High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations

We introduce a high resolution fifth-order semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations. The numerical fluxes of the scheme are constructed by Hermite polynomials which can be obtained by using the short-time assignment of the first derivatives. The extensions of the proposed semi-discrete Hermite central-upwind scheme to multidimensional cases are straightforward. The accuracy, efficiency and stability properties of our schemes are finally demonstrated via a variety of numerical examples.     

Constructing permutation polynomials from piecewise permutations

We present a construction of permutation polynomials over finite fields by using some piecewise permutations. Based on a matrix approach and an interpolation approach, several classes of piecewise permutation polynomials are obtained.     

CALCULATION FORMULAS FOR PRINCIPAL STRESSES

在前人工作的基础上,运用一元三次方程的理论直接求解应力状态的特征方程,得到了实用的主应力计算公式.     

Cubic C8: An Observable Allotrope of Carbon?

Ab initio and DFT calculations are used to investigate the structure, electronic properties, spectra and reactivity of cubic C₈, which is predicted to be aromatic according to Hirsch′s rule. Although highly strained and with a small amount of diradical character, the carbon cube represents a surprisingly deep minimum and should therefore be observable as an isolated molecule. It is, however, predicted to be very reactive, both with itself and triplet oxygen. Calculated IR, Raman, and UV/Vis spectra are provided to aid identification of cubic C₈ should it be synthesized.     

Universal mappings for certain classes of operators and polynomials between Banach spaces

A well‐known result of J. Lindenstrauss and A. Pełczyński (1968) gives the existence of a universal non‐weakly compact operator between Banach spaces. We show the existence of universal non‐Rosenthal, non‐limited, and non‐Grothendieck operators. We also prove that there does not exist a universal non‐Dunford–Pettis operator, but there is a universal class of non‐Dunford–Pettis operators. Moreover, we show that, for several classes of polynomials between Banach spaces, including the non‐weakly compact polynomials, there does not exist a universal polynomial.     

On eight-dimensional unital division algebras over finite fields

The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry.     

IrIII‐based Octahedral Metalloligands Derived Primitive Cubic Frameworks for Enhanced CO2/N2 Separation

We developed a metalloligand strategy to construct porous frameworks, viz. the combined use of Ir^III‐based octahedral metalloligands and the linear unit [Ni(cyclam)] easily afforded two isostructural complexes 1 and 2 with primitive cubic frameworks. Both complexes show good CO₂/N₂ separation property.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.