关于单调函数的一个定理

根据积分中值定理:如果函数f(x)在区间(a,b)内连续,则对(a,b)内任意两点x_1,x_2(x_1<x_2),至少存在一点ξ(x_1<ξ<x_2),使等式成立。许多学者自然会将以上结论改成这样的一个问题:对区间(a,b)内每一点ξ,能否找到两点x_1,x_2(x_1<ξ<x_2),使(1)式成立?回答是否定的。例f(x)=x^2,在(-1,1)上连续,取ξ=0,则x_1,x_2∈(-1,1),当x_1<ξ<x_2时,恒有∫_(x_2)^(x_2)f(x)dx=f(ξ)≠0。

微分中值定理的反问题

本文指出并修正了文[2]中结论的错误．讨论了函数在严格凸条件下及在点严格凸条件下的微分中值定理的反问题。

连续T—模族{T_p(x,y)}

本文给出了一类连续T-模T_p(x,y),探讨了它的性质及一些结论。

积分中值定理的反问题初探

本文利用凸函数的概念和性质，对积分中值定理的反问题进行了探讨，主要结论有１．设ｆ（ｘ）是（ａ，ｂ）内的严格凸实值函数，ｇ（ｘ）是（ａ，ｂ）内的严格回实值函数，且ｆ（ｘ）、ｇ（ｘ）均在（ａ，ｂ）上严格递增，则是（ａ，ｂ）上关干ｘ的严格递增函数。２．设ｆ（ｘ）是定义在（ａ，ｂ）内的严格单增连续函数，ｇ（ｘ）是（ａ，ｂ）内严格单减的连续函数，且ｆ（ｘ）＞０，ｇ（ｘ）＞０，则对ξ∈（ａ，ｂ）可找到两点ｘ１，ｘ２∈（ａ，ｂ），ｘ１＜ξ＜ｘ２使３．设ｆ（ｘ）是定义在（ａ，ｂ）上的严格单增连续函数，则对ξ∈（ａ，ｂ），可找到两点ｘ１，ｘ２∈（ａ，ｂ）。

Upper Bound and Lower Bound Estimate of Monotone Increasing Fractal Function

Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f（x）（it is a monotone increasing fractal function） and its some applications.

Effect of MgO and SiO_2 on surface tension of fluoride containing slag

Surface tensions of slag addition Mg O and Si O2 based on conventional 70%CaF 2-30%Al2O3 and 60%Ca F2-20%Ca O-20%Al2O3(mass fraction) at 1300 °C, 1400 °C and 1500 °C were investigated. Influence mechanism of Mg O and Si O2 on slag surface tension was also analyzed. Results indicate that surface tension decreases with the increase of Mg O content in the case of the Mg O content(mass fraction) less than 8%, however, when Mg O content(mass fraction) is from 8% to 30%, surface tension increases with the increase of Mg O content. When Si O2 content(mass fraction) is from 2% to 8%, surface tension decreases with the increase of Si O2 content. Additionally, the relationship between surface tension and optical basicity is a monotonically increasing linear function. Research findings can provide important reference for slag design and the study of slag-metal interfacial tension.

Microscopic Theory of Nonlinear Spin Waves in Ferromagnets

Considering the attractive interaction between ferromagnet, we propose the model of magnon-pairs, which two magnons with opposite wave vectors in a Heisenberg is suitable for low-temperature environment. A dressed magnon is an energy quantum of the magnon-pairs whose energy is a monotonically increasing function of absolute temperature. Based on the model, we re-investigate the excitation mechanism and thermodynamic properties of the Heisenberg ferromagnet. The correction factor e（O） plays an important role in studying the low-temperature properties of a ferromagnet.

A three-process quantum engine cycle consisting of a two-level system

Based on the thermodynamic properties of isoenergetic,adiabatic and isothermal quantum processes,it is shown that it is possible to combine the three processes into a quantum engine cycle.The efficiency of the three-process cycle can be derived and is dependent on the highest and lowest temperatures.The efficiency in some operation regions does not demonstrate a monotonically increasing function of the temperature difference.When the highest temperature of the cycle is larger than the critical temperature,which can be determined by the characteristics of the three-process cycle,a unique region where the efficiency decreased with the increase of the temperature difference exists.

TYPE X MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION

The author considers the asymptotic behavior of solutions of a class of ordinary dmerentialequations x = F(x) in the nonnegative orthant R7. Suppose that F(o) = o, Fi(x1,..., xn) isnondecreasing in xk for all k≠ i and that F possesses an order-increasing invarian function.Then it is shown that every bounded solution to such a system converges to a single equilibrium.