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.     

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.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

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.     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

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.     

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.     

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.     

水动力-热动力学的极值定律

本文对水动力学和更普通性的连续介体动力学中以连续方程与运动方程所表达的现有诸经典守恒定律以外,提出另一最大能量消散率定律.这一定律的推论就是应用水力学中培纶格-波丝最小储存能学说. 凡在运动中消散了的机械能皆转化成为热能,储存在物体里.能量之消散当一定时刻一定温度都使产熵增加.所以,从最大能量消散率可引出热力学第二定律的一个新概念,即机械运动的产熵率也总是一个可能的最大值. 文中建议的这个连续介体极值定律,可从变分原理推导出来,重订热力学第二定律则可藉微观分析加以证明.两者合成水动力-热动力学极值定律     

Mathematics in the Memoirs of the Lisbon Academy of Sciences in the 19th century

From the end of the 18th century until the appearance of the first issue of the Jornal de Sciencias Mathematicas e Astronomicas in 1877, the Lisbon Royal Academy of Sciences, founded in 1779, was the main publisher in Portugal of periodicals that included mathematical papers. In this article I will give an overview of the mathematical papers which appeared in the Academy's Memoirs during the 19th century, in the context of the scientific output published in its pages. We will characterize the community of mathematicians around the Academy's journal and the changes in background and in themes researched throughout the century.     

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.     

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.     

On variations in the solutions of integro-differential equations of mixed problems of elasticity theory for domain variations

The behaviour of the solution of the boundary value problem for a pseudodifferential equation (PDE), Green's function of this problem, and also some of their local and global characteristics, during variation of the domain is investigated. Formulas are proposed that enable the solution of a broad class of PDE in a domain to be expressed in terms of the solution in the near domain. Local characteristics of the solution are expressed in terms of the local characteristics of the solution in the near domain. A double asymptotic form of Green's function for both arguments tending to the domain boundary occurs in the variation formula. The variation of this double asymptotic form as the domain varies is expressed in terms of this same asymptotic form. The system of variation formulas obtained is closed. It enables the PDE solution in the domain to be reduced to the solution of an ordinary differential equation in functional space. The local characteristics of the solution can also be found by this method without calculating the solution itself. If there is sufficient symmetry in the initial operator, then conservation laws in the Noether sense are obtained for its Green's function and its asymptotic form. The behaviour of the quantities under investigation is studied under inversion.

The investigation of variations of the solutions of problems for the variation of the domain occurs in the paper by Hadamard /1/, who studied the variation in conformal mapping and obtained a formula similar to (1.4). The formula for the variation of the solution of the boundary value problem for an elliptic differential equation is obtained in /2/. Variation formulas for the case of the operator of the problem about a crack and a circular domain are obtained in /3, 4/. The Irwin formula /5/ is obtained from formulas (1.4) and (1.21) by substitution.     

Study of mechanical relaxation processes in ladder organosilicon polymers

Dynamic viscoelastic properties of ladder polyorganosiloxanes have been studied by the method of induced resonance oscillations in the temperature range from –150 to 300°C and in the frequency range from 8 to 300 Hz. Two broad maxima of mechanical losses were observed for all the polymers studied independently of their chemical structure, a low-temperature maximum in the –150 to 0°C region and a high-temperature maximum in the 0 to 250°C region. It was found that the introduction of alkyl groups into polyphenylsilsesquioxanes does not noticeably affect the position and nature of the low-temperature relaxation peaks but in certain cases leads to an increase in the dynamic modulus in polyphenylalkylsilsesquioxanes, compared with the modulus of polyphenylsilsesquioxane in the same temperature region. In the high-temperature region, a distinct dependence is observed of the relaxation peak on the length and the content of alkyl groups in the polymer. It has been found that increase in the length and the content of alkyl groups is accompanied by a shift in the peak in the direction of low temperatures and a decrease in the value of the modulus. Hypotheses have been suggested on the nature of the shifts which lead to the relaxation peaks observed in the ladder polyorganosiloxanes.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 804–809, September–October, 1973.     

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.     

Multiple structural changes in the tail behavior: Evidence from stock index futures returns

The study provides an approach of nonlinear analysis for detecting multiple structural changes in the tails of financial returns distributions. The proposed approach can simultaneously determine the number of structural breaks in a series of tail-indexes and estimate the mean tail-index levels in distinct regimes. The method is applied to the tail behavior of DJIA futures returns. The sample period covered various recent financial crises, and ran from October 1999 to December 2003, enabling assessment of the relationships between changes in the tail shape of returns distribution and known extreme events in financial markets. The empirical results demonstrate the existence of at least one break point in the left and common tails of the DJIA futures returns distribution during the sample period, and the mean tail-index levels in different regimes classified by estimated break points display an increase in the left and common tails that coincides the phenomenon of gradually decreasing financial turbulence in DJIA futures contracts. The empirical evidence indicates that the structural changes in the tail behavior of the distribution of DJIA futures returns are associated more with negative shocks than positive ones, creating differences in risk management between long and short investors in futures markets.     

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.