Ladders, description

Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system s composition at equilibrium. When we need a more exact quantitative description of the equilibrium condition, a ladder diagram may not be sufficient. In this case we can find an algebraic solution. Perhaps you recall solving equilibrium problems in your earlier coursework in chemistry. In this section we will learn how to set up and solve equilibrium problems. We will start with a simple problem and work toward more complex ones. 

Ladder diagrams provide a simple graphical description of a solution s predominate species as a function of solution conditions. They also provide a convenient way to show the range of solution conditions over which a buffer is most effective. For ex-... 

One example of a structure (8) is the space of polynomials, where the ladder of subspaces corresponds to polynomials of increasing degree. As the index / of Sj increases, the subspaces become increasingly more complex where complexity is referred to the number of basis functions spanning each subspace. Since we seek the solution at the lowest index space, we express our bias toward simpler solutions. This is not, however, enough in guaranteeing smoothness for the approximating function. Additional restrictions will have to be imposed on the structure to accommodate better the notion of smoothness and that, in turn, depends on our ability to relate this intuitive requirement to mathematical descriptions. 

Figure 6.4. Fragmentation spectrum of a tryptic peptide obtained from bovine serum albumin. Peptide sequence LGEYGFQNALIVR, monoisotopic [M + H]+ = 1479.796, monoisotopic [M+2H]2+ =740.402. Upper panel full scan MS spectrum. Lower panel MS/MS spectrum of a doubly-charged ion at 740.7 m/z with a ladder of y ions, the distances between which correspond to amino acid residues (upper row of letters). A shorter series of b ions is also seen (lower row of letters). See Fig. 6.5 for description of nomenclature. Note the often observed phenomenon where multiply-charged ions lose the charge during fragmentation process and, therefore, have higher m/z values than the original parent ion.

Circa 428-347 The life of Plato, the great philosopher and mystic, who contributes the four qualities to the alchemical theory of the elements, provides the first description of the ladder of the seven planets, and provides a theory of the threefold structure of the soul. 

Some empirical studies demonstrated that this research model was an acceptable initial tool in understanding travel motivation (Kim, 1997 Lee, 1998 Loker-Murphy, 1995 Mills, 1985). As Ryan (2002b 50) reports, the evidence was not always clear cut but at a descriptive level it has an obvious appeal. Furthermore, it has been proposed that the travel career ladder can be utilised as a blueprint for the design of motivational studies for special markets such as for ecotourists and for theme park patrons (Blayney, 1998 Pearce Rutledge, 1994). 

A single deviation from the perfect ladder structure, and thus the formation of single standed subunits, produces the point of attack for chemical decomposition as, induced by thermolysis or hydrolysis. An additional complication arises because one often compares macroscopic properties, deduced from TGA or DSC measurements, for example, with the spectroscopic description of the molecular structure. Even if the spwtroscopic characterization of the ladder polymere, say by C-NMR spectroscopy, is supported by the inclusion of well-defined low molecular weight model components, the limit of detection for structural defects will not exceed about 1 %. Such a degree of inhomogeneity, however, may be disastrous for many material properties. 

Further progresses in comprehension would profit from more systematic comparisons of the charge transfer organic conductors and superconductors with their oxide counterparts. The example give by H. Schultz should here be followed after starting with D. Jerome a study of electron correlations in the organics that led finally to D. Jerome s and C. Bourbonnais work described here, H. Schultz centred his own activity on very similar problems in oxides, where he was one of the first to give a satisfactory description of ladder compounds. 

Christy AG, Alberius-Henning P, Lidin SA (2001) Computer modelling and description of nonstoichiometric apatites Cd5./2(V04)3li. and Cd5 /2(P04)3Bri as modified chimney-ladder stmctures with ladder-ladder and chimney-ladder couphng. J Sohd State Chem 156 88-100 Claike RS, Altschuler ZS (1958) Determination of the oxidation state of uranium in apatite and phosphorite deposits. Geochim Cosmochim Acta 13 127-142... 

Individual and organizational factors are each investigated separately using a total of 11 anchored descriptive rating scales called ladders. Seven ladders are used to diagnose individual factor issues and 4 ladders comprise the organizational factors evaluation. By asking a series of yes/no and open-ended questions of the... 

The description of the energetics of a single bubble, and of the density inside and around it, is not sufficient to describe collective phenomena, such as ebullition or separation of a bubble layer. The description of a single bubble is at a low level in a ladder of models, each introducing new concepts and enlarging the space (and time) scale of the model. 

Readily accessible surface is not a precise description, but is interpreted here to mean those surfaces which could be casually contacted by a person who may not be associated with the transport operation. For example, the use of a ladder might make surfaces accessible, but this would not be cause for considering the surfaces as readily accessible. In the same sense, surfaces between closely spaced fins would not be regarded as readily accessible. If fins are widely spaced, say the width of a person s hand or more, then the surface between the fins could be regarded as readily accessible. 

An alternative description of the observed phenomena can be obtained by the dressed atom model [80]. In this approach the eigenvalues of the global system atom + field, the dressed states, are sought. The strong pump beam dresses the atom with laser photons which leads to energy levels split by the Rabi frequency. The resonances discussed in Fig. 20 then arise naturally as transitions between the (infinite) ladder of dressed states. The dressed atom model delivers a physically comprehensible description of atomic energy levels in strong fields and the reader is referred to Ref. 80 for a detailed presentation. 

---