Modifying the matrix

This experiment shows how modifying the matrix of the solution containing the analyte can dramatically improve the shape of the titration curve. 

Finally, another alternative to continuum regression has been put forward by Wise and de Jong [18]. Their continuum power-PLS (CP-PLS) method modifies the matrix X = USV into X " = i.e. the singular values are raised to a... 

It is possible to modify the matrix hydrophilicity-lipophilicity balance (HLB) by using different alkyl-modified trialkoxysilanes as co-reagents with tetraethylorthosilicate (TEOS), to greatly alter (reduce) the release rate of heparin, as then water access to the entrapped drug is considerably reduced (Figure 2.10).4... 

The results of extracting these herbicides from celite versus soil, display a marked difference (as seen by comparing Table VII to Table VIII). The only difference between the extraction from celite and the extraction from soil was the matrix itself, all other conditions were identical. This raises the question is the water modifying the solvent or modifying the matrix ... 

A model for sorption and transport of gases in polymers has to specifically account for the fact that the presence of sorbed gases in the polymer modifies the matrix (7, 9). In developing the matrix model we are guided by the physical evidence relating to the mechanism of sorption and transport. The matrix model is consistent with the following observations and assumptions ... 

S denotes a summation over discrete levels and integration over the continuum. In this general discussion, we omit the contribution from the exchange process (Fig. 9 f) which will only modify the matrix elements in Eq. (12), and we also omit the ground-state... 

There are alternative ways of modifying the matrix to remove the interference. Organic compounds have been shown to be effective. Regan and Warren [41] studied potential interferences on lead determinations in water. 100 mg l-1 of calcium, magnesium, strontium and barium were added to lead solutions in hydrochloric acid and nitric acid. The most severe interferences... 

There are many review articles concerning application of USE in food technology [57] and for isolation of bioactive substances from herbs and other plant materials [58], as well as leaching of heavy metals from environmental and industrial samples [59]. Application of ultrasound during sequential extraction of trace elements significantly shortens the whole procedure however, for satisfactory efficiency it is necessary to increase the temperature and modify the matrix. 

On the other hand, if the composition of the matrix varies or the content of the clement increases to the point of modifying the matrix, the law of proportionality no longer holds and corrections must be calculated taking into account these matrix effects. 

In the program it is only necessary to modify the matrix elements of the one-electron part of tire Hamiltonian h j by adding the dipole moment integrals ... 

Let us try to modify the matrix-vector multiplication algorithm from section 6.4.1 to improve the scalability. The poor scalability was a result of the relatively large communication overhead incurred by using a row distribution for the matrix A. When A is distributed by rows, all elements of the b or c vector must visit (or be stored by) each process during the computation if b and c are replicated, no data exchange is required for b, but an all-to-all broadcast is required to replicate c at the end of the computation if both vectors are distributed, no communication is required for c but all elements of b must visit all processes during the execution. 

Usually it is not opportune to calculate the Jacobian J at each iteration (particularly for large-dimension problems). Rather it should be done only when there are convergence problems in the system solution. When J is modified, the matrix G must also be updated and refactorized. 

The absorption of moisture predominantly modifies the matrix-dependent properties of a composite and this tends to reduce the tempera-... 

In addition, each object examined in this study had only two orientations 0° and 180°. The matrix representation of the rotated object (180° counterclockwise rotation) was obtained by simply modifying the matrix of the original object shown in the above-mentioned equation. Then the matrix of the rotated object... 

In contrast to thermal treatments, chemical treatments make available a wider range of transformations and reaction conditions which would modify the matrix. These chemical modifications can be targeted at the functional monomer (Sec. III.A) or the crosslinker (Sec. III.B). 

If efficient active sites shall be created by stabilizing the molecular species at the surface of a well-defined phase, as in the case of V0x/Ti02 - anatase catalysts, the better activity in NO SCR was achieved by cocondensation of the dopant alkoxide with the surface groups of preformed colloidal particles of the matrix precursor, followed by gelation [76]. A similar approach of modifying the matrix precursor sol with dopant molecules yielded well-dispersed tantalum species at the silica surface, efficient in selective oxidation of pyrimidine thioether [77]. 

A Tc-electron model is necessarily oversimplified because, among other reasons, it lies upon the so-called a — n separation. This means that the n electrons are described by an effective model Hamiltonian as discussed in the previous sections while the effect of the a electrons (a core) is taken into account only by modifying the matrix elements of the effective Hamiltonian for the n electrons. Another drastic simplification is the first-neighbor approximation discussed also in the previous sections. These approximations may considerably limit the power of the... 

When a new formation is penetrated, the initial pressure will always be equal to the reservoir pore pressure. However, in this book and in the code, we will leave this input completely general, if only for code flexibility and the possibility that the program will be used in special experimental situations. Once the pressure field in space is obtained for a particular time step, it must be copied into the pressure array for the earlier pressure before pressures can be recursively advanced and integrated in time. The bookkeeping of an earlier time pressure array means that an additional Fortran dimension statement, plus more allocated memory, will be required. Aside from new input statements required for fluid compressibilities, we will need to modify the matrix coefficients B and W as required by Equations 20-23 and 20-37. That is, the -2 of Equation 20-37 is to be replaced by the term - 2 - c )pc(Ax)2/(kAt) of Equation 20-23, while the... 

The adhesion between the fibers and matrix can be improved by either modifying the surface of the fibers to make them more compatible with the matrix, or by modifying the matrix with a coupling agent that adheres well to both the fibers and the matrix. The addition of a sufficient amount of Na2SOj to NaOH can assist... 

In this work. Zirconium based UHTCs were applied to modify the matrix of Cp/SiC composites and fabricate ultra-high-temperature coatings for C/SiC composites. The properties and microstructures were studied as well. 

An alternative approach to improving upon GRT-thermoplastic composite properties is to add materials that will enhance the properties of the matrix, and thus the overall composite. Ideally the added modifier would result in a S5mer-gistic effect the improvement in composite properties being greater than those of the matrix alone. A potentially even more attractive route is the use of an additive that not only modifies the matrix properties but also increases interaction (adhesion) between the matrix and the GRT particles. 

An alternative approach, to be used either with E or AR glass fibres, was to modify the matrix in order to improve the resistance of the fibres, either by lowering the alkalinity level (e.g. silica fume additions high alumina cement) or by sealing the matrix (e.g. polymer modified cements). The long-term performance of the GRC composite is still the major criterion by which its quality is assessed, and considerable effort is continuously being made to improve the service life of such materials. These topics will be discussed in detail in Sections 8.4-8.6. The production methods and the properties of the composites will be dealt with in Section 8.3. 

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