Hilbert space factorization and partial measurements

A quantum system whose state vector belongs to a finite-dimensional Hilbert space is considered. If this space has a dimension that is a composite number, one can factor the space into a tensor product of sub-spaces. An observable that acts only in one of these subspaces is called a partial measurement. Some of the properties and the interpretation of such partial measurements are discussed.     

AM1 study of conformations of oxocane and 1,3-dioxocane

Summary AM1 semi-empirical SCF MO calculations are reported for important conformations of oxocane (1) and 1,3-dioxocane (2). The boat-chair conformation of1 (BC-1) is found to be the most stable form, whereas the crown family conformation is calculated to be 3.7 kJ·mol^–1 less stable. The boat-boat form of1 is 15.9 kJ·mol^–1 less stable thanBC-1. The boat-chair conformation of2 (BC-1,3) is calculated to be the most stable form of 1,3-Dioxocane. The crown-family conformation and the boat-boat geometry of this compound are 4.2 and 8.3 kJ mol^–1 less stable thanBC-1,3.

---

AM1-Rechnungen zu den Konformationen von Oxocane und 1,3-Dioxocan

Zusammenfassung Die wesentlichen Konformationen von Oxocan (1) und 1,3-Dioxocan (2) wurden mittels semiempirischer AM1-Rechnungen (SCF MO) untersucht. Die Wanne-Sessel-Konformation von1 (BC-1) ist am stabilsten; Konformationen aus der Klasse der Kronen sind um 3.7 kJ·mol^–1 energiereicher. Die Wanne-Wanne-Konformation von1 ist um 15.9 kJ·mol^–1 instabiler alsBC-1. Die Wanne-Sessel-Konformation von2 (BC-1,3) ist das stabilste Konformer von 1,3-Dioxocan. Kronenkonformationen und Wanne-Wanne-Geometrien sind um 4.2 und 8.3 kJ·mol^–1 energiereicher alsBC-1,3.

     

A new wavelet method for solving the Helmholtz equation with complex solution

The Helmholtz equation which is very important in a variety of applications, such as acoustic cavity and radiation wave, has been greatly considered in recent years. In this article, we propose a new efficient computational method based on the Legendre wavelets (LWs) expansion together with their operational matrices of integration and differentiation to solve this equation with complex solution. Because of the fact that both of the operational matrices of integration and differentiation are used in the proposed method, the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problems. As an applied example, “propagation of plane waves” is investigated to demonstrate the validity and applicability of the presented method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 741–756, 2016     

Organocatalytic synthesis of α-hydroxy and α-aminophosphonates

A new and highly flexible procedure is described for the synthesis of α-amino- and α-hydroxy phosphonates. In the presence of a catalytic amount of oxalic acid (10 mol %), trimethyl phosphite reacts with aldehydes or imines (generated in situ from an aldehyde and an amine) to yield the corresponding coupled products in good yield.     

Oxidative amidation of aromatic aldehydes with amine hydrochloride salts catalyzed by silica‐coated magnetic carbon nanotubes (MagCNTs@SiO2)‐immobilized imine–Cu(I)

Mesoporous silica‐coated magnetic carbon nanotubes were prepared; their surface functionalization, followed by reaction with CuI, were carried out to develop a Cu‐grafted functionalized mesoporous material. This system is able to catalyze oxidative amidation of aromatic aldehydes with amine hydrochloride salts, generating amide derivatives in moderate to good yields. Magnetic properties of this catalyst led to easy separation as well as providing significant recyclability. Copyright © 2013 John Wiley & Sons, Ltd.     

Ag‐nanoparticle embedded p(AA) hydrogel as an efficient green heterogeneous Nano‐catalyst for oxidation and reduction of organic compounds

P(AA)‐Ag heterogeneous catalyst system comprised of Ag nanoparticles embedded within hydrogel matrices has been described for the selective aerobic oxidation of alcohols and reduction of nitro phenols in water. P(AA)‐Ag nanocomposite was characterized by Fourier transform infrared (FT‐IR), scanning electron microscopy (SEM), transmission electron microscopy (TEM), thermal gravimetric analysis (TGA), X‐Ray photoelectron spectroscopy (XPS) and inductively coupled plasma atomic emission spectrometer (ICP). Catalytic activity of p(AA)‐Ag catalyst was investigated in the aerobic oxidation of primary alcohols and reduction of nitro compounds by emphasizing the effect of different parameters such as temperature, catalyst amount, substituent effect, etc. The catalyst was easily recovered from the reaction medium and it could be re‐used for other three runs without significant loss of activity.     

Phosphated tungstate: An efficient new solid phosphoric acid catalyst for the synthesis of heterocyclic nitrones

Phosphated tungstate as a new, reusable and efficient solid phosphoric acid catalyst was synthesized and used to promote the reaction of diaminoglyoxime with various aromatic aldehydes. The prepared phosphated tungstate was characterized using various techniques including X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, Fourier transform infrared spectroscopy and thermal analysis. A wide variety of heterocyclic nitrones were obtained under mild reaction conditions and in high yields by using the prepared catalyst.     

An Efficient Synthesis of Stable Phosphorus Ylides Derived from Triphenylphosphine,Dialkyl Acetylenedicarboxylates,and an NH-Acid

Stable crystalline phosphorus ylides were obtained in excellent yields from the 1:1:1 addition reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of strong NH-acids, such as benzotriazole, 5-methylbenzotriazole, 5-chlorobenzotriazole, pyrrole, 2-acetylpyrrole, pyrrole-2-carboxaldehyde, 4-nitro-acetanilide, 4-methoxyacetanilide, 4-bromoacetanilide, 4-methylacetanilide, 2-methyl-acetanilide, and 2,6-dimethylacetanilide. These stable ylides exist in a solution as a mixture of two geometrical isomers as a result of the restricted rotation around the carbon–carbon partial double bond resulting from the conjugation of the ylide moiety with the adjacent carbonyl group.     

Thermodynamics of a 3 — D charged rotating hairy black hole

In this paper, we consider a charged rotating black hole in three dimensions with a scalar charge, and discuss thermodynamics quantities. We find effects of the black hole parameters on the temperature, entropy, free energy, total energy and specific heat. We also investigate the stability of the black hole and study phase transition. We consider the first law of thermodynamics and find that satisfied.