Subordinate series

With this theoretically predicted spectrum we compare that actually observed. The empirical set of terms of any one spectrum is arranged by spectroscopists in a number of term series 1 an individual term is denoted by its number in the term series and by the name of this series. The usual designation of these term series is derived from the historical designation of the corresponding line scries s (sharp or second subordinate series), p (principal series), d (diffuse or first subordinate series), / (fundamental series, often called also b, Bergmann scries), g (called sometimes / or / ), etc. There is therefore a scries of s-terms, one of p-, d-, f-. . . terms further, each of these may be multiple, but this possibility we shall disregard for the time being. ... 

The largest existing term corresponds to the orbit of the electron in the normal state and gives a measure of the ionisation potential. If this term is an s-term, as is the case for several of the simpler spectra, the ionisation potential is the frequency of the limit (n—cc) of the principal series multiplied by A if the largest term is a p-tetm, the ionisation potential is the frequency of the common limit of the two subordinate series multiplied by A. Simple spectra are also known for which a d-term corresponds to the normal state (e.g. Sc++). 

Neben-quantenzahl, /. secondary (or subsidiary) quantum number, -raum, m. additional space anteroom, -reaktlon, /. by-reaction, side reaction, secondary reaction, -rechnung, /. auxiliary calculation, -reihe,/. = Neben-serie. -rohr, n. side tube (or pipe), branch tube (or pipe). -roUe, /. subordinate r61e. -sache, /. secondary matter. 

Chlorite is abundant in Cu-Pb-Zn-rich deposits but is scarce in Au-Ag-rich deposits. Fe chlorite is the most common and Fe-Mg chlorite is subordinate (Shirozu, 1969). Almost all of the chlorite is classified as orthochlorite which can be regarded as part of the clinochlore-daphnite solid solution series. In general, chlorite is intimately associated with sulfide minerals such as sphalerite, galena, pyrite, chalcopyrite, and pyrrhotite. A 7 A septechlorite was reported from the Toyoha Pb-Zn deposits (Sawai, 1980). Interstratified chlorite-smectite and vermiculite-saponite are rather common minerals in Au-Ag deposits (e.g., Yoneda and Watanabe, 1981), but they have not yet been reported from other deposits. 

There is also a sixth member of this series, known as uranium Y (46, 50, 56, 59), which was discovered in 1911 by G. N. Antonoff, who was working under Sir Ernest Rutherford at the University of Manchester. He afterward returned to St. Petersburg. Uranium Y, like uranium Z, belongs to a subordinate branch of the family. Frederick Soddy attributed Antonoff s success, not to the special chemical process adopted, but to the lapse of a suitable period of time between successive separations" (75). Thus in the uranium series uranium 1 breaks down to form uranium Xj, and this in turn disintegrates to form the successive products uranium X2, uranium Z, uranium 2, and uranium Y. 

Another series was subsequently launched by John Wiley Sons, who also assembled a distinguished advisory board (Fig. 9), theirs consisting of Tom Chilton and his visionary subordinate, Tom Drew, from Du Pont, Donald B. Keyes of the University of Illinois, Kenneth M. Watson of Universal Oil Products near Chicago, and Olaf A. Hougen of the University of Wisconsin. The latter two authored in 1931 a salutary text on Industrial Chemical Calculations, precursor of their pivotal three volumes on Chemical Process Principles. Hougen and Watson held that process problems are primarily chemical and physicochemical in nature, whereas unit-operation problems are for the most part physical [46]. (Incidentally, Wiley Sons did not claim for their series even the second edition of Hitchcock and Robinson s book, which they published.)... 

Branched chain a linear series of carbon atoms occurring in paraffinic hydrocarbons and some alcohols that is isomeric with its straight chain counterpart and has a subordinate chain of one or more carbon atoms ... 

The multifractal behavior of time series such as SRV, HRV, and BRV can be modeled using a number of different formalisms. For example, a random walk in which a multiplicative coefficient in the random walk is itself made random becomes a multifractal process [59,60], This approach was developed long before the identification of fractals and multifractals and may be found in Feller s book [61] under the heading of subordination processes. The multifractal random walks have been used to model various physiological phenomena. A third method, one that involves an integral kernel with a random parameter, was used to model turbulent fluid flow [62], Here we adopt a version of the integral kernel, but one adapted to time rather than space series. The latter procedure is developed in Section IV after the introduction and discussion of fractional derivatives and integrals. 

Thus, we observe that when the memory kernel in the fractional Langevin equation is random, the solution consists of the product of two random quantities giving rise to a multifractal process. This is Feller s subordination process. We apply this approach to the SRV time series data discussed in Section II and observe, for the statistics of the multiplicative exponent given by Levy statistics, the singularity spectrum as a function of the positive moments... 

The sharp, diffuse and fundamental series are occasionally called respectively the second subordinate, first subordinate and Bergmann... 

Medical Units. The FM 8-10 series fully describes medical operations during deployment. Refer to these manuals for the mission and capabilities of the Theater Army Surgeon, Medical Command, and subordinate units. 

Fig. 15.7 Association between the odor of a familiar conspecific and one of three attributes (rank, body size, and shell quality) in Pagurus longicarpus (after Gherardi et al. 2005). The authors observed the response of a test crab to a well-fitting empty shell in the presence of seawater conditioned by the odor of two familiar conspecifics, analyzed separately for 5 min for each odor in random order. Three series of experiments were conducted same body size and same shell quality (1), different body size and same shell quality (2), and same body size and different shell quality (3). The better crab (and the worse crab) was the dominant (and subordinate) crab in (1),...

A series of orders and plans established the general command and control structure of the CTF. These orders and plans also transmitted sufficient authority and guidance to subordinate component conunands and operational units so that they could then develop the local procedures that were necessary to bridge the gap between general mission orders and specific subunit operations. 

The calculation of credit enhancement for notes in a master trust transaction seems more complicated than in a traditional pass-through transaction because subordinated notes from an earlier series are expected to be redeemed before the senior notes of later series. However, if the mortgages were to perform poorly, the trigger events ensure that all outstanding junior notes would only be repaid after all the senior notes. So the credit enhancement can be calculated as the aggregate balance of subordinate notes as a proportion of the total notes outstanding. 

Finally, the MMS-CG collaboration on workplace safety inspection had failed to become a coordinated and effective program because of jurisdictional confusion. As previously discussed, OCSLA assigned workplace safety to the CG despite its lack of qualification for this role, caused withdrawal of OSHA, which is more highly qualified, and assigned overall rig safety to MMS. Sorting out responsibilities between the agencies has been difficult and led to a series of interagency memoranda. More difficulty was created by maritime law and issues such as whether a semi-submersible rig is a vessel and thereby requires CG safely certification and a subordinate role for the MMS. 

The Cation Hofmeister Series The nature of the cations of the salts used for the denaturation of proteins also plays a role, subordinate to the dominating role of the anions, establishing for a given anion the series according to Cacace et al. [98] ... 

Materials Materials used in this study are listed in table 1. A series of new polymer coating 20 are composed essentially of a copolymer having perfluoroalkyl chain and hydrophobic filler. Subordinate No.-l, -2 and -3 indicate 80, 100 and 200 phr of filler contents, respectively. The copolymer was synthesized by means of radical polymerization of comonomer, perfluoro (meth)acrylates and vinyltrimethoxysil-ane. Chemical structure of repeat unit is described as follows ... 

The initial and boundary conditions for A define themselves, from those to which E and B are subordinated. Since the equations that satisfy the vector potential A are linear, A can be expanded in a series of plane waves. This expression is [145]... 

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