Characterizations of optimality in convex programming: the nondifferentiable case

Primal, dual and saddle-point characterizations of optimality are given for convex programming in the general case (nondifferentiable functions and no constraint qualification).     

Ab initio modelling of the interaction of H interstitials with grain boundaries in bcc Fe

Hydrogen that is accumulated within the grain boundaries can lead to a decrease of the critical strain required to fracture the material. The paper presents results of ab initio modelling of hydrogen–grain boundary interaction in ferromagnetic bcc iron. Modelling was performed using density functional theory with generalised gradient approximation (GGA’96), as implemented in WIEN2k package. Three fully relaxed tilt grain boundaries, Σ5(310), Σ5(210) and Σ3(111), were studied. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two ‘grains’. Calculated formation energies of grain boundaries is 1.44, 1.83 and 1.46 J/m² and the maximum binding (trapping) energies of hydrogen to the boundaries are 0.43, 0.83 and 0.39 eV, respectively. These values are close to other researchers’ data. The higher value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical atom configurations resulting from mutual rigid shift of the two grains that was necessary to be introduced to provide optimal distances between Fe atoms, unlike the other two boundary types.     

Defects within the landau theory: A perturbation approach

We discuss the continuum medium theory that enables us to find the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters. The theory is invalid in the immediate vicinity of the phase transition temperature and for high concentration of defects. The possibilities of interpretation of experimental data on the basis of the theory are also discussed.     

Surplus division and investment incentives in supply chains: A biform-game analysis

In this paper, we use a biform-game approach for analyzing the impact of surplus division in supply chains on investment incentives. In the first stage of the game, firms decide non-cooperatively on investments. In the second stage, the surplus is shared according to the Shapley value. We find that all firms have inefficiently low investment incentives which, however, depend on their position in the supply chain. Cross-subsidies for investment costs can mitigate, but not eliminate the underinvestment problem. Vertical integration between at least some firms.yields efficient investments, but may nevertheless reduce the aggregated payoff of the firms. We show how the size of our effects depends on the structure of the supply chain and the efficiency of the investment technology. Various extensions demonstrate that our results are qualitatively robust.     

Two-Dimensional Layered Metallic VSe2/SWCNTs/rGO Based Ternary Hybrid Materials for High Performance Energy Storage Applications

In this work, the ternary hybrid structure VSe₂/SWCNTs/rGO is reported for supercapacitor applications. The ternary composite exhibits a high specific capacitance of 450 F g⁻¹ in a symmetric cell configuration, with maximum energy density of 131.4 Wh kg⁻¹ and power density of 27.49 kW kg⁻¹. The ternary hybrid also shows a cyclic stability of 91 % after 5000 cycles. Extensive density functional theory (DFT) simulations on the structure as well as on the electronic properties of the binary hybrid structure VSe₂/SWCNTs and the ternary hybrid structure VSe₂/SWCNTs/rGO have been carried out. Due to a synergic effect, there are enhanced density of states near the Fermi level and higher quantum capacitance for the hybrid ternary structure compared to VSe₂/SWCNTs, leading to higher energy and power density for VSe₂/SWCNTs/rGO, supporting our experimental observation. Computed diffusion energy barrier of electrolyte ions (K⁺) predicts that ions move faster in the ternary structure, providing higher charge storage performance.     

Synthesis,spectroscopic, DFT,biological studies and molecular docking of oxovanadium (IV), copper (II) and iron (III) complexes of a new hydrazone derived from heterocyclic hydrazide

A new Schiff base hydrazone (Z)‐2‐(2‐aminothiazol‐4‐yl)‐N′‐(2‐hydroxy‐3‐methoxybenzylidene) acetohydrazide (H₂L) and its chelates [VO (HL)₂]·5H₂O, [Cu (HL)Cl(H₂O)]·2H₂O and [Fe(L)Cl(H₂O)₂]·3H₂O have been isolated and characterized using different physico‐chemical methods, for example infrared (IR), electron paramagnetic resonance (EPR), thermogravimetric analysis and DTG in the solid state, and ¹H‐NMR, ¹³C‐NMR and UV in solution. Magnetic and UV–visible measurements proposed that the coordination environments are square pyramidal, tetrahedral and octahedral geometries for oxovanadium (IV), Cu (II) and Fe (III), respectively. The ligand acts as mono‐negative NO towards oxovanadium (IV) and Cu (II) ions, and bi‐negative ONO for Fe (III) ion. The geometries of the ligand and its complexes were performed using Gaussian 9 program with density functional theory. The EPR spectral data of oxovanadium (IV) and Cu (II) chelates confirmed the mentioned geometries. The molecular modeling was done, and illustrated bond lengths, bond angles, molecular electrostatic potential, Mulliken atomic charges and chemical reactivity for the inspected compounds. Theoretical IR and ¹H‐NMR of the free ligand were calculated. Furthermore, thermodynamic and kinetic parameters for thermal decomposition steps were studied. Docking study of H₂L was applied against the proteins of both bacterial strains Staphylococcus aureus and Escherichia coli, as well as the protein of xanthine oxidase as antioxidant agent by Schrödinger suite program utilizing XP glide protocol. Furthermore, antimicrobial, antioxidant and DNA‐binding activities of the compounds have been carried out.     

On Electrostatics,Covalency, and Chemical Dashes: Physical Interactions versus Chemical Bonds

The increasing availability of real-space interaction energies between quantum atoms or fragments that provide a chemically intuitive decomposition of intrinsic bond energies into electrostatic and covalent terms [see, for instance, Chem. Eur. J. 2018 , 24, 9101] provides evidence for differences between the physicist's concept of interaction and the chemist's concept of a bond. Herein, it is argued that, for the former, all types of interactions are treated equally, whereas, for the latter, only the covalent short-range interactions have actually been used to build intuition about chemical graphs and chemical bonds. This has led to the bonding role of long-range Coulombic terms in molecular chemistry being overlooked. Simultaneously, blind consideration of electrostatic terms in chemical bonding parlance may lead to confusion. The relationship between these concepts is examined herein, and some notes of caution on how to merge them are proposed.     

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Previously, master equation (ME) simulations using semiclassical transition state theory (SCTST) and high-accuracy extrapolated ab initio thermochemistry (HEAT) predicted rate constants in excellent agreement with published experimental data over a wide range of pressure and temperatures ≳250 K, but the agreement was not as good at lower temperatures. Possible reasons for this reduced performance are investigated by (a) critically evaluating the published experimental data and by investigating; (b) three distinct ME treatments of angular momentum, including one that is exact at the zero- and infinite-pressure limits; (c) a hindered-rotor model for HOCO that implicitly includes the cis- and trans-conformers; (d) possible empirical adjustments of the thermochemistry; (e) possible empirical adjustments to an imaginary frequency controlling tunneling; (f) including or neglecting the prereaction complex PRC1; and (g) its possible bimolecular reactions. Improvements include better approximations to factors in SCTST and using the Hill and van Vleck treatment of angular momentum coupling. Evaluation of literature data does not reveal any specific shortcomings, but the stated uncertainties may be underestimated. All ME treatments give excellent fits to experimental data at T ≥ 250 K, but the discrepancy at T < 250 K persists. Note that each ME model requires individual empirical energy transfer parameters. Thermochemical adjustments were unable to match the experimental H/D kinetic isotope effects. Adjusting an imaginary frequency can achieve good fits, but the adjustments are unacceptably large. Whether PRC1 and its possible bimolecular reactions are included had little effect. We conclude that none of the adjustments is an improvement over the unadjusted theory. Note that only one set of experimental data exists in the regime of the discrepancy with theory, and data for DO + CO are scanty.     

The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision.