正项级数敛散性新的根式判别法

基于几何级数的敛散性和比较判别法,给出判断正项级数敛散性的一个新的根式判别法,并举例说明其应用.     

The BMO L space and Riesz transforms associated with Schrödinger operators

Let L =△ ＋ V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Fefferman-Stein type decomposition of BMOL functions.     

Fundamentals of Computational Conformal Geometry

Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.     

The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.     

The classification of maximal inverse monoids of matrices

Semigroup Forum - Let $${\mathbb {F}}$$ be a field. The set $$M_{n}({\mathbb {F}})$$ of all $$n \times n$$ matrices over $${\mathbb {F}}$$ forms a monoid under usual matrix multiplication. We...     

Density functional calculations on 13-atom Pd12M （M= Sc-Ni） bimetallic clusters

The geometric structures,electronic and magnetic properties of the 3d transition metal doped clusters Pd12M(M=Sc-Ni) are studied using the semi-core pseudopots density functional theory.The groundstate geometric structure of the Pd12M cluster is probably of pseudoicosahedron.The Ih-Pd12M cluster has the most thermodynamic stability in five different symmetric isomers.The energy gap shows that Pd12M cluster is partly metallic.Both the absolutely predominant metal bond and very weak covalent bond might exist in the Pd12M cluster.The magnetic moment of Pd12M varies from 0 to 5 μB,implying that it has a potential application in new nanomaterials with tunable magnetic properties.     

Photo-electrochemical analysis of passive film formed on X80 pipeline steel in bicarbonate/carbonate buffer solution

Photo-electrochemical measurement was used to explore the formation potential, formation time, chloride ions concentration, applied potential and pH value of the solution on the electronic property of passive film formed on X80 pipeline steel in 1 M NaHCO₃/0.5 M Na₂CO₃ buffer solution. The results showed that the photocurrent is positive, indicating an n-type semiconductor character of the passive film, the photocurrent increased with increasing the formation potential, prolonging the formation time, decreasing chloride ions concentration, rising applied potential and decreasing the pH value of the solution. Capacitance measurement exhibited a positive slope of Mott-Schottky plot, and the slopes of Mott-Schottky plots increased with the increasing formation potential, showing a decrement of the donor density of the passive film.     

Determination of arterial wall shear stress

The arteries can remodel their structure and function to adapt themselves to the mechanical environment. In various factors that lead to vascular remodeling, the shear stress on the arterial wall induced by the blood flow is of great importance. However, there are many technique difficulties in measuring the wall shear stress directly at present. In this paper, through analyzing the pulsatile blood flow in arteries, a method has been proposed that can determine the wall shear stress quantitatively by measuring the velocity on the arterial axis, and that provides a necessary means to discuss the influence of arterial wall shear stress on vascular remodeling.     

Quasi-linear PDEs and forward–backward stochastic differential equations: Weak solutions

In this paper, we study the existence, uniqueness and the probabilistic representation of the weak solutions of quasi-linear parabolic and elliptic partial differential equations (PDEs) in the Sobolev space $H_{\rho }^1({\mathbb{R}}^d)$. For this, we study first the solutions of forward–backward stochastic differential equations (FBSDEs) with smooth coefficients, regularity of solutions and their connection with classical solutions of quasi-linear parabolic PDEs. Then using the approximation procedure, we establish their convergence in the Sobolev space to the solutions of the FBSDES in the space $L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^d)?L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^k)?L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^{k\times d})$. This gives a connection with the weak solutions of quasi-linear parabolic PDEs. Finally, we study the unique weak solutions of quasi-linear elliptic PDEs using the solutions of the FBSDEs on infinite horizon.