Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.      

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.     

A proposal for a convertible stadium roof structure derived from Watt-I linkage

In this paper, a novel convertible stadium roof structure is introduced, which has been derived from a special geometric configuration of Watt-I linkage, a 1-DoF mechanism used in robot technologies as anthropomorphic fingers. The proposed structure can offer a wide range of different shape configurations according to the environmental conditions and spatial needs, thus offering several aesthetic and functional advantages over existing solutions. This paper serves as a feasibility investigation of this concept, mainly from geometric and structural point of view. To that affect, first kinematic analysis and geometric design of this linkage are introduced. Then, structural analyses of the proposed structure with realistic dimensions and loading conditions are performed in three different geometric configurations, in order to discuss strength and stiffness limitations. Finally, potential cover materials and actuators are briefly discussed.     

Recovery rates in investment-grade pools of credit assets: A large deviations analysis

We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate function and show that it has a natural interpretation as the favored way to rearrange recoveries and losses among the different types. Numerical examples are also provided.     

APN permutations on and Costas arrays

We study PN and APN functions over the integers modulo n. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on where p is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.     

Accurate Interaction Energies of CO2 with the 20 Naturally Occurring Amino Acids

We have performed a series of highly accurate calculations between CO₂ and the 20 naturally occurring amino acids for the investigation of the attractive noncovalent interactions. Different nucleophilic groups present in the amino acid structures were considered (α-NH₂, COOH, side groups), and the stronger binding sites were identified. A database of accurate reference interactions energies was compiled as computed by explicitly-correlated coupled-cluster singles-and-doubles, together with perturbative triples extrapolated to the complete-basis-set limit. The CCSD(F12)(T)/CBS reference values were used for comparing a variety of popular density functionals with different basis sets. Our results show that most density functionals with the triple-zeta basis set def2-TZVPP align with the CCSD(F12)(T)/CBS reference values, but errors range from 0.1 kcal/mol up to 1.0 kcal/mol.     

Direct Hydrogenation of Dinitrogen and Dioxygen via Eley–Rideal Reactions

Most Eley–Rideal abstraction reactions involve an energetic gas‐phase atom reacting directly with a surface adsorbate to form a molecular product. Molecular projectiles are generally less reactive, may dissociate upon collision with the surface, and thus more difficult to prove that they can participate intact in abstraction reactions. Here we provide experimental evidence for direct reactions occurring between molecular N₂⁺ and O₂⁺ projectiles and surface‐adsorbed D atoms in two steps: first, the two atoms of the diatomic molecule undergo consecutive collisions with a metal surface atom without bond rupture; and second, the rebounding molecule abstracts a surface D atom to form N₂D and O₂D intermediates, respectively, detected as ions. The kinematics of the collisional interaction confirms product formation by an Eley–Rideal reaction mechanism and accounts for inelastic energy losses commensurate with surface re‐ionization. Such energetic hydrogenation of dinitrogen may provide facile activation of its triple bond as a first step towards bond cleavage.     

Electrocatalytic Hydrogen Evolution Using A Molecular Antimony Complex under Aqueous Conditions: An Experimental and Computational Study on Main-Group Element Catalysis

Electrocatalytic hydrogen gas production is considered a potential pathway towards carbon-neutral energy sources. However, the development of this technology is hindered by the lack of efficient, cost-effective, and environmentally benign catalysts. In this study, a main-group-element-based electrocatalyst, SbSalen , is reported to catalyze the hydrogen evolution reaction (HER) in an aqueous medium. The heterogenized molecular system achieved a Faradaic efficiency of 100 % at −1.4 V vs. NHE with a maximum current density of −30.7 mA/cm². X-ray photoelectron spectroscopy of the catalyst-bound working electrode before and after electrolysis confirmed the molecular stability during catalysis. The turnover frequency was calculated as 43.4 s⁻¹ using redox-peak integration. The kinetic and mechanistic aspects of the electrocatalytic reaction were further examined by computational methods. This study provides mechanistic insights into main-group-element electrocatalysts for heterogeneous small-molecule conversion.