Functional analysis

Functional analysis is a technique, which consists of researching and characterizing the functions provided by a product to satisfy the needs of a usei (NF-EN 1325-1). The functional analysis used in our approach considers the functions (expressed in active form) that the product must ftdfill this is an external functional analysis or functional analysis of need. 

BS/EN/IEC 61839 2000 states that other function representations may be more suitable than the hierarchical method proposed. It would, therefore, be consistent with relevant standards to deploy a method such as Cognitive Work Analysis 

Cognitive Work Analysis is comprised of five individual methods and the first, woik domain analysis (WDA), is the means by which this functional analysis can be performed. The work domain analysis phase involves describing or modeling the system in which the activity under analysis takes place. A work domain analysis is used to identify the functional purpose and structure of the work domain in terms of the overall system goals, the processes adopted, and the artifacts used within the system. In modeling a system in this way, the system constraints that modify activity within the work domain are specified. These constraints can of course greatly influence the selection of automation strategies and allocation of function. 

The use of an abstraction hierarchy (AH) provides a graphical representation of the work domain where the AH represents the system at a number of levels. At the highest level, the AH captures the system s reason for being, its functional purpose, while at the lowest level it captures the physical objects in the system s environment. In between are levels of abstraction that relate more specifically to functions and which can form the basis for an alternative approach to function analysis. The five different layers in an AH are defined briefly in Table 7.2. 

In summary, conventional hierarchical functional analysis tends to focus on the what of a system What is it and what does it do The abstraction hierarchy, on the other hand, takes a much wider perspective by looking at the why and the how. Whereas traditional functional analysis methods excel at what should happen, this complementary approach is useful at looking at what could happen Could automation serve this purpose better than a human or vice versa  

Once the estabhshed requirements baseline variations and conflicts are satisfactorily resolved, the requirements baseline is considered valid. This validated requiremraits baseline is thrai used as input to functional analysis (6.3) and documented in the integrated database. 

The enterprise shall perform functional analysis to accomplish the following two related objectives  

The enterprise analyzes each system function to determine the responses (output) of the system to stimuli (inputs) necessary to accomplish system objectives. 

Analyses are conducted to understand the functional behavior of the system under varions conditions and to assess the integrity of the functional architecture. Analyses should involve the simulation or stimulation of functional models utilizing operational scenarios that expose the models to a variety of stressful and non-stressful situations that reflect anticipated operational usage and environments. 

As system functions are decomposed into functions, interfaces between interacting functions are created. The enterprise identifies these interfaces and defines their functional interactions, such as start and end states or inputs and outputs. 

The presence of some functions in the structures of organic derivatives may be detected by some redox reactions. Many of them have been evoked in the preceding chapters. 

Primary alcohols are oxidized in well-defined conditions by chromic anhydride CrOs, giving the corresponding carboxylic acids, while chromium reduces from state+VI to + III. In the same conditions, secondary alcohols give the corresponding ketones and tertiary alcohols give orange-colored chromic esters. This color contrasts with the green color of chromic salts obtained with both previous alcohols. 

Aldehydes are reductants. They are oxidized, for example, by the complex ion tetraiodomercurate-(n) (Nessler s reagent). The mercury of the complex is reduced to the metallic state. Aldehydes also reduce the ammoniacal silver nitrate (Tollens reagent) with the formation of metallic silver. Concerning this point, let s us recall that aldoses are also reductants. For example, they reduce cupric copper to cuprous copper (Fehling s reagent). Ketoses also exhibit this property. In this case, this is due to the presence of the group enediol in their structure. 

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Joe T and Albrecht A C 1993 Femtosecond time-resolved coherent anti-Stokes Raman spectroscopy of liquid benzene a Kubo relaxation function analysis J. Chem. Phys. 99 3244-51... 

Toby B FI and Egami T 1992 Accuracy of pair distribution function analysis applied to crystalline and noncrystalline materials Aota Crystaiiogr.k 48 336-46... 

Reddy, J. N., 1986. Applied Functional Analysis and Variational Methods in Engineering, McGraw-Hill, New York. 

A. W. Norman, R. Bouillon, and M. Thomasset, eds.. Vitamin D, Structure, Function Analysis and Clinical Application, Proceedings of the Eighth Workshop on Vitamin D, Paris, July 5, 1991, Walter de Gmyter, Berlin, 1991. 

Elements of Applicable Functional Analysis, Marcel Dekker,... 

Hille, E. Methods in Classical and Functional Analysis, Addison-Wesley, Reading, MA (1972). 

Introductory Functional Analysis with Applications, Wiley, New... 

Wouk, A. A Cour se of Applied Functional Analysis. Interscience, New York (1979). 

Functional analysis. The methodology enables eaeh part to be elassified as essential A parts or non-essential B parts. Given this awareness, redesigns ean be evolved around the essential eomponents, from whieh redueed part eount normally results. 

Functional analysis gives a Design Efficiency = Essential Parts/Total Parts > 60%... 

Table 9. Functionality analysis of HSi-PaMeSt prepared by the HSi(CH3)2CH2CH2

Reduction from Functional Form to Algebraic Form is considered here to belong more properly to functional analysis rather than to numerical analysis, and neither an effective survey nor a representative sample of methods is possible in a few pages. Nevertheless, one or two general remarks may be in order. 

A good modem treatment of approximation, especially linear, is in [6], and reference may be made also to [3]. For a more elaborate treatment of matrix methods, see [4]. In [13] can be found an excellent collection of articles by various authors on a number of topics, including a good brief treatment of stability, and an introduction to functional analysis as it applies to computational practice. Perhaps the best treatment of the QD algorithm is by Henrici in [9]. 

A. E. Taylor, Introduction to Functional Analysis, p. 98, John Wiley and Bonn, Inc., New York, 1958 B. Friedman, Principles and Techniques of Applied Mathematics, p. 125, John Wiley and Sons, Inc., New York, 1956. 

Functionalization yields have to be checked carefully by comparing the effective number average molecular weight Mn with its value calculated from the functional content of the sample, under the assumption that each macromolecule carries one function (two if a bifunctional initiator is used). Low molecular weight samples are preferred, as the functional analysis would otherwise lack accuracy. In all examples quoted high functionalization yields have been attained. 

Before the advent of modem computer-aided mathematics, most mathematical models of real chemical processes were so idealized that they had severely limited utility— being reduced to one dimerrsion and a few variables, or Unearized, or limited to simplified variability of parameters. The increased availability of supercomputers along with progress in computational mathematics and numerical functional analysis is revolutionizing the way in which chemical engineers approach the theory and engineering of chemical processes. The means are at hand to model process physics and chenustry from the... 

II. Principles of Quantum Mechanics. This section defines the state of a system, the wave function, the Schrddinger equation, the superposition principle and the different representations. It can be given with or without calculus and with or without functional analysis, depending on the mathematical preparation of the students. Additional topics include ... 

Our account of the theory of difference schemes is mostly based on elementary notions from functional analysis. In what follows we list briefly widespread tools adopted in the theory of linear operators which will be used in the body of this book. 

Balakrishnan, A. (1976) Applied Functional Analysis. Springer New-York-Berlin-Heidelberg. 

Kantorovich, L. and Akilov, G. (1977) Functional Analysis in Normed Spaces. Nauka Moscow (in Russian). 

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