Periodic solution of a higher dimensional ecological system

The main purpose of this article is to study the periodicity of a Lotka-Volterra''s competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix''s spectral theory and inequality $|x(t)|\leq x(t_{0})+\int_{0}^{\omega }|\dot{x}(t)|{\rm d}t$. Some examples and their simulations show the feasibility of our main result.     

分数年龄生存函数的估计

本文主要讨论了生存函数的插值问题,使用了非节点端点的三次样条插值和α-power插值两种方法对生存函数进行了插值,并与传统的三种插值假设：死亡均匀分布假设、常数死亡力假设、Balducci假设做了比较.另外,我们对α-power插值中的α进行了拟合,并通过误差分析表明先对α拟合后再进行α-power插值,其插值的误差将会变得非常小,几乎与样条插值相仿.     

Regiocontrolled intramolecular cyclizations of carboxylic acids to carbon-carbon triple bonds promoted by acid or base catalyst

We systematically investigated, for the first time, the relationship between regioselectivity and acid/base effects in the cyclization reactions between carboxylic acids and carbon-carbon triple bonds. We found novel acid- and base-promoted cyclizations to selectively give isocoumarin or pyran-2(2H)-one and phthalide or furan-2(5H)-one skeletons, respectively, and established a catalytic version of regioselective heterocyclic ring synthesis. Density functional theory calculations and application to a short route to thunberginol A were also described. [reaction: see text].     

Notes on the products of the lower topology and Lawson topology on posets

In this paper, we investigate the relation between the lower topology respectively the Lawson topology on a product of posets and their corresponding topological product. We show that (1) if S and T are nonsingleton posets, then Ω(S×T)=Ω(S)×Ω(T) iff both S and T are finitely generated upper sets; (2) if S and T are nontrivial posets with σ(S) or σ(T) being continuous, then Λ(S×T)=Λ(S)×Λ(T) iff S and T satisfy property K, where for a poset L, Ω(L) means the lower topological space, Λ(L) means the Lawson topological space, and L is said to satisfy property K if for any x∈L, there exist a Scott open U and a finite F⊆L with x∈U⊆↑F.     

Hardy–Carleson Measures and Their Dual Poisson–Szegö Transforms

Recently Choe et al. have introduced the notion of dual Berezin transforms and used it to obtain new characterizations of the Carleson measures for the weighted Bergman spaces over the unit ball in C ⁿ . Continuing our investigation on the Hardy spaces, we obtain new characterizations of the Carleson measures for the Hardy spaces by means of the dual Poisson–Szegö transforms introduced by Koosis. Compared with the results for the weighted Bergman spaces, our results for the Hardy spaces not only show an similarity, but also reveal a new characterization.     

A heuristic approach for deriving the priority vector in AHP

This paper proposes an approach for deriving the priority vector from an inconsistent pair-wise comparison matrix through the nearest consistent matrix and experts judgments, which enables balancing the consistency and experts judgments. The developed algorithm for achieving a nearest consistent matrix is based on a logarithmic transformation of the pair-wise comparison matrix, and follows an iterative feedback process that identifies an acceptable level of consistency while complying with experts preferences. Three numerical examples are examined to illustrate applications and advantages of the developed approach.     

o-C8 Carbon: a New Allotrope of Superhard Carbon

An orthonormal crystal of carbon with PMMA space group (o-C₈) was found to be a stable superhard carbon allotrope by particle swarm optimization algorithm and density functional calculations. The phonon spectrum calculations demonstrate that the o-C₈ carbon phase is dynamically stable. The volume compression calculations show that it is highly incompressible, with bulk modulus of 298.6 GPa. The calculations demonstrate that it is a low-density superhard material with density of 2.993 g/cm³ and Vickers hardness of 82.4 GPa.     

Image formation in holographic tomography

Tomography has been applied to holographic imaging systems recently to improve the 3D imaging performance. However, there are two distinct ways to achieve this: either by rotation of the object or by rotation of the illumination beam. We provide a transfer function analysis to distinguish between these two techniques and to predict the 3D imaging performance in holographic tomography when diffraction effects are considered. The results show that the configuration of rotating the illumination beam in one direction while fixing the sample leads to different 3D imaging performance as compared to the configuration of rotating the sample. The spatial frequency cutoff is nonisotropic in the case of rotating the illumination, and a curved line of singularity is observed. Rotating of the sample, on the contrary, has more symmetry in spatial frequency coverage but has a single point of singularity. The 3D transfer function derived can be used for 3D image reconstruction.     

HYLLERAASIAN WAVE FUNCT/ON OF 2s2 1S OF HELIUM

A variatioual calculation of the energy of the 2s^{2 1}S state of helium has been carried out with the use of a wave function of the Hylleraasian type. The wave function is ψ=e^-0.2278s{1-0.17079s-0.063155u-0.013869t² +0.010044u²+0.0064785s²} where s,t u are in units of 4 times the first Bohr radius of hydrogen. The energy is E(2s^{2 1}S)=-1.5412Rh. compared with the value -1.4400 Rh obtained by the method of self-consistent field.