Mathematics, historical survey

The pi theorem is often associated with the name of Buckingham (4), because he introduced this term in 1914, but the proof of it was accomplished in the course of a mathematical analysis of partial differential equations by Federmann in 1911 see Ref. 5, Chap. 1.1, A Brief Historical Survey. 

The Editors feel that they should note other positive responses by mathematicians to Ya.B. s book as well. In 1968 the RSFSR Ministry of Education, on the recommendation of the Scientific Council of the AS USSR Institute of Applied Mathematics chaired by M. V. Keldysh, recommended the book Higher Mathematics for Beginners and its Applications to Physics as a textbook for physico-mathematical schools and elective study. A very prominent American mathematician, Lippman Bers, wrote, Finally, I would like to indicate how I was influenced by two very nonstandard books on mathematical analysis a historical survey written by the outstanding mathematician O. Toeplitz, and a textbook written by a well-known physicist, Ya. Zeldovich (unfortunately not yet available to the British or American reader). ... 

After a short historical survey the fundamentals of signal transducers and the present state of thermometric, optoelectronic, and piezoelectric biosensors are presented. The most relevant electrochemical techniques are outlined in detail because electrochemical transducers are predominant. The aim of the second section is to provide information on the function of the biocomponents used in biosensors, primarily enzymes, but also antibodies and chemoreceptors. Special attention is paid to the methods of immobilization of the biomaterial and to the discussion and mathematical modeling of the interplay of biochemical reactions with mass transfer processes in immobilized enzyme electrodes. 

The above remarks have been more of a setting of the scene than a historical survey. In the subsequent sections, topicality and experimental evidence are further emphasized, at the risk of an inadequate coverage of the classic calculations and eternal verities of the subject. It is partly out of respect for the available basic literature that such a policy was adopted. We should mention Slater (for an authoritative and exhaustive survey), Callaway (for a general account of the theory), and Ziman (for a recent summary of various mathematical techniques and their interrelationships) as three such sources to which the reader may turn for guidance, as did the author on occasion. In particular, considerations of space and the spirit of this treatise have precluded the inclusion of much mathematical detail, and rather than setting forth an incomplete description of this, inviting misunderstanding, it has been avoided almost entirely. 

With this, we complete a historical survey of the development of the theory of an elementary act and go over to a discussion of fundamental concepts of the modern theory without adhering to chronological order and without mentioning the special features of the treatment of any problem by different authors. Our aim is to present, in a qualitative form, the fundamental physical concepts and to discuss the possibilities of their experimental verification. The mathematical apparatus of the theory and some special physical problems remain beyond the scope of the present review. ... 

Although there have been abundant records of decision analyses based on multiple criteria in human history, putting the analyses in a formal mathematical setting is fairly new. Though stiU young, the literature of such mathematical treatments has exploded during the last three decades. The interested reader is referred to Stadler (1979, 1981), Steuer et al (1996) for surveys and historic notes. 

The applied field research methods (survey, description, observation, work with maps) and Earth remote sensing, as well as methods of mathematical, conceptual modeling and mapping. Theoretical analysis is based on the theory of reflection and systemic and chorological approach, methodological statements of historical geography by V.I. Paranin (Paranin 1990, 1998, Paranina 2012c). 

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