Character weight matrix

Character-state weight matrices have usually been estimated more or less by eye, but they can also be derived from a rate matrix. For example, if it is presumed that each of the two transitions occurs at double the frequency of each transversion, a weight matrix can simply specify, for example, that the cost of A-G is 1 and the cost of A-T is 2 (Fig. 14.5). (The parsimony method dictates that the diagonal elements of the matrix, or the cost of having the same base in different sequences, be zero. This proves to be a shortcoming of parsimony this will be discussed further below.) In the subsequent tree-building step, this set of assumptions will minimize the overall number of transversions and tend to cluster sequences differing mainly by transitions. 

The different temperature dependences of Ti in weak and strong magnetic fields are undoubtedly associated with the effect of the phenolic adsorbent matrix, since the weight fractions of water in the foam bulk are equal. The adsorbent effect is also revealed by the two-component character of relaxation curves (Fig. 13). Thus, the short component has a relaxation time of Ti = 0.15 — 0.20 s and is practically independent of temperature. The authors explain its existence by the presence of water in 20-100 A large cells which is strongly bonded to the matrix ... 

One of the important issues addressed in our simulations is the character of clusters under study. Are these clusters solid or liquid rmder experimental conditions If they arc liquid, then the distribution wc observe in the pick-up and consequently in the photodissociation simulations corresponds to a statistical distribution at a. given temperature. If, however, the cluster is solid then both in the simulations and in the cxj)eriment we observe a quasi-stationary state with a very long lifetime rather than an equilibrium thermodynamical state. This question can be resolved by means of the instantaneous normal modes (INM) density of states (DOS) spectrum. To calculate INM DOS wc construct the Hessian matrix in a mass-weighted atomic Cartesian coordinate basis of N atoms with /r=. r, y, z. The 3N eigenvectors in the form Ci -.Cjj,Cj-,C2, C2/,C2-,.c.vj.,ca/j,c.v de-... 

We carried out non-spin-polarized molecular orbital calculations using a DV-Xa code called SCAT (7). In the DV-Xa method, matrix elements in the secular equation are derived from the weighted sum of integrand values at sampling points. Hence numerical atomic orbitals can be used as basis sets. These atomic orbitals were generated on each iteration in atomic-like potentials derived from spherically averaging the molecular potential around each nucleus (7). The numerical wave functions thus obtained can be used efficiently for the molecular orbitals and have a practical character making them suitable for... 

The term bitumen (also, on occasion, referred to as native asphalt and extra heavy oil) includes a wide variety of reddish-brown to black materials of semisoUd, viscous to brittle character that can exist in nature with no mineral impurity or with mineral matter contents that exceed 50% by weight. Bitumen is frequently found filling pores and crevices of sandstone, limestone, or argillaceous sediments, in which case the organic and associated mineral matrix is known as rock asphalt. 

In what follows, bold characters are used for denoting matrices the matrix of the absorbances of the sample will be denoted by A, the matrix of the absorbances of the standard solutions by As, the matrix of the concentrations of chemical components in the analysed sample and in the standard solutions by C and Cs, respectively the matrix of the molar absorptivities by E and the matrix of the contribution weight of the standard solutions, generating the absorbance of the sample, by P. In order to comprehend more easily the matrix formalism, the symbol of matrices is followed (between right brackets) by the specification of the number of rows and columns in the respective matrix. Therefore, matrix As, made up of A rows and N columns, is denoted as follows As,[A,N]. Relations (1) and (2) are equivalent to matrix expressions (3) and (4). 

Montaudo, G., Montaudo, M. S., Puglisi, C., and Samperi, F. Molecular weight determination and structural analysis in polydisperse polymers by hyphenated gel permeation chromatography matrix-assisted laser desorption ionization— Time of flight mass spectrometry. Int. J. Polym. Anal. Charact. 3, 177, 1997. 

Examples of stab resistant body armour are often quite different in constractional character. For example, some comprise a matrix of overlapping metal or composite plates located between fabric layers (based on para-aramid or UHMW polyethylene), others are based on more flexible aramid woven textiles which have been coated with silicon carbide particles to blunt the knife point and others incorporate fine tungsten wire within a knitted fabric matrix. Copying the ancient chain mail concept, similar fine mail constructed from stainless steel or titanium wire may be included as a layer. Obviously the overall weight and thickness of the resulting armour is of crucial importance for the comfort of the wearer but this will be determined largely by the magnitude of the threat. 

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