INDEX subtraction

B, J, C, N) performs the desired calculation I and J are singly dimensional integer arrays, the contents of which point to elements of the A and B arrays respectively. For the present purpose A and B would be identical and would contain the atomic coordinates. The integer variable N determines the number of indexed subtractions performed. The overall operation performed... 

An additional complication in the PIMC simulations arises when Bose or Fermi statistics is included in the formalism. The trace in the partition function allows for paths which may end at a particle index which is different from the starting index. In this way larger, closed paths may build up which eventually spread over the entire system. All such possible paths corresponding to the exchange of indistinguishable particles have to be taken into account in the partition function. For bosons these contributions are summed up for fermions the number of permutations of particle indices involved decides whether the contribution is added (even) or subtracted (odd) in the partition function. 

Next, observations xi. ..x are classed by first subtracting the x-value of the lower boundary of bin 1, a, and then dividing the difference by the class width w. The integer INT((x,-a)/M +l) gives the class number (index) j. The number of events per class is counted and expressed in form of an absolute, a relative, and a cumulative result (E, 100 E/n, resp. 100 H(E/n)). 

To characterize the difference between two chromatograms, an overall mismatch index and a list of the areas, helglits, and positions of the main peaks in the difference chromatogram are provided. The difference chromatogram is the result of subtracting the standard chromatogram for that class of specimen from the chromatogram of the specimen. 

Recently, this problem has been approached by reverting to reading the color of the bilirubin directly. This used to be called an "Icterus Index", in which the color of the serum was compared to a dilute dichromate solution (39). However, the new approach has been to use two wavelengths. This can be used in either of two different procedures. In one procedure the reading is made at the peak for bilirubin which is at 453 nm and at an isosbestic point for hemoglobin (40). The effect on the reading due to hemoglobin is subtracted from the bilirubin value. Commercial instruments based on this principle have not been successful. 

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

The index of hydrogen deficiency is defined as the number of pair of hydrogen atoms that must be subtracted from the molecular formula of the corresponding alkane to give the molecular formula of the compound under consideration. 

Fluctuations in refractive index occur within a volume element and arise from variations in density and concentration. The former are responsible for scattering by the solvent and may be ignored in the present context since solution and solvent scatterings are subtracted. Regarding the dissolved polymer, it is only necessary, therefore, to consider scattering caused by local fluctuations in concentration. 

The second reason for acid-digestion is the determination of the total soil elemental content of, e.g. potassium, phosphorus or trace elements. This is seldom done for potassium in normal soil samples, mainly because the total K in soils is of no value as an index to the availability of K to plants, nor is it always of value in tracing the movement or accumulation of applied fertilizer K (Pratt, 1965). The unreactive soil phosphorus is obtained by subtracting the naturally leached reactive phosphorus from the total phosphorus, and a method for determining the latter by extraction with sulphuric acid and potassium persulphate is cited by Turner and FHaygarth (2000). They analysed... 

Subtractively normalized interfacial FTIR has been employed [242] to study the changes in the surface coordination of pyridine molecules on Au(lll). It has been deduced from the experiments that pyridine molecule is positioned upright at positive potentials and its plane rotates somewhat with respect to the electrode surface. In situ FTIR has also been used [243] to investigate adsorption of pyridine on Au(lll), Au(lOO), andAu(llO) electrodes. For the low-index electrodes, the behavior of band intensity located at 1309 cm and corresponding to the total adsorbed pyridine, agreed with the surface excess results obtained earlier from chronocoulometry. 

The value of each phase constant (i.e., X, Y, Z, U, and S ) is determined by subtracting the retention index of the probe on a squalane stationary phase (Isq) from the retention index of the probe on the stationary phase being characterized (Ijp). For example, the phase constant of benzene (X ) would be calculated as shown in Equation 4.2. 

To check this by a specific example, consider the 431 rhombohedral reflection. To find the lH index in terms of rhombohedral indices, we must travel from O to O by way of rhombohedral axes, that is, via OD, DK, and KO it is evident from Fig. 243 b that from O to D we cross four planes (hn), from D to K three planes (kR), and from AT to O one plane (lR), so that in all eight planes are crossed (hRA-kR- lR). For hll9 we have to go from O to A to get there by way of rhombohedral axial directions, the simplest course is via OD and DA from O to D four planes are crossed, while from D to A three planes are crossed, but these have to be subtracted because we are returning towards the original plane through 0 (or, in other... 

Current IUPAC and Chemical Abstracts nomenclature has been employed in this index with the former given preference. Substitutive nomenclature has been given preference over radicofunc-tional, additive, subtractive, conjunctive or replacement nomenclature, except where this becomes unwieldy. With many bicyclic and polycyclic compounds bearing heteroatoms, standard bicyclic or polycyclic oxa, aza, and thia replacement nomenclature has often been used. With certain functional groups, where the names are rather complex and probably not familiar to most organic chemists, such as ylides, those compounds have simply been named as sulfur, tellurium and arsonic ylides. Metal catbenes have been treated similarly. With more complex functionality and many heterocycles, the Beilstein Commander Crossfire nomenclature system has been used with certain modifications. 

This is the form chosen for implementation in Fig. 10.17. The control variable is mouth half-pressure hm, and h = h m - p+b is computed from the incoming bore pressure using only a single subtraction. The table is indexed by h, and the result of the lookup is then multiplied by h Finally, the result of the multiplication is subtracted from h m to give the outgoing pressure wave into the bore. The cost of the reed simulation is only two subtractions, one multiply, and one table lookup per sample. 

The current is sampled at the end of each potential pulse and the net response (/sw) is given by the subtraction of the current corresponding to a pulse with odd index (forward current, 7f) and the signal of the following pulse with even index (reverse or backward current, 7r) (see Scheme 7.3) ... 

Extensive work investigating the stress-optical rule has also been performed on polymer solutions [101]. Here the rule can be successfully applied if the solvent contributions to the birefringence are properly subtracted. Care must be taken, however, to avoid form birefringence effects if there is a large refractive index contrast between the polymer and the solvent. 

Iterative deconvolution Recursive deconvolution Subtractive deconvolution Positional scanning/indexing Mutational surf other methods... 

The function in Example 4.4 can be used to autoscale a data matrix. The function determines the size of the argument, its mean vector, and its standard deviation vector. On the last fine, a MATLAB programming trick is used to extend the mean vector and standard deviation vector into matrices having the same number of rows as the original argument prior to subtraction and division. The expression ones < r, i) creates an r x 1 column vector of ones. When used as an index in the statement mn (ones(r,1), ), it instructs MATLAB to replicate the mean vector r times to give a matrix having the dimensions r x c. 

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