Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

The paper proposes a method to calculate the natural frequencies of ribbed cylindrical shells with local axisymmetric deflections. The influence of initial imperfections of two types on the minimum frequencies of vibration is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 63–72, September 2008.     

十六烷基甲苯磺酸钠的界面性能研究

用自制的3种十六烷基甲苯磺酸钠,研究了其正构烷烃/水体系的界面性能。分别考察了磺酸盐支化程度及浓度等内部因素以及外加助剂脂肪醇类型和无机盐浓度等外界因素对磺酸盐最小烷烃碳数n_min以及界面张力值的影响。结果表明,磺酸盐支化程度增加,其n_min变大,最低界面张力值变小;而随着磺酸盐浓度的增加,界面张力值先下降后上升;随着助剂脂肪醇碳链长度的增加,其n_min逐渐变大;无机盐的影响则表现为随着盐浓度的增加界面张力值先下降后上升,超低界面张力值出现在一个适宜的盐浓度范围内。     

计算最小支撑出树的一种简便算法

本文通过对网络中有向支撑出树性质的研究,提出了在有向网络图中寻找以某一定点为根的最小有向支撑出树一种较简便的计算方法,并给出了应用该算法进行实际操作的一个算例．     

对称的运输问题及其逆问题

本文对［１,２,６］中提出的运输问题进行了推广,并提出了一个强多项式算法,从而改进了原有的结果．同时对对称的运输问题的逆问题进行了研究,并借助于最小费用循环流技术得到了一个强多项式算法．     

Approximated solutions in rational form for systems of differential equations

In this paper we present a technique to study the existence of rational solutions for systems of differential equations — for an ordinary differential equation, in particular. The method is relatively straightforward; it is based on a rationality characterisation that involves matrix Padé approximants. It is important to note that, when the solution is rational, we use formal power series “without taking into account” their circle of convergence; at the end of this paper we justify this. We expound the theory for systems of linear first-order ordinary differential equations in the general case. However, the main ideas are applied in numerical resolution of partial differential equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

关于多项式最大公因式的进一步探讨

在［１］中有这样一个结论,对于 Ｐ［ｘ］中任意两个多项式 ｆ（ｘ）、ｇ（ｘ）,在 Ｐ［ｘ］中存在一个 最大公因式 ｄ（ｘ）,且ｄ （ｘ）可以表示成ｆ （ｘ）、ｇ （ｘ）的一个组合,即有 Ｐ［ｘ］中的多项式 ｕ（ｘ）、ｖ（ｘ）,使： ｄ（ｘ）＝ ｕ（ｘ）ｆ（ｘ）＋ ｖ（ｘ）ｇ（ｘ） （１）本文将对ｕ（ｘ）、ｖ（ｘ）作进一步的分析,从而得出有关ｕ（ｘ）、ｖ（ｘ）的一些新的结论,以作为上述结论的补充     

多模奇相干态光场中的N-Y最小测不准态与N-H最小测不准态

本文根据新近建立的多模辐射场的广义非线性等阶高阶压缩理论,对多模奇相干态光场|Ψ,o〉_q中的N次方Y压缩、N次方H压缩、N-Y最小测不准态以及N-H最小测不准态等进行了详细研究.结果表明:1)当压缩阶数N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-Y最小测不准态;当N为奇数时,态|Ψ,o〉_q既不处于N-Y最小测不准态,也不呈现N次方Y压缩效应.2)当q & #183;N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-H最小测不准态;当q & #183;N为奇数时,态|Ψ,o〉_q既不处于N-H最小测不准态,也不呈现N次方H压缩效应.3)多模奇相干态|Ψ,o〉_q恒处于N-Y最小测不准态与恒处于N-H最小测不准态的条件明显不同,两者存在着严格的区别.     

多模偶相干态光场中的N次方Y压缩与N次方H压缩特性研究

本文根据新近建立的多模辐射场的广义非线性等阶高阶压缩理论,对多模偶相干态光场冲|ψ,e〉_q中的N次方Y压缩、N次方H压缩、N-Y最小测不准态以及N-H最小测不准态等进行了详细研究。结果表明:1)当N为偶数时,态|ψ,e〉_q恒处于N-Y最小测不准态;当N为奇数时,态|ψ,e〉_q在一定条件下存在着周期性变化的、任意阶的N次方Y压缩效应,2)当q·N为偶数时,态|ψ,e〉_q恒处于N-H最小测不准态。当q·N为奇数时,在另外的条件下,态|ψ,e〉_q存在着周期性变化的、任意阶的N次方H压缩效应。3)N次方Y压缩效应与N次方H压缩效应两者的压缩程度和深度均与几率幅y_q^(e)、压缩参数R_j、各模的初始相位ψ_j(或者初始相位和∑_j=1^qψ_j)、压缩阶数N及腔模总数q等非线性相关,后者与上述诸参量的非线性关联程度要比前者的更强。     

电位差计测量温差电动势的回归分析

对电位差计测量温差电动势实验采用回归分析法处理,让学生学会用实验的方法建立变量间函数公式。     

Derived Functors of Hom Relative to Flat Covers

We study the derived functors of Hom that are computed by using flat resolutions of Hom. These are denoted ⁿ. We compare these with the usual Extⁿ's and show that ¹⊂ Ext¹and indicate (using MacLane's terminology) why the class of associated short exact sequences is a proper class. When the ring is a Dedekind domain we classify the N such that ⁿ(–, N) = 0 and show that unlike the situation for other classically defined right derived functors of Hom, Hom is not balanced relative to the two classes of modules that make ¹ vanish.