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.     

2-Cyanoacrylates in the conjugate addition of trifluoroacetic acid and nucleophilic reagents

In the presence of trifluoroacetic acid, ethyl 2-cyanoacrylate readily reacts with nucleophilic reagents, such as 2-chloro-1,3,2-benzodioxaphosphole, (EtO)₃P, (EtO)₂PCl, Ph₂PCl, Ph₃P, and thiourea. In these reactions the acid proton enters position 2 of the cyanoacrylate, whereas the nucleophilic component enters position 3, in accordance with the electron density distribution in the acrylate. In the absence of trifluoroacetic acid the above reagents, except 2-chloro-1,3,2-benzodioxaphosphole, cause ethyl 2-cyanoacrylate polymerization. The interaction of ethyl 2-cyanoacrylate with 2-chloro-1,3,2-benzodioxaphosphole and trifluoroacetic acid is the first example of a 2-cyanoacrylate taking part in the acid-initiated electrophilic conjugate addition of a weak nucleophile.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1245–1247, July, 1993.     

Synthesis and Electrospray Ionization Mass Spectra of N-（1,3, 2-Dioxaphosphorinan-2-ylmethyl）thiophosphoramidates

N-（1,3,2-Dioxaphosphorinan-2-ylmethyl）thiophosphoramidates were synthesized and determined by NMR spectra and positive ion electrospray ionization mass spectrometry （ESI-MS） in conjunction with tandem mass spectrometry （MS/MS）. The fragmentation pathways were investigated. The results show that these characteristic ions in ESI mass spectra are useful in the structural determination of N-（1,3,2-dioxaphosphorinan-2-ylmethyl）- thiophosphoramidates.     

Alkynenitriles: stereoselective chelation controlled conjugate addition-alkylations

Chelation-controlled conjugate addition of Grignard reagents to γ-hydroxyalkynenitriles stereoselectively generates tri- and tetra-substituted alkenenitriles. t-BuMgCl-initiated deprotonation of hydroxyalkynenitriles followed by addition of a second Grignard reagents triggers a facile conjugate addition leading to a cyclic magnesium chelate. Protonation of the chelate stereoselectively generates trisubstituted nitriles whereas the addition of t-BuLi causes conversion to an ‘ate’ complex that allows alkylation with aldehyde electrophiles. The chelation-controlled conjugate addition-alkylation generates tri- and tetra-substituted alkenenitriles that are otherwise difficult to synthesize.     

YBa2Cu3O7 electro-magnetic optic effects in Ba L2,3 X-ray absorption near Tc

The onset of electro-magnetic optic effects, observed at the Ba L_2,3 edges synchrotron X-ray absorption by a YBa₂Cu₃O₇ single crystal, 20 K above the transition temperature to superconductivity, T_c ∼ 92 K is used to identify the role played by the Ba donor layer in the transition to superconductivity in the CuO₂ layers. Negative permeability leads to Faraday rotation of the transmitted beam below T = 112 to 56 K for the 22 μm thick single crystal (c-axis orientation of 8π/18 relative to ε_X-rays) and sharp changes in the density of empty final states lead to zero transmitted radiation in an interval ΔE at the given orientation. The temperature dependence: ΔE(L₂) = 1.4, 3.5 and 3.9 eV, while ΔE(L₃) = 5.3, 6 and 7 eV at T = 92, 74 and 63 K, respectively, indicates that the width of the empty final states bands increases as T decreases. ΔE(L₃)/ΔE(L₂) = 3.8 at 92 K to 1.8 at 63 K also indicates that the d_5/2 symmetry bands fill faster than those of d_3/2 symmetry below T_c, providing the first experimental evidence of unpaired spin-orbit states in the Ba donor layer of a superconductor. These effects, characteristic of ferromagnetic and anti-ferromagnetic materials near a resonance absorption, signal the onset of a Mott transition. The interaction between the layer states is described using 1D conjugate molecular orbitals.     

Indium Mediated Conjugate Addition of Allyl Bromide to Nitroalkenes in DMF—H2O Media

Allylindium bromide prepared by metallic indium and allyl bromide was added to nitroalkenes to give conjugate addition compounds in moderate to good yields in an aqueous media.     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

A quasi‐dynamic procedure for coupled thermal simulations

This paper outlines the development and adaptation of a coupling strategy for transient temperature analysis in a solid via a conjugate heat transfer method. This study proposes a quasi‐dynamic coupling procedure to bridge the temporal disparities between the fluid and the solid. In this approach, dynamic thermal modeling in the solid is coupled with a sequence of steady states in the fluid. This quasi‐dynamic algorithm has been applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate using the severe thermal conditions of a solid propellant rocket. Two different coupled thermal computations have been performed. In the first one—referred to as the reference computation—the coupling period is equal to the smallest solid time constant. In the second one, a very large coupling period is used. The results show that the procedure can predict accurate transient temperature fields at a reasonable computational cost. The simulation CPU time is approximately reduced by up to 90%, while maintaining a very good accuracy. All the details of the numerical test case are given in the paper. This application illustrates the capabilities and the overall efficiency of this coupled approach in a solid transient problem using long term simulations of time dependent flows. Copyright © 2013 John Wiley & Sons, Ltd.