亚纯函数正规族与分担集（英文）

In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and     

2-Harmonic Maps Between Riemannian Manifolds and Conservation Laws (Ⅱ)

For harmonic map f: M→N,P.Baird and J. Eells have successfully foundout its stress-energy tensor S_f=e(f)g- f*h,which is called 1-stress-energy tensorin order to differ from what we’ll develop later.In view of the original defini-tion of 2-harmonic maps,people would ask what is the associated 2-stress-energytensor and the second conservation law of 2—harmonic maps.     

■_4VK_n的Smarandachely邻点可区别正常边染色（英文）

Let f be a proper edge coloring of G using k colors.For each x∈V(G),the set of the colors appearing on the edges incident with x is denoted by S_f(x)or simply S(x)if no confusion arise.If S(u)■S(v)and S(v)■S(u)for any two adjacent vertices u and v,then f is called a Smarandachely adjacent vertex distinguishing proper edge coloring using k colors,or k-SA-edge coloring.The minimum number k for which G has a Smarandachely adjacent-vertex-distinguishing proper edge coloring using k colors is called the Smarandachely adjacent-vertex-distinguishing proper edge chromatic number,or SAedge chromatic number for short,and denoted byχ'_(sa)(G).In this paper,we have discussed the SA-edge chromatic number of K_4∨K_n.     

Hom-李代数表示的一个补充（英文）

本文给出了Hom-李代数上新的一系列上边缘算子,证明了这些上边缘算子所对应的上同调群都是同构的.接着,本文研究了这些上边缘算子的性质,得到:向量空间g上的Hom-李代数结构与Λg~*■V上的一系列上边缘算子是一一对应的.     

完全分配格上的覆盖粗糙集模型

将集合论中的覆盖概念抽象到完全分配格L上,利用它定义格L上关于覆盖的上(下)近似算子,给出格L上覆盖粗糙集模型.文中先讨论格L上覆盖的相关性质,进而研究了覆盖上(下)近似算子的性质,得到若干结果.     

退位减法很有趣

最近,我们学习了数学退位减法,老师教的方法是：在退位减法中,因为被减数个位上的数小于减数个位上的数,先从被减数十位上借1,和个位上的数凑成十几,减去减数个位上的数,成为答数的个位数,然后把十位数减去1移到答数的十位数上。     

图上作业法的改进

这篇文章利用表上作业法来说明图上作业法的被检查圈可以大大减少,实际上,图上作业法与表上作业法是等价的,作者所获得的结论也可由图上作业法的性质直接证明.和本文相反,我们也可以一切从图上作业法出发,然后再引出表上作业法的性质来.一般说来,从图形出发证明较简,因为有较多的几何直观性.     

从上半平面Hardy空间到增长型空间和Bloch空间上的加权复合算子的有界性

研究了从上半平面的Hardy空间到增长型空间和Bloch空间上的加权复合算子有界性的充要条件,给出了上半平面增长型空间上的加权复合算子有界性的充要条件,利用上半平面增长型空间和圆盘增长型空间之间的同构,获得了圆盘增长型空间上的加权复合算子有界性的充要条件.     

超级画板中的仿射变换

1引言"斜光到晓穿朱户",月光把窗玻璃上的几何图形投影到地板上,窗玻璃上的线段投影到地板上还是线段,点在线段上,投影后仍然如此,平行线段还是平行线段;但直角可能变成锐角或钝角,圆就变成     

关于模糊数空间的上确界度量化问题

讨论了模糊数空间的上确界度量化问题,指出了已有上确界度量,即一致Hausdorff度量的不足。利用区间数和模糊数的关系,给出了模糊数空间上的一种新的上确界度量,即EW-型上确界度量,并通过实例验证了其有效性和合理性。讨论了EW-型上确界度量的相关性质,并证明了EW-型上确界度量同样使模糊数空间成为完备的度量空间。     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Cross section for capture of a particle by a spherically symmetric body and different types of finite motion in the relativistic theory of gravitation

Conclusions It is clear that all properties of the metric (1) that can be formulated in the language of its invariants are identical when these properties are considered in general relativity and in the RTG. For example, the expressions for the cross section for capture of particles by a black hole in general relativity and a sufficiently compact body in the RTG are identical. Similarly, when we consider finite motion of particles in the RTG and in general relativity there are analogous sets of different types of motion of the particles (there is only the characteristic difference in the coordinate r characterized by the relation (6)).We note that circular orbits in the gravitational field of a spherically symmetric body were considered in the framework of the RTG in [3], and it was found that these orbits exist for r>2 and are Lyapunov stable for r>5. A relation characterizing the Thomas precession identical to the corresponding expression obtained in general relativity was also obtained in [3]. Thus, differences between general relativity and the RTG can appear only in properties that are not formulated in the language of the invariants of the metric (1). Therefore, if, for example, we consider the problem of the scattering of a particle by a spherically symmetric compact body in the framework of the RTG and general relativity, then we cannot find a difference between the theories of gravitation, since the expressions for the capture cross sections are the same.Institute of Theretical and Experimental Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 85, No. 1, pp. 150–154, October, 1990.     

Representations of Nature of Science in Selected Histories of Science in the Integrated Science Textbooks in China

This study aimed to examine the representations of nature of science (NOS) in the eight histories of science selected from three series of integrated science textbooks used in junior high school in China. Ten aspects of NOS were adopted in the analytical framework. It was found that NOS had not been well treated in the selected histories of science in the three series of science textbooks. Specifically, it was found that the empirical and inferential aspects were treated better than other aspects, and discrepancies existed among the three series of science textbooks and among the eight histories of science in terms of dealing with the target NOS aspects. Implications for addressing NOS in historical materials in science textbooks were discussed in the final part of this paper.     

Geochemical studies in the uranium prospect at Umra,Rajasthan

With the objective of investigating the geochemistry of the natural waters of the uranium prospect at Umra, Rajasthan, the concentrations of uranium, nickel, cobalt, copper, vanadium, etc., in the natural waters have been determined and their distribution patterns have been interpreted in the light of the geology of the area, the climatic and hydrological conditions prevalent there and the geochemical behaviour of the elements concerned. It is found that there is a marked contrast in the uranium content of winze and well-waters. The presence of copper in waters despite their high pH is ascribed to the tendency of copper to form colloidal suspension of basic carbonates. The observation, that vanadium is present in the secondary uranium-vanadium minerals but is absent in the waters, could be explained in the light of the geochemical behaviour of the element. The concentration of cobalt in most of the water samples and its absence in some is traceable to the controlling effect of pH on the mobility of cobalt. Nickel in waters might have been ‘scavenged’ and absorbed on hydrated iron oxides, which explains the absence of nickel in waters. Mention is made of the health hazard involved in drinking water from one of the wells with high content of uranium.     

Mathematics as a study of pattern and beauty via computational graphics

The paper questions the present mode of computer usage, with its emphasis on numerical problem solving, in the typical first degree course in mathematics. The role of ‘ pleasure in visual pattern ‘ in the growth of the analytical faculties of the human mind is discussed. It is suggested that the key role the computer has to play in the education of mathematicians concerns the development of the awareness of shape and in providing pleasure in pattern.

     

Mathematical modelling of social obesity epidemic in the region of Valencia,Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic.

We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general strategies to reverse the increasing trend of obesity are suggested.

The obese population in the region of Valencia is increasing (11.6% in 2000 and 13.48% in 2005) and the future is worrisome. Our model predicts that 15.52% of the population in Valencia will be obese by 2011. Model sensitivity analysis suggests that obesity prevention strategies (healthy advertising campaigns) are more effective than obesity treatment strategies (physical activity) involving the obese and overweight subpopulation in controlling the increase of adulthood obesity in the region of Valencia.     

Geometric Invariant Theory in a Model-Independent Analysis of Spontaneous Symmetry and Supersymmetry Breaking

Functions which are covariant or invariant under the transformations of a reductive linear algebraic group can be advantageously expressed in terms of functions defined in the orbit space of the group, i.e. as functions of a finite set of basic invariant polynomials. This fact and the tools of geometric invariant theory can be exploited in many physical contexts where the study of covariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry and/or supersymmetry breaking in possibly supersymmetric quantum field theories of elementary particles, in the analysis of phase spaces and structural phase transitions in solid state physics (Landau's theory), in covariant bifurcation theory, in crystal field theory and in most areas of solid state theory where use is made of symmetry adapted functions. We shall present some elements of geometric invariant theory and illustrate some of the possible applications in the study of spontaneous symmetry and supersymmetry breaking.