Half Inverse Riordan Arrays and Their Related Vertical Recurrence Relation

We discuss two different procedures to study the half Riordan arrays and their inverses. One of the procedures shows that every Riordan array is the half Riordan array of a unique Riordan array. It is well known that every Riordan array has its half Riordan array. Therefore, this paper answers the converse question: Is every Riordan array the half Riordan array of some Riordan arrays? In addition, this paper shows that the vertical recurrence relation of the column entries of the half Riordan array is equivalent to the horizontal recurrence relation of the original Riordan array''s row entries.     

On the Applications of the Linear Recurrence Relationships to Pseudoprimes

We present here some results on the applications of linear recursive sequences of order $2$ to the Fermat pseudoprimes, Fibonacci pseudoprimes, and Dickson pseudoprimes.     

不带微商的边界型求积公式

本文在不带微商项的条件下,对一些特殊区域构造了具有最高代数精确度的边界型求积公式。还对某些较广泛的区域解决了构造3次边界型或非边界型求积公式的“最少结点数”的问题。 首先,我们在立方体区域上将Sadowsky的42点5次边界型求积公式的结点个数减少到32点,并证明了要构造立方体区域上的5次边界型对称求积公式,结点个数不能少于32。文中还构造出n维双层球壳区域上具有最高(3次)代数精度和最少结点个数((2n+2)点)的边界型求积公式。因此,[5]中构造出的3维双层球壳区域上的8点3次边界型求积公式是“最少结点数”的求积公式。最后,证明了对于2维、3维轴对称区域(即关于所有坐标轴都对称的区域)构造3次求积公式,至少分别用到4个和6个结点。对于n维球域构造3次求积公式至少要用到2n个结点。 本文出现的求积公式都是不带微商项的。     

自正则Chung型重对数律的精确渐近性

设X,X_1,X_2,…为零均值、非退化、吸引域为正态吸引场的独立同分布随机变量序列,记S_n=■X_j,M_n=■|S_k|,V_n~2=■X_j~2,n≥1.证明了当b>-1时,■δ~(-2(b 1))■(log log n)~P/(n log n)P(Mn/V_n≤ε~(π~2)/(8lgo log n)~(1/2)) =4/πГ(b 1)■~(-1)~k/(2k 1)~(2b 3).     

Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems

How, in a discretized model, to utilize the duality and complementarity of two saddle point variational principles is considered in the paper. A homology family of optimality conditions, different from the conventional saddle point conditions of the domain-decomposed Hellinger-Reissner principle, is derived to enhance stability of hybrid finite element schemes. Based on this, a stabilized hybrid method is presented by associating element-interior displacement with an element-boundary one in a nonconforming manner. In addition, energy compatibility of strain-enriched displacements with respect to stress terms is introduced to circumvent Poisson-locking.

     

Infrared spectrum and bonding in uranium methylidene dihydride, CH2=UH2

Uranium atoms activate methane upon ultraviolet excitation to form the methyl uranium hydride CH3-UH, which undergoes alpha-H transfer to produce uranium methylidene dihydride, CH2=UH2. This rearrangement most likely occurs on an excited-quintet potential-energy surface and is followed by relaxation in the argon matrix. These simple U+CH4 reaction products are identified through isotopic substitution (13CH4, CD4, CH2D2) and density functional theory frequency and structure calculations for the strong U-H stretching modes. Relativistic multiconfiguration (CASSCF/CASPT2) calculations substantiate the agostic distorted C1 ground-state structure for the triplet CH2=UH2 molecule. We find that uranium atoms are less reactive in methane activation than thorium atoms. Our calculations show that the CH2=UH2 complex is distorted more than CH2=ThH2. A favorable interaction between the low energy open-shell U(5f) sigma orbital and the agostic hydrogen contributes to the distortion in the uranium methylidene complexes.     

Predictions of the geometries and fluorescence emission energies of oxyluciferins

The complete active space self-consistent field (CASSCF) method and multiconfigurational second-order perturbation theory (CASPT2) have been used to study the structures and spectra of oxyluciferins (OxyLH2). The ground and lowest-lying singlet excited states geometries have been optimized using CASSCF. CASPT2 has been used to predict relaxed emission energies. The focus is on the lowest-lying singlet excited states of the anionic keto and enol forms of OxyLH2(-1) at the optimized excited-state geometries. The planar keto and enol forms of OxyLH2(-1) are minima on both the S0 and the S1 potential energy surfaces. The twisted keto and enol forms of OxyLH2(-1) are transition states on the S0 and S1 potential energy surfaces. The S1 --> S0 fluorescence emission energies are in the range of 54.2-58.4 kcal/mol for the anionic planar keto forms of OxyLH2, and in the range of 55.7-63.2 kcal/mol for the anionic enol forms of OxyLH2. S0 and S1 potential energy surfaces and thus are not implicated in the emission spectra in the gas phase.     

三角形单元协调与非协调位移的能量正交关系

基于组合稳定化变分原理,周天孝提出的组合杂交法是绝对收敛和稳定的,它给出了一种系统化的增强应力／应变方法,并建立了一簇低阶仿射等价的ｎ＿ｃｕｂｅ（ｎ＝２,３）单元·本文论证了单元上应力插值为线性,位移插值为协调线性部分和非协调二次部分之和的三角形组合杂交单元其协调部分与非协调部分的能量正交关系,进而得到此三角形单元刚度矩阵等同于协调的三角形线性元刚度矩阵,即非协调部分无应变增强特性     

The energy orthogonal relation between conforming and non-conforming displacements of triangular element

Based on the variational principle of combinative stability, combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower-order elements which are affine-equivalent ton-cube (n=2,3). The energy orthogonal relation between the conforming part and the non-conforming part of displacements interpolation functions in triangular element is given, in which the stress is interpolated by linear polynomials on each element, but the displacements are interpolated by the sum of conforming linear and non-conforming quadratic polynomials. Furthermore, this element is equivalent to the conforming triangular linear element, that is, the non-conforming parts have no contribution to enhanced strains.     

Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept

Methodology and Computing in Applied Probability - Lieberman and Phillips (J Time Ser Anal 35(6):592–623 2014, J Econ 196(1):99–110 2017) proposed a stochastic unit root model, where...