Functional Analysis Technique symbols

For a statistical analysis of copolymer sequences, different mathematical techniques are used. For mathematically oriented researchers, a copolymer sequence might be considered as a string of symbols whose correlation structure can be characterized completely by all possible monomer-monomer correlation functions. Since the correlations at long distances are typically small, it is important to use the best possible estimates to measure the correlations, otherwise the error due to a finite sample size can be as large as the correlation value itself. 

The analysis of the positron annihilation lifetime spectra is a very important aspect of using the PAL techniques to analyze polymers. Without proper data analysis interpretation of data might be misleading and important scientific information will be lost. In PAL studies of polymers the PAL spectrum can be analyzed in two ways (1) a finite lifetime analysis or (2) continuous lifetime analysis. In the finite lifetime analysis the PAL spectra is resolved into a finite number of negative exponentials decays. The experimental data y(t) is expressed as a convoluted expression (by a symbol ) of the instalment resolution function R(t) and a finite number (n) of negative exponentials ... 

Density functional theory (DFT) as applied to adsorption is a classical statistical mechanic technique. For a discussion of DFT and classical statistical mechanics, with specific applications to surface problems, the text book by Davis [1] is highly recommended. (Here the more commonly used symbol for number density p(r) is used. Davis uses n(r) so one will have to make an adjustment for this text.) The calculations at the moment may be useful for modeling but are questionable for analysis with unknown surfaces. The reason for this is that the specific forces, or input parameters, required for a calculation are dependent upon the atoms assumed to be present on the surface. For unknown surfaces, a reversion to the use of the Brunaver, Emmett and Teller (BET) equation is often employed. 

The SLIM language allows to describe discrete dynamics, real time, and continuous dynamics, both in a qualitative and in a probabilistic fashion. A formal semantics allows to precisely characterize the complete set of nominal and non-nominal behaviours of the model, and opens up the possibility to apply a wealth of formal verification techniques for various forms of analysis. These include symbolic model checking for functional verification and formal requirements analysis, FTA and FMEA, testability, and performance analysis. 

The activities described in the previous sections are supported by an integrated platform, which incorporates extensions of existing tools in a uniform environment. Verification and validation functionalities of the toolset are based on symbolic model checking techniques. In particular, the tool set builds upon the NuSMV [26] symbolic model checker, the MRMC [25] probabilistic model checker, and the RAT [29] requirements analysis tool. The architecture of the tool set is shown in Fig. 6. 

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