The Seminal Ideas

The experimental observation consists of the analysis of radiation eminating from an orifice in a hollow cavity kept at a ffxed temperature. The partition formula by frequency is obtained on integration over allowed modes of vibration, 

In statistical thermodynamics, which treats energy as a continuous function, = kT for each mode of the Boltzmann distribution. The radiation 

This means that an infinite amount of thermal energy needs to be converted into radiant energy to establish an equihbrimn at short wavelength. 

To overcome the problem it was necessary to assmne that radiant energy occms as multiples of discrete rmits, proportional to the frequency, = hi/ the proportionality factor is known as Planck s constant. The 

Solution of the black-body problem had an immediate knock-on effect on two other unsolved problems of classical physics, the photoelectric effect and the interpretation of atomic spectra. 

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Second, Max Dresden, who was both my thesis advisor and loyal friend. As Jay was the perfect teacher of high school physics, so Max was the quintessential physics professor. Max opened my eyes to the deej) mystery we call the universe, and taught me that the path to truth is indistinguishable from the path to beauty. The seminal idea and outline of this book-its major themes, chapters, and overall organization -benefitted greatly from Max s experience and wise counsel. I have followed our bible of ideas ever since Max and I lovingly crafted a skeletal version of it prior to our first meeting with a potential publisher over a decade ago. 

The Zintl-Klemm concept evolved from the seminal ideas of E. ZintI that explained the structural behavior of main-group (s-p) binary intermetaUics in terms of the presence of both ionic and covalent parts in their bonding description [31, 37]. Instead of using Hume-Rother/s idea of a valence electron concentration, ZintI proposed an electron transfer from the electropositive to the electronegative partner (ionic part) and related the anionic substructure to known isoelectronic elemental structures (covalent part), e.g., TK in NaTl is isoelectro-nic with C, Si and Ge, and consequenUy a diamond substructure is formed. ZintI hypothesized that the structures of this class of intermetallics would be salt-like [16b, 31 f, 37e]. 

It would be hard to write a definitive account of the development of extended sampling methods we will not attempt to do so. The seminal ideas are probably correctly attributed to Torrie and Valleau [22], who coined the terminology umbrella sampling. The huge literature of subsequent advances and rediscoveries may be rationalized a little by dividing it into two, according to how the macrostates to be weighted are defined. 

A little-known paper of fundamental importance to modern atomic theory was published by Hantaro Nagaoka in 1904 [10]. Apart from oblique citation, it was soon buried and forgotten. With hindsight it deserved better than that. It contained the seminal ideas underlying the nuclear model of the atom, the standing-wave nature of orbital electrons and radiationless stationary states. It was so far ahead of contemporary thinking that later imitators either failed to appreciate its significance, or pretended to be unaware of it. 

Barton and Cohen (48) were the first to suggest the seminal idea that dienones could be intermediates in the biosynthesis of aporphine alkaloids from benzylisoquinolines, since such dienones could rearrange to the aporphine nucleus either through a dienone-phenol or a dienol-benzene rearrangement as shown in the scheme on the following page. 

It would be hard to write a definitive account of the development of extended sampling methods we will not attempt to do so. The seminal ideas... 

Section 3 introduces the seminal ideas about schema mapping generation, and the early algorithms developed in the framework of the Clio project [Miller et al. 

The seminal ideas relating to the oxidative coupling of phenols have found very widespread application, and yet the actual mechanism of coupling in vivo remains obscure. In new work, it has been found that extracts of Papaver somniferum which had peroxidase activity were unable to catalyse the conversion, by phenol oxidative coupling, of reticuline into salutaridine. 

The most attractive part of the wave-field vacuum is that it provides a natmal explanation to the vexing question of action at a distance. The seminal idea stems from the work of Tetrode (1922) who concluded that... 

The seminal idea is trivial the function is integrated within a generic interval. If error control is satisfectory, the portion of the integral is added to the global integral otherwise, the interval is split into two subintervals (usually, but not necessarily, of the same width) and the same procedure is recursively invoked twice. 

The seminal idea on which active set methods are based is rather simple and is the same, albeit with several variants, as the one adopted in the Attic method as well as in the Simplex method for linear programming starting from a point where certain constraints are active (all the equality constraints and some inequality constraints), we search for the solution to this problem as if all the constraints are equalities. During the search, it, however, may be necessary to insert other inequality constraints that were previously passive and/or remove certain active inequality constraints as they are considered useless based on their Lagrange parameters. The procedure continues until KKT conditions are fulfilled. 

The seminal idea on which the SLP is based is trivial. Consider the problem (13.1)-(13.3). Suppose we know a feasible point x and linearize the objective function and constraints ... 

The uniqueness of Groves mechanisms provides an additional simplification to the efficient mechanism design problem when dominant strategy implementations are required. It is sufficient to consider the family of Groves mechanisms, and look for functions hi -) that provide Groves payments that satisfy all of the desired constraints. The Vickrey-Clarke-Groves (VCG) mechanism is an important special case, so named because it reflects the seminal ideas due to Vickrey [100] and Clarke [26]. The VCG mechanism maximizes expected revenue across all strategyproof efficient mechanisms, subject to ex post individual-rationality (IR) constraints. Ex post IR provides ... 

The first solution was proposed by Warshel in 1976 [19] at the semi-empirical level and by Rivail and Assfeld [20] 20 years later at the ab initio level of theory. The seminal idea is to divide the large molecular system into two communicating parts, one considered as the active part (where the electronic phenomenon takes place) is small and is described with Quantum Mechanics (QM) methods, the other, considered as the surronndings, contains the remaining thonsands of atoms and is then treated with Molecnlar Mechanics (MM) Force Fields. This is the principle of the so-called QM/MM methods, which rely on the locality of the electroiuc phenomenon under investigation [9]. 

By combining the catalytic and template effect of copper(I), Leigh et al. have developed a new powerful tool, which permits to use only catalytic amounts of the template agents for the synthesis of mechanically interlocked architectures. In theory, this concept can be applied to many other metal-mediated reactions, such as cross-couplings, condensations or other cycloaddition reactions.This new development may be the seminal idea that could lead to a whole new range of catenane- and rotaxane-forming protocols. 

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