Effect of strain on charge density wave order in α-U

The effect of strain on charge density wave (CDW) order in $\alpha$-U is investigated within the framework of relativistic density-functional theory. The energetical stability of $\alpha$-U with CDW distortion is enhanced by the tensile strain along $a$ and $b$ axes, which is similar to the case of negative pressure and normal. However, the tensile strain along $c$ axis suppresses the energetical stability of CDW phase. This abnormal effect could be understood from the emergence of a new one-dimensional atomic chain along $c$ axis in $\alpha$-U. Furthermore, this effect is supported by the calculations of Fermi surface and phonon mode, in which the topological objects and the dynamical instability show opposite behaviors between strains along $a$/$b$ and $c$ axes.     

Supramolecular Arrangement and DFT analysis of Zinc(II) Schiff Bases: An Insight towards the Influence of Compartmental Ligands on Binding Interaction with Protein

We report, for the first time, a detailed crystallographic study of the supramolecular arrangement for a set of zinc(II) Schiff base complexes containing the ligand 2,6-bis((E)-((2-(dimethylamino)ethyl)imino)methyl)-4-R-phenol], where R=methyl/tert-butyl/chloro. The supramolecular study acts as a pre-screening tool for selecting the compartmental ligand R of the Schiff base for effective binding with a targeted protein, bovine serum albumin (BSA). The most stable hexagonal arrangement of the complex [Zn − Me] (R=Me) stabilises the ligand with the highest FMO energy gap (ΔE=4.22 eV) and lowest number of conformations during binding with BSA. In contrast, formation of unstable 3D columnar vertebra for [Zn − Cl] (R=Cl) tend to activate the system with lowest FMO gap (3.75 eV) with highest spontaneity factor in molecular docking. Molecular docking analyses reported in terms of 2D LigPlot+ identified site A, a cleft of domains IB, IIIA and IIIB, as the most probable protein binding site of BSA. Arg144, Glu424, Ser428, Ile455 and Lys114 form the most probable interactions irrespective of the type of compartmental ligands R of the Schiff base whereas Arg185, Glu519, His145, Ile522 act as the differentiating residues with ΔG=−7.3 kcal mol⁻¹.     

一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

全局优化问题的一个新的无参数填充函数

求全局最优化问题的填充函数算法被提出以来，参数的选取和调整一直是制约算法有效性的因素。如何在实际的计算过程中选取合适的参数，直接影响和决定了运算速度和效率。因此，构造不含参数的填充函数就显得极为重要。提出一个新的无参数的填充函数，对其理论性质进行了分析，并给出相应的填充函数算法，数值计算验证了算法的有效性。