连续自然数幂的二项分解

对根据新定义的二元方数,结合组合数导出连续自然数n次幂的二项分解,从而得出连续自然数n次幂的二项分解公式,并利用其探究了波文猜想。

The Least Square Solutions to the Quaternion Matrix Equation AX=B

A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.

Morphological evolution and growth kinetics of Kirkendall voids in binary alloy system during deformation process-Phase field crystal simulation study

The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.

Two-dimensional Numerical Simulation of an Elastic Wedge Water Entry by a Coupled FDM-FEM Method

Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method （FDM） and finite element method （FEM） was developed to analyze the fluid structure interaction （FSI） problem. The FDM, in which the Constraint Interpolation Profile （CIP） method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting （THINC/SW） scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary （IB） method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.

Screening influencing factors of blood stasis constitution in traditional Chinese medicine

Objective To study the influencing factors of blood stasis constitution and provide a basis for treating blood stasis-related diseases by traditional Chinese medicine(TCM) constitution identification.Methods Data were collected using the self-developed TCM constitution identification platform based on B/S model by the project team. The obtained data were divided into blood stasis constitution and normal constitution groups. The differences of the categorical type influencing factors(gender, birth mode, feeding mode within four months of birth, family history, marital status, eating habits, sleeping habits, exercise habits, emotional state, stress situation, and living environment) and the quantitative type influencing factors(sleep time, age,and mother’s age at birth) on the constitution of the two groups were analyzed. In the singlefactor analysis, the Pearson’s chi-square test was selected for the categorical variable, and the independent sample t test and Mann-Whitney U nonparametric test were selected for the quantitative variables according to whether they conformed to the positive-terrestrial distribution;the binary logistic stepwise regression method was selected for the multi-factor analysis.Results The data of 318 cases were collected from the TCM composition identification platform, and 159 cases of blood stasis constitution were used as the experimental group and 159 cases of normal constitution were used as the control group. The Pearson’s chi-square test yielded significant differences(P < 0.05) in the effects of gender, pressure situation, family history, living environment, emotional state, exercise habits, and dietary habits on blood stasis constitution. The independent samples t test yielded differences in sleep duration between the blood stasis constitution and normal constitution populations(P < 0.05), which meant sleep duration of the blood stasis constitution population was less than that of the normal constitution population. The Mann-Whitney U nonparametric test results accepted the original hypothesis that there was no difference in the distribution of age and mother’s age at birth across constitution types(P > 0.05). Binary logistic regression analysis showed that gender, family history, marital status, living environment, exercise habits, and emotional state were risk factors for blood stasis constitution(P < 0.05).Conclusion Gender, family history, living environment, emotional state, and exercise habits were significant influencing factors of blood stasis constitution. Blood stasis constitution populations can pay more attention to these influencing factors in their daily life for the prevention and reconciliation of blood stasis constitution.

Numerical Method on Load Sharing Problem of Thick Laminate Joints

Accurately and efficiently predicting the load sharing of multi^bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional （2D） finite element method （FEM） is introduced to meet such a demand. The deformation contributions of the joint zone are analyzed and calculated separately, including the shearing deformation of the fasteners shank, the bending deformation of the fasteners shank, and the bearing deformation of the fasteners and joint plates. These deformations are all transferred and incorporated into the components of the fastener＇s flexibility. In the 2D finite element model, the flexibilities of the beam elements and bush elements are used to simulate different components of the fastener＇s flexibility. The parameters of the beam elements which include the bending moment of inertia and intersection area, and the parameters of the bush elements which include the stiffness in different directions, are all obtained through equalizing the fasteners flexibilities. In addition, the secondary bending effect introduced by the single-lap joints is also taken into account to verify the flexibilities of the fasteners in practical application. The proposed FEM is testified to be more accurate than the traditional 2D FEMs and more efficient than the three-dimensional （3D） FEM in solving load sharing problem of multi-bolt single-lap thick laminate joints. With the increase of joint plates＇ thickness, the advantages of the proposed method tend to be more obvious. The proposed 2D FEM is an effective tool for designing bolted joints in large-scale composite structures.