关于若干整数分拆问题(英文)

Y.Alavi,A.J.Boals,G.Chartrand,P.Erds和O.R.Oellermann提出下面的猜想:已知整数a1,a2,…,ak,满足n≤ai≤2n-2,1≤i≤k,且a1+a2+…+ak=n(n+1)/2,则S={1,2,…,n}包含有k个互不相交子集S1,S2,…,Sk,满足ai=Σ(Si),1≤i≤k。推广该猜想,得到下面的定理:已知整数a1,a2,…,ak,满足ai≥n,1≤i≤k,且a1+a2+…+ak≤n(n+1)/2,则S={1,2,…,n}包含有k个互不相交子集S1,S2,…,Sk,满足ai=Σ(Si),1≤i≤k。由此定理易推出K.Ando,S.Gervacio和M.Kano证明的一个主要定理。参考文献中的一个错误同时被更正。

Clinical significance of connective tissue growth factor in hepatitis B virus-induced hepatic fibrosis

AIM:To determine the utility of connective tissue growth factor(CCN2/CTGF) for assessing hepatic fibrosis in hepatitis B virus(HBV)-induced chronic liver diseases(CLD-B).METHODS:Enzyme-linked immunosorbent assay was used to measure CCN2 in sera from 107 patients with chronic hepatitis B(CHB) and 39 patients with HBVinduced active liver cirrhosis and 30 healthy individuals.Liver samples from 31 patients with CHB,8 patients with HBV-induced liver cirrhosis and 8 HBV carriers with normal liver histology were examined for transforming growth factor β-1(TGF-β1) or CCN2 mRNA levels by in situ hybridization,and computer image analysis was performed to measure integrated optimal density(IOD) of CCN2 mRNA-positive cells in liver tissues.Histological inflammation grading and fibrosis staging were evaluated by H and E staining and Van Gieson's method.RESULTS:Serum CCN2 concentrations were,respectively,4.0-or 4.9-fold higher in patients with CHB or active liver cirrhosis as compared to healthy individuals(P < 0.01).There was good consistency between the levels of CCN2 in sera and CCN2 mRNA expression in liver tissues(r = 0.87,P < 0.01).The levels of CCN2 in sera were increased with the enhancement of histological fibrosis staging in patients with CLD-B(r = 0.85,P < 0.01).Serum CCN2 was a reliable marker for the assessment of liver fibrosis,with areas under the receiver operating characteristic(ROC) curves(AUC) of 0.94 or 0.85 for,respectively,distinguishing normal liver controls from patients with F1 stage liver fibrosis or discriminating between mild and significant fibrosis.CONCLUSION:Detection of serum CCN2 in patients with CLD-B may have clinical significance for assessment of severity of hepatic fibrosis.

Classification and Identification of Nuclear, Biological or Chemical Agents Taken from Remote Sensing Image by Using Neural Network

In the context of new risks and threats associated to nuclear, biological and chemical （NBC） attacks, and given the shortcomings of certain analytical methods such as principal component analysis （PCA）, a neural network approach seems to be more accurate. PCA consists in projecting the spectrum of a gas collected from a remote sensing system in, firstly, a three-dimensional space, then in a two-dimensional one using a model of Multi-Layer Perceptron based neural network. It adopts during the learning process, the back propagation algorithm of the gradient, in which the mean square error output is continuously calculated and compared to the input until it reaches a minimal threshold value. This aims to correct the synaptic weights of the network. So, the Artificial Neural Network （ANN） tends to be more efficient in the classification process. This paper emphasizes the contribution of the ANN method in the spectral data processing, classification and identification and in addition, its fast convergence during the back propagation of the gradient.

Local Data Analysis for Eliminating End Restraint of Triaxial Specimen

A data processing method was proposed for eliminating the end restraint in triaxial tests of soil. A digital image processing method was used to calculate the local deformations and local stresses for any region on the surface of triaxial soil specimens. The principle and implementation of this digital image processing method were introduced as well as the calculation method for local mechanical properties of soil specimens. Comparisons were made between the test results calculated by the data from both the entire specimen and local regions, and it was found that the deformations were more uniform in the middle region compared with the entire specimen. In order to quantify the nonuniform characteristic of deformation, the non-uniformity coefficients of strain were defined and calculated. Traditional and end-lubricated triaxial tests were conducted under the same condition to investigate the effects of using local region data for deformation calculation on eliminating the end restraint of specimens. After the statistical analysis of all test results, it was concluded that for the tested soil specimen with the size of 39.1 mm × 80 ram, the utilization of the middle 35 mm region of traditional specimens in data processing had a better effect on eliminating end restraint compared with end lubrication. Furthermore, the local data analysis in this paper was validated through the comparisons with the test results from other researchers.

A comprehensive fractal char combustion model

The char combustion mechanisms were analyzed and a comprehensive fractal char combustion model was developed to give a better understanding and better predictions of the char combustion characteristics. Most of the complex factors affecting the char combustion were included, such as the coupling effects between the pore diffusion and the chemical reactions, the evolution of the char pore structures and the variation of the apparent reaction order during combustion, the CO/CO_2 ratio in the combustion products and the correction for oxy-char combustion. Eleven different chars were then combusted in two drop tube furnaces with the conversions of the partly burned char samples measured by thermogravimetric analysis. The combustion processes of these chars were simulated with the predicted char conversions matching very well with the measured data which shows that this char combustion model has good accuracy. The apparent reaction order of the char combustion decreases, stabilizes and then increases during the combustion process. The combustion rates in the oxy-mode are generally slower than in the air-mode and the effect of the char-CO_2 gasification reaction becomes obvious only when the temperature is relatively high and the O_2 concentration is relatively low.

Micromechanical analysis of damage evolution in splitting test of asphalt mixtures

A methodology was presented relating the microstructure of asphalt mixtures to their damage behavior. Digital image techniques were used to capture the asphalt mixture microstructure, and the finite element method was used to simulate the damage evolution of asphalt mixture through splitting test. Aggregates were modeled to be linearly elastic, and the mastics were modeled to be plastically damaged. The splitting test simulation results show that the material heterogeneity, the properties of aggregates and air voids have significant effects on the damage evolution approach. The damage behavior of asphalt mixture considering material heterogeneity is quite different from that of the conventional hypothesis of homogeneous material. The results indicate that the proposed method can be extended to the numerical analysis for the other micromechanical behaviors of asphalt concrete.

Interface contact profiles of a novel locking plate and its effect on fracture healing in goat

Objective： To evaluate the interface characteristics of the new-designed locking plate （LP） and limited contact-dynamic compression plate （LC-DCP） and compare the fracture healing between LP and LC-DCP in a goat tibia fracture model. Methods： Eight-hole LP and LC-DCP were applied to fix fresh goat tibiae in a reproducible manner. The average pressure, force and interface contact area were calculated using Fuji prescale pressure sensitive film interposed among the plate and the bone and image analysis system, Eighthole LP and LC-DCP were applied to each tibia in a goat tibia fracture model. The fracture healing was evaluated by X-ray photography at postoperative 8 weeks. The goats were sacrificed at postoperative 12 weeks. Three-point bending test was conducted in the tibiae. Results： The interface contact of LP system was smaller than that ofLC-DCP （P〈0.05）, while interface contact force of LP system was higher than that of LC-DCP （P〈0.05）. Radiographs revealed that the fracture line disappeared in the LP group, while the fracture line was visible in DCP group at postoperative 8 weeks. At postoperative 12 weeks, the bending strength and bending load of fractured tibia were higher in LP group than in DCP group, respectively.