The structure and vibrational features of proton disolvates in water–ethanol solutions of HCl: the combined spectroscopic and theoretical study

The infrared (IR) spectra of water–ethanol (EtOH) solutions of HCl are measured over a wide range of acid concentration at fixed H₂O―EtOH ratios (1 : 1, 1 : 2, and 1 : 40). In these systems, different proton disolvates with (quasi)symmetrical H‐bonds are formed. Their structure and vibrational features are revealed by the density functional theory method coupled with the polarizable continuum model of solvation. In dilute acidic solutions, the Zundel‐type H₅O₂⁺ ion is mainly formed. In concentrated HCl solutions, the ions (H₂O···H···O(H)Et)⁺ and (Et(H)O···H···O(H)Et)⁺ with the quasi‐symmetrical O···H⁺···O unit having O···O separation <2.45 Å appear. The first ion characterized by the IR‐intensive band around 1800 cm^?1 is mainly formed in the 1 : 1 water–ethanol systems. The second ion exists in the 1 : 2 and 1 : 40 water–ethanol systems. Its spectroscopic signatures are the groups of the IR‐intensive bands around 800 and 1050 cm^?1. In highly concentrated HCl solutions with the 1 : 40 water–ethanol ratio, a neutral Et(H)O···H⁺···Cl^? complex exists. Copyright © 2013 John Wiley & Sons, Ltd.     

Brightening single-photon emitters by combining an ultrathin metallic antenna and a silicon quasi-BIC antenna

Bright single-photon emitters(SPEs)are fundamental components in many quantum applications.However,it is difficult to simultaneously get large Purcell enhancements and quantum yields in metallic nanostructures because of the huge losses in the metallic nanostructures.Herein,we propose to combine an ultrathin metallic bowtie antenna with a silicon antenna above a metallic substrate to simultaneously get large Purcell enhancements,quantum yields,and collection efficiencies.As a result,the brightness of SPEs in the hybrid nanostructure is greatly increased.Due to the deep subwavelength field confinement(mode size<10 nm)of surface plasmons in the ultrathin metallic film(thickness<4 nm),the Purcell enhancement of the metallic bowtie antenna improves by more than 25 times when the metal thickness decreases from 20 nm to 2 nm.In the hybrid nanostructures by combining an ultrathin metallic bowtie antenna with a silicon antenna,the Purcell enhancement(Fp≈2.6×10⁶)in the hybrid nanostructures is 63 times greater than those(≤4.1×10⁴)in the previous metallic and hybrid nanostructures.Because of the reduced ratio of electromagnetic fields in the ultrathin metallic bowtie antenna when the high-index silicon antenna is under the quasi-BIC state,a high quantum yield(QY≈0.70)is obtained.Moreover,the good radiation directivity of the quasi-BIC(bound state in the continuum)mode of the silicon antenna and the reflection of the metallic substrate result in a high collection efficiency(CE≈0.71).Consequently,the overall enhancement factor of brightness of a SPE in the hybrid nanostructure is EF?≈Fp×QY×CE≈1.3×10⁶,which is 5.6×10² times greater than those(EF?≤2.2×103)in the previous metallic and hybrid nanostructures.     

Filament sets, aposyndesis, and the decomposition theorem of Jones

Applications of the work introduced by the authors in a recent article, Filament sets and homogeneous continua, are given to aposyndesis and local connectedness. The aposyndetic decomposition theorem of Jones is generalized to spaces with the property of Kelley.

     

Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

On small homotopies of loops

Two natural questions are answered in the negative:

• “If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic?”

• “Can adding arcs to a space cause an essential curve to become nulhomotopic?”

The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and π₁-shape injective.

The structures and electronic absorption spectra of substituted phenyldiacetylenes: experimental and theoretical studies

The results of experimental and theoretical investigation of the electronic absorption spectra of substituted phenyldiacethylenes are presented. The bands in the experimental spectra were assigned in detail using quantum chemical calculations of the electronic structures and spectra of the molecules. The influence of the interaction of the substituents on the spectral parameters of the systems under study was analyzed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1947–1953, October, 2007.     

Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation

We consider some types of packet discretization for continuous spectra in quantum scattering problems. As we previously showed, this discretization leads to a convenient finite-dimensional (i.e., matrix) approximation for integral operators in the scattering theory and allows reducing the solution of singular integral equations connected with the scattering theory to some suitable purely algebraic equations on an analytic basis. All singularities are explicitly singled out. Our primary emphasis is on realizing the method practically.     

A note on a result by M. Bognár concerning the Hahn--Mazurkiewicz Theorem

Summary In this note we use Theorem 2.4 in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1]to give a very short proof of a recent result due to M. Bognár (Theorem A in [3]). We also prove that Bognár's result is in fact equivalent to the classical Hahn-Mazurkiewicz Theorem. Finally we give generalizations in the non-compact setting.     

有限线状连续带电体二维平面电场的计算机模拟

利用切线法和扫描法绘制一些有限线状连续带电体所在平面的电力线和等势线。