Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues

We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian,

     

Salicylaldehyde based oxazolidines as catalysts for the asymmetric addition of diethylzinc to aldehydes

A series of oxazolidines have been prepared by condensation of N‐isopropyl norephedrine with a variety of salicylaldehyde derivatives. Despite the stereochemical relationship of (1R,2S)‐norephedrine with (1R,2S)‐ephedrine, the resultant oxazolidines 12‐14 were determined to have a stronger stereochemical relationship with (1S,2S)‐pseudoephedrine based oxazolidines. The resultant oxazolidines were used as catalytic ligands in the addition of diethylzinc to several aldehydes. It was determined that the oxazolidine derivative 12 gave the highest yield and a moderate enantioselectivity.     

Raman scattering in ZrB<Subscript>12</Subscript> cage glass

High-precision measurements of the Hall effect and Raman scattering have been performed for single crystals of ZrB₁₂ superconductor in the wide temperature range of 5–300 K. For ZrB₁₂, the boson peak with ω_max ~ 100 cm^–1 has been observed for the first time within the low-frequency range of the Raman spectrum I(ω). The sizes of vibrational clusters with the correlation length ranging from 25 to 35 Å are estimated. The relation between the renormalization of the low-frequency density of vibrational states accompanying the transition to the cage-glass phase (T* ~ 90 K) and the enhancement of superconductivity in ZrB₁₂ is discussed.     

High‐Affinity Proton Donors Promote Proton‐Coupled Electron Transfer by Samarium Diiodide

The relationship between proton‐donor affinity for Sm^II ions and the reduction of two substrates (anthracene and benzyl chloride) was examined. A combination of spectroscopic, thermochemical, and kinetic studies show that only those proton donors that coordinate or chelate strongly to Sm^II promote anthracene reduction through a PCET process. These studies demonstrate that the combination of Sm^II ions and water does not provide a unique reagent system for formal hydrogen atom transfer to substrates.     

Energy characteristics of nitrooxazolidines and their radicals

Russian Chemical Bulletin - The standard molar enthalpies of combustion for three methyl and dimethyl nitrooxazolidine derivatives in the liquid and crystalline states were determined using a...     

Pictet–Spengler Synthesis of Quinoline‐Fused Porphyrins and Phenanthroline‐Fused Diporphyrins

Doubly and quadruply quinoline‐fused porphyrins were effectively synthesized through a reaction sequence consisting of Suzuki–Miyaura coupling of β‐borylated porphyrins with 2‐iodoaniline and subsequent Pictet–Spengler cyclization. These quinoline‐fused porphyrins display red‐shifted absorption bands and higher electron‐accepting abilities. This synthetic protocol also allowed the synthesis of phenanthroline‐fused porphyrin dimers, which bound either a Ni^II or Zn^II cation. The resultant metal complexes displayed further red shifted absorption spectra and molecular twists to effect an almost perpendicular arrangement of the two porphyrins.     

The Electrochemistry of Viologens with Various Alkyl Substituents and The Dimerization of Their 1e- Reduced Species in the Absence and Presence of Various Cyclodextrins

We present EQCM study for the electrochemical behavior of various 1-methyl-1'-alkylvilogen (C₁C_nV:n=1, 7-10, 12, 14,16, 18). In some viologens, we discussed the mechanism of CD-induced comproportionation reaction as well as electrodeposition pathway based on the EQCM and the spectroelectrochemical experimental results.     

A Learning Algorithm for the Control of Continuous Action Set-Point Regulator Systems

The convergence properties for reinforcement learning approaches, such as temporal differences and Q-learning, have been established under moderate assumptions for discrete state and action spaces. In practice, however, many systems have either continuous action spaces or a large number of discrete elements. This paper presents an approximate dynamic programming approach to reinforcement learning for continuous action set-point regulator problems, which learns near-optimal control policies based on scalar performance measures. The continuous-action space (CAS) algorithm uses derivative-free line search methods to obtain the optimal action in the continuous space. The theoretical convergence properties of the algorithm are presented. Several heuristic stopping criteria are investigated and practical application is illustrated by two example problems—the inverted pendulum balancing problem and the power system stabilization problem.     

A proposition on memes and meta-memes in computing for higher-order learning

In computational intelligence, the term ‘memetic algorithm’ has come to be associated with the algorithmic pairing of a global search method with a local search method. In a sociological context, a ‘meme’ has been loosely defined as a unit of cultural information, the social analog of genes for individuals. Both of these definitions are inadequate, as ‘memetic algorithm’ is too specific, and ultimately a misnomer, as much as a ‘meme’ is defined too generally to be of scientific use. In this paper, we extend the notion of memes from a computational viewpoint and explore the purpose, definitions, design guidelines and architecture for effective memetic computing. Utilizing two conceptual case studies, we illustrate the power of high-order meme-based learning. With applications ranging from cognitive science to machine learning, memetic computing has the potential to provide much-needed stimulation to the field of computational intelligence by providing a framework for higher order learning.     

Complex Classical Fields: A Framework for Reflection Positivity

We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our method generalizes Osterwalder and Schrader’s construction of Euclidean fields. We allow complex-valued classical fields in the case of quantum field theories that describe neutral particles. From an analytic point-of-view, the key to using our method is reflection positivity. We investigate conditions on the Fourier representation of the fields to ensure that reflection positivity holds. We also show how reflection positivity is preserved by various spacetime compactifications of ${\mathbb{R}^{d}}$ in different coordinate directions.