Some researches on multivariate Lagrange interpolation along the sufficiently intersected algebraic manifold

In this article, Lagrange interpolation by polynomials in several variables is studied. Particularly on the sufficiently intersected algebraic manifolds, we discuss the dimension about the interpolation space of polynomials. After defining properly posed set of nodes (or PPSN for short) along the sufficiently intersected algebraic manifolds, we prove the existence of PPSN and give the number of points in PPSN of any degree. Moreover, in order to compute the number of points in PPSN concretely, we propose the operator ? _k with reciprocal difference.     

Gelfand-Kirillov dimension of some primitive abundant semigroups

In this paper, the growth and Gelfand-Kirillov dimension of some primitive abundant semigroups are investigated. It is shown that for certain primitive abundant (regular) semigroup S, S as well as the semigroup algebra K [S] has polynomial growth if and only if all of its cancellative submonoids (subgroups) T as well as K[T] have polynomial growth. As applications, it is shown that if S is a finitely generated primitive inverse monoid having the permutational property, then clK dim K[S] = GK dim K[S] = rk(S).     

The effect of ghost forces for a quasicontinuum method in three dimension

We study the efect of"ghost forces"for a quasicontinuum method in three dimension with a planar interface."Ghost forces"are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region.Numerical results suggest that"ghost forces"may lead to a negilible error on the solution,while lead to a fnite size error on the gradient of the solution.The error has a layer-like profle,and the interfacial layer width is of O(ε).The error in certain component of the displacement gradient decays algebraically from O(1)to O(ε)away from the interface.A surrogate model is proposed and analyzed,which suggests the same scenario for the efect of"ghost forces".Our analysis is based on the explicit solution of the surrogate model.     

Fixed Point Theorems for Mean Nonexpansive Mappings in CAT(0) Spaces

In this article, we prove the existence of fixed points and the demiclosed principle for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces. We also obtain a Δ-convergence theorem and a strong convergence theorem of Ishikawa iteration for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces.     

On sums of sparse prime subsets

For arbitrary c00, if A is a subset of the primes less than x with cardinality δx(logx)-1, δ≥(logx)-c0, then there exists a positive constant c such that the cardinality of A+A is larger than cδx(loglogx)-1.     

广义线性McCoy环

称环R是右线性McCoy的,如果R[x]中非零线性多项式f（x）,g（x）满足I（x）g（x）=0,则存在非零元素r∈R使得f（x）r=0．设a是环R的自同态,通过用斜多项式环R[x;a]中的元素代替一般多项式环R[x]中的元素而引入a-线性McCoy环的概念．讨论了a-线性McCoy环的基本性质和扩张性质．     

Environmental dispersion in a three-layer wetland flow with free-surface

To further address the characteristic of contaminant transport in wetlands of a multi-layer structure, environmental dispersion of a pulsed contaminant emission into a steady flow is analytically explored in this paper for the typical case of a respectively vegetated or packed three-layer wetland dominated with free-water-surface-effect. The hierarchical structure for the critical length and duration of the contaminant cloud is illustrated for the dispersion of typical contaminant constituents.     

双参数 C-半群

引入单参数C-半群和双参数C0-半群,给出了更一般的双参数C-半群和无穷小生成元的定义,应用双参数半群与单参数半群的关系和双参数半群的性质,给出了双参数C-半群的阶全微分,偏微分,指数有界性,和双参数C-半群是由C、A1和A2唯一确定的闭稠定线性算子的一个充分条件.     

Side-Arm Assisted Anilido-Imine Based Rare-Earth Metal Complexes for Isoprene Stereoselective Polymerization

Anilido-imine ligands o-C₆H₄(NHAr₁)(CH=NAr₂), in which Ar₁ is 2,6-diisopropylbenzyl group and Ar₂ contains fluorine (HL₁) or methoxyl (HL₂) group on ortho-position of phenyl substituent, were synthesized for constructing rare-earth metals based complexes of 1a–1c (HL₁ based Sc, Lu, Y) and 2a–2c (HL₂ based Sc, Lu, Y). Based on their NMR spectra and X-ray single-crystal structures, the side-arm group of -F and -OMe is identified to chelate to the corresponding central metal. The twisted angles between two planes formed by chelated heteroatoms (N, N, F for HL₁ and N, N, O for HL₂) are observed, in which the largest dihedral angle (53.3°) for HL₁-Y and the smallest dihedral angle (44.32°) for HL₂-Sc are detected. After being activated by AlⁱBu₃ and [Ph₃C][B(C₆F₅)₄], these catalysts showed great activity for isoprene polymerization. Bearing the same ligand HL₁, smaller scandium based complex 1a and middle size of lutetium based 1b provided lower cis-1,4-selectivity (57.3% and 64.2%), larger yttrium complex 1c displayed high cis-1,4-selectivity (84%). Chelating by crowded HL₂, small size of scandium complex 2a provided impressive trans-1,4-selectivity (93.0%), middle lutetium based 2b displayed non-selectivity and larger yttrium complex 2c showed clear cis-1,4-selectivity (83.3%). Moreover, 2a/AlⁱBu₃ system showed the quasi-living chain transfer capability.     

DLSTM-Based Successive Cancellation Flipping Decoder for Short Polar Codes

Polar code has been adopted as the control channel coding scheme for the fifth generation (5G), and the performance of short polar codes is receiving intensive attention. The successive cancellation flipping (SC flipping) algorithm suffers a significant performance loss in short block lengths. To address this issue, we propose a double long short-term memory (DLSTM) neural network to locate the first error bit. To enhance the prediction accuracy of the DLSTM network, all frozen bits are clipped in the output layer. Then, Gaussian approximation is applied to measure the channel reliability and rank the flipping set to choose the least reliable position for multi-bit flipping. To be robust under different codewords, padding and masking strategies aid the network architecture to be compatible with multiple block lengths. Numerical results indicate that the error-correction performance of the proposed algorithm is competitive with that of the CA-SCL algorithm. It has better performance than the machine learning-based multi-bit flipping SC (ML-MSCF) decoder and the dynamic SC flipping (DSCF) decoder for short polar codes.