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Matrix Representation (matrix + representation)
Selected AbstractsMatrix Representation of Polymer Chain Size Distributions, 3 , Case Studies for Linear Polymerization Mechanisms at Transient ConditionsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 4-5 2008Heloísa L. Sanches Abstract The mass balance equations used to describe different polymerization systems are represented and analyzed with the help of a general matrix framework previously developed. Some of its properties were presented in previous works and are illustrated here in three examples. The first example regards the dynamics of a copolymerization reactor. It is shown that terminal and penultimate models may predict qualitatively different responses in batch reactions. The second example also regards the dynamics of copolymerization reactions. It is shown how manipulation of initial conditions and monomer feed rates can be used to keep copolymer composition constant throughout the batch. The third example concerns the existence of oscillating chain size distributions when there are multiple monomer insertion steps. [source] Matrix Representation of Polymer Chain Size Distributions, 2,MACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2007Fundamental Analysis of Linear Polymerization Mechanisms at Transient Conditions Abstract Analysis of the mass balance equations that describe a reaction system may be useful to provide information about its dynamics, such as the restricted set of compositions that can be achieved from a given set of initial compositions and the effect of feeding reactants to the reaction environment along the reaction course. Since these results may be important for the formulation of reaction policies, this work presents the properties of a matrix polymerization model previously developed and extended to describe transient conditions. This model is based on the definitions of two matrices: the consumption matrix (A,,,Kt), which contains information about chemical transformations among the many active polymer species in the system, and the propagation matrix Kp, which contains information about chain growth. It is shown that the set of mass balance equations that describes the dynamics of active chemical species in polymerization reactions has a stable and unique solution, which is bounded if feed rates are also bounded. It is also shown that the set of compositions that may be reached through manipulation of the feed rates is restricted and may not include all possible chemical compositions. Finally, it is shown that the obtained molecular weight distributions are special multiple time convolutions of the initiation rates. [source] A phylogenetic supertree of the bats (Mammalia: Chiroptera)BIOLOGICAL REVIEWS, Issue 2 2002KATE E. JONES ABSTRACT We present the first estimate of the phylogenetic relationships among all 916 extant and nine recently extinct species of bats (Mammalia: Chiroptera), a group that accounts for almost one-quarter of extant mammalian diversity. This phylogeny was derived by combining 105 estimates of bat phylogenetic relationships published since 1970 using the supertree construction technique of Matrix Representation with Parsimony (MRP). Despite the explosive growth in the number of phylogenetic studies of bats since 1990, phylogenetic relationships in the order have been studied non-randomly. For example, over one-third of all bat systematic studies to date have focused on relationships within Phyllostomidae, whereas relationships within clades such as Kerivoulinae and Murinae have never been studied using cladistic methods. Resolution in the supertree similarly differs among clades: overall resolution is poor (46.4% of a fully bifurcating solution) but reaches 100% in some groups (e.g. relationships within Mormoopidae). The supertree analysis does not support a recent proposal that Microchiroptera is paraphyletic with respect to Megachiroptera, as the majority of source topologies support microbat monophyly. Although it is not a substitute for comprehensive phylogenetic analyses of primary molecular and morphological data, the bat supertree provides a useful tool for future phylogenetic comparative and macroevolutionary studies. Additionally, it identifies clades that have been little studied, highlights groups within which relationships are controversial, and like all phylogenetic studies, provides preliminary hypotheses that can form starting points for future phylogenetic studies of bats. [source] The correlation contracted Schrödinger equation: An accurate solution of the G -particle-hole hypervirialINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 14 2009D. R. Alcoba Abstract The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd-order correlation transition matrix elements into the 2-body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti-Hermitian part of the CCSE. A comparative analysis of the GHV and the anti-Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg-like unitary transformation to the G -particle-hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. The correlation energies obtained are within 98.80,100.09% of the full-configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Normal form representation of control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002Daizhan Cheng Abstract This paper is to investigate the normal form representation of control systems. First, as numerical tools we develop an algorithm for normal form expression and the matrix representation of the Lie derivative of a linear vector field over homogeneous vector fields. The concept of normal form is modified. Necessary and sufficient conditions for a linear transformation to maintain the Brunowsky canonical form are obtained. It is then shown that the shift term can always be linearized up to any degree. Based on this fact, linearization procedure is proposed and the related algorithms are presented. Least square linear approximations are proposed for non-linearizable systems. Finally, the method is applied to the ball and beam example. The efforts are focused on the numerical and computer realization of linearization process. Copyright © 2002 John Wiley & Sons, Ltd. [source] A species-level phylogenetic supertree of marsupialsJOURNAL OF ZOOLOGY, Issue 1 2004Marcel Cardillo Abstract Comparative studies require information on phylogenetic relationships, but complete species-level phylogenetic trees of large clades are difficult to produce. One solution is to combine algorithmically many small trees into a single, larger supertree. Here we present a virtually complete, species-level phylogeny of the marsupials (Mammalia: Metatheria), built by combining 158 phylogenetic estimates published since 1980, using matrix representation with parsimony. The supertree is well resolved overall (73.7%), although resolution varies across the tree, indicating variation both in the amount of phylogenetic information available for different taxa, and the degree of conflict among phylogenetic estimates. In particular, the supertree shows poor resolution within the American marsupial taxa, reflecting a relative lack of systematic effort compared to the Australasian taxa. There are also important differences in supertrees based on source phylogenies published before 1995 and those published more recently. The supertree can be viewed as a meta-analysis of marsupial phylogenetic studies, and should be useful as a framework for phylogenetically explicit comparative studies of marsupial evolution and ecology. [source] Analytical model for double split ring resonators with arbitrary ring widthMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2008Vitaliy Zhurbenko Abstract For the first time, the analytical model for a double split ring resonator with unequal width rings is developed. The proposed models for the resonators with equal and unequal widths are based on an impedance matrix representation and provide the prediction of performance in a wide frequency range. A phase compensation is implemented to adjust for the difference in length of the two rings, resulting in an accurate calculation of the resonant frequencies. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 511,515, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23104 [source] Blocking Two-level Factorial ExperimentsQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 3 2007Murat Kulahci Abstract Blocking is commonly used in experimental design to eliminate unwanted variation by creating more homogeneous conditions for experimental treatments within each block. While it has been a standard practice in experimental design, blocking fractional factorials still presents many challenges due to differences between treatment and blocking variables. Lately, new design criteria such as the total number of clear effects and fractional resolution have been proposed to design blocked two-level fractional factorial experiments. This article presents a flexible matrix representation for two-level fractional factorials that will allow experimenters and software developers to block such experiments based on any design criterion that is suitable with the experimental conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Geometrical and algebraic approach to central molecular chirality: A chirality index and an Aufbau description of tetrahedral moleculesCHIRALITY, Issue 7 2006Salvatore Capozziello Abstract On the basis of empirical Fischer projections, we develop an algebraic approach to the central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral tetrahedron can generate in S and R absolute configurations. They constitute a matrix representation of the O(4) orthogonal group. According to this representation, given a molecule with n chiral centres, it is possible to define an "index of chirality , , {n, p}", where n is the number of stereogenic centres of the molecule and p the number of permutations observed under rotations and superimpositions of the tetrahedral molecule to its mirror image. The chirality index not only assigns the global chirality of a given tetrahedral chain, but indicates also a way to predict the same property for new compounds, which can be built up consistently. Chirality 18:462,468, 2006. © 2006 Wiley-Liss, Inc. [source] Algebraic structure of central molecular chirality starting from Fischer projectionsCHIRALITY, Issue 5 2003Salvatore Capozziello Abstract The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and inversions is identified. The result can be generalized to chains of connected tetrahedrons. Chirality 15:466,471, 2003. © 2003 Wiley-Liss, Inc. [source] | ||||||||||||||||