the SOL/divertor plasma. Indeed, neoclassical self-diffusion process, the resultant effect of the combination of magnetic drift and Coulomb collisions with background ions, has already been included in the IMPGYRO model. In the present paper, prior to implementing the detailed model of neoclassical transport process into IMPGYRO, we have investigated the effect of neoclassical selfdiffusion in a realistic tokamak geometry with lower single null X-point. We also use a model with guiding center approximation in order to compare with the IMPGYRO full orbit model. The preliminary calculation results of each model have shown differences in the perpendicular average velocity of impurity ions at the top region of the SOL. The mechanism which leads to the difference has been discussed. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time-fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time-stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor-corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper provides a unified treatment to the problems of constrained minimum-time trajectory generation, fault detection and isolation and (after a fault has been detected and identified) trajectory reconfiguration, in an integrated scheme using a differential flatness and B-splines parameterisation. Using the flatness/B-splines parameterisation, the problem of minimum-time constrained trajectory planning is cast into a feasibility-search problem in the splines control-points space, in which the constraint region is characterised by a polytope. A close approximation of the minimum-time trajectory is obtained by systematically searching the end-time that makes the constraint polytope to be minimally feasible. Fault detection is carried out by using B-splines in an FIR filter implementation. Thus, the three problems (namely, trajectory generation, fault detection and trajectory reconfiguration), which are traditionally dealt with separately, are solved in a unified manner, using the same mathematical/computational tools. This, not only offers a unified solution but also simplifies the use of mathematical libraries in the coding of algorithms for real-time applications. All through the paper, a case-study consisting in a nonlinear input-constrained double-tank system is analysed in order to illustrate the techniques in an intuitive manner. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of a parabolic partial differential equation with non-local and time-dependent boundary conditions arising from ductal carcinoma in situ model. Approximation solution of the present problem is implemented by the Ritz-Galerkin method, which is a first attempt at tackling parabolic equation with such non-classical boundary conditions. In the process of dealing with the difficulty caused by integral term in non-local boundary condition, we use a trick of introducing the transition function G( x, t) to convert non-local boundary to another non-classical boundary, which can be handled with the Ritz-Galerkin method. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we focus on high-dimensional similarity join (HDSJ) using MapReduce paradigm. As the volume of the data and the number of the dimensions increase, the computation cost of HDSJ will increase exponentially. There is no existing effective approach that can process HDSJ efficiently, so we propose a novel method called symbolic aggregate approximation (SAX)-based HDSJ to deal with the problem. SAX is the abbreviation of symbolic aggregate approximation that is a dimensionality reduction technique and widely used in time series processing, we use SAX to represent the high-dimensional vectors in this paper and reorganize these vectors into groups based on their SAX representations. For the very high-dimensional vectors, we also propose an improved SAX-based HDSJ approach. Finally, we implement SAX-based HDSJ and improved SAX-based HDSJ on Hadoop-0.20.2 and perform comprehensive experiments to test the performance, we also compare SAX-based HDSJ and improved SAX-based HDSJ with the existing method. The experiment results show that our proposed approaches have much better performance than that of the existing method. [ABSTRACT FROM AUTHOR]

In their recent work, Jiang and Yang studied six classical Likelihood Ratio Test statistics under high-dimensional setting. Assuming that a random sample of size n is observed from a p-dimensional normal population, they derive the central limit theorems (CLTs) when p and n are proportional to each other, which are different from the classical chi-square limits as n goes to infinity, while p remains fixed. In this paper, by developing a new tool, we prove that the mentioned six CLTs hold in a more applicable setting: p goes to infinity, and p can be very close to n. This is an almost sufficient and necessary condition for the CLTs. Simulations of histograms, comparisons on sizes and powers with those in the classical chi-square approximations and discussions are presented afterwards. [ABSTRACT FROM AUTHOR]

The minimax approximation is of special importance for the design of filters. As to the minimax approximation by a rational function, the characteristics of the best approximations are well developed. However, least-squares approximation is often used instead due to the simplicity of calculation. Nevertheless, no theoretical result has been published as to how close and how good the achieved approximation results are compared to those of the best (optimal) minimax approximation. This paper deals with the least p-th approximation (p &ges;2, even) by a rational function and gives a fairly simple theoretical lower bound for the ratio of the maximum error(s) of the minimax approximation to those of the least p-th approximation (usually local minima). This paper proves that on a weak but practical assumption, Nishi's result on the least p-th approximation by linear function is also valid for the approximation by rational function. Numerical examples show that the least p-th approximation for p = 8 or 16 is usually enough to achieve a good approximation to the minimax approximation. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(3): 21–32, 2001 [ABSTRACT FROM AUTHOR]

Finite element analysis is a widely used simulation technique in steel design to analyze the structural behavior of structural components, such as beams, columns or connections. The major steps involved in finite element simulations are the definition of the basic parameters and the discretization in elements of the component, also known as preprocessing; the analysis of the model and the post‐processing by the representation and the interpretation of the obtained results. On the particular case of bolted connections, the most time‐consuming of these three phases is that of preprocessing, because on traditional finite element technology is required that the real geometry of the CAD model is simplified to be meshed and analyzed; this task is specifically severe and requires paying close attention on the case of components affected to concentration stresses. Nowadays, different techniques have been proposed and developed with this objective: reduce costs in terms of time and specialized human resources because the workflow is easier and simpler. One of these methods are the known as the meshfree methods, that do not require connection between nodes and are based on the interaction of the points of the geometry with the neighbors, so the processor analyzes taken as base the real CAD geometry and no simplifications are needed. On this paper is exposed the meshless method based on the theory of external approximations as an alternative to the classic finite element method. This method is based on the theory where all parts of the assembly are considered as different elements, and the approximation of displacements inside is arbitrary and not only by polynomials. The convergence of the simulation model is based on the external equilibrium of the assembly. The method is applied to a practical case: the simulation of the T‐stub connection. The T‐stub component corresponds to one T‐shaped steel profile bolted through their flanges and loaded through their web until collapse, and its behavior is similar to the tension zone of beam to column bolted end plate connections. The analysis of strength, stiffness and ductility have been widely investigated experimentally, by simulation and theoretically, and they are obtained from the force‐displacement characteristic curve. Information presented by Bursi and Jaspart on the paper "Benchmarks for finite element modelling of bolted steel connections" are considered to elaborate the models and to compare the results. [ABSTRACT FROM AUTHOR]