Ruin Probabilities for Risk Models with Constant Interest

Ukrainian Mathematical Journal - We consider continuous-time risk models with m-dependent claim sizes and constant interest rate. Under certain special conditions, we obtain the upper bound for the...     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Halide Anion Triggered Reactions of Michael Acceptors with Tropylium Ion

Tropylium bromide undergoes noncatalyzed, regioselective additions to a large variety of Michael acceptors. In this way, acrylic esters are converted into β-bromo-α-cycloheptatrienylpropionic esters. The reactions are interpreted as nucleophilic attack of bromide ions at the electron-deficient olefins and the approach of the tropylium ion to the incipient carbanion. Quantum chemical calculations were performed to elucidate the analogy to the amine- or phosphine-catalyzed Rauhut–Currier reactions. Subsequent synthetic transformations of the bromo-cycloheptatrienylated adducts are reported.     

Activation of α-Fe2O3 for Photoelectrochemical Water Splitting Strongly Enhanced by Low Temperature Annealing in Low Oxygen Containing Ambient

Photoelectrochemical (PEC) water splitting is a promising method for the conversion of solar energy into chemical energy stored in the form of hydrogen. Nanostructured hematite (α-Fe₂O₃) is one of the most attractive materials for a highly efficient charge carrier generation and collection due to its large specific surface area and the short minority carrier diffusion length. In the present work, the PEC water splitting performance of nanostructured α-Fe₂O₃ is investigated which was prepared by anodization followed by annealing in a low oxygen ambient (0.03 % O₂ in Ar). It was found that low oxygen annealing can activate a significant PEC response of α-Fe₂O₃ even at a low temperature of 400 °C and provide an excellent PEC performance compared with classic air annealing. The photocurrent of the α-Fe₂O₃ annealed in the low oxygen at 1.5 V vs. RHE results as 0.5 mA cm⁻², being 20 times higher than that of annealing in air. The obtained results show that the α-Fe₂O₃ annealed in low oxygen contains beneficial defects and promotes the transport of holes; it can be attributed to the improvement of conductivity due to the introduction of suitable oxygen vacancies in the α-Fe₂O₃. Additionally, we demonstrate the photocurrent of α-Fe₂O₃ annealed in low oxygen ambient can be further enhanced by Zn-Co LDH, which is a co-catalyst of oxygen evolution reaction. This indicates low oxygen annealing generates a promising method to obtain an excellent PEC water splitting performance from α-Fe₂O₃ photoanodes.     

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.     

Dual sufficient characterizations of transversality properties

Positivity - This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to develop a general scheme for quantitative...     

Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality...     

Tomographic probability representation for quantum fermion fields

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto the probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are described by fermionic tomographic symbols. The product of the operators acting on the fermion states is mapped onto the star-product of the fermionic symbols. The kernel of the star-product is obtained. The antisymmetry of the fermion states is formulated as a specific symmetry property of the tomographic joint probability distribution associated with the states.