Probabilistic models for stochastic elliptic partial differential equations

Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically.     

Study on High-Temperature Spectra of Asymptotic Asymmetric-Top Molecule O3

The line intensities of 001-000 transition of the asymptotic asymmetric-top O₃ molecule at several temperatures are calculated by directly calculating the partition functions and regarding the rotationless transition dipole moment squared as a constant. The calculated values of the total internal partition sums (TIPS) are consistent with the data of HITRAN database with -0.61% at 296 K. The calculated line intensity data at 500 K and 3000 K are also in excellent agreement with the data in HITRAN database with less than 0.659% and 5.458% at 500 K and 3000 K, which provide a strong support for the calculations of partition function and line intensity at high temperature. Then we extend the calculation to higher temperatures. The line intensities and simulated spectra of ν₃ band of the asymptotic asymmetric-top O₃ molecule at 4000 and 5000 K are reported. The results are of significance for the studying of the molecular high-temperature spectrum including experimental measurements and theoretical calculations.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains*

Let B_E be a bounded symmetric domain realized as the unit open ball of JB*-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE) to weighted Hardy space H_v^∞ in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(B...     

周毓麟先生在计算数学领域的成就与贡献——纪念周毓麟院士百年诞辰

本文从计算数学的视角,介绍周毓麟先生在离散泛函分析方法和大型科学计算方法等领域的研究工作.     

The minimal excludant and Schmidt's partition theorem

In this work, we study Schmidt's partition theorem in a combinatorial manner, and find a strong refinement which connects the minimal excludant of ordinary partitions to the length of Schmidt's partitions. As a byproduct, we obtain a bivariate form of an identity recorded in Ramanujan's lost notebook.     

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.     

The Weierstrass–Mandelbrot Process Revisited

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot–Weierstrass process is a complex fractional Brownian motion.     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.