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In this paper, we have described the optical model of light field in vision correcting display providing clear image to farsighted vision at a close viewing distance. Relationship between display and retina images was expressed to the matrix form based on the optical model of light transportation. We reconstructed retina image by optimizing the display image for the given matrix relationship. By analyzing the image quality of corrected image according to an optical gap between pin-hole and pixel arrays, we obtained the proper optical gap maximizing the correction of farsighted vision in our design condition.

Electronic tattoos (E-tattoos), which can be intimately mounted on human skin for noninvasive and high-fidelity sensing, have attracted the attention of researchers in the field of wearable electronics. However, fabricating E-tattoos that are capable of self-healing and sensing multistimuli, similar to the inherent attributes of human skin, is still challenging. Herein, a healable and multifunctional E-tattoo based on a graphene/silk fibroin/Ca2+ (Gr/SF/Ca2+) combination is reported. The highly flexible E-tattoos are prepared through printing or writing using Gr/SF/Ca2+ suspension. The graphene flakes distributed in the matrix form an electrically conductive path that is responsive to environmental changes, such as strain, humidity, and temperature variations, endowing the E-tattoo with high sensitivity to multistimuli. The performance of the E-tattoo is investigated as a strain, humidity, and temperature sensor that shows high sensitivity, a fast response, and long-term stability. The E-tattoo is remarkably healed after damage by water because of the reformation of hydrogen and coordination bonds at the fractured interface. The healing efficiency is 100% in only 0.3 s. Finally, as proof of concept, its applications for monitoring of electrocardiograms, breathing, and temperature are shown. Based on its unique properties and superior performance, the Gr/SF/Ca2+ E-tattoo may be a promising candidate material for epidermal electronics.

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura (Inverse Problems 2009; 25:015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd.

Based on the idea of the spectral visual response fitting, the visual difference between the spectral reflectance factor function of the standard and specimen was proposed in this paper. Basic equations used in the recipe formulation as well as recipe correction were derived based on the spectral visual response fitting in matrix form and an algorithm for the least-squares match has been developed. The iterative procedure for the recipe correction has been established in this algorithm. Twenty standards were used in our numerical experiments. The experimental results showed that the average colour difference against for the standards under the five different illuminants (D65, A, F1, F2 and F3) was smaller than one based on other spectrophotometric fittings, balanced the colour differences better and produced lower metamerism.

Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein–protein interactions. There have been efforts to identify and analyze these protein–protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein–protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein–protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6–0.3 for capsids from different families with the same T-number and similar subunit fold; and

The present paper refers to the definition of the torsional stiffness radii of multistorey tall buildings using both the continuous and the discrete model of the structure. The magnitude of the torsional stiffness radius of a building is the most important structural characteristic in order to explain the torsional behaviour of a building during an earthquake as it directly affects the building's torsional flexibility. The importance of the torsional flexibility of buildings is recognized by contemporary Seismic Codes that propose a grid of torsional provisions in order to avoid soft-storey operation due to floor torsional vibrations around a vertical axis. However, contrary to single-storey buildings, the torsional stiffness radius of multistorey buildings is not defined directly because both the translational and torsional stiffness of these buildings are expressed in matrix form. In the present paper, this weakness has been overcome using the continuous model of the structure, from which the torsional stiffness radius of a general monosymmetric multistorey tall system arises via a closed mathematical equation. The discrete model of the structure has numerically verified this closed mathematical equation. Copyright © 2007 John Wiley & Sons, Ltd.

This article is concerned with the recent merger of five German unions to form the new multi-industry union, ver.di. Its focus is on the effects of the merger and on developments in the post-merger phase. The article explores the various internal problems of the new union, concentrating on those that flow from the adoption of a matrix form of organisation. It deals also with the external relations of ver.di, with other unions and with the central organisation of German trade unions, the DGB. Central conclusions here are that the creation of ver.di is likely to exacerbate competition amongst German unions and further erode the position of the peak association.

This paper presents a linear algebraic procedure in obtaining (6−n) reciprocal screws from an n-screw system of a robotic manipulator. The procedure starts by formulating the reciprocal relationship between a screw system and its reciprocal screw system in matrix form, and augmenting the screw matrix which is assembled with n screws in the screw system. Vectors of cofactors of the augmented row are then produced and the partitioning of the screw matrix is implemented to generate each of the (6−n) reciprocal screws. The theory developed in this paper provides a novel and simple procedure to obtain reciprocal screws from any screw system. The paper illustrates applications to cases with different screw systems. © 2003 Wiley Periodicals, Inc.

In this paper we give the generalization of the score tests covering the case of ties and we give examples where the expressions in matrix form are completely specified for the weighted tests and the score tests for the case of r groups. It is worth mentioning that although the score tests are not generally included in the commercial software, these tests should be used if it can be assumed that the censoring mechanism is equal in the r groups or if there is no censoring (Lawless, 1982). We establish the equivalence between "numerators" of these families of tests. As result of this equivalence we define four new tests that complete the classification of score and weighted tests. The Kruskal-Wallis test (1952) appears as a particular case of the score tests for the case of non-censoring. A simulation study has been done in order to compare the performance of the tests described in this paper. An example is included to make the understanding of the paper easier.

Diagonalization of the 3-D governing equations, transverse field construction, field dependence on the perpendicular coordinate, fields within annuli, compact recursion equations in matrix form, and 3-D EH and HH dyadic Green's function elements are treated. Explicit dependence on substrate thickness is given. Magnetic walls are imposed for nonport contour regions. Published 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 18: 219–227, 1998.

In elasticity theory involving anisotropic materials, the rotational transformation of stress, strain and constitutive relations is of major importance. Also, when these problems are represented in matrix form there are several different contracted notations used to express the stress and strain tensors as column matrices. In general, the contracted notations used lead to unnecessary complications and may lead to errors. In the paper, contracted forms which yield orthonormal rotational transformations are advocated. These transformations are illustrated for stress, strain, modulus and compliance and are also applicable for strength transformation. The gains to be made are procedural and mathematically simple, leading to easier understanding.

The complex variable boundary element method (CVBEM) developed by Hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains. A cut is made in the doubly connected domain, and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations. Cauchy–Riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when Neumann and Robin conditions are imposed on the boundaries. The resulting nodal equations are expressed in matrix form, and coding rules and methods for checking the matrix elements are developed. Three solution methods (implicit, explicit and hybrid) are described, and by means of examples, the efficacy of these methods is discussed and compared.

The system of time-dependent Hartree-Fock equations allowing the calculation the of nth harmonic generation is established by using the same method used in a former paper in the same conditions. These equations are still subjected to orthonormalization conditions. Then by using a recurrence method, we express these equations in matrix form, as well as the orthonormalization conditions; and, as in the former paper, we then replace the solution of the matrix equation subjected to a constraint by that of a free equation. Finally the elimination of the spin variables allows a further simplification. So we obtain an equation allowing the calculation of the nth harmonic generation.

In order to apply the TDHF equations in the matrix form we established previously, we conceive a model for which the static Hartree–Fock equations are rigorously solved; so we study problems only linked to the TDHF method, independent of any further approximation (for example, of LCAO type). This model is made of a spherical box containing electrons subject to a particular potential. We solve, numerically, the TDHF equations at different orders, and we calculate the third order hyperpolarizability tensor. We then compare our results with the ones given by a variation-perturbation method.

The Schrodinger equation, describing the motion of a high-energy electron in a crystal foil, can be solved exactly with appropriate boundary conditions. The formal analytical solution in matrix form however is not suitable for numerical calculations but can be expanded in a series of terms proportional to subsequent powers of the electron wavelength. In the case of fast electron scattering, the electron wavelength decreases so that, to a good approximation, the series can be cut off after the low order terms, yielding a relatively simple expression. This expression reveals two corrections to the dynamical solution of Howie and Whelan, which was obtained by neglecting second order derivative terms in the Schrudinger equation. From an analysis of these corrections, an investigation of the validity of the Howie-Whelan solntion could be performed as function of the cqwtal thickness and an estimation for the thickness limit could be derived. Die Schrodingergleichung, die die Bewegung eines Elektrons hoher Energie in einer Kristallschicht beschreibt, last sich mit geeigneten Randbedingungen exakt losen. Die formale analytische Losung in Matrixform ist nicht geeignet fur numerische Rechnungen, last sich jedoch in eine Reihe von Termen entwickeln, die wachsenden Exponenten der Elektronenwellenlange proportional sind. Im Falle der Streuung schneller Elektronen nimmt die Elektronenwellenlange so ab, das in guter Naherung die Reihe nach den Termen niedriger Ordnung abgebrochen merden kann und sich ein relativ einfacher Ausdruck ergibt. Dieser Ausdruck ergibt zwei Korrekturen zur dynamischen Losung von Howie und Whelan, die durch Vernachllassigung von zweiten Ableitungen in der Schrodingergleichung erhalten wurde. Aus der Analyse dieser Korrekturen kann eine Untersuchung der Gultigkeit der Howie-Whelan-Losung in Abhlangigkeit von der Kristalldicke durchgefuhrt und eine Berechnung der Grenzdicke abgeleitet merden.

This paper examines some problems in the recent experience with regional accounts in Argentina. In Section I a detailed exploration of the possibility of an adaptation of the UN System of National Accounts to any one regional division of a country is presented. The proposal is introduced in matrix form, compatible with the SNA. In Section II selected problems in the definition of the concept of residence and their implications, particularly in the production accounts, are discussed. The presentation is based upon examples for the construction sector, interregional transport, the services of public administration, and the branches of public enterprises resident outside the region. In Section III the principal conclusions of the usefulness, possibility and priorities of regional accounts in Argentina are noted.

A new empirical mathematical method for inter-element effect corrections in XRF analysis is presented. It is based on a special theoretical description of XRF phenomena called OMX (operator model of x-ray fluorescence), presuming a discrete layer model of the sample structure and using mathematical operators to describe the interaction between sample layers and exciting radiation. The operators formed generally as spectral distributions may be simplified into the matrix form for practical application. The effectiveness of the proposed method was verified experimentally by analysing samples of glass and glass raw materials.

One major task of the sciences of human behavior is to formulate working ideas that make sense of rich sets of data gathered by present-day techniques. A closely related concern is the development of methods of analysis relevant to the underlying theory. Awareness of the interplay among techniques of gathering data, methods of analysis, and theoretical framework fosters the clarification and reformulation of each element in a scientific operation. Techniques can be useful timesavers once variables have been identified and relationships have been demonstrated. Following a theoretical orientation the present paper reports an original method of organizing and presenting sociometric data for research and professional purposes. The graphic outcome of the operations is a sociograph. It not only arranges members of the population systematically in discernible cliques and other sub-groupings but also indicates cleavages in the structure of the group being studied. Positive and negative valuations of one another by individuals within a real-life situation provide the firstorder data. They are employed to obtain data cards, to yield the graphic presentation in matrix form, and to calculate indices of peer status independently of any external variables. A subsequent paper upon age-mate acceptance and indices of peer status treats the last of the three operations.

Eine Gruppe von erstgradigen Differentialgleichungen, die man in Matrizenform geschrieben hat, lost man bekanntlich an Hand des sog. Matrizanten auf. Man teilt die Koeffizientenmatrix A des betreffenden Differentialgleichungssystems in Untermatrizen so, das die Untermatrizen, die auf der Diagonale liegen, quadratisch werden. Mit Hilfe der Storungsrechnung bildet man jetzt den Matrizanten fur A. In der hergeleiteten Form sind die Matrizanten der obenerwahnten diagonalen Untermatrizen die Hauptbauteile, die die ubrigen zwei Untermatrizen miteinander „koppeln”. Als Anwendung wird das Problem der gekoppelten Biege- und Torsionsschwingungen betrachtet. A system of differential equations of the first order written in matrix form, may be solved in the well-known way by means of the so-called matrizant: The matrix A of the coefficients of the given system of differential equations is partitional into submatrices in such a way that the submatrices on the diagonal are square matrices; the matrizant for A is found by using perturbation theory. In the form derived here the matrizants of the abovementioned submatrices on the diagonal are the main elements which are coupled by the remaining two submatrices. The theory is applied to the problem of coupled flexural and torsional oscillations.

Die Bewegungsgleichungen des Kristallgitters einer isotopischen Legierung konnen in einer ubersichtlichen Matrizenform dargestellt werden [1]. Diese Matrizenformulierung ermoglicht es, die Berechnung der Frequenzmomente in ein geometrisch-kombinatorisches Problem zu uberfuhren. Bei der Beschrankung auf Radialkrafte gewinnt dieses Problem eine besonders anschauliche geometrische Form. The equations of motion for the crystal lattice of an isotopic alloy may be formulated in a simple matrix form [1]. This matrix form renders possible to transform the computation of the moments of frequency-spectrum into a geometric-combinatorical problem. For radial forces only, the geometric formulation of this problem is particularly instructive.

The density, thermal expansion behavior, and transformationrange viscosity of barium germanate glasses containing 0 to 9 mol% BaO were measured. The addition of BaO to GeO/sub 2/ resulted in phase separation at all BaO concentrations. The results of the property measurements indicate that glasses containing up to 3 mol% BaO consist of a matrix of essentially pure GeO/sub 2/ with barium-rich droplets. Glasses containing 6 mol% BaO or more consist of two interconnected vitreous phases. The morphology of glasses containing between approximately 3.5 and 5.5 mol% BaO can be altered from the droplet/matrix form to that of two continuous phases by the appropriate heat treatment.