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Purpose: The purpose of this paper is to conveniently and accurately design partial knitting knitted fabrics based on matrix transformation. Design/methodology/approach: Using mathematical modeling, the pattern diagram block matrix and process design matrix of partial knitting knitted fabrics are established, and the process knitting diagram with parameter information is generated. Based on the establishment of the mathematical model of the process knitting diagram, a loop deformation method based on three-dimensional (3D) coordinate point matrix transformation is proposed. Findings: The matrix transformation method can provide a suitable deformed loop mode for partial knitting knitted fabrics and helps to generate a 3D modeling diagram conveniently. Originality/value: This paper proposed a method of design and modeling of partial knitting knitted fabric based on matrix transformation. Taking the 3D modeling effect of conventional partial knitting as an example to test the modeling method, the results show that after matrix transformation, the loop model can realize the rapid transformation and calculation of the coordinates of the control point and generate a 3D modeling diagram. [ABSTRACT FROM AUTHOR]

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the "t-matrix" model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This "t-matrix" model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts. [ABSTRACT FROM AUTHOR]

This article aims to introduce some modern algebraic structures as hyper super matrices. The classical algebra and matrices cannot process higher-dimensional information with several levels of ambiguity and uncertainty. Hence, it is necessary to establish such superalgebraic structures that can organize and classify the uncertain and incomplete information floating in parallel higher dimensions as facts, events, or realities. To achieve the desired goal, a particular construction of Hypersoft Matrix (HS-Matrix) and Subjectively Whole Hyper-SuperSoft Matrix (SWHSS-Matrix) is offered in a plithogenic Fuzzy environment initially, and some aggregation operators are formulated. A Local-Global-Universal Combined Consciousness State Ranking Model is formulated as an application. As the classification of non-physical phenomena like state of physical health or Consciousness has not yet been addressed in the area of decision making therefor the proposed model will open a new dimension of classification of the non-physical part of the universe in which one can select the most suitable possible reality from several parallel realities which would be useful in the field of artificial intelligence. This model classifies the accumulated states of matter bodies (subjects). And gives a possible description of the Combined-Consciousness State of a Universe. In addition, it offers a local ranking by observing the information through several angles of vision, just like a human mind does, and a universal ranking by classifying the accumulated states. Furthermore, the final Global Ranking is achieved by constructing a percentage frequency-matrix and an authenticity measure of the order is offered. A numerical example is constructed to describe SWHSS-Matrix and LGU-Ranking Model. Some pie graphs are used to describe the individual states, accumulated states, and the ultimate accumulated universal state of all given subjects (a Combined Conscious State of Universe). [ABSTRACT FROM AUTHOR]

The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the 1-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the 2-D case of Toeplitz-block Toeplitz (TBT) matrices, described a minimal information, which is necessary to recover the inverse matrices, and gave a complete characterisation of the inverse matrices. Now, we develop our approach for the more complicated cases of the block TBT-matrices and of the 3-D Toeplitz matrices. Some important special cases are treated as well. [ABSTRACT FROM AUTHOR]

Least square regression is a very popular supervised classification method. However, two main issues greatly limit its performance. The first one is that it only focuses on fitting the input features to the corresponding output labels while ignoring the correlations among samples. The second one is that the used label matrix, i.e. , zero–one label matrix is inappropriate for classification. To solve these problems and improve the performance, this paper presents a novel method, i.e. , inter-class sparsity based discriminative least square regression (ICS_DLSR), for multi-class classification. Different from other methods, the proposed method pursues that the transformed samples have a common sparsity structure in each class. For this goal, an inter-class sparsity constraint is introduced to the least square regression model such that the margins of samples from the same class can be greatly reduced while those of samples from different classes can be enlarged. In addition, an error term with row-sparsity constraint is introduced to relax the strict zero–one label matrix, which allows the method to be more flexible in learning the discriminative transformation matrix. These factors encourage the method to learn a more compact and discriminative transformation for regression and thus has the potential to perform better than other methods. Extensive experimental results show that the proposed method achieves the best performance in comparison with other methods for multi-class classification. [ABSTRACT FROM AUTHOR]

The simulation of light scattering by particles on a substrate with the T -matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from the substrate. In practice, the plane wave expansion (i.e., the Sommerfeld integrals) needs to be truncated at a maximal in-plane wavenumber κ max . An appropriate selection of κ max is essential: counter-intuitively, the overall accuracy can degrade significantly if the integrals are truncated with a too large value. In this paper, we propose an empirical formula for the selection of κ max and discuss its application using a number of example simulations with dielectric and metallic oblate spheroids on dielectric and metallic substrates. The computed differential scattering cross sections are compared to results obtained from the discrete-sources method. [ABSTRACT FROM AUTHOR]

The T -matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T -matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously. [ABSTRACT FROM AUTHOR]

Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of m × n rank-2 matrices and n × n skew-symmetric rank-2 matrices. Our approach is to use tropical geometry to reduce this to a problem about phylogenetic trees which we then solve. In particular, we give a combinatorial description of the collections of pairwise distances between several taxa that may be arbitrarily prescribed while still allowing the resulting dissimilarity map to be completed to a tree metric. [ABSTRACT FROM AUTHOR]

An effective nonlinear model reduction approach, empirical Gramians balanced reduction approach, is studied, to reduce the computation complexity in nonlinear power system model application. The realization procedure is: firstly, computing the empirical controllable and observable Gramians matrices of nonlinear power system model, secondly, by these two matrices, computing the balance transformation matrix to obtain the balanced system model of the original model, then, computing the controllable and observable matrices of the balanced system to obtain the diagonal Hankel singular matrix. Finally, deciding the lower-order subspace to obtain the reduced power system model. A 15-machine power system model is taken as an example to perform the reduction simulation analysis. [ABSTRACT FROM AUTHOR]

We study the effect of three types of graft transformations to increase or decrease the distance spectral radius of connected uniform hypergraphs, and we determine the unique k -uniform hypertrees with maximum, second maximum, minimum and second minimum distance spectral radius, respectively. [ABSTRACT FROM AUTHOR]

Abstract: This paper is the sixth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists several earlier publications not incorporated in the original database and previous updates. [Copyright &y& Elsevier]

We consider matrix structures in the quantum N-body problem that generalize the Faddeev components for resolvents, T-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of T-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators. [ABSTRACT FROM AUTHOR]

Abstract: We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-conquer (BD&C) algorithm as well as the block twisted factorization (BTF) method on the other hand. The BD&C algorithm does not require tridiagonalization of the original band matrix at all, and the current version of the BTF method tridiagonalizes the original band matrix only for computing the eigenvalues. Avoiding the tridiagonalization process sidesteps the cost of backtransformation of the eigenvectors. Beyond that, we discovered another disadvantage of the backtransformation process for band matrices: In several scenarios, a lot of gradual underflow is observed in the (optional) accumulation of the transformation matrix and in the (obligatory) backtransformation step. According to the IEEE 754 standard for floating-point arithmetic, this implies many operations with subnormal (denormalized) numbers, which causes severe slowdowns compared to the other algorithms without backtransformation of the eigenvectors. We illustrate that in these cases the performance of existing methods from Lapack and Plasma reaches a competitive level only if subnormal numbers are disabled (and thus the IEEE standard is violated). Overall, our performance studies illustrate that if the problem size is large enough relative to the bandwidth, BD&C tends to achieve the highest performance of all methods if the spectrum to be computed is clustered. For test problems with well separated eigenvalues, the BTF method tends to become the fastest algorithm with growing problem size. [Copyright &y& Elsevier]

Abstract: This paper is a sequel to “Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases” (). We present a new fraction-free algorithm for the computation of a diagonal form of a matrix over a certain non-commutative Euclidean domain over a computable field with the help of Gröbner bases. This algorithm is formulated in a general constructive framework of non-commutative Ore localizations of -algebras (OLGAs). We use the splitting of the computation of a normal form for matrices over Ore localizations into the diagonalization and the normalization processes. Both of them can be made fraction-free. For a given matrix over an OLGA , we provide a diagonalization algorithm to compute and with fraction-free entries such that holds and is diagonal. The fraction-free approach allows to obtain more information on the associated system of linear functional equations and its solutions, than the classical setup of an operator algebra with coefficients in rational functions. In particular, one can handle distributional solutions together with, say, meromorphic ones. We investigate Ore localizations of common operator algebras over and use them in the unimodularity analysis of transformation matrices . In turn, this allows to lift the isomorphism of modules over an OLGA Euclidean domain to a smaller polynomial subring of it. We discuss the relation of this lifting with the solutions of the original system of equations. Moreover, we prove some new results concerning normal forms of matrices over non-simple domains. Our implementation in the computer algebra system Singular:Plural follows the fraction-free strategy and shows impressive performance, compared with methods which directly use fractions. In particular, we experience a moderate swell of coefficients and obtain simple transformation matrices. Thus the method we propose is well suited for solving nontrivial practical problems. [Copyright &y& Elsevier]

A simplified calibration procedure using T-matrix concept is presented for two-port vector network analyzer (VNA) with three measurement channels. Compared with Short-Open-Load-Thru (SOLT) calibration method based on 10-term error model where 10 error terms must be solved and saved at each frequency, the proposed method need define fewer characteristic variables. Moreover, a length- unknown 50Ω line can be used instead of a random single-port standard, for example, substituting Load standard with 50Ω line in SOLT calibration procedure. Via the simplified calibration procedure, the scattering parameters of a two-port device under test (DUT) can be finally obtained. Experimental verification is carried out, and good agreement is observed. [ABSTRACT FROM AUTHOR]

In this paper, we study the teleportation of arbitrary N-qudit state with the tensor representation. The necessary and sufficient condition for realizing a successful or perfect teleportation is obtained, as will be shown, which is determined by the measurement matrix Tδ and the quantum channel parameter matrix X. The general expressions of the measurement matrix Tδ are written out and the quantum channel parameter matrix X are discussed. As an example, we show the details of three-ququart state teleportation. [ABSTRACT FROM AUTHOR]

The optical response of a particle composed of a dielectric core surrounded by a densely packed shell of small metal spheres is simulated with the superposition T-matrix method for realistic material parameters. In order to compute the electric and magnetic particle polarizabilities a single expansion T-matrix is derived from a particle centered T-matrix. Finally the permeability of a medium comprising such particles is found to deviate considerable from unity resulting in a noticeable optical response. [ABSTRACT FROM AUTHOR]

Abstract: In this study, a novel positioning model of a double-CCD cameras calibration system, with an Alternate-Eight-Matrix (AEM) Look-Up-Table (LUT), was proposed. Two CCD cameras were fixed on both sides of a large scale screen to redeem Field Of View (FOV) problems. The first to the fourth AEMLUT were used to compute the corresponding positions of intermediate blocks on the screen captured by the right side camera. In these AEMLUT for the right side camera, the coordinate mapping data of the target in a specific space were stored in two matrixes, while the gray level threshold values of different position were stored in the others. Similarly, the fifth to the eighth AEMLUT were used to compute the corresponding positions of intermediate blocks on the screen captured by the left side camera. Experimental results showed that the problems of dead angles and non-uniform light fields were solved. In addition, rapid and precision positioning results can be obtained by the proposed method. [Copyright &y& Elsevier]

We demonstrate behaviour of the momentum space screened Coulomb t-matrix, obtained by a numerical solution of the three-dimensional Lippmann--Schwinger equation. Examples are given for different types of screening. They prove that it is possible to obtain numerically a reliable threedimensional screened Coulomb t-matrix, what is important in view of its application in few-body calculations. [ABSTRACT FROM AUTHOR]

Abstract: The derivation of the Sh-matrices using the T-matrix method allows the shape-dependent parameters to be separated from size- and refractive-index-dependent parameters. This separation also allows for the surface integrals to be solved analytically for many particle morphologies. In this manuscript we provide analytical expressions for the Sh-matrices that contain the shape information for cube-like particles. Resulting analytical expression for the T-matrix elements can be found directly from these expressions. We verify the results by comparing the light-scattering obtained using the method of Sh-matrices with that using the discrete dipole approximation (DDA). [Copyright &y& Elsevier]

A scatterer is regarded as a one-port device, and an associated generalized transition matrix is defined uniquely to describe the relationships between the rotated tangential scattered field components and the rotated tangential incident field components on a specified reference surface. The reference surface can be moved to proper surfaces with regular shapes, or even be extended to include a group of scatterers with arbitrary shapes and different materials. Furthermore, scatterers connected with perfectly electric conducting (PEC) plates can also be handled with this one-port device model. Numerical results in two dimensions are provided to show that the generalized transition matrix is effective in analyzing large-scale scattering systems. [ABSTRACT FROM AUTHOR]

By exploiting the theory of ordinary differential equations together with certain properties of higher transcendental functions, a useful analytical expression for the integral transform of the Green's function for motion in Coulomb-Yamaguchi potential is derived via the r-space approach. This integral transform is applied to construct an analytical expression for off-shell Jost solution in its 'maximal reduced form' involving confluent and Gaussian hypergeometric functions. Corresponding Jost functions automatically follow from this solution. Finally, as another application of the off-shell Jost solution, the off-shell T-matrix is calculated by using a modified relation between off-shell physical wave function and T-matrix which does not involve the potential explicitly, thereby avoiding certain difficult integrals, and expressed it in terms of rational functions and simple hypergeometric functions which is in exact agreement with the results given previously by other authors. [ABSTRACT FROM AUTHOR]

Abstract: We use the Sh-matrix formalism that contains the shape-dependent parameters of the T-matrix to derive an analytical solution for the light scattering from a finite cylinder containing a spherical cavity. The integral expressions for the Sh-matrix elements are simpler than those of the T-matrix elements and the case of a sphere embedded in a finite cylinder these integrals can be solved analytically. [Copyright &y& Elsevier]

We propose a generalized T-matrix definition that facilitates the conversion between the S-parameter and T-parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of en- trance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare T-matrix and do not have the same number of entrance and exit ports. Through careful selection of the T-matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the S-parameter and T-parameter for multiport networks. This symmetry extension allows a practical means to cascade and deembed such networks. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper we proposed a decompositioning method to compute scattering by aggregated cylindrical fibres using a multiple scattering T-matrix approach. In this paper we extend this approach to scatterers lacking rotational symmetry. To investigate the capability of this method a square prism and a cube are decomposed into a number of subscatterers and scattering of the original particle shape is computed using multiple scattering. The results are validated using discrete dipole approximation (DDA). [Copyright &y& Elsevier]

A new method of analysis of an arbitrary configuration of elliptical cylinders is presented. The treatment of such a problem is based on a combination of the cylindrical and elliptical coordinates systems. This approach is applied to the formulation of the scattered field at the surface of equivalent cylinder surrounding dielectric or metal elliptical object. To analyse the arbitrary set of elliptical cylinders, the iterative scattering procedure is used. A good agreement of the proposed method with the commercial FD simulator is achieved. [ABSTRACT FROM AUTHOR]

Abstract: Light scattering is a useful tool in optical particle characterization. It can help to understand the nature of single particles as well as systems or clusters of particles; information about particle sizes, materials or shapes can be gathered. In this paper we investigate the application of light scattering studies to the analysis of a sintering process of silver nanoparticles. For this we first simulate the scattering behavior of two silver spheres. Then we assume sintering between them, leading to a single particle with a concave, peanut-like shape. We approximate this shape by a Cassini-oval. For light scattering studies we use an advanced T-matrix algorithm, the Nullfield Method with Discrete Sources. This method proved to be capable of simulating light scattering by concave particles. To make sure that the calculated data are correct we do comparative simulations using the Discrete Sources Method. [Copyright &y& Elsevier]

The resonance and radiation characteristics of a spherical microstrip with its circular metallic patch located inside a coating, possessing an arbitrary number of layers, are investigated. The developed methodology combines the Legendre transform with a T-matrix method. The appropriate basis functions for the surface current on the patch are chosen according to the cavity model. The complex resonant frequencies are the singular points of a homogeneous linear system, resulting by following a Galerkin's technique. The numerical results of this article propose novel multi-layered spherical microstrip configurations. More precisely, a new type of excitation that concerns an amplifying layer located between core and patch is proposed. The control mechanism of the amplifying capability via the layer's thickness and dielectric constant is reported. Moreover, the behavior of a microstrip with two airgaps that are surrounded by a zero-index material is analyzed. Finally, a coating's continuous distribution, following a “shifted” Luneburg law, is treated by a step approximation of the radial function of its dielectric constant, and the achieved high quality factor of such a microstrip is discussed. [ABSTRACT FROM AUTHOR]

An analysis for axisymmetric steady-state response of an arbitrarily thick, isotropic, and functionally graded circular cylindrical shell of infinite length subjected to an axially moving normal ring load is presented. The mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell according to a power law distribution. The problem solution is derived by using Fourier transformation with respect to a moving reference frame in conjunction with the T-matrix solution technique that involves a system global transfer matrix, formed by applying continuity of the displacement and stress components at the interfaces of neighbouring layers. The analytical results are illustrated with numerical examples in which a metal-ceramic functionally graded material (FGM) pipe, composed of aluminium and zirconia, is subjected to a normal ring load travelling along the tube at constant speed. Four types of pipes are configured, i.e. a ceramic-rich composition with the ceramic at the inner (or outer) interface, and also a metal-rich composition with the metal at the inner (or outer) interface of the pipe. The presented model is used to determine the critical velocity of the moving load as a function of shell thickness for the selected material compositional gradient profiles. The effects of load velocity and shell thickness on the basic dynamic field quantities such as the mid-plane radial displacement and hoop stress amplitude along the pipe axis are also evaluated and discussed. Moreover, the response curves for the FGM shells are compared with those of equivalent bi-laminate shells containing comparable total volume fractions of constituent materials. Limiting cases are considered and good agreements with the solutions available in the literature are obtained. [ABSTRACT FROM AUTHOR]

An inverse eigenvalue problem concerns the reconstruction of a matrix from prescribed spectral data. The spectral data involved may consists of the complete or only partial information of eigenvalues or eigenvectors. The objective of an inverse eigenvalue problem is to construct a matrix from a certain specific structures as well as its given spectral properties. On the study of inverse problems for Jacobi matrices, a series of conclusions have been made. In this paper, we will construct a T-matrix and a Jacobi matrix Dora its mixed type eigenpairs. In fact, it is shown that for a given positive vector x = (xn, ..., xn)t and a real positive number, lambda; there exists a unique T-matrix and a unique Jacobi matrix which they are related to each other. This kind of problem are of great value for many applications, including control theory, vibration theory and structural design. [ABSTRACT FROM AUTHOR]

The viscoelastic properties of phase‐separated poly(methyl methacrylate) (PMMA) and poly(styrene–co‐maleic anhydride) (SMA) blend systems have been investigated. It is shown that the samples of initial off‐symmetric and symmetric compositions show different characteristic viscoelastic properties, which are the reflections of different internal morphologies. Except for the well‐known characteristic deviations of the storage modulus at low frequencies, other rheological functions such as weighted relaxation spectrum, van Gurp–Palmen plots, and Cole–Cole plots also show significantly different shapes corresponding to droplet‐matrix and co‐continuous morphology. Based on these findings we propose that such characteristic fingerprints can be used for inferring the internal structure. [ABSTRACT FROM AUTHOR]

A two-channel problem is considered within a method based on first-order differential equations that are equivalent to the corresponding Schrödinger equation but more convenient for dealing with resonant phenomena. Using these equations, it is possible to calculate directly the Jost matrix for practically any complex value of the energy. The spectral points (bound and resonant states) can therefore be located in a rigorous way, namely, as zeros of the Jost matrix determinant. When calculating the Jost matrix, the differential equations are solved and thus, at the same time, the wave function is obtained with the correct asymptotic behavior analytically embedded in the solution. The method offers a very accurate way of calculating not only total widths of resonances but their partial widths as well. For each pole of the S-matrix, its residue can be calculated rather accurately, which makes it possible to obtain the Mittag–Leffler-type expansion of the S-matrix as a sum of the singular terms (representing the resonances) and the background term (contour integral). As an example, the two-channel model by Noro and Taylor is considered. It is demonstrated how the contributions of individual resonance poles to the scattering cross section can be analyzed using the Mittag–Leffler expansion and the Argand plot technique. This example shows that even poles situated far away from the physical real axis may make significant contributions to the cross section. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [ABSTRACT FROM AUTHOR]

A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688–2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721–734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O(N log N) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N∼102–104 for different wave numbers are presented. © 2005 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Abstract: Two modifications of the T-matrix method developed earlier for layered scatterers are extended by a procedure of analytical averaging of cross-sections for randomly oriented particles. One of the approaches uses spheroidal coordinates and field expansions in terms of the spheroidal wave functions and is practically equivalent to the separation of variables method formulated for spheroids. The applicability of the suggested approaches is discussed, and some numerical results are presented. [Copyright &y& Elsevier]

Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-α-particle model interacting via the deep αα potential by Buck, Friedrich, and Wheatley is investigated. [ABSTRACT FROM AUTHOR]

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is an extension of the tree-metric theorem to more general dissimilarity maps. In particular, we show that a tree with n leaves is reconstructible from the weights of the m-leaf subtrees provided that n ≥ 2m — 1. [Copyright &y& Elsevier]

We show that the Ocneanu algebra of quantum symmetries, for an ADE diagram (or for higher Coxeter–Dynkin systems, like the Di Francesco–Zuber system) can be, in most cases, deduced from the structure of the modular T matrix in the A series. We recover in this way the (known) quantum symmetries of su(2) diagrams and illustrate our method by studying those associated with the three genuine exceptional diagrams of type su(3), namely, E[sub 5], E[sub 9], and E[sub 21]. This also provides the shortest way to the determination of twisted partition functions in boundary conformal field theory with defect lines. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The development of algorithms and methods for modelling flowsheets in the field of granular materials has a number of challenges. The difficulties are mainly related to the inhomogeneity of solid materials, requiring a description of granular materials using distributed parameters. To overcome some of these problems, an approach with transformation matrices can be used. This allows one to quantitatively describe the material transitions between different classes in a multidimensional distributed set of parameters, making it possible to properly handle dependent distributions. This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes. The finite volume method for spatial discretization and the second-order Runge–Kutta method were used to obtain the complete discretized form of the PBE and to calculate the transformation matrices. The proposed method was implemented in the flowsheet modelling framework Dyssol to demonstrate and prove its applicability. Hence, it was revealed that this new approach allows the modelling of complex processes involving materials described by several interconnected distributed parameters, correctly taking into consideration their interdependency. [ABSTRACT FROM AUTHOR]

A T-rnatrix used for image scrambling is proposed and its periodicity is proved. The T-matrix has a simple conformation and a period twice as long as the Arnold matrix. It can be applied to image encryption and pre-processing in image processing such as image watermarking algorithms. Two examples of applications are given. [ABSTRACT FROM AUTHOR]

A key integral in the derivation of the size-dependent Maxwell–Garnett (MG) formula presented in the subject paper is not only nonconvergent, but also unnecessary. The correct derivation of the MG formula, based on the so-called Fikioris approach, has been available for several years. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 228–229, 2000. [ABSTRACT FROM AUTHOR]

Presents reply to comments on the article "Comparison of Long-Wavelength T-Matrix Multiple-Scattering Theory and Size-Dependent Maxwell -- Garnett Formula."