On lower iteration complexity bounds for the convex concave saddle point problems

Mathematical Programming - In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: $$\min _x\max...     

Modulating Charge Carrier Efficient Separation Enabled by Lewis Base Modification in Paper-based Photoelectrochemical Sensor

The separation efficiency of charge carriers determines the analytical sensitivity of the paper-based photoelectrochemical sensor. Herein, the Lewis base modification strategy is proposed to promote the carrier separation through an in-situ ion exchange method. Firstly, three-dimensional paper-based hierarchically TiO₂ (PHT) arrays are prepared with the one-step hydrothermal method. With the aid of Lewis base, the photo-induced charge separation efficiency and the photocurrent signal are obviously increased. Ultimately, sensitive sensing of prostate specific antigen (PSA) is achieved and the linear range is 1 pg/mL–100 ng/mL with the detection limitation of 0.3 pg/mL.     

Nonlinear vibration response of a complex aeroengine under the rubbing fault

Nonlinear Dynamics - Rolling bearing and squeeze film damper will introduce structural nonlinearity into the dynamic model of aeroengine. Rubbing will occur due to the clearance reduction design of...     

A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

Weak Galerkin finite element methods with or without stabilizers

The purpose of this paper is to investigate the connections between the weak Galerkin (WG) methods with and without stabilizers. The choices of stabilizers directly affect the convergence rates of the corresponding WG methods in general. However, we observed that the convergence rates are independent of the choices of stabilizers for these WG elements with stabilizers being optional. In this paper, we will verify such phenomena theoretically as well as numerically.

     

Coexistence of double-parameter nonlinear dynamics and metastable chaos for bistable asymmetric composite laminated square panel under combined external and parametric excitations

Nonlinear Dynamics - This paper studies the double-parameter multi-pulse jumping chaotic vibrations and metastable chaos of the bistable asymmetric composite laminated square panel under combined...     

Synthesis and Structural Characterization of a Di-nuclear Uranyl Complex with Quinoline-6-carboxylate

Crystallography Reports - A di-nuclear uranyl complex with the formula of [(UO2)2(L)4(H2O)2]?4H2O (1) (HL = quinoline-6-carboxylic acid) was synthesized hydrothermally and characterized by...     

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

On Almost Interval Preserving Linear Operators

Siberian Mathematical Journal - A lattice homomorphism between quasi-Banach lattices is known to be compact if and only if it is a sum of a series of rank one lattice...