Spectral Analysis and Solvability of Volterra Integro-Differential Equations

Doklady Mathematics - Integro-differential equations with unbounded operator coefficients in a Hilbert space are studied. The equations under consideration are abstract hyperbolic equations...     

General Formation of Macro-/Mesoporous Nanoshells from Interfacial Assembly of Irregular Mesostructured Nanounits

Mesoporous core–shell nanostructures with controllable ultra-large open channels in their nanoshells are of great interest. However, soft template-directed cooperative assembly to mesoporous nanoshells with highly accessible pores larger than 30 nm, or even above 50 nm into macroporous range, remains a significant challenge. Herein we report a general approach for precisely tailored coating of hierarchically macro-/mesoporous polymer and carbon shells, possessing highly accessible radial channels with extremely wide pore size distribution from ca. 10 nm to ca. 200 nm, on diverse functional materials. This strategy creates opportunities to tailor the interfacial assembly of irregular mesostructured nanounits on core materials and generate various core–shell nanomaterials with controllable pore architectures. The obtained Fe,N-doped macro-/mesoporous carbon nanoshells show enhanced electrochemical performance for the oxygen reduction reaction in alkaline condition.     

Measurement of Residual Dipolar Couplings of Organic Molecules in Multiple Solvent Systems Using a Liquid-Crystalline-Based Medium

Residual dipolar coupling (RDC), a robust anisotropic NMR parameter for structural elucidation of organic molecules, is only accessible in an anisotropic environment. Herein, we introduce a novel alignment medium based on the molecular self-assembly of oligopeptide amphiphile (OPA). This medium is compatible with different intermediate and polar solvent systems, such as CD₃OD, [D₆]DMSO, and D₂O. The preparation of the OPA-based medium is simple and rapid, while only very weak background signals were observed from OPAs. Furthermore, we show that the purity of OPA has only a minor influence on the quality of the RDC data. These advantages allow RDC measurements of organic molecules with different polarities and solubilities with high efficiency and accuracy.     

Direct Intermediate Regulation Enabled by Sulfur Containers in Working Lithium–Sulfur Batteries

Polysulfide intermediates (PSs), the liquid-phase species of active materials in lithium–sulfur (Li-S) batteries, connect the electrochemical reactions between insulative solid sulfur and lithium sulfide and are key to full exertion of the high-energy-density Li-S system. Herein, the concept of sulfur container additives is proposed for the direct modification on the PSs species. By reversible storage and release of the sulfur species, the container molecule converts small PSs into large organosulfur species. The prototype di(tri)sulfide-polyethylene glycol sulfur container is highly efficient in the reversible PS transformation to multiply affect electrochemical behaviors of sulfur cathodes in terms of liquid-species clustering, reaction kinetics, and solid deposition. The stability and capacity of Li-S cells was thereby enhanced. The sulfur container is a strategy to directly modify PSs, enlightening the precise regulation on Li-S batteries and multi-phase electrochemical systems.     

Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

Synthesis of lupeol derivatives and their antileishmanial and antitrypanosomal activities

The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by ¹H NMR, ¹³C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC₅₀ = 12.48 μg/mL) and the lowest cytotoxic derivative (CC₅₀ = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase.     

On the performance of band-limited asynchronous DS-CDMA over nakagami-m channels

In this paper we investigated the BER performance of DS-CDMA using various chip-waveforms, which include three time-limited chip-waveforms and two band-limited chip-waveforms. Closed-form formulae were derived for evaluating the achievable bit-error rate performance with the aid of the standard Gaussian approximation, when communicating over a Nakagami-m channel. The time-limited waveforms impose a low implementational complexity, since they maybe over sampled and read from a look-up table. However, they are outperformed by the frequency-domain raised-cosine waveform as well as the optimum waveform specifically designed by Cho and Lehnert for achieving the lowest possible bit error rate     

Surface space-charge waves in open guiding structures

Basic definitions related to the main electrodynamic characteristics of surface space-charge waves are formulated. These characteristics and their relationships with the geometric dimensions of guiding structures (a dielectric cylinder and a planar metal-dielectric waveguide) are determined.     

A closed-form solution for the distribution of the sum of Nakagami-m random phase vectors

The distribution of the modulus of the sum of random phase vectors, is of great practical importance in several applications which deal with sums of sinusoidal signals (wireless multipath transmissions, radars, optical communications, etc). In this letter, simple closed-form expressions are presented for the probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF) and the moments of the envelope distribution of the sum of L non-identical random Nakagami-m phase vectors with integer fading parameters. Moreover, the average over this distribution of the Gaussian Q-function and of the squared Q-function, are also presented in closed-form