Vollständige Lösung der unbestimmten GleichungX 3q+Y3=1 in ganzèn Zahlen

Ohne ZusammenfassungDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischerDer detaillierte Beweis des in dieser Note enthaltenen Satzes ist 1915 in russischer     

An analysis of setup cost reduction in a two stage system

This paper investigates the impact of investing in setup cost reduction in a two stage manufacturing process. Closed form relationships are developed for the cases of investment in primary stage setup cost reduction, investment in finishing stage setup cost reduction, and simultaneous investment in setup cost reduction in both stages. Numerical results are presented which compare each of the models to the basic model. These results indicate that when investment in both stages is feasible, it is most effective to simultaneously invest in setup cost reduction. Failing this, the next best alternative is to invest in setup cost reduction in the finishing stage.     

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.     

Asymptotic expansion of solutions in a rolling problem

Asymptotic methods in the theory of differential equations and in nonlinear mechanics are commonly used to improve perturbation theory in the small oscillation regime. However, in some problems of nonlinear dynamics, in particular for the Higgs equation in field theory, it is important to consider not only small oscillations but also the rolling regime. In this article we consider the Higgs equation and develop a hyperbolic analogue of the averaging method. We represent the solution in terms of elliptic functions and, using an expansion in hyperbolic functions, construct an approximate solution in the rolling regime. An estimate of accuracy of the asymptotic expansion in an arbitrary order is presented.     

Approaches and practices in developing school mathematics textbooks in China

In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new developments in compiling and publishing high school mathematics textbooks. Implications obtained from Chinese practices in textbook development are then discussed in a broad context.     

The product representation theorem for interlaced pre-bilattices: some historical remarks

This note aims to unravel the history of the Product Representation Theorem for Interlaced Pre-bilattices. We will see that it has its lattice-theoretic roots in early attempts to solve one of the problems in Birkhoff’s Lattice Theory. The theorem was presented in its full generality by Czédli, Huhn and Szabó at a conference in Szeged, Hungary in 1980 (and published in 1983). This was several years before Ginsberg introduced bilattices at a conference on artificial intelligence in 1986 and in his foundational paper in 1988.     

On Problems in the Calculus of Variations in Increasingly Elongated Domains

This paper deals with minimization problems in the calculus of variations set in a sequence of domains, the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. The authors study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.     

Promoting number theory in high schools or birthday problem and number theory

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.     

Education for Operational Research. A Practitioner's Viewpoint

University education for operational research in Britain is making great and welcome strides forward, but there has been little open discussion of its aims in relation to the advance of the profession. Progress in operational research, and in its application to the really worth-while problems of industry in particular, depends primarily on strengthening the industrial operational research group in its “front line” role. We need a research study of the teaching and practice of industrial operational research, in relation to effectiveness. We need “collaborative” programmes of operational research education in which the university and the industrial operational research group each contribute, in a man's training over a period of years, in the ways in which each is most competent. We need emphasis on “breadth” as well as “depth” in operational research education, and greater attention to the mutual contributions of operational research, teaching and practice, and the teaching and development of management. An impressionist sketch of a programme which might meet these needs is put forward for discussion of principles and feasibility.     

The existence and uniqueness of<Emphasis Type="Italic">q</Emphasis>-process in random environment

We introduce some basic concepts such as random (sub-)transition function, q-function in random environment, g-process in random environment and some basic lemmas. For any continuous g-function in random environment, we prove that the g-process in random environment always exists, and that any g-process in random environment satisfies the random Kolmogorov backward equation and the minimal g-process in random environment always exists. When g is a continuous and conservative g-function in random environment, the necessary and sufficient conditions for the uniqueness of g-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous g-processes in random environments are considered.     

Supporting Statistics in the Workplace: Experiences with two Hospitals

This paper provides some rejections on the promotion of lifelong learning in statistics in the workplace. The initiative from which the rejections are drawn is a collaboration between a university and two public hospitals, of which one of the stated aims is to develop statistical skills among the hospitals' researchers. This is realized in the provision of 'biostatistical clinics' in which workplace teaching and learning of statistics takes place in one-on-one or small group situations. The central issue that is identified is the need to accommodate diversity: in backgrounds, motivations and learning needs of workplace learners (in this case medical researchers), in the workplace environments themselves and in the projects encountered. Operational issues for the statistician in providing such training are addressed. These considerations may reject the experiences of the wider community of statisticians involved in service provision within a larger organization.     

Community operational research issues and public art practice: the art director system

The key issues of community operational research, outlined in a paper by Ritchie, have relevance to community projects in general and, we argue, a particular relevance to public art. We illustrate this relevance by describing eight case studies in public art, four in Japan and four in the west, and by considering the projects in a three-way factorial design, make a case for the art director system in the management of public art projects.     

角蛋白16和17在部分表皮肿瘤中的表达和意义

目的 研究角蛋白16 和17（K16、K17）在部分表皮肿瘤中的表达和意义。方法 采用免疫组化法检测K16、K17在正常皮肤、脂溢性角化病、日光性角化病、皮角、基底细胞癌、鳞状细胞癌中的表达。结果 K16、K17 在正常皮肤表皮各层呈阴性表达;在脂溢性角化病表皮各层中除了角质层外大多呈阳性表达;在日光性角化病表皮K16 均不表达,K17 除了角质层外在其他各层也不表达;K16 在皮角表皮棘层呈强阳性表达,但在其他各层均呈阴性表达,K17 在皮角表皮各层基本呈阳性或强阳性表达;在基底细胞癌中,K16、K17除了在棘层呈弱阳性表达外,在其他各层均呈阴性表达;在鳞状细胞癌中,K16 在基底层呈阴性表达,但在其他各层及K17 在表皮全层均呈阳性或强阳性表达。K16 除基底层外在肿瘤表皮其他各层表达比较差异均有统计学意义（均P＜0.05）;K17 在表皮各层表达差异均有统计学意义（均P＜0.05）。结论 K16、K17的表达状况可为表皮肿瘤的鉴别诊断提供病理学方面的依据。     

The role of examples in forming and refuting generalizations

Acknowledging students’ difficulty in generalizing in general and expressing generality in particular, we assert that the choice of examples that learners are exposed to plays a crucial role in developing their ability to generalize. We share with the readers experiences in which examples supported generalization, and elucidate the strategies that worked for us in these circumstances, presuming that similar strategies could be helpful with other students in other settings. We further share several pitfalls and call for caution in avoiding them.     

Harmonic wavelets in boundary value problems for harmonic and biharmonic functions

We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

Sphalerite geothermometry

Kullerud’s method of formation-temperature determination has been applied to the polymetallic sulphide deposits of Sadon in Northern Caucasus, U.S.S.R. The sulphide ore occurs at three places, separated by a few kilometers from each other. They are Sadon, Zgid and Holst. Mineralogical assemblage is sphalerite, galena, pyrite and pyrrhotite. It is found that sphalerites from the above three places were formed mainly within a temperature range of 120–500° C. The temperature data are represented in the form of histograms. The occurrence of more than one maximum in each histogram may indicate ore deposition in more than one stage. From the histograms, it is concluded that in Sadon, ore deposition took place in three stages: in Zgid, in only one stage and in Holst, in two stages. These conclusions are in agreement with those arrived at by others by mineragraphic studies.