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

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]

The tensor-product ( TP) model transformation is a numerical technique that finds a convex representation, akin to a Takagi-Sugeno ( TS) fuzzy model, from a given linear parameter varying ( LPV) model of a system. It samples the LPV model over a limited domain, which allows the use of the higher order singular value decomposition ( HOSVD) and convex transformations that leads to the TS representation of the LPV model. In this paper, we discuss different strategies that could be used on the sampling step of the TP model transformation (which in turn lead to different membership function properties of a TS fuzzy model). Additionally, this paper discusses how the other steps could be used to reduce the number of rules of a given TS fuzzy model. In cases where nonzero singular values were discarded in the rule reduction, we also show how to obtain an uncertain model that covers the original. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide. [ABSTRACT FROM AUTHOR]

Several methods have been proposed to determine a high-resolution NNR spectrum from limited data. This paper attempts to improve and extend the NMR spectrum estimation method using a complex Kalman filter, which was pro- posed previously by Nishlyama and Mita. In the proposed NMR spectrum estimation using the Kalman filter, extra data were required in addition to that to be used in the spectrum estimation, in the approximate determination of the spin-spin relaxation time. Hence, the previously reported NMR spectrum estimation is not based strictly on the same condition as that of the discrete Fourier transform. This paper improves this point, and the extra data are obtained by extrapolation by the AR model. This makes it possible to compare the method with the discrete Fourier transform based on the same number of data. It is shown that when the spectrum is limited to a certain frequency band, the proposed method gives an NMR spectrum with twice higher frequency resolution by reducing the effect of the spin-spin relaxation time and the effect of discrete approximation. In the proposed method, the spin-spin relaxation time of the nucleus, corresponding to the frequency resolution that is twice higher than usual, is determined by a linear interpolation of the spin-spin (relaxation time which is obtained approximately by discrete Fourier transform. [ABSTRACT FROM AUTHOR]

This paper presents a unified theory for the nonuniform sampling theorem for the low-pass band-limited waveform. In most practical cases, the mean interval of the sampling points is in the so-called oversampling state. One can also assume that there exists a certain period in the sampling point sequence. Those properties of the sampling point sequence are assumed in this paper. Yen has derived a sampling theorem for the case where the sampling-point sequence has a period. In his theorem, however, the interpolation function has a spectrum which is a stepwise discontinuous function, not suited to the realization of the interpolation function by a digital or other similar filters. One of the greatest features of the sampling theorem proposed in this paper is that the interpolation function has a continuous spectrum. The problem has been discussed by one of the authors for the case where the sampling frequency and the band-end frequency of the waveform are in an integer ratio. In this paper, the sampling theorem is derived in a unified and integrated form without imposing such a condition. The variance of the approximation error is also derived for the case where a statistically independent additive error is superposed on the sampled value, and it is shown that the proposed sampling theorem is better in that respect. The discussion is extended to the multidimensional band-limited waveform, and a sampling theorem is shown which has an interpolation function with a continuous spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new constrained interpolation profile (CIP) method that is stable and accurate but requires less amount of computation compared to existing CIP-based solvers. CIP is a high-order fluid advection solver that can reproduce rich details of fluids. It has third-order accuracy but its computation is performed over a compact stencil. These advantageous features of CIP are, however, diluted by the following two shortcomings: (1) CIP contains a defect in the utilization of the grid data, which makes the method suitable only for simulations with a tight CFL restriction; and (2) CIP does not guarantee unconditional stability. There have been several attempts to fix these problems in CIP, but they have been only partially successful. The solutions that fixed both problems ended up introducing other undesirable features, namely increased computation time and/or reduced accuracy. This paper proposes a novel modification of the original CIP method that fixes all of the above problems without increasing the computational load or reducing the accuracy. Both quantitative and visual experiments were performed to test the performance of the new CIP in comparison to existing fluid solvers. The results show that the proposed method brings significant improvements in both accuracy and speed. [ABSTRACT FROM AUTHOR]

This paper discusses a routing scheme for an autonomous distributed wireless network (mobile ad-hoc networking) using an ultra-wideband (UWB) system. The UWB system is a kind of spread-spectrum communication system which has the function of measuring the distance between the transmitter and the receiver with high accuracy. Using this distance measurement function, the received energy per bit is kept constant by adjusting the spreading factor according to the transmission distance. This paper considers a packet-forwarding scheme based on the above feature of the UWB system, where the spreading factor is adjusted according to the distance between the transmitter and the receiver. The objective is to realize higher throughput than in single-hop transmission by using multihop transmission which controls the maximum transmission distance. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(2): 22–30, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20082 [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson-like equations and generalized double-layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE-based distance function approximations. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient and systematic algorithm for the solution of electromagnetic scattering and radiation problems over a wide frequency interval. The algorithm is based on the evaluation of the Padé approximant of the solution vector, constructed at a minimum number of expansion frequencies within the interval of interest. The bisection algorithm introduced in this paper is robust. It keeps the approximation error bounded by a predefined constant over the entire frequency band. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 376–380, 1999. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors proposed a design method for representing the window function by the C-spline function, which is a linear combination of the B- spline functions. By using that design method, a window function is obtained which has the same mainlobe bandwidth and the highest sidelobe level as the Hanning window or Blackman window, but a faster sidelobe fall-off. However, the design method for the new window function is not practical due to the fact that the description of the design specification is premature and the optimal dimension is not specified. This paper aims at the realization of a practical design method by improving those points. A design method is proposed in which the specification for the high-frequency range is given in terms of the sidelobe fall-off, and the specification for the low-frequency range is given in terms of the desired frequency characteristics in the logarithmic scale, together with the tolerable approximation error, represented by the mean-square error. The optimal dimension is determined, in the iterative approximation increasing the dimension to reduce the error in regard to the desired frequency characteristics, as the minimum dimension that reduces the err- or to the tolerable value. The usefulness of the proposed design method is demonstrated by a design example for the window function, which has a better characteristic than those of Kaiser-Bessel, Gauss and Hanning windows. [ABSTRACT FROM AUTHOR]

This paper proposes a method of stable approximation based on the phase characteristics, utilizing the properties of phase and the stability of discrete-time all-pole-type transfer function. The feature of the method is that the characteristics to be approximated can be modeled by the ω-coordinate (real-frequency) of the interpolating points and a real coefficient parameter. When the method is used in the approximation in the time domain, the characteristics of the nonminimum phase system can also be approximated by the transfer function with zeros and by the processing using complex cepstrum. The extension of the method to the two-dimensional signal processing is also discussed, although the discussion has to be limited to the separable case. [ABSTRACT FROM AUTHOR]

Rigorous full-wave analysis techniques are presently receiving much attention in the design of MICs and, in particular, of MMICs due to increasing circuit packing densities and structural complexity. In this paper, the problems associated with such techniques and previous related work are briefly outlined in the introduction. To obtain self-consistency, the electrodynamic Green's functions and related terms are then formulated for the shielded (M)MIC problem. The final operator equation for the numerical solutions derived and the associated functions space are presented and discussed. The central portion of the paper describes a new numerical solution using a discretized Green's function database technique. The resulting linear system of equations is solved by direct inversion for geometrical complexities involving up to about 1000 unknowns; for a higher number of unknowns, an iterative solution is generated. As an alternative to the database technique developed, a variety of spectral domain iterative solutions has been written and tested as well. This includes application of the conjugate gradient method to the normal operator equation (CON algorithm), an implicit iterative Galerkin approximation called the modified planar conjugate gradient technique (MPCG) and monotonically convergent iteration procedure being a version of the conjugate residual algorithm (CR). Supplementary to this, the extraction of (M)MIC design data from the numerical 3D solutions obtained and error considerations are presented. The paper concludes with a variety of analysis examples of medium to high geometrical complexity and with verification of some results by comparison with measurements and with numerical data from other sources. CPU times required on typical workstations (MicroVAX, HP 9000, etc.) are moderate, thus rendering the techniques presented as useful in the solution of MIC and MMIC design problems. [ABSTRACT FROM AUTHOR]

This paper considers the set of waveforms for which the weighted power-of-p (1 < p < +∞) integral of the Fourier spectrum is bounded. Since different weight functions can be used in different frequency bands, as long as they are positive, the restriction of the waveform by the power-of-p integral is sufficiently general. It is assumed that the waveform belonging to such a set is added to several given linear time-invariant filters. A theory of the optimum approximation of the original waveform is established using the sampling sequences of the corresponding outputs. The measure of the original waveform is established using the sampling sequences of the corresponding outputs. The measure of the approximation error is defined as the upper limit of the absolute value of the difference between the original and the approximating waveforms when the original waveforms are changed one by one over the whole set of waveforms. Considering the sampling points, which substantially affect the approximation at a fixed time t, a theorem is presented which indicates that there exists a waveform which has zero value at all such sampling points and has the absolute value of the approximation error which reaches the above upper limit. It is shown also that a similar result can be established for the multidimensional waveform. In this paper, it is shown that the proposed method of linear approximation is better than any other approximation using the same sample values, including the nonlinear signal processing, as long as the forementioned set of waveforms and the measure for the approximation error are considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the CPatch, a curved primitive that can be used to construct arbitrary vector graphics. A CPatch is a generalization of a 2D polygon: Any number of curves up to a cubic degree bound a primitive. We show that a CPatch can be rasterized efficiently in a hierarchical manner on the GPU, locally discarding irrelevant portions of the curves. Our rasterizer is fast and scalable, works on all patches in parallel, and does not require any approximations. We show a parallel implementation of our rasterizer, which naturally supports all kinds of color spaces, blending and super‐sampling. Additionally, we show how vector graphics input can efficiently be converted to a CPatch representation, solving challenges like patch self intersections and false inside‐outside classification. Results indicate that our approach is faster than the state‐of‐the‐art, more flexible and could potentially be implemented in hardware. [ABSTRACT FROM AUTHOR]

In this paper, we use the asymptotical analysis to construct the asymptotic approximation of the solution with internal transition layer of the boundary value problem for a reaction‐diffusion equation on the segment in case of discontinuous reactive and diffusive terms. The internal layer is located in the vicinity of a single point of discontinuity of the mentioned terms. We also investigate the existence and stability of such solution. For the last purpose, we use the asymptotical method of differential inequalities. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we develop an equivalent approximation approach to obtain the Hamilton‐Jacobi‐Bellman (HJB) equations of intertemporal decision problems under uncertainty. An implicit discount function is adopted in the derivation of the rate of change of value function for the HJB equations to provide the broadest coverage of time preferences. Meanwhile, we provide an illustrative example for application by revisiting the intertemporal consumption and portfolio decisions problem. Furthermore, we verify the validity of our approach in robustness tests by incorporating exponential, nonconstant, and stochastic hyperbolic discounting functions, respectively. The HJB equations and their resulting decision rules in the finite and infinite planning horizons have confirmed that our approach provides an efficient and reliable alternative to acquire the HJB equations in the intertemporal economic issues under uncertainty. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a method for finding an approximate solution of a class of 2D fractional optimal control problems with fractional‐order dynamical system is discussed. In the proposed method, the fractional derivative is expressed in the Caputo sense. The method consists of expanding unknown functions as the elements of two‐dimensional (2D) Müntz‐Legendre wavelets. The 2D Müntz‐Legendre wavelets are constructed and their properties are presented. The operational matrix of fractional‐order integration for these wavelets is utilized to reduce the solution of 2D fractional optimal control problem to an optimization problem, which can then be solved easily. Some results concerning the error analysis are obtained. Finally, two illustrative test problems are included to demonstrate the validity and applicability of the technique. Moreover, our achievements are compared with the previous results to show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

SUMMARY Most engineering applications involving solutions by numerical methods are dependent on several parameters, whose impact on the solution may significantly vary from one to the other. At times an evaluation of these multivariate solutions may be required at the expense of a prohibitively high computational cost. In the present paper, an adaptive approach is proposed as a way to estimate the solution of such multivariate finite element problems. It is based upon the integration of so-called nested Padé approximants within the finite element procedure. This procedure includes an effective control of the approximation error, which enables adaptive refinements of the converged intervals upon reconstruction of the solution. The main advantages lie in a potential reduction of the computational effort and the fact that the level of a priori knowledge required about the solution in order to have an accurate, efficient, and well-sampled estimate of the solution is low. The approach is introduced for bivariate problems, for which it is validated on elasto-poro-acoustic problems of both academic and more industrial scale. It is argued that the methodology in general holds for more than two variables, and a discussion is opened about the truncation refinements required in order to generalize the results accordingly. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the classical error estimates of nonconforming Crouzeix-Raviart type finite elements for the Stokes equations. By introducing some quasi-interpolation operators and using the special properties of these nonconforming elements, it is proved that their consistency errors can be bounded by their approximation errors together with a high-order term, especially which can be of arbitrary order provided that f in the right-hand side is piecewise smooth enough. Furthermore, we show an interesting result that both in the energy norm and L2 norm the consistency errors are dominated by the approximation errors of their finite element spaces. As byproducts, we derive the error estimates in both energy and L2 norms under the regularity assumption ( u, p) ∈ H1 + s(Ω) × H s(Ω) with any s ∈ (0,1], which fills the gap in the a priori error estimate of these nonconforming elements with low regularity [ABSTRACT FROM AUTHOR]

SUMMARY The multiport scattering (S-) parameter matrix is increasingly utilized to compose models of large bit-width interconnect systems with broadband characteristics (frequency range of zero to tens of gigahertz) to perform increasingly accurate signal-integrity and power-integrity simulations. The search for an optimal solution space often requires generation of S-parameter models of interconnect systems for various signal/ground pin mappings, a process that can be computationally costly if the structure is electromagnetically solved for each distinct pin mapping. To expedite this model-generation process, we propose a method in which an N-port structure is electromagnetically solved only once to yield an N × N S-matrix; then, a linear system is formulated and solved to yield an ( N − M) × ( N − M) post-suppressed S-matrix (where M is the number of suppressed ports). This approach results in significant computational savings through elimination of electromagnetic field-solver runs for each distinct pin mapping. Included in this paper is a discussion about the limitations of this technique and several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided. [ABSTRACT FROM AUTHOR]

Summary: The goal of this paper is to create a fruitful bridge between the numerical methods for approximating PDEs in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear systems. Among the main objectives are the design of new, efficient iterative solvers and a rigorous analysis of their convergence speed. The link we have in mind is either the structure or the hidden structure that the involved coefficient matrices inherit, both from the continuous PDE and from the approximation scheme; in turn, the resulting structure is used for deducing spectral information, crucial for the conditioning and convergence analysis and for the design of more efficient solvers. As a specific problem, we consider the incompressible Navier–Stokes equations; as a numerical technique, we consider a novel family of high‐order, accurate discontinuous Galerkin methods on staggered meshes, and as tools, we use the theory of Toeplitz matrices generated by a function (in the most general block, the multilevel form) and the more recent theory of generalized locally Toeplitz matrix sequences. We arrive at a somehow complete picture of the spectral features of the underlying matrices, and this information is employed for giving a forecast of the convergence history of the conjugate gradient method, together with a discussion on new and more advanced techniques (involving preconditioning, multigrid, multi‐iterative solvers). Several numerical tests are provided and critically illustrated in order to show the validity and the potential of our analysis. [ABSTRACT FROM AUTHOR]

In the last decade, theoretical and applied studies were done in order to provide a suitable definition of fractional derivative, which meets all the requirement of a derivative in its primary sense. It was concluded by some eminent researchers that the Riemann‐Liouville version was the most suitable. However, many numerical approximation of fractional derivative were done with Caputo version. This paper addresses the numerical approximation of fractional differentiation based on the Riemann‐Liouville definition, from power‐law kernel to generalized Mittag‐Leffler‐law via exponential‐decay‐law. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical treatment of a fourth‐order fractional diffusion‐wave problem. Our proposed method includes the use of parametric quintic spline in the spatial dimension and the weighted shifted Grünwald‐Letnikov approximation of fractional integral. The solvability, stability, and convergence of the numerical scheme are rigorously proved. It is shown that the theoretical convergence order improves those of earlier work. Simulation is further carried out to demonstrate the numerical efficiency of the proposed scheme and to compare with other methods. [ABSTRACT FROM AUTHOR]

From a mathematical point of view, phase field theory can be understood as a smooth approximation of an underlying sharp interface problem. However, the smooth phase field approximation is not uniquely defined. Different phase field approximations are known to converge to the same sharp interface problem in the limiting case-if the thickness of the diffuse interface converges to zero. In this respect and focusing on numerics, a question that naturally arises is as follows: What are the convergence rates of the different phase field models? The paper deals precisely with this question for a certain family of phase field models. The focus is on an Allen-Cahn-type phase field model coupled to continuum mechanics. This model is rewritten into a unified variational phase field framework that covers different homogenization assumptions in the diffuse interfaces: Voigt/Taylor, Reuss/Sachs and more sound homogenization approaches falling into the range of rank-one convexification. It is shown by means of numerical experiments that the underlying phase field model-that is, the homogenization assumption in the diffuse interface-indeed influences the convergence rate. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper demonstrates the capability of our previously published undoped Double-Gate (DG) MOSFET explicit and analytical compact model to also forecast the effect of the volume inversion (VI) on the intrinsic capacitances. For that purpose, we present simulation results for these capacitances. We show now that the model presents an accurate dependence on the silicon layer thickness, consistent with two-dimensional numerical simulations, for both thin and thick silicon films. As opposed to our previous work, here we test the capacitance model for three different film thicknesses and also show that the transition from VI regime to dual gate behaviour is well simulated. We demonstrate in this paper that even if the current drive and transconductance are enhanced in VI regime, our results show that intrinsic capacitances are higher as well, which may limit the high-speed (delay time) behaviour of DG MOSFETs under VI regime. The good agreement between the numerical simulations and our model shows the high potential of our complete DG MOSFET model. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well-known that there is no integrable relation between the twist of a rigid body and its finite motion. Moreover, the reconstruction of the body's motion requires to solve a set of differential equations on the rigid body motion group. This is usually avoided by introducing local parameters (e.g. Euler angles) so that the problem becomes an ordinary differential equation on a vector space (e.g. kinematic Euler equations). In this paper the original problem on the motion group is treated. A family of approximation formulas is presented that allow reconstructing large rigid body motions from a given velocity field up to a desired order, where a k-th order reconstruction requires the first k - 1 time derivatives of the velocity. Such reconstruction formulas could be used whenever the velocity field is accessible. As an example the formulas are applied to the rotation update in a momentum preserving time stepping scheme for the dynamic Euler equations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss basic properties, a least-squares problem for row extended matrices and the associated approximation problem. First, we obtain their basic properties by applying their particular structure. Then we derive a general representation of the solutions to the least-squares problem, and we obtain an expression for the solution to the associated approximation problem. Finally, we provide a perturbation analysis and a perturbation bound for the best approximate solution. The results are illustrated by numerical examples. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a general parametric lifetime model for predicting fatigue behaviour at any stress level and amplitude (for example, at any combination of σmax and σmin pair) in the high-cycle fatigue regime. The problem of the design of the experimental laboratory test required for such a prediction is dealt with. The surprising and relevant result is that running two groups of tests for two different constant stress levels of σmax or σmin is sufficient to predict the whole collection of Wöhler fields for any possible stress level. However, some combinations of tests, such as one for a fixed value of σmax and one for a fixed value of σmin, are shown to be insufficient. Closed formulas for obtaining any Wöhler field from the results of the experiments corresponding to the two different fixed values of σmax or σmin are given. Together the proposed model and lab tests allow any fatigue analysis to be performed in the current investigation. One example of application illustrates the proposed method. [ABSTRACT FROM AUTHOR]

The YUV 4:2:0 format is a representative format for color images in international standards. In this format, both color difference components U and V reduce the number of pixels in the horizontal and vertical directions by one-half. Consequently, this reduction degrades the color difference components. At a relatively high bit rate, the degradation produced by reducing the number of pixels is often worse than the degradation that depends on the coding. Thus, processing to compensate for the degradation due to the format transform becomes necessary. The pixels of the color difference components reduced once on the encoding side are determined by interpolation on the decoding side. The typical interpolation methods are bilinear interpolation, bicubic interpolation, and interpolation by a finite impulse response (FIR) filter. When these interpolation methods were applied to interpolate the color difference components in the YUV 4:2:0 format, blur and lower saturation were produced in the colors in the color difference components returned to the original number of pixels. In this paper, we propose a method that uses information in the luminance component not having a reduced number of pixels to interpolate the color difference components in the YUV 4:2:0 format. Consequently, color blurring is prevented in the edges of the image, and an objective is to improve the saturation in the entire image. We based the proposed method on bilinear interpolation and bicubic interpolation, and formulated an interpolation method using the luminance component as an extended form. The proposed method and the bicubic interpolation are compared in both objective and subjective evaluations, and demonstrate the effectiveness of the proposed method. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(9): 1–10, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20218 [ABSTRACT FROM AUTHOR]

In this paper, we consider the field produced by a line current behind a layer of left-handed material (LHM). Our purpose is to show that any slab of LHM (except the known case ℇ = -1 and μ = -1) when is illuminated by a point source has infinite number of focal points with approximately same smearing as the recently studied LHM layer with ℇμ = 1. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 64–67, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11128 [ABSTRACT FROM AUTHOR]

In this paper, an asymptotic formula using Newton and Chebyshev interpolations is developed and presented. With this formula, the coupling coefficient between suspended plate antennas with an inclined ground plane is estimated. The accuracy of this formula is validated by full-wave analysis in terms of the simulation results obtained using the Zeland IE3D software package. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 19–22, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11114 [ABSTRACT FROM AUTHOR]

Generally, in image segmentation or object extraction, the edge image of the target object has a substantial effect on the extraction accuracy. In this paper, we focus on the characteristics of the currents flowing in an electrical circuit and propose a technique to interpolate and enhance the edges of a still image by simulating this circuit behavior and apply this technique to image segmentation. The proposed technique constructs a resistor circuit by mapping the edge intensity of each point in the edge image to a resistance, applies a suitable voltage to this circuit, and determines the distribution of the flowing current. Based on the property that the current concentrates in the path that minimizes the sum of the resistances, the current distribution that was obtained is inversely transformed again into the edge intensities in order to enhance weak edges and interpolate broken edges. In several experiments, the proposed technique produced better results than other edge interpolation and enhancement techniques. And when used with the watershed algorithm, highly accurate segmentation was obtained. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(9): 22–33, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10085 [ABSTRACT FROM AUTHOR]

The IDO method, known as a numerical method suitable for partial differential equations containing an advection term, is improved in terms of its accuracy. In the method proposed in this paper, the order of Hermite interpolation is increased with a parameter h in order to deal with the higher order differential coefficients as independent variables. (In the conventional IDO method, h = 3 for calculation of the advection term and h = 5 for calculation of the diffusion term.) When this method is applied to a one-dimensional advection-diffusion equation, it is found that the numerical error is reduced to about 1/5 of that in the conventional IDO method if h = 7 is used. By using two mutually overlapping grid systems, the scheme becomes stable. Further stability is achieved by applying the time-splitting method. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(8): 11–18, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10124 [ABSTRACT FROM AUTHOR]

Enlargement processing of digital images is usually carried out by means of an interpolation function obtained by simplification of the sinc function. However, in such an interpolation method, restoration of the high-frequency components lost in digitizing the images is not carried out at all. Hence, the enlargement causes blurring for images with many edges and detailed signals. For one-dimensional signals, Carrato and colleagues have proposed an interpolation method in which the discontinuities of the step edge signals are preserved while other signals are linearly interpolated. In this method, no blurring occurs in the expansion processing of strong frames of the images. However, Carrato's method has the following problems. (1) Only the step edges in the image signals are taken into account so that consideration of the detailed signals is insufficient. (2) Extension of the one-dimensional interpolation method given by Carrato to a two-dimensional interpolation method has a problem in interpolation at the center of the lattice. In this paper, a method is proposed to accomplish improvement of Carrato's method. With regard to problem (1), the interpolation not only is effective for the step edge signals but also preserves the apex of the peak and valley signals. With regard to problem (2), improvement is planned by directly deriving the interpolation value from the original signals. The proposed interpolation processing is accomplished by describing the processing sequence by a rule. The proposed method consists of two sets of fuzzy reasoning. The proposed method and the conventional interpolation method are compared from the numerical and visual perspectives and the effectiveness of the proposed method is clarified. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 57–66, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1140 [ABSTRACT FROM AUTHOR]

In this paper we briefly present the results obtained in our paper (Talay and Zheng 2002a) on the convergence rate of the approximation of quantiles of the law of one component of (X[sub t]), where (X[sub t]) is a diffusion process, when one uses a Monte Carlo method combined with the Euler discretization scheme. We consider the case where (X[sub t]) is uniformly hypoelliptic (in the sense of Condition (UH) below), or the inverse of the Malliavin covariance of the component under consideration satisfies the condition (M) below. We then show that Condition (M) seems widely satisfied in applied contexts. We particularly study financial applications: the computation of quantiles of models with stochastic volatility, the computation of the VaR of a portfolio, and the computation of a model risk measurement for the profit and loss of a misspecified hedging strategy. [ABSTRACT FROM AUTHOR]

This paper analyzes the accuracy of count data estimated by the point-in-polygon method. A point-in-polygon interpolation model is proposed, based on a stochastic distribution of points and the target zone, in order to represent a variety of situations. The accuracy of estimates is numerically investigated in relation to the size of the target zone and the distribution of points, and the optimal location of representative points is discussed. The major findings of this paper are as follows: (1) though the relative accuracy of estimates generally increases monotonously with the size of the target zone, the monotoneity is often disturbed by the periodicity in the spatial configuration of source zones and the point distribution; (2) the point-in-polygon and the areal weighting interpolation methods have the same accuracy of estimates when points are concentrated in less than 12-15 percent area around the representative point in source zones; (3) the point-in-polygon method is not so robust against the locational gap between points and the representative point; (4) the optimal location of representative points is given by the spatial median of points. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we introduce a simple; but an effective algorithm to detect and image the precise location of moving targets behind obstacles based on one-transmitter and two-receiver configuration. The problem geometry together with the formulation details of the algorithm are given. The performance of the algorithm is first evaluated by synthesizing a numerical scenario that is simulated by moving ideal scatterers. Then, the success and the validity of the algorithm are being assessed by an error analysis study that calculates the error associated by the approximations. The algorithm is tested with measured data obtained by an experimental set-up for detecting a human movement behind the wall. Resultant two-dimensional consecutive images indicate that this algorithm can be effectively used for pinpointing the moving targets in TWR or similar through-the-obstacle radar applications with good fidelity. © 2017 Wiley Periodicals, Inc. Microwave Opt Technol Lett 59:1252-1259, 2017 [ABSTRACT FROM AUTHOR]

Consider a set of waveforms whose Fourier spectra are band-limited within a certain frequency band. We assume that the weighted Lp integrals (i

This paper presents a synthesis method for active RC filters with multiple pass-bands, The synthesis procedure is based on a signal-flow graph representation and frequency transformation applied to a passive LCR filter. It should be noticed that an active RC filter with multiple passbands is amenable to the finite gainband product effects of an operational amplifier. This is really true if adjacent passbands are close. Hence an effective technique is developed for reducing the finite GB product effects. An experimental result concerning the two-passband filter derived from a third-order Chebyshev filter also is included. [ABSTRACT FROM AUTHOR]

This paper proposes a method of two dimenslonal analysis for the thickness-flexural vibration, where the one-dimensional finite-element method (FEM) is applied to the planar equation. This approach aims at application to the analysis of the flexural spurious vibrations of strip rectangular AT-cut plate often used in practice. The feature of the proposed method is that the two-dimensional coupled vibration can be analyzed by applying twice the one-dimensional FEM. in other words, the one-dimensional FEM is applied to the eigenmode guided by the X-edge, as well as to the resonant expression derived from the boundary condition on the Z'-edge. As a result, the considered matrix is reduced greatly in size compared to the direct analysis by the two-dimensional FEM. The result of calculation for the change of the resonant frequency due to the change of the Z'-edge ratio is compared to the result of experiment, and the usefulness of the proposed method is demonstrated. It is shown also that most of the spurious vibrations depending on the Z'-edge ratio are flexural vibrations, which is a new finding. [ABSTRACT FROM AUTHOR]

The spline interpolation using the sampling bases has a feature of real-time computation which is not observed in other methods since the result of interpolation is derived directly from the sampled value sequence. Then it is necessary that the sampling function should be truncated in a finite interval. This paper aims to clarify the relation in this method between the error in the result of interpolation due to the truncation and the length of the truncation interval. The result is summarizes in a correspondence table for the truncation interval length and the error. In the proposed interpolation method, the truncation interval length to ensure the given tolerable range of error can be determined using the correspondence table. [ABSTRACT FROM AUTHOR]

Originally irreducible polynomials were obtained essentially by checking the irreducibility of a randomly chosen polynomial. Recently, irreducible polynomials of a specified form have been produced and a transformation of the variable has been applied to produce a systematic method of deriving irreducible polynomials. In this paper, we consider Irreducible polynomials from the viewpoint of cyclotomic polynomials. We define conditions for the existence of irreducible cyclotomic polynomials and show that these polynomials have some specified forms. Additionally, it is shown that an infinite number of irreducible polynomials can be generated which satisfy those conditions. [ABSTRACT FROM AUTHOR]

Assume that signal f(t) is impressed on N parallel time-invariant liner networks Hm(ω) (m = 1∼N), and consider the uniformly sampled values gm(nT) (m=1∼N; n=0, ± 1, ±2; T > 0) of the output signal gm(t) (m=1∼N). This paper discusses the following problem from a unified viewpoint. The response g(t), when the signal f(t) is passed through the given filter H(ω), is to be approximated by and expression y (t) which is the sum of the forementioned sample value multiplied by time functions ø mn(t) (m-1 ∼ N; n=0, ± 1, ± 2,). It is assumed that the signal f(t) belongs to the set 1 of the signals for which the weighted square integral of the Fourier spectrum F(ω) is not greater than a positive number A. In the foregoing, ømn(t) is called the interpolation function. First, it is shown that given Hm(ω)(m=1∼N), the time-limited interpolation function, which minimizes the upper limit emax(t) of the error e(t) =g(t) - y(t) over all f(t) belonging to T, is obtained by shifting the impulse responses øm(t) (m=1∼N) of certain N linear time-invariant interpolation filters øm (ω) (m=1∼N) and øm(ω) (m=1∼N) are optimized so that the measure emax(t) of the error is minimized, the upper and the lower bounds of the optimal emax(t) are shown. Considering an application where N is large, the optimization is discussed in the sense that the equivalent multiplicity is reduced at the sacrifice of the approximation error. [ABSTRACT FROM AUTHOR]

This paper describes a method for estimating and forecasting reliability from attribute data, using the binomial model, when reliability requirements are very high and test data are limited. Integer data - specifically, numbers of failures - are converted into non-integer data. The rationale is that when engineering corrective action for a failure is implemented, the probability of recurrence of that failure is reduced; therefore, such failures should not be carried as full failures in subsequent reliability estimates. The reduced failure value for each failure mode is the upper limit on the probability of failure based on the number of successes after engineering corrective action has been implemented. Each failure value is less than one and diminishes as test programme successes continue. These numbers replace the integral numbers (of failures) in the binomial estimate. This method of reliability estimation was applied to attribute data from the life history of a previously tested system, and a reliability growth equation was fitted. It was then 'calibrated' for a current similar system's ultimate reliability requirements to provide a model for reliability growth over its entire life-cycle. By comparing current estimates of reliability with the expected value computed from the model, the forecast was obtained by extrapolation. [ABSTRACT FROM AUTHOR]

As lower-order approximation methods for discrete-time linear systems, Mullis and Roberts have proposed two methods: the socalled modified least-square approximation (MLSA), and the interpolatory approximation (IA). The characteristics of the two methods were investigated considering their relationships. In this paper, a lower-order approximation method for continuous-time linear systems is presented in a form corresponding to MLSA, with its property, algorithm and state-space representation discussed in correspondence with the discrete-time case. The approximation can also be regarded as corresponding to IA, and thus the proposed method is called the continuous-tie Mullis-Roberts-type approximation (CMRA). The latter half of this paper presents a formulation for the limiting case (as sampling time → 0) from a lower-order approximation method for discrete-time systems to one for continuous-time systems. Thus it is shown that CMRA is obtained as a common limit of MLSA and LA, thereby providing a physical interpretation to the formal correspondence between CMRA and MLSA/IA. [ABSTRACT FROM AUTHOR]

The local neighborhood search method is one of the efficient strategies for approximation algorithms for many combinatorial problems contained in the NP-complete class. To evaluate this kind of approximation method, the average case analysis is considered to be better than the worst case analysis. This paper considers the 0 - 1 knapsack problem, one of the representative problems included in the NP-complete class of problems. Then the behavior of the local neighborhood search method is analyzed for the problem using a flow model we proposed on a previous occasion. By comparing the analytical result for the 0 - 1 knapsack problem instances with up to 200 variables, we show that the flow model is useful as the means of analyzing the behavior of the local neighborhood search method for the 0 - 1 knapsack problem. [ABSTRACT FROM AUTHOR]

This paper discusses a least-squares error design of 2-D digital filters under a peak error constraint. Initially we present a filter design procedure in which the peak error constraint is satisfied by iterating the design based on a weighted least-squares error criterion to update the weights. The computational complexity required in the filter design is then reduced by switching from the above procedure to the Lagrange method of unknown constants during the course of iteration. Finally, the trade-off between square error and absolute peak error is verified by using a numerical example. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(9): 75–82, 1998 [ABSTRACT FROM AUTHOR]