切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up 技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用, 证明了Marstrand定理.

连续函数微切集的存在性定理

该文研究了在Hausdorff度量及分布意义下连续函数之微切集的存在性问题,证明了连续的典型函数具有丰富的(万有)微切集结构.这一结果推广了Z.Buczolich的相关结论.

Varifolds的某些Rectifiability特征

该文证明下面的定理:设一Varifold V具有特征0<lim_(r→0)(μV(Cr(x)))/(r^n)<∞,那么,V是Rectifiable的.另外,该文还给出了一个Varifold的结构表示定理.

Totally Geodesic Invariant Subm anifolds of Contact Metric Manifold

The purpose of this paper is to give a sufficient and necessary condition of totally geodesic on invariant submanifold of contact metric manifold and is to generalize the results in [3] and [4].

Corrosion damage evolution and mechanical properties of carbon fiber reinforced aluminum laminate

Fiber metal laminates(FMLs),a kind of lightweight material with excellent comprehensive performance,have been successfully applied in aerospace.FMLs reinforced with carbon fiber have better mechanical properties than those with glass or aramid fiber.However,carbon fiber binding metal may lead to galvanic corrosion which limits its application.In this paper,electrochemical methods,optical microscope and scanning electron microscope were used to analyze the corrosion evolution of carbon fiber reinforced aluminum laminate(CARALL)in corrosive environment and explore anti-corrosion ways to protect CARALL.The results show that the connection between carbon fiber and aluminum alloy changes electric potential,causing galvanic corrosion.The galvanic corrosion will obviously accelerate CARALL corroded in solution,leading to a 72.1%decrease in interlaminar shear strength,and the crevice corrosion has a greater impact on CARALL resulting in delamination.The reduction of interlaminar shear strength has a similar linear relationship with the corrosion time.In addition,the adhesive layers between carbon fiber and aluminum alloy cannot protect CARALL,while side edge protection can effectively slow down corrosion rate.Therefore,the exposed edges should be coated with anti-corrosion painting.CARALL has the potential to be used for aerospace components.

Eddy generation and evolution in the North Pacific Subtropical Countercurrent(NPSC) zone

The seasonal generation and evolution of eddies in the region of the North Pacific Subtropical Countercurrent remain poorly understood due to the scarcity of available data.We used TOPEX/POSEIDON altimetry data from 1992 to 2007 to study the eddy field in this zone.We found that velocity shear between this region and the neighboring North Equatorial Current contributes greatly to the eddy generation.Furthermore,the eddy kinetic energy level(EKE) shows an annual cycle,maximum in April/May and minimum in December/January.Analyses of the temporal and spatial distributions of the eddy field revealed clearly that the velocity shear closely related to baroclinic instability processes.The eddy field seems to be more zonal than meridional,and the energy containing length scale shows a surprising lag of 2-3 months in comparison with the 1-D and 2-D EKE level.A similar phenomenon is observed in individual eddies in this zone.The results show that in this eddy field band,the velocity shear may drive the EKE level change so that the eddy field takes another 2-3 months to grow and interact to reach a relatively stable state.This explains the seasonal evolution of identifiable eddies.

Excisional hemorrhoidal surgery and its effect on anal continence

AIM:To investigate the role of anal cushions in hemorrhoidectomy and its effect on anal continence of the patients.METHODS:Seventy-six consecutive patients(33 men and 43 women) with a mean age of 44 years were included.They underwent Milligan-Morgan hemorrhoidectomy because of symptomatic third-and fourth-degree hemorrhoids and failure in conservative treatment for years.Wexner score was recorded and liquid continence test was performed for each patient before and two months after operation using the techniques described in our previous work.The speed-constant rectal lavage apparatus was prepared in our laboratory.The device could output a pulsed and speed-constant saline stream with a high pressure,which is capable of overcoming any rectal resistance change.The patients were divided into three groups,group A(< 900 mL),group B(900-1200 mL) and group C(> 1200 mL) according to the results of the preoperative liquid continence test.RESULTS:All the patients completed the study.The average number of hemorrhoidal masses excised was 2.4.Most patients presented with hemorrhoidal symptoms for more than one year,including a mean duration of incontinence of 5.2 years.The most common symptoms before surgery were anal bleeding(n = 55),prolapsed lesion(n = 34),anal pain(n = 12) and constipation(n = 17).There were grade Ⅲ hemorrhoids in 39(51.3%) patients,and grade Ⅳ in 37(48.7%) patients according to Goligher classification.Five patients had experienced hemorrhoid surgery at least once.Compared with postoperative results,the retained volume in the preoperative liquid continence test was higher in 40 patients,lower in 27 patients,and similar in the other 9 patients.The overall preoperative retained volume in the liquid continence test was 1130.61 ± 78.35 mL,and postoperative volume was slightly decreased(991.27 ± 42.77 mL),but there was no significant difference(P = 0.057).Difference was significant in the test value before and after hemorrhoidectomy in group A(858.24 ± 32.01 mL vs 574.18 ± 60.28 mL,P = 0.011),but no obvious difference was noted in group B or group C.There was no significant difference in Wexner score before and after operation(1.68 ± 0.13 vs 2.10 ± 0.17,P = 0.064).By further stratified analysis,there was significant difference before and 2 months after operation in group A(2.71 ± 0.30 vs 3.58 ± 0.40,P = 0.003).In contrast,there were no significant differences in group B or group C(1.89 ± 0.15 vs 2.11 ± 0.19,P = 0.179;0.98 ± 0.11 vs 1.34 ± 0.19,P = 0.123).CONCLUSION:There is no difference in the continence status of patients before and after Milligan-Morgan hemorrhoidectomy.However,patients with preoperative compromised continence may have further deterioration of their continence,hence Milligan-Morgan hemorrhoidectomy should be avoided in such patients.

Theoretical predictions of viscosity of methane under confined conditions

Density functional theory has been confirmed as a reliable approach in the descriptions of inhomogeneous fluids.By integrating the density functional theory into the revised local average density model, a theoretical approach is constructed to investigate the local shear viscosity in the confined conditions. In the density functional theory,the weighted density approximation for attractive part and the modified fundamental measure theory for repulsion contribution are adopted to accurately describe the inhomogeneous systems. By comparing with simulation data, the theoretical model is tested. In this work, the shear viscosities of methane are calculated in different external fields(on a hard wall, a solvophobic wall and in slit pores with different widths). In addition, the effects of temperature on the local density and viscosity are also considered. It shows that the effect of temperature on the shear viscosity is more obvious on solid surfaces. The calculation provides an approach to determine the viscosity under confined conditions, which is extremely significant in real industrial applications.

The formation mechanism and the influence factor of residual stress in machining

Residual stresses generated in cutting process have important influences on workpiece performance. The paper presents a method of theoretical analysis in order to explicate the formation mechanism of residual stresses in cutting. An important conclusion is drawn that the accumulated plastic strain is the main factor which determines the nature and the magnitude of surface residual stresses in the workpiece. On the basis of the analytical model for residual stress, a series of simulations for residual stress prediction during cutting AISI 1045 steel are implemented in order to obtain the influences of cutting speed, depth of cut and tool edge radius on surface residual stress in the workpiece. And these influences are explained from the perspective of formation mechanism of residual stress in cutting. The conclusions have good applicability and can be used to guide the parameters selection in actual production.

Dimension of Slices Through Fractals with Initial Cubic Pattern

In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L^m. When μV《 L^m, the connection of the local dimension ofμVand the box dimension of slices is given.