Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

ABSTRACT

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.     

含非完整界面的功能梯度压电材料Ⅲ型裂纹问题

本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题．此裂纹垂直于非完整界面，采用弹簧型力电耦合界面模型模拟非完整界面．界面两侧材料的性质，如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化．运用积分变换法将裂纹面条件转换为奇异积分方程，并使用Gauss-Chebyshev方法对其进行数值求解．根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系．     

A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

Double‐crosslinked reversible redox‐responsive hydrogels based on disulfide–thiol interchange

We present novel redox‐responsive hydrogels based on poly(N‐isopropylacrylamide) or poly(acrylamide), consisting of a reversible disulfide crosslinking agent N,N′‐bis(acryloyl)cystamine and a permanent crosslinking agent N,N′‐methylenebisacrylamide for microfluidic applications. The mechanism of swelling/deswelling behavior starts with the cleavage and reformation of disulfide bonds, leading to a change of crosslinking density and crosslinking points. Raman and ultraviolet‐visible spectroscopy confirm that conversion efficiency of thiol–disulfide interchange up to 99%. Rheological analysis reveals that the E modulus of hydrogel is dependent on the crosslinking density and can be repeatedly manipulated between high‐ and low‐stiffness states over at least 5 cycles without significant decrease. Kinetic studies showed that the mechanical strength of the gels changes as the redox reaction proceeds. This process is much faster than the autonomous diffusion in the hydrogel. Moreover, cooperative diffusion coefficient (D_coop) indicates that the swelling process of the hydrogel is affected by the reduction reaction. Finally, this reversibly switchable redox behavior of bulky hydrogel could be proven in microstructured hydrogel dots through short‐term photopatterning process. These hydrogel dots on glass substrates also showed the desired short response time on cyclic swelling and shrinking processes known from downsized hydrogel shapes. Such stimuli‐responsive hydrogels with redox‐sensitive crosslinkers open a new pathway in exchanging analytes for sensing and separating in microfluidics applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2590–2601     

Some research problems on the hadamard product and singular values of matrices

We pose some problems on the Hadamard product and singular values of matrices.     

Modified Gauss rules for approximate calculation of some strongly singular integrals

The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented.     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.