Factor contributions, matrix

Ramirez, J. Fenselau, C. Factors contributing to peak broadening and mass accuracy in the characterization of intact spores using matrix-assisted laser desorption/ionization coupled with time-of-flight mass spectrometry. J. Mass Spectrom. 2001,36, 929-936. 

This dilemma could be overcome by the hypercycle model hypercycles are in fact not theoretical concepts, but can be observed (in a simple form) in today s organisms, where an RNA virus transfers the information for an enzyme in the host cell, which is able to carry out the preferred synthesis of new virus RNA. This RNA synthesis is supported by host factors, and an RNA minus-strand is formed. The following RNA replication affords a plus-strand. The process corresponds to a double feedback loop and involves the enzyme coded by the RNA matrix and the information present in the matrix in the form of a nucleotide sequence. Both factors contribute to the replication of the matrix, so that there is second-order autocatalysis (Eigen et al., 1982). 

This notation is more convenient, since in (j,.IMIsy) the states of the pair i and j are specified while the subscripts in specify the location of the element in the /th row and Mi column. The symbol (s,IMIS , ) is the factor contributed to the GPF by the nn pair i and / + 1, being in states s,. and s- j, respectively. This matrix element is obtained by multiplying the matrix M by a row vector on the left and by a column vector on the right. Since (s,l and b j) are unit vectors, this multiplication produces the element of the matrix that corresponds to the state of the nn pair i and I + 1. 

Some of the variation of the responses about their mean is caused by variation of the factors. The effect of the factors as they appear in the model can be measured by the differences between the predicted responses (y,) and the mean response (y,). For this purpose, it is convenient to define a matrix of factor contributions, F. 

Other strong advantages of PCR over other methods of calibration are that the spectra of the analytes have not to be known, the number of compounds contributing to the signal have not to be known on the beforehand, and the kind and concentration of the interferents should not be known. If interferents are present, e.g. NI, then the principal components analysis of the matrix, D, will reveal that there are NC = NA -I- NI significant eigenvectors. As a consequence the dimension of the factor score matrix A becomes (NS x NC). Although there are NC components present in the samples, one can suffice to relate the concentrations of the NA analytes to the factor score matrix by C = A B and therefore, it is not necessary to know the concentrations of the interferents. 

Considerable effort has been spent to explain the effect of reinforcement of elastomers by active fillers. Apparently, several factors contribute to the property improvements for filled elastomers such as, e.g., elastomer-filler and filler-filler interactions, aggregation of filler particles, network structure composed of different types of junctions, an increase of the intrinsic chain deformation in the elastomer matrix compared with that of macroscopic strain and some others factors [39-44]. The author does not pretend to provide a comprehensive explanation of the effect of reinforcement. One way of looking at the reinforcement phenomenon is given below. An attempt is made to find qualitative relations between some mechanical properties of filled PDMS on the one hand and properties of the host matrix, i.e., chain dynamics in the adsorption layer and network structure in the elastomer phase outside the adsorption layer, on the other hand. The influence of filler-filler interactions is also of importance for the improvement of mechanical properties of silicon rubbers (especially at low deformation), but is not included in the present paper. 

Each term of equations (6)-(8) is factorized into parts that can be related to the electronic and vibrational wavefrmctions and excitation frequency. The electronic contribution (matrix elements of /x° and /u. ), weighted with the differential energy denominators — vo + Tu). determines the total enhancement of all the normal vibrations for a given... 

In summary, the quantity of soft coke seems to increase with the surface area in the small-pore range (zeolite and matrix), while the stripping rate is determined inversely by the accessibility of the catalyst sites and increases with larger and nonconstrained pore systems. We can conclude that for delta coke limited RFCC catalyst selection it will be essential to assess the diferences in all the factors contributing to commercial delta coke. 

Many factors contribute to ventricular remodehng, including neurohormonal factors (e.g., activation of the renin-angiotensin-aldosterone and sympathetic nervous systems), hemodynamic factors, mechanical factors, and changes in gene expression. This process affects both cardiomyocytes (cardiomyocyte hypertrophy, loss of cardiomyocytes) and the extracellular matrix (increased interstitial fibrosis), thereby promoting both systohc and diastohc dysfunction. ... 

The diffusion equations just used are simplifications of more complex processes. The F factor was empirically derived and must take into account those matrix pore geometric factors contributing to decreases in diffusion rates. Such factors may include pore tortuosity, dead-end pores, and pore constrictions. Initial modeling studies suggest that constrictions, in particular, have large effects in retarding release (8,9). 

The breakthrough volxame trends for many sorbate types on the porous polymeric sorbents indicate a limited trapping capacity in the supercritical fluid CO2 above 200 atmospheres. Fractionation and selective retention on these sorbents seems only possible below this specified pressure limit for the odoriferous solutes examined in this study. Adsorbent surface area appears to be the most significant factor contributing to the retention of sorbates on these sorbents as well as activated carbon. For certain synthetic adsorbents (Tenax, XAD-2) employed in this study, pressure-induced morphological changes in the polymer matrix lead to an increase in the sorption capacity, and hence to an increase in breakthrough volumes at intermediate pressures. 

The chemical properties of a protein fimctional group are strongly influenced by its local environment, such as polarity of the microenvironment, hydrogen bonding effect, field/electrostatic effect, as well as steric and matrix effects. These factors contribute to the selectivity and specificity of chemical modifications. Several strategies can be adapted to enhance the selectivity and specificity ... 

The distribution of the various factors in each SWM sample was obtained by squaring individual molecular marker compoimds of the factor loading matrix, where the sum of the squared loadings for all factors of a particular waste sample equals 1.00 (communality which is the proportion of the total variance in a particular sample that is e3q>lained by Aose factors). The individual squared loading of one factor represents the fraction that factor contributes to the solid waste sample (if a sample has a factor 1 loading of 0.4 then (0.4) =0.16, or 16% of the sample is from factor 1). 

Although the sample, in most instances, constitutes a very small portion of the overall volume in the capillary once injected (< 1%), the matrix of the sample has profound effects in CE. This is due to two main factors contribution of the sample to the total current conductance and also due to its interaction with the capillary walls (especially proteins). On the basis of how the sample is prepared and how the separation buffer is selected, sample matrix effects can be either favorable or detrimental to the analysis [5]. Peak shape, separation, quantification, and reproducibility are affected greatly by sample matrix. 

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