Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

一种基于特征分解的图像融合方法

一幅图像可以分解成几何特征不同的纹理部分和卡通部分,基于这两大特征提出了一种图像融合方法.利用卡通和纹理特征的差异,通过学习分别得到卡通字典和纹理字典.在融合过程中,分别利用特定的卡通和纹理字典对源图像的卡通和纹理部分进行融合,融合后的卡通和纹理部分经简单相加得到融合图像.实验结果表明,所提方法是有效的.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．