Number-count set

In his derivation, Frieden uses the concept of a number-count set nm, each member representing the number of photons counted in a spectral interval. The total number of photons m= x nm is taken as known to be N. In terms of frequencies vm, the values of the object spectrum are given by om = nmhvm, where h is Planck s constant. The number of normal modes or degrees of freedom available for occupation by photons of frequency vw is labeled zm. The Bose-Einstein degeneracy factor... [Pg.116]

Frieden finds the probability of a given number-count set nj in the absence of empirical data to be given by an Mfold integral ... [Pg.116]

Here the values qm represent the prior spectrum and p(ql9..qM) is the known probability of a given spectrum (set of qm). The number-count-set estimate hm, and hence the object estimate dm, is obtained by maximizing P by the usual methods of finding extrema. [Pg.116]

These M + 1 equations in M + 1 unknowns p and Xm may be solved by the Newton-Raphson method, in which the unknowns are iteratively adjusted until the right and left sides of the equations agree. The object spectrum number-count set hm and noise em are then computed by substitution of p and the Xm into Eqs. (31) and (32). [Pg.117]

The deconvolved or restored object that we seek is the most probable number-count set nm. This is called the maximum-likelihood (ML) estimate of the object. It obeys simply... [Pg.235]

The sample collected from the crystaUizer was diluted with filtered electrolyte (2.0 wt% aqueous NaCl) and decanted to separate the fines from the coarse crystals. The dilution and decantation were repeated 5-7 times till 200 ml of the decanted sample was obtained. Preliminary tests by hoh (8) have shown tiiat these repeated decantantions were sufficient to recover at least 95% of the fines present in the original sample. Both the fine and coarse fractions were then analysed with the Coulter Counter using a 50 p.m orifice tube for the former and a 280 im orifice tube for the latter. By adjusting the Coulter Counter s settings, a set of particle number counts at different sizes (successive sizes differing by a factor of 21/3) was made for each of the 2 orifice tubes used. [Pg.333]

The subgraph count set (SCS) is a vector descriptor where each entry is the number of time-specific subgraphs obtained by cutting one bond at a time in an - H-depleted molecular graph [Oberrauch and Mazzanti, 1990] ... [Pg.92]

There are now many computer programs that calculate octanol-water logP from molecular structure. They are usually based on a regression analysis fitting of observed logP values to a set of molecular descriptors, for example counts of atoms of different atomic numbers, counts of atoms of a specific atom type (distinguishing sp3, sp2, and spl carbon, or... [Pg.72]

Step 2 Number of signals. Count the number of signals to determine the minimum number of sets of equivalent carbons in the compound. [Pg.397]

The principle of cardinality The last number to be assigned to an object during counting denotes the cardinality of die counted set. [Pg.91]

Amino acid adjacency matrices, which in addition to the information on abundance of individual amino acids also give the count of successive pairs of amino acids, are accompanied by some loss of information, in the view that information on the location of various pairs is not known. A remedy for this loss of information is to record the locations of pairs of adjacent amino acids rather than just their occurrence. In this way, the AAA matrix of Matrix 13.13 has a new form shown in Matrix 13.4, in which we show only the portion of the matrix involving elements G-V. The modified AAA matrix shown in Matrix 13.5 is associated with the sequence of the first 45 amino acids of the human ND6 protein. Observe the elements (G, L) and (G, F) that have in the corresponding AAA matrix the abundance count 2, are now replaced by two sequential numbers. Although many matrix elements of the modified AAA matrix may remain to be single numbers, in general, the elements of the modified AAA matrix are not numbers, but sets, that is, collections of numbers. In Matrix 13.5, we show the same portion of the AAA matrix for the second protein of Table 13.10. [Pg.348]

These supraicosahedral boranes were subsequently investigated by Fowler using the pairing principle from tensor surface harmonic theory (section II.E). The predicted anomalous electron counts for BieHie, BigHig, and B22H22, namely, 2n or 2/7 -I- 4 rather than 2n + 2 skeletal electrons, were shown to be forced by symmetry for either T or Td clusters with an odd number of sets of four equivalent cage atoms or Cm or Cmv m > 3) clusters with an odd number of cage atoms on the Cm axis. [Pg.31]

The first line of the connection table, called the counts line (see Figure 2-21), specifies how many atoms constitute the molecule represented by this file, how many bonds arc within the molecule, whether this molecule is chiral (1 in the chiral flag entry) or not, etc. The last-but-onc entry (number of additional properties) is no longer supported and is always set to 999. The last entry specifics the version of the Ctab format used in the current file. In the ease analyzed it is V2000". There is also a newer V3000 format, called the Extended Connection Table, which uses a different syntax for describing atoms and bonds [50. Because it is still not widely used, it is not covered here. [Pg.49]

The water analysis is incomplete unless the number of coliform bacteria present is determined as well. A multiple-tube fermentation technique can be used to enumerate positive presumptive, confirmed, and fecal coliform tests. Results of the tests are expressed in terms of the most probable number (MPN). That is, the count is based on a statistical analysis of sets of tubes in a series of serial dilutions. MPN is related to a sample volume of 100 ml. Thus, an MPN of 10 means 10 coliforms per 100 ml of water. [Pg.462]

Figures 13.25-13.28 show the ultrahigh resolution separations in chloroform of polystyrene standards, polytetramethylene glycol, urethanes and isocyanates, and epoxy resins, respectively. Multiple column sets of anywhere from two to six columns in series have been used for well over a year with no apparent loss of efficiency. The 500- and 10 -A gels can easily tolerate 15,000 psi or more. In fact, the limiting factor in the number of columns that can be used in series is generally the pump or injector in the FIPLC system. A pump capable of 10,000 psi operation should allow the use of a column bank of 10-12 50-cm columns with a total plate count of 500,000 or more.

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