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.     

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.     

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.     

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.     

Entanglement,fidelity and quantum chaos in cavity QED

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom–field system as a quantum–classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Chaos manifests itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with prominent fractal-like behavior and in the quantum atom–field degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom–field resonance correlate strongly. It is shown that the Jaynes–Cummings dynamics can be unstable in the regime of chaotic walking of an atom in the quantized field of a standing wave in the absence of any other interaction with environment. Quantum instability manifests itself in strong variations of quantum purity and entropy and in exponential sensitivity of fidelity of quantum states to small variations in the atom–field detuning. It is quantified in terms of the respective classical maximal Lyapunov exponent that can be estimated in appropriate in–out experiments. This result provides a quantum–classical correspondence in a closed physical system.     

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。     

The antiplane problem of the motion of a point shear load over a two-layer elastic base at a constant velocity

The problem of modelling the motion of a force disturbance in an elastic medium that is heterogeneous over its depth is investigated. It is in an antiplane formulation in a moving system of coordinates that all possible versions of the ratio of the velocity of motion of the surface point shear load to the velocities of the shear waves in the layers of the two-layer elastic base are examined. Cases of a subsonic regime (SBR) in the upper and lower layers, of a supersonic regime (SPR) in the upper layer and an SBR in the lower layer, and of an SBR in the upper layer and an SPR in the lower layer are studied using the Fourier transform and the theory of residues. The last two cases are extremely interesting from the mathematical point of view, as here, on the boundary between the layers, the solutions of elliptic and hyperbolic equations meet, and previously unknown features arise in the displacements that,it seems, should also occur in the solution of the corresponding plane problem. The case of an SPR in the upper and lower layers is investigated using a special method for successive allowance for the incident, reflected and refracted shock wave fronts. In all cases, expressions are obtained for the displacements in the layers, and their characteristic features are investigated.     

The effective conductivity of a randomly inhomogeneous medium

Using a representation of the solution to the diffusion equation in a randomly inhomogeneous medium in the form of a Feynman path integral an explicit expression is obtained for the effective conductivity in a space of arbitrary dimension. A calculation of the path integral only turns out to be possible in the case of a large-scale limit. In particular, it is shown that in the three-dimensional case the expression for the effective conductivity does not admit of an expansion in terms of the conductivity variance. This indicates that the use of standard perturbation theory in the form of an expansion in terms of the conductivity fluctuations is incorrect.     

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.     

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.     

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.     

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.

     

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.     

Rawlsian altruism with perfect discrimination leads to social efficiency

Recent studies draw attention on the highly specialized capacity of human beings in recognizing altruists versus cheaters in social interactions. These results hint at the existence of specialized abilities that support discriminating behavior in strategic interactions. In this paper, we explore the implications of discriminating behavior in the study of the indirect evolutionary selection of selfish versus altruistic motivations in the context of generic 2×2 base games, and in particular for coordination and cooperation scenarios. We find that inequality averse (Rawlsian) altruism can enforce under rather general conditions socially optimal outcomes, including cases where selfishness cannot, such as in prisoner’s dilemmas. Inequality seeking (Nietzschian) altruism in no case improves upon Rawlsian altruism in terms of social optimality of outcomes, and often does worse. In the cooperation scenario in particular, Nietzschean altruism never manages to implement the cooperative outcome. Under perfect discrimination, moreover, inequality averse (Rawlsian) altruism often evolves at the expense of selfishness. These results suggest that the development of sophisticated discrimination abilities may be strongly adaptive in supporting fairness-oriented forms of pro-sociality in humans in the context of social dilemmas and coordination problems.