New Approach to Calculating the Double Coaxial Resonator with a Shortening Capacitance

Russian Physics Journal - The double coaxial resonator with a shortening capacitance is calculated by the partial volume method. The double resonator is represented by two single coaxial resonators...     

Optimization in a Nonlinear Lanchester-Type Model Involving Supply Units $$^* $$

Journal of Applied and Industrial Mathematics - In this paper, we introduce a nonlinear Lanchester-type model involving supply units. The model describes a battle where the Blue party consisting of...     

Infinite-dimensional Log-Determinant divergences between positive definite Hilbert–Schmidt operators

Positivity - The current work generalizes the author’s previous work on the infinite-dimensional Alpha Log-Determinant (Log-Det) divergences and Alpha-Beta Log-Det divergences, defined on the...     

Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

Journal of Nonlinear Science - We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $$L^2$$ weak...     

Regularized Divergences Between Covariance Operators and Gaussian Measures on Hilbert Spaces

Journal of Theoretical Probability - This work presents an infinite-dimensional generalization of the correspondence between the Kullback–Leibler and Rényi divergences between Gaussian...     

On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.     

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f ^nm (z)f ^nd (qz + c))^(k) for meromorphic functions in a non-Archimedean field.     

Design of Hollow Nanoreactors for Size- and Shape-Selective Catalytic Semihydrogenation Driven by Molecular Recognition

Mimicking the structures and functions of cells to create artificial organelles has spurred the development of efficient strategies for production of hollow nanoreactors with biomimetic catalytic functions. However, such structure are challenging to fabricate and are thus rarely reported. We report the design of hollow nanoreactors with hollow multishelled structure (HoMS) and spatially loaded metal nanoparticles. Starting from a molecular-level design strategy, well-defined hollow multishelled structure phenolic resins (HoMS-PR) and carbon (HoMS-C) submicron particles were accurately constructed. HoMS-C serves as an excellent, versatile platform, owing to its tunable properties with tailored functional sites for achieving precise spatial location of metal nanoparticles, internally encapsulated (Pd@HoMS-C) or externally supported (Pd/HoMS-C). Impressively, the combination of the delicate nanoarchitecture and spatially loaded metal nanoparticles endow the pair of nanoreactors with size–shape-selective molecular recognition properties in catalytic semihydrogenation, including high activity and selectivity of Pd@HoMS-C for small aliphatic substrates and Pd/HoMS-C for large aromatic substrates. Theoretical calculations provide insight into the pair of nanoreactors with distinct behaviors due to the differences in energy barrier of substrate adsorption. This work provides guidance on the rational design and accurate construction of hollow nanoreactors with precisely located active sites and a finely modulated microenvironment by mimicking the functions of cells.