Abstract:
In the title complex, [Ni(C9H5O6)2(C11H10N4)2]·8H2O, the NiII ion exhibits site symmetry 2. It has a distorted octahedral coordination defined by two N atoms from two symmetry-related 1-[(1H-benzimidazol-1-yl)methyl]-1H-imidazole ligands and four O atoms from two symmetry-related 3,5-dicarboxybenzoate anions. In the crystal, the complex molecules and solvent water molecules are linked via O—H...O, O—H...N and N—H...O hydrogen bonds, forming a three-dimensional structure. There are also a number of C—H...O interactions present.

Abstract:
According to the Shell-Model Monte Carlo method, basing on the Random Phase Approximation and the linear response theory, we carried out an estimation on electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni , $^{56}$Mn ,$^{56}$Cr and $^{56}$V in strong electron screening (SES)in presupernova. The EC rates are decreased greatly and even exceed $21.5\%$ in SES. We also compare our results with those of Aufderheide (AFUD), which calculated by the method of Aufderheide in SES. Our results are agreed reasonably well with AUFD at higher density-temperature surroundings (e.g. $\rho_7>60, T_9=15.40$) and the maximum error is $\sim $0.5$\%$. However, the maximum error is $\sim $13.0$\%$ at lower density surroundings (e.g. $^{56}$Cr at $\rho_7=10, T_9=15.40, Y_e=0.41$ ). On the other hand, we also compared our results in SES with those of FFN's and Nabi's, which is in the case without SES. The comparisons show that our results are lower more than one order magnitude than FFN's, but about $7.23\%$ than Nabi's.

Abstract:
Using the theory of relativity in superstrong magnetic fields (SMFs) and nuclear shell model, we carry out estimation for electron capture (EC) rates on iron group nuclei in SMFs. The rates of change of electronic abundance (RCEA) due to EC are also investigated in SMFs. It is concluded that the EC rates of most iron group nuclides are increased greatly by SMFs and even exceeded by nine orders of magnitude. On the other hand, RCEA is influenced greatly by SMFs and even reduced by more than eight orders of magnitude in the EC reaction.We also compare our results with those of Fuller et al.(FFN) and Aufderheide et al.(AUFD) in the case with and without SMFs. The results show that our results are in good agreement with AUFD's, but the rates of FFN's are about close to one order of magnitude bigger than ours in the case without SMFs. On the contrary, our calculated rates for most nuclides in SMFs are increased and even exceeded as much as for nine and eight orders of magnitude of compared to FFN's and AUFD's results, which is in the case without SMFs, respectively.

Abstract:
In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation $axy-x-y=n$ in which $a$ is fixed and and $n$ varies.

Abstract:
Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops the general Hausdorff measure theory of dual approximation on non-degenerate manifolds. In particular, they established the divergence part of the theory based on their general ubiquity framework. However, the convergence counterpart of the project remains wide open and represents a major challenging question in the subject. Until recently, it was not even known for any single non-degenerate manifold. In this paper, we settle this problem for all curves in $\mathbb{R}^2$, which represents the first complete theory of its kind for a general class of manifolds.

Abstract:
In this paper, we establish asymptotic formulae with optimal errors for the number of rational points that are close to a planar curve, which unify and extend the results of Beresnevich-Dickinson-Velani and Vaughan-Velani. Furthermore, we complete the Lebesgue theory of Diophantine approximation on weakly non-degenerate planar curves that was initially developed by Beresnevich-Zorin in the divergence case.

Abstract:
In order to analyze the dynamical mechanism of the abnormal activity of the subtropical high, the variables in the partial differential vortex equations based on the heat force and the whorl movement dissipation effect, are separated in space and time with Galerkin methods. Aiming at resolving the problem of the insufficiency and shortcoming of the conventional method in the choice of space-basis function, we set forth the research idea of using the expirical orthogonal function (EOF) and the genetic algorithm combined with inversion of the space-basis function from the actual sequence of data fields. After the EOF of the daily time series of the subtropical high potential fields, the first three major typical space fields whose cumulative variance contribution is more than 90 percent as the fitting object are chosen, and a group of trigonometric function is selected as the general space-basis function. And then, the dual-constraint function is formulated with the complete orthogonality between space-basis function and the least square of error of general space-basis function and EOF typical field. Then the genetic algorithm is introduced to carry out the curved surface fitting and coefficient optimization of the basis function, and through inversion, an objective and reasonable ordinary differential dynamical model of subtropical high is obtained. Furthermore, through the EOF and inversion of history sensible heat field data, an ordinary differential dynamical model of subtropical high which objectively takes into account of the distribution of thermal factors is set up. Finally, based on the above obtained nonlinear dynamical model, the complicated dynamic behaviors and mechanism of the subtropical high under the impact of heat force are analyzed and discussed, also some new opinions are obtained. For example, the east-west sensitive heat intensity and the configuration distribution and the east-west sensitive heat difference are important factors that lead to a complex configuration (such as the subtropical high double-ridges phenomenon) of the subtropical high flow field and potential field. The heliacal season radicalization heat and the east-west sensitive heat distribution of the East Asia are the important reasons that lead to the subtropical high mutations and the subtropical high flow abnormality, such as the subtropical high north leap and west extend.

Abstract:
With the development of location technologies, advanced LBS-based ITS increasingly requires the capability of database technologies to manage the continuously arrived vehicles' location, traffic jam and other interrelated information of large amounts of traffic in the following years. And some burst arrival stream data will challenge the real-time performance and the allocation of limited resource. However, choosing a desirable database operator scheduling strategy can significantly improve the performance of the system. The path capability strategy was chosen and improved as ITS' operator scheduling strategy to meet the real-time response and the minimal memory requirement of the system.