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     

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.     

Rolling in the Higgs model and elliptic functions

Asymptotic methods in nonlinear dynamics such as, for example, the Krylov-Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs equation in field theory, not only the small-oscillation regime but also the rolling regime is of interest. Both slow- and fast-rolling regimes are important in the Friedmann cosmology. We present an asymptotic method for solving the Higgs equation in the rolling regime. We show that to improve the perturbation theory in the rolling regime, expanding a solution known in terms of elliptic functions not in trigonometric functions (as with the averaging method in the small-oscillation regime) but in hyperbolic functions turns out to be effective. We estimate the accuracy of the second approximation. We also investigate the Higgs equation with damping.     

Asymptotic behavior of the correlation coefficients of transverse momenta in the model with string fusion

In the framework of the model with fusion of quark–gluon strings on the transverse lattice, we find the asymptotic behavior of the correlation coefficients between observables in separated rapidity intervals with a high string density in a realistic case with an inhomogeneous distribution of strings in the impact parameter plane. We calculate the asymptotic forms for three types of correlations: between the average transverse momenta of particles with rapidity in these intervals, between the average transverse momentum of particles in one rapidity interval and the multiplicity of particles in another, and also between the multiplicities of charged particles in these intervals. We show that the previously found independence of the asymptotic form of the correlation coefficient between the average transverse momenta from the variance in the number of particles produced in string fragmentation holds only in the case of a uniform distribution of strings in the transverse plane. We also show that the found general expressions for the long-range correlation coefficients in the particular case with a uniform distribution of strings in the transverse plane become the formulas previously obtained by another method applicable only in this simple case.     

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。     

Reasoning about variation in the intensity of change in covarying quantities involved in rate of change

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratio-based. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change.     

Socio-economic and cultural mediators of mathematics achievement and between-school equity in mathematics education at the global level

This paper aims at identifying and understanding how and to what extent socioeconomic and cultural factors mediate mathematics achievement and between-school equity in mathematics education among countries. First, under the assumption that equity and quality of education are independent constructs, the construct of equity-in-quality in mathematics education is developed. Second, the 18 countries that were identified in the previous work of the author Jurdak in (Toward equity in quality in mathematics education. Springer, New York, 2009) as being diverse in mathematics education will serve as study cases to illustrate, compare, and contrast the mediatory role of socio-economic and cultural factors in mathematics achievement and between-school equity in mathematics education. The results show that the differences in mathematics achievement and between-school equity in mathematics education at the country level are associated with, and can be accounted for in some cases, by socioeconomic and cultural factors.     

Quasihyperbolic geodesics in convex domains

We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesies are quasiconvex in the norm metric in convex domains in all normed spaces.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.