一类具有连续变量的二阶中立型差分方程的振动性

研究时滞差分方程解的性质在理论和应用中是非常重要的。本文用分析的方法研究了一类具有连续变量的二阶中立型差分方程解的振动性,给出了该类方程解振动和差分算子振动的几个充分条件。     

稀疏效应下功能性反应系统的数学研究

本文考虑一类具有稀疏效应和Ｈｏｌｌｉｎｇ第ＩＩ型动能反应的捕食一食饵系统ｘ＝ａｘ（ｘ－Ｌ）ｋ－ｘ／ｋ－ｂｘｙ／１＋ｈｘ，ｙ＝－ｃｙ＋ｄｘｙ／１＋ｈｘ其中ａ，Ｌ，ｋ，ｂ，ｈ，ｃ，ｄ的为正常数，Ｌ＜ｋ，假定Ｌ＞０充分小，如果（１）的正平衡点稳定，则其外围不存在极限环；如果（１）正平衡点不稳定，讨论了Ｈｅｔｅｒｏｃｌｉｎｉｃ分枝以及极限的环的唯一性，特别当Ｌ＝０时，正平衡点稳定则一定全局渐近稳定，正平衡     

一类变分方程解的显式结构及应用

运用分析方法证明了一类应用于随机控制的对称变分方程解的存在性并给出解的显式结构,是对刘坤会（１９９２）与孙世良（１９９７）文的实质性推广。     

一类二阶非线性差分方程的振动性质

从解的渐近状态着手,将所述方程的所有非平凡解分成互不相交的四类,应用分类讨论方法和分析方法,讨论了一类广泛的二阶非线性差分方程解的振动性质,建立了两个新的振动性定理,推广并改进了已有文献中的相关结果。     

某些具有偏差变元的抛物型方程的解的振动性

探讨了某些具有偏差变元的抛物型方程解的振动性,得到这些方程解为振动的充分条件,以扩育了傅希林（1994）,崔宝同（1996）,陈宁（1999）文中的某些定理,亦是作者1999年文的继续,主要结果是定理2、定理3与定理5。     

一类非线性振动系统的周期解及次调和解

本文讨论了一类在自然界广为存在的非线性振动系统的复杂运动规律，通过建立一新判断函数Ｘ（Ａ，θ），推广了Ｓ．Ｌｅｆｓｃｈｅｔｚ的周期理论，并用得到的系列定理分析了非线性一类振动系统，所得理论证明包含了Ｓ．Ｌｅｆｅｃｈｅｔｚ理论的结果。     

时滞差分方程中Razumikhin型稳定性定理的改进

本文用Ｌｙａｐｕｎｏｖ函数来研究时滞差分方程解的稳定性,得到了包含经典的Ｒａｚｕｍｉｋｈｉｎ型稳定性定理作为其推论的结果,且避免了求Ｒａｚｕｍｉｋｈｉｎ条件中辅助函数Ｐ的困难。     

一类非椭圆算子的基本解和Pohozaev恒等式

本文给出了一类次椭圆算子（Ｈｅｉｓｅｎｂｒｇ群上的Ｋｏｈｎ－Ｌａｐｌａｃｅ算子为其特例）的基本解和Ｐｏｈｏｚａｅｖ恒等式。     

带有非奇异核分数阶差分方程的比较原理及解的不确定性分布

比较原理对于研究分数阶方程的性质具有重要的作用。首先，证明了 ABR 型分数阶差分方程的比较原理。其次，利用比较原理，建立了不确定性分数阶差分方程的解与其 $\alpha$-路径之间的联系。接着，给出了 ABR 型不确定性分数阶差分方程解的不确定性分布。最后，具体的实例验证了主要结论的正确性。     

φ形式的Khintchine不等式

推广Ｋｈｉｎｔｃｈｉｎｅ不等式，对于一类φ函数，得到φ－１Σｎ１φ（｜ａｊ｜）≤ｃ１２ｎΣε１…Σεｎ｜ε１ａ１＋…＋εｎａｎ｜其中εｉ＝±１，Σ对所有（ε１，…，εｎ）取值作为应用，得到Ｈ１函数的小波级数的一个φ不等式：∫Ｒｎφ－１Σλ∈Ｆφ（｜（ｆ，ψλ）ψλ（ｘ）｜）ｄｘ≤ｃ     

Estimation of Parameters of Universal Distribution of Moments of Failure of Products

A method is proposed for estimating the parameters of a mixture of exponential and Weibull distributions for which the accuracy of preliminary estimates obtained by graphical analysis is refined in accordance with the criterion of maximum likelihood. The efficiency of the proposed method is supported by the results of statistical modeling.     

Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons

A novel method for the determination of the optical properties of tissue from time-domain measurements is presented. The data analysis is based on the evaluation of the first moment and the second centralized moment, i.e., the mean time of flight and the variance of the measured distribution of times of flight (DTOF) of photons injected by short (picosecond) laser pulses. Analytical expressions are derived for calculation of absorption and of reduced scattering coefficients from these moments by application of diffusion theory for infinite and semi-infinite homogeneous media. The proposed method was tested on experimental data obtained with phantoms, and results for absorption and reduced scattering coefficients obtained by the proposed method are compared with those obtained by fitting of the same data with analytical solutions of the diffusion equation. Furthermore, the accuracy of the moment analysis was investigated for a range of integration limits of the DTOF. The moment analysis may serve as a comparatively fast method for evaluating optical properties with sufficient accuracy and can be used, e.g., for on-line monitoring of optical properties of biological tissue.     

Estimation of potentialities of methods of summation of direct measurement errors

Conventional methods for summation of direct measurement errors are considered. Conditions under which these methods provide consistent results are stated. It is proposed to utilize for characteristic of the total error, its interval estimator or the half-sum of the value obtained by adding up its arithmetic and geometric random errors.Translated from Izmeritel'naya Tekhnika, No. 4, pp. 10–12, April, 1995.     

空压机轴承箱蜗壳温度探头油封改造

由于空压机进气侧轴承箱蜗壳温度探头密封效果不好,使空压机及其后续管道受到油污染。后将温度探头的O形圈密封改为骨架油封,杜绝了轴承箱漏油问题。文章简介空压机的结构和技术参数,详细介绍了骨架油封的制作和优点。     

Characteristics of mechanical properties of materials in studies of conditions of attainment of marginal states

It is shown that conditions of attainment of marginal states in the material of structural components are formulated on the basis of analysis of force and deformation criteria of formation and development of destruction. The parameters of these criteria are data on types of structural materials, standard and special characteristics of their mechanical properties, structural forms of considered elements of the equipment, and their operating stress loading. In this case, the construction of a system of state equations for describing interrelation of current damage, external actions, and responses to them is based on the concept of calculating variations in properties of materials at all stages of the design life cycle.     

Determination of parameters of microstructural inhomogeneity of deformation of metals by the method of modeling

The article suggests a method of evaluating the microstructural inhomogeneity of deformation of metals by modeling. The method includes the measurement of deformations of metal according to meshes of a dividing grid with small base and the calculation of the distribution parameters of microdeformations in model representation. It is shown that the modeling method makes it possible objectively to evaluate the microinhomogeneity of deformation of metals independently of the chosen mesh size of the dividing grid. New structural characteristics are introduced: the base and wave of variation expressing the degree of crumbling or amalgamation of metal grains by inhomogeneity of deformation.Translated from Problemy Prochnosti, No. 7, pp. 40–44, July, 1991.     

Analysis of the rate of propagation of the wave of change of boiling modes

An approximate analytical expression is derived for the velocity of the front of the wave of change of boiling modes on a rod and on a plate. The impact of the Thomson effect and of the heater orientation in the gravity field is included. Adequate agreement is demonstrated between the derived relations and experimental data.     

水三相点复现的不确定度评定

水三相点是开尔文热力学温度的唯一基准点，也是ITS-90国际温标重要的定义固定点。因此，水三相点不确定度分析对整个温标的建立、温度量值传递起着至关重要的作用。近3年来，中国计量科学研究院研制出一系列高质量的水三相点容器，加强了水三相点的研究，为不确定度的分析提供了更为可靠的实验依据。同时，不确定度的分析也是客观评价新研制容器性能的一个重要指标。因此，根据实验结果对新研制容器所复现的水三相点进行了不确定度评定。评定结果表明，其扩展不确定度为0．16mK(k=2．69，P=0．99)。