The bang–bang theorem via Baire category: a dual approach

The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point \({\bar x}\), we consider those which minimize an auxiliary linear functional \({\phi}\). For all \({\phi}\) in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.     

In situ preparation of polymeric cobalt phthalocyanine–decorated TiO2 nanorods for efficient photocatalytic CO2 reduction

The integration of photosensitizers with low-cost and non-toxic metal oxides is a promising strategy to design heterogeneous photocatalysts for CO₂ reduction. Herein, p–n heterojunction photocatalysts (T-CoPPcs) consisting of p-type polymeric cobalt phthalocyanines (CoPPcs) as a photosensitizer coupled with n-type TiO₂ nanorods were fabricated through a facile, eco-friendly, one-pot hydrothermal reaction. In this process, CoPPcs were grown on n-type TiO₂ nanorods, whereas protonated titanate nanorods began converting to the highly crystalline anatase phase with small crystals on the TiO₂ surfaces. The introduction of CoPPcs not only improved the solar light utilization but also accelerated the separation and migration of charge carriers via the p–n heterojunction with the strong interfacial contact Ti–O–Co bond. The increases in crystallinity and surface area of TiO₂ nanorods also contributed to the enhanced photoactivities of T-CoPPcs. The CO₂ photoreduction of the synthesized materials was evaluated in CO₂-saturated MeCN/water using [Co(bpy)₃]²⁺ as a cocatalyst and triethanolamine as a hole scavenger. The optimized nanocomposite exhibited a remarkable CO generation rate of 4.42 mmol/h/g with a high selectivity of 85.3% and outstanding catalytic stability. The influences of cocatalyst concentration, water content, catalyst loading, and hole scavenger concentration were optimized for efficient CO₂ reduction. The photocatalytic CO₂ conversion efficiency of the present system is found to be higher than that of TiO₂-based materials reported in the literature. We believe that this research into a heterostructural design strategy and photocatalytic system may be an inspiration for the development of photocatalytic CO₂-to-CO conversion.     

The isomeric ratios in photonuclear reactions of natural tellurium induced by bremsstrahlungs with endpoint energies in the giant dipole resonance region

We have determined the isomeric ratios in ¹²⁰Te(γ, n)^119m,gTe, ¹²²Te(γ, n)^121m,gTe, ¹²⁸Te(γ, n)^127m,gTe and ¹³⁰Te(γ, n)^129m,gTe photonuclear reactions of natural tellurium induced by bremsstrahlungs with end-point energies in the giant dipole resonance (GDR) region. The investigated samples were irradiated at electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The gamma spectra of the samples irradiated were measured with spectroscopic system consisting of 8192 channel analyzer and high-energy resolution (180 keV at gamma ray 1,332 keV of ⁶⁰Co) HP(Ge) semiconductor detector Canberra. The GENIE2000 (Canberra) computer program was used for data processing. The results were discussed and compared with those of other authors.     

Singular gradient flow of the distance function and homotopy equivalence

Let $M$ be a Riemannian manifold and let $\varOmega $ be a bounded open subset of $M$ . It is well known that significant information about the geometry of $\varOmega $ is encoded into the properties of the distance, $d_{\partial \varOmega }$ , from the boundary of $\varOmega $ . Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if $x_0$ is a singular point of $d_{\partial \varOmega }$ then the generalized characteristic starting at $x_0$ stays singular for all times. As an application, we deduce that the singular set of $d_{\partial \varOmega }$ has the same homotopy type as $\varOmega $ .     

Monte-Carlo calculations for neutron yield from photonuclear reactions following bremsstrahlung in tungsten target

The photonuclear reactions of (γ, xn) or (γ, xnp) types can be used to produce high-intensity neutron sources for research and applied purposes. In this work a Monte-Carlo calculation has been used to evaluate the production yields of neutrons from the (γ, n) and (γ, 2n) reactions following the bremsstrahlung produced by 100 and 200 MeV electron beams on the tungsten target. Our calculations indicated that the neutron yield is an increasing function of the target thickness in a considered range from 1.5 to 2.5 mm.     

A synthesis of new 7-amino-substituted 4-aminopyrazolo[1,5-a][1,3,5]triazines via a selective three-component triazine ring annulation

3-Amino-substituted 5-aminopyrazoles were found to be suitable substrates for the synthesis of new 4-aminopyrazolo[1,5-a][1,3,5]triazines (5-aza-9-deaza-adenines) when used in the one-pot, three-component reaction with cyanamide and triethyl orthoformate under microwave irradiation. The reaction proceeded selectively and its scope was demonstrated by the preparation of a library of 4-aminopyrazolo[1,5-a][1,3,5]triazines. Some structural aspects of the prepared compounds were investigated using dynamic NMR spectroscopy and X-ray crystallography. The operational simplicity, short reaction time, and good reproducibility are attractive features of the developed robust and practical approach for the synthesis of 7-amino-substituted 4-aminopyrazolo[1,5-a][1,3,5]triazines.     

Design of type-II interband cascade lasers for terahertz emission

We report the design of type-II interband cascade (IC) lasers emitting at terahertz (THz) range. The band structures are obtained using an eight-band k · p finite difference method with strain effects, which accounts for the coupling between the conduction and valence bands. Also, a detailed analysis of the interband transition energy in the type-II IC laser structures as a function of layer thickness is carried out using the self-consistent Schrödinger–Poisson calculations. The calculations show that the promising type-II IC lasers operating at 2.3 THz can be reached.     

Configuration of subgroups in the special linear group over a skew field with infinite center

Let T be a skew field with infinite center, let be the special linear group over T of degree 3, and let be the subgroup of diagonal matrices with unit Dieudonee determinant. It is proved that for each intermediate subgroup H, H , there exists a net of order n such that ( H N().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 5–12, 1989.In conclusion, the author would like to thank his instructor Z. I. Borevich, as well as N. A. Vavilov, for their assistance.     

吡咯锂的合成、表征及晶体结构

Development of clean energy is an urgent requirement because of the depletion of fossil energy sources and increasingly severe environmental pollution. However, the lack of safe and efficient hydrogen storage materials is one of the bottlenecks in the implementation of hydrogen energy. Liquid organic hydrogen carriers (LOHCs) have been recognized as potential materials for the storage and transportation of hydrogen owing to their high gravimetric and volumetric hydrogen densities, reversible hydrogen absorption and desorption ability, and ease of widespread implementation with minimal modification on the existing fueling infrastructure. While some LOHCs such as cycloalkanes and N-heterocycles have been developed for hydrogen storage, they require a high hydrogen release temperature due to the large enthalpy change of dehydrogenation. In our previous work, a metallation strategy was proposed to improve the thermodynamic properties of liquid organic hydrogen carriers for hydrogen storage, and a series of metalorganic hydrides were synthesized and investigated. Among them, sodium phenoxide-cyclohexanolate pair, lithium carbazolide-perhydrocarbazolide, and sodium anilinide-cyclohexylamide pair showed promising dehydrogenation thermodynamics and improved hydrogen storage properties. Sodium pyrrolide and sodium imidazolide were also synthesized. However, pyrrolides were not well characterized, and the structure of lithium pyrrolide was not resolved. In the present study, we synthesized sodium and lithium pyrrolides by ball milling and wet chemical methods. One equivalent of hydrogen could be released from the reaction of pyrrole and metal hydrides, indicating the replacement of H by metal. The formation of pyrrolides was confirmed by nuclear magnetic resonance (NMR), X-ray diffraction (XRD) and ultraviolet-visible spectroscopy analyses. The ¹H signals attributed to C－H in the NMR spectra of the alkali metal pyrrolides shifted upfield due to the replacement of the H of N－H with a stronger electron-donating species (Li or Na), resulting in a greater shielding environment upon metallation. The absorption peaks of lithium and sodium pyrrolides showed red shifts, and the intensities became obviously stronger in the UV-Vis spectra, suggesting an enhancement of the conjugation effect, in accordance with theoretical calculations. The structure of lithium pyrrolide was determined by the combined direct space method and first-principles calculations on XRD data and Rietveld refinement. This molecule crystallizes in the monoclinic P2₁/c (14) space group, with lattice parameters of a = 4.4364(7) Å, b = 11.969(2) Å, c = 8.192(2) Å, β = 108.789(8)°, and V = 411.8(2) ų (1 Å = 0.1 nm). Each Li⁺ cation is surrounded by three pyrrolides via cation－N σ bonding with two pyrrolides and a cation–π interaction with the third pyrrolide, where the Li⁺ is on the top of the π face. Our experimental findings are different from the theoretical prediction in the literature.