Radiation: Waves or particles? A quantized approach to time

A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units t_o=h/m_oc² for a particle at rest, and of similar interval unit s_o when in relative motion, with conventional relativistic corrections.

For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. t_o and s_o are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept.     

A second quantized formulation of valence bond theory

Valence bond theory is formulated in terms of second quantized operators and is related to the theory of the unitary group of spin-free orbital transformations. The construction of Weyl basis states, the evaluation of matrix elements, and the application to a linked-diagram valence bond perturbation theory are all discussed.     

Second-order quantized Hamilton dynamics coupled to classical heat bath

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.     

A canonical averaging in the second-order quantized Hamilton dynamics

Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.     

A ring-expansion approach to roseophilin

[reaction: see text] Preparation of a cyclopentenone-fused pyrrolophane, which serves as a model for the tricyclic core of roseophilin (1), is described. The synthetic scheme features a palladium-catalyzed annulation and oxidative cleavage sequence to provide a macrocyclic ketoester (17). Modified Paal-Knorr pyrrole synthesis and Friedel-Crafts acylation complete the pyrrolophane model system (20).     

A synthetic approach to enfumafungin

The stereospecific synthesis of the dienophile subunits 5 was achieved from the butenolide 6. Ester 19 was obtained in 67% overall yield (2 steps), with no intermediate purification, by a sodium chlorite oxidation of the corresponding aldehyde in buffered conditions, followed immediately after extraction, by a Mitsunobu reaction of the relatively labile acid 3 with alcohol 13. The synthesis of the α,β-unsaturated aldehydes 22 and 23 is also reported. Tentative IMDA reactions of 22 and 23 were examined in thermal conditions, or with a Lewis acid catalysis, and results are reported herein.     

A mannich-like approach to naphthyridinomycin

A concise route to a potential tetracyclic precursor of the title compound is described. The key step is the intramolecular interpolation of a formyl equivalent between an N-methyl group and a carbon atom α-to a ketone.     

Synthetic approach to malibatol A

[reaction: see text] A synthetic approach to malibatol A featuring a novel benzofuran synthesis is described.     

A retro-Claisen approach to dolabriferol

[reaction: see text] The protected precursor 30 to dolabriferol was generated by a DBU-induced, ester-forming, retro-Claisen process. The required linear carbon chain present in 22 was synthesized by a stereoselective lithium aldol reaction. The necessary aldehyde and ketone fragments were synthesized using stereocontrolled aldol reactions with the ethyl (S)-lactate derived ketone 13.     

A new approach to prostanoids

A new asymmetric approach to 11-deoxyprostanoids is presented.     

A comprehensive approach to argumentation

A reasoning model, based on the logic of argumentation, is described. The model represents argumentation as a directed graph in which nodes and arcs can be colored using an ordinal set of weightings and in which the attributes of both nodes and arcs can be modified. It is thus able to deal with the undercutting or augmenting of arguments. Weightings can be propagated through the graph to generate unique weightings for any node or arc. The model is able to deal with contradiction. It can incorporate numerical methods and is able to handle qualitative and quantitative reasoning.     

A new approach to isochromanes

Some isochromane derivatives exhibit hypotensive,¹ antitumor,² and growth-regulating³ activities; some others have a specific effect on the dopaminergic system.⁴     

A biomimetic approach to lanthionines

The asymmetric sulfa-Michael additions of appropriately protected L- and D-cysteine derivatives to new chiral dehydroamino acid derivatives have been developed as key steps in the synthesis of biologically important cysteine derivatives, such as lanthionine (Lan) and β-methyllanthionine (MeLan), which are unusual bis-α-amino acids found in the emerging lantibiotics such as nisin.     

A direct approach to alpha-trifluoromethylamines

[reaction: see text] S-[1-(N-Acetylamino)-2,2,2-trifluoroethyl]-O-ethyl dithiocarbonate (6), a readily available xanthate, adds efficiently to various functionalized olefins to give the corresponding adducts 8 via a radical chain reaction initiated by a small amount of lauroyl peroxide.