Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates

This work focuses on optimal controls of diffusions in an infinite horizon. It has several distinct features in contrast to the existing literature. The discount factor is allowed to be randomly varying and state dependent. The existence and uniqueness of the viscosity solution to the associated Hamilton–Jacobi–Bellman equation are established. The verification theorem is also obtained. Because closed-form solutions are virtually impossible to obtain in most cases, we develop numerical methods. Using the Markov chain approximation methods, numerical schemes are constructed; viscosity solution methods are used to prove the convergence of the algorithm. In addition, examples are given for demonstration purpose.     

Malliavin calculus for regularity structures: The case of gPAM

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in $L^2$-directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times.     

Lattices with Defining Relations Close to Distributivity

We consider the 3-generated lattices whose generators enjoy the defining relations of the type a∨(b∧c) = (a∨b)∧(a∨c). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.     

Anisotropic Mixed-Norm Hardy Spaces

We introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces.     

Local laws for non-Hermitian random matrices

The product of m ∈ N independent random square matrices whose elements are independent identically distributed random variables with zero mean and unit variance is considered. It is known that, as the size of the matrices increases to infinity, the empirical spectral measure of the normalized eigenvalues of the product converges with probability 1 to the distribution of the mth power of the random variable uniformly distributed on the unit disk of the complex plane. In particular, in the case of m = 1, the circular law holds. The purpose of this paper is to prove the validity of the local circular law (as well as its generalization to the case of any fixed m) in the case where the distribution of the matrix elements has finite absolute moment of order 4 + δ,δ > 0,. Recent results of Bourgade, Yau, and Yin, of Tao and Vu, and of Nemish are generalized.     

Moyennes effectives de fonctions multiplicatives complexes

We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing’s classical estimates and extending those of Halász. Several applications are derived, including estimates for the difference of mean-values of so-called pretentious functions, local laws for the distribution of prime factors in an arbitrary set, and weighted distribution of additive functions.     

A remark on boundary level admissible representations

We point out that it is immediate by our character formula that in the case of a boundary level the characters of admissible representations of affine Kac–Moody algebras and the corresponding W-algebras decompose in products in terms of the Jacobi form ${?}_{11}(\tau ,z)$.     

Correction to: Effects of environmental factors on key kinetic parameters relevant to pitting corrosion

Journal of Solid State Electrochemistry -     

Novel silver(I)N-heterocyclic carbene complexes bearing 2-(4-hydroxyphenyl)ethyl group: Synthesis,characterization, and enzyme inhibition properties

Herein, novel silver-based N-heterocyclic carbene (NHC) complexes bearing 2-(4-hydroxyphenyl)ethyl group were synthesized. Novel Ag(I)NHC complexes were synthesized from the 2-(4-hydroxyphenyl)ethyl-substituted benzimidazolium salts and silver oxide via in situ deprotonation method. The successful formation of all Ag(I)NHC complexes was proved by using ¹H NMR, ¹³C NMR, FTIR spectroscopy, and elemental analysis techniques. In addition, their inhibitory effects have been investigated of these substances on acetylcholinesterase (AChE), α-glycosidase (α-Gly), human carbonic anhydrase I (hCA I), and human carbonic anhydrase II (hCA II) enzymes. It has been seen that all compounds have a better ability to inhibit compared with existing tried inhibitors. Among these, the best inhibitor against AChE enzyme is 1g (K_i : 9.54 ± 0.98 μM and IC₅₀ : 17.40), and against α-Gly, 1c showed the highest effect (K_i 3.09 ± 0.36 μM and IC₅₀ 7.91). The best inhibitor against hCA I and hCA II enzymes are 1c and 1g compounds. For hCA I and hCA II, IC₅₀ values were calculated as 17.85 and 9.06 μM and K_i values were measured as 5.45 ± 2.02 and 8.99 ± 2.02 μM, respectively.     

Inversion of the Deactivation Efficiency of Excited States upon Selective Photoexcitation of the Uranyl Ion Complex with D-Tryptophan in Aqueous and Methanol Solutions

High Energy Chemistry - The quenching of fluorescence (FL) of uranyl ion $${\text{UO}}_{2}^{{2 + }}$$ and tryptophan Trp during their selective intracomplex photoexcitation in aqueous and methanol...