Direction 461 - multiplication

The order of operations directs multiplication to be done next, left to right. The answer will be left in terms of it. 

Order of operations directs multiplication to be done next, left to right. 

Recent Achievements in Apparently Direct Multiple Electron Transfers... 

The word variation has a special definition in mathematics. When two numbers vary directly, it means that one of the numbers is a direct multiple of the other. The numbers 7 and 21 vary directly, because 21 is three times 7. When two numbers vary inversely, it means that one number is some multiple of the reciprocal of the other. 

Upon illumination, semiconductor particles become charged, allowing even for electrophoretic mobility under an applied electrical field When appropriately prepared, colloidal TiO2 can apparently accumulate charge to effect directly multiple quanta redox reactions The efficiency of such charge accumulation is surely related to doping level for the doping level can alter band positions and may improve the efficiency of photoinduced electron transfer. For example, the dispersal of FcjOa... 

Equation (2.31) is readily verified by explicitly performing the submatrix multiplications and comparing with the result obtained by direct multiplication of S and T this is left as an exercise for the reader. 

Some properties of direct multiplication (called also Kronecker or tensor multiplication) are given in Appendix A. 

Direct multiplication of matrices, which are subscripted with composite indices, is carried out in the same manner as that of doubly-subscripted matrices e.g. the direct product in equation (93a) can be expressed as ... 

Record calibration data with standard deviation in Data Table 19.2. The software for the instrument directs multiple passes/runs on each sample and reports standard deviations for the measurements calculated from replicate results. Obtain a hard copy of the results. Then record the sample data in Data Table 19.3. 

Pauling, L. (1985) Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals, Nature 317, 512. 

For a few layers, N small, direct multiplication is practical. For an extended multilayer, tricks from optics and solid-state physics come in handy. 

Assigned signals ( C chemical shift and C — H direct multiplicity) and/or a list of coupled signals from the 2D NMR spectra. 

Either the current SV or the SS atoms forming the extension bond are quaternary carbon atoms, i.e., have a C — H direct multiplicity equal to 1... 

One can find relations between the rotors by the direct multiplication. As an example,... 

Dry deposition not measured directly, -multiple complex variables (e.g. biochemical and geochemical reactions) must be considered in the model development. -Difficult to investigate the influence of surface characteristics. 

Once the choice of basis functions for the irreducible representations of Dto has been made, the 3-J symbols can be calculated as integrals analogously to the 3-/ symbols (Sect. 4). Therefore, they may also be calculated from the corresponding 3-1 symbols of R3 using a positive constant of renormalization. The scheme for direct multiplication of the irreducible representations of D[Pg.232]

Scheme of direct multiplication of the irreducible representations of Da>. where A > A. From this table the multiplication schemes for the other point groups can be derived using the relationships discussed in Sect. 7. The antisymmetrized direct product (E ) is always A2 and this is true also of all the dihedral sub-groups of -Doo... 

The procedure is continued, plate by plate, until a plate is reached at which a liquid of feed composition is being intro liced a total of four plates is required. The results just obtained can be applied to any size unit, as long as direct multiples of the feed and product rates and holdup volumes are used. 

The First Tether-directed Multiple Functionalization of C Formation of Higher Adducts with Novel Addition Patterns... 

Zallen, J. A., Yi, B. A., and Bargmarm, C. I. (1998) The conserved immunoglobulin superfamily member SAX-3/Robo directs multiple aspects of axon guidance in C. elegans. Cell 92, 217-227. 

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