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This paper deals with the analysis of the orthogonality of a monic polynomial sequencedefined as a linear combination of a sequence of monic orthogonal polynomialswithwherefor. Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials. We obtain the connection between the Jacobi matrices associated withand, respectively, by using an LU factorization. Some special cases of the above type relation are analysed. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of similarity matrix, which has been used to define similarity between nodes of two graphs, to the case of colored graphs, where the coloring is either on the nodes or on the edges of both graphs. The proposed method tries to find the optimal matching between the nodes or edges of both graphs but only performs the comparison when their colors are the same. The proposed cost function nevertheless uses the connectivity between all nodes and edges of both graphs. We then also show how to extend this to the notion of low rank similarity matrix, by defining it as a constrained optimization problem. [ABSTRACT FROM AUTHOR]

After a quick review of the most used numerical indicators for evaluating research, we present an integrated model for ranking scientific publications together with authors and journals. Our model relies on certain adjacentcy matrices obtained from the relationship between papers, authors, and journals. These matrices are first normalized to obtain stochastic matrices and then are combined together using appropriate weights to form a suitable irreducible stochastic matrix whose dominant eigenvector provides the desired ranking. Our main contribution is a in-depth analysis of various strategies for choosing the weights, showing their probabilistic interpretation and showing how they affect the outcome of the ranking process. We also prove that, by solving an inverse eigenvector problem, we can determine a weighting strategy in which the relative importance of papers, authors, and journals is chosen by the final user of the ranking algorithm. The impact of the different weighting strategies is analyzed also by means of extensive experiments on large synthetic datasets. [ABSTRACT FROM AUTHOR]

In this study, the effect of heat treatment on barrier and functionality of polyolefin-coated papers was investigated. The aim was to find the optimal improvements on barrier without losing the applicability of the materials due to physical damages. The results of the study proved considerable improvement in barrier characteristics of the structures. Both water vapor and oxygen transmission rates of LDPE-coatings decreased linearly following the set-temperature until 200°C. At this point, the treatment caused a continuing decrease in oxygen transmission achieving 10 × lower transmission levels than the untreated structure, whereas moisture transport faced corresponding but lower increase. This was considered to be caused by the difference in diameter of the H2O and O2 molecules; the smaller water molecules are able to penetrate between spherulites, whose size increased due to higher treatment temperature followed by cooling. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of local asymptotic stability for a competitive Lotka–Volterra system with time-varying delays. By employing a linear matrix inequality (LMI) approach, we not only prove that the local asymptotic stability of the positive equilibrium for the Lotka–Volterra type competitive system will be preserved for suitable delays under a well known condition, but also obtain the maximal allowable length of delays by using Matlab’s Control Systems Toolbox to solve a feasible LMI. Compared with some known results, our estimate on the length of delays is less conservative. [Copyright &y& Elsevier]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In the first part an solver for a semiseparable matrix of semiseparability rank p is derived, and in a second part we derive an solver for a band matrix with bandwidth . Both solvers are constructed in a similar way: firstly a Yule–Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side. Finally, a combination of the above methods is presented to solve linear systems with semiseparable plus band coefficient matrices. The overall complexity of this solver is plus lower order terms. In the final section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods. [Copyright &y& Elsevier]

Abstract: Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input–output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles. [Copyright &y& Elsevier]

Abstract: This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions. [Copyright &y& Elsevier]

This paper focuses on the reliable fuzzy control design problem for fuzzy control systems with time delay. Based on linear matrix inequality (LMI) approach, a method for designing a reliable fuzzy controller is presented. The resulting fuzzy control systems are reliable in the sense that asymptotic stability is achieved not only when all control components are operating well, but also in the presence of some component failures. A reliable fuzzy control design scheme via state feedback is proposed in terms of LMIs. The result is extended to the case of observer-based reliable fuzzy control. Two illustrative examples are given to illustrate the validity of the proposed design procedures. [Copyright &y& Elsevier]

The present review paper examines the use of different types of polymeric matrix composites in hard tissue replacement applications. The review presents the actual state of the art in the fields of bioinert composites for permanent applications, biodegradable matrix composites for temporary applications and the emerging area of injectable composites. In all cases some recent developments are also discussed. The paper starts with an introduction to locate the reader. Bone–analogue composites are then extensively discussed. Several other systems based on an inert polymeric matrix are described, focusing on their proposed applications. A great emphasis is afterwards given to biodegradable matrix systems. The most widely used synthetic bioresorbable systems are analysed and compared with an example of natural origin degradable composites–starch based composites. Finally, composite systems that are non-processable by melt based routes and in many cases injectable are discussed in detail, including several recent developments on this emerging area of research. [Copyright &y& Elsevier]

We model the folding of ordinary paper via piecewise isometries R2→R3. The collection of crease lines and vertices in the unfolded paper is called the crease pattern. Our results generalize the previously known necessity conditions from the more restrictive case of folding paper flat (into R2); if the crease pattern is foldable, then the product (in a non-intuitive order) of the associated rotational matrices is the identity matrix. This condition holds locally in a multiple vertex crease pattern and can be adapted to a global condition. Sufficiency conditions are significantly harder, and are not known except in the two-dimensional single-vertex case. [Copyright &y& Elsevier]

In state-space systems, since the minimum statistical sensitivity structures obtained by the equivalent transformations are generally completely dense, they have defects and the numbers of parameters are very large. If this point can be improved, realizations with lower sensitivity and fewer parameters are obtained. This paper presents a synthesis of new minimum statistical sensitivity structures with fewer parameters as one such realization. First, to compare sensitivities of various realizations, assuming that only noninteger elements in the coefficient matrices contain small variations, the statistical sensitivity is defined. Since the sensitivity is invariant under the orthogonal transformations, using the symmetry of the coefficient matrices of the balanced realizations which are the members of the minimum statistical sensitivity structures, it is shown that a minimum statistical sensitivity structure can be realized with fewer parameters by defining an appropriate orthogonal transformation matrix. The number of parameters required in the proposed structure depends on the pole-zero configuration of the transfer function. Finally, various realizations are compared using numerical examples. As the parameters decrease, the insensitive elements increase. Therefore, the realization proposed in this paper has the lowest sensitivity. [ABSTRACT FROM AUTHOR]