Ultraviolet Finiteness of Chiral Perturbation Theory in Two-Dimensional Quantum Electrodynamics

We consider the perturbation theory in the fermion mass (chiral perturbation theory) in the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction has the exponential form and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.     

A polarographic study of mercuric cyanide complexes with alkali halides

The processes by which the movements of the surface of the earth due to its rotation around the polar axis can influence the atmosphere above are considered in detail. It emerges that the fast-moving areas in the equatorial belt on the surface of the earth play a highly important role in determining the behaviour of the atmosphere. The jet-stream in the sub-tropical regions, the westerly zonal winds in the region of middle latitudes and the easterly surface-winds in the equatorial belt are explained on this basis and shown to stand in close relationship with each other. The winds observed in the polar belt are also discussed and explained.     

Steenrod squares in Cotor

It is first shown that the comparison theorem in relative homological algebra is the only tool to be used for introducing Steenrod operations in Cotor as well as in Ext. Then, the interaction of the operations in both functors is discussed in full detail. Some basic properties of the operations are given in the last section of the paper.The authors would like to thank a referee for his suggestion to reorganize their paper in the present form.This work is supported in part by NSF research grant GP-9585.     

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.     

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.     

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.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

Exploring gender factors related to PISA 2003 results in Iceland: a youth interview study

Students’ mathematical achievement in Iceland, as reported in PISA 2003, showed significant and (by comparison) unusual gender differences in mathematics: Iceland was the only country in which the mathematics gender gap favored girls. When data were broken down and analyzed, the Icelandic gender gap appeared statistically significant only in the rural areas of Iceland, suggesting a question about differences in rural and urban educational communities. In the 2007 qualitative research study reported in this paper, the authors interviewed 19 students from rural and urban Iceland who participated in PISA 2003 in order to investigate these differences and to identify factors that contributed to gender differences in mathematics learning. Students were asked to talk about their mathematical experiences, their thoughts about the PISA results, and their ideas about the reasons behind the PISA 2003 results. The data were transcribed, coded, and analyzed using techniques from analytic induction in order to build themes and to present both male and female student perspectives on the Icelandic anomaly. Strikingly, youth in the interviews focused on social and societal factors concerning education in general rather then on their mathematics education.     

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.     

An overview on the history of actuarial calculus in Portugal until the late 19th century

Pension funds, namely survivors' pension funds were established in Portugal in the late 18th century, in mutual benefit societies. The first Portuguese life assurance companies were created in the first half of the 19th century but their activity was not very extensive. Only in the 20th century did both institutions become actuarially-based. In this paper, we provide an overview of the development of actuarial calculus in Portugal until the late 19th century, in order to contextualise the scientific progress of those institutions, mainly the former. This paper lays the groundwork for further research on the history of actuarial calculus in Portugal.     

我国制造业背景下质量管理活动的量表开发研究

质量管理的测度是质量管理实证研究的基础,但我国在此领域还处于起步阶段。以重庆市制造业企业为样本,采用基于偏最小二乘法的证实性因子分析方法,对我国制造业企业的质量管理活动进行了实证度量。结论显示,我国制造业企业质量管理活动包含六个方面的主要内容:企业高层的支持、员工的参与、供应商关系、重视客户、产品设计和流程管理。研究给出了具体的我国质量管理活动的测度量表。     

Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared

We compare different approaches to the construction of the quantum mechanics of a particle in the general Riemannian space and space–time via quantization of motion along geodesic lines. We briefly review different quantization formalisms and the difficulties arising in their application to geodesic motion in a Riemannian configuration space. We then consider canonical, semiclassical (Pauli–De Witt), and Feynman (path-integral) formalisms in more detail and compare the quantum Hamiltonians of a particle arising in these models in the case of a static, topological elementary Riemannian configuration space. This allows selecting a unique ordering rule for the coordinate and momentum operators in the canonical formalism and a unique definition of the path integral that eliminates a part of the arbitrariness involved in the construction of the quantum mechanics of a particle in the Riemannian space. We also propose a geometric explanation of another main problem in quantization, the noninvariance of the quantum Hamiltonian and the path integral under configuration space diffeomorphisms.     

Continuous modal control of linear multicoupled objects

A modal control method is considered in which the spectrum of the closed-loop system is continuously deformed in such a way that the spectrum of the open-loop object transforms into the desired spectrum. The algorithm of the continuous modal control is synthesized. The conditions for spectral control in the method are obtained. The approach is based on similar ideas to those in /1/, but a different class of controls is considered here. Moreover, by using the appratus of Lyapunov functions, specified in the one-parameter family of the deformed spectrum, the deviation between the required spectrum and the closed-loop system spectrum can be minimized in the Euclidean metric, in the case when the wanted spectrum cannot be obtained in the closed-loop system.     

Effect of disperse mineral fillers on the strain-strength properties and crack resistance of cured polyesters

Conclusion The tendency of disperse mineral fillers toward aggregation, with the formation of a continuous framework of particles, when filler content is greater than the SCC is manifest in a sharp increase in the difference between the relative viscosity of polyester binder-pastes in the uncured state and the relative elastic modulus in the cured state. It is also manifest in an increase in the relative modulus and a reduction in crack growth energy in cured composites. In this case, there is an especially large increase in the size of the characteristic defect, which ultimately determines the reduction in the breaking stress. The modification of binder-pastes with surfactants increases filler dispersion and makes it possible to increase the strength of cured composites.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 819–824, September–October, 1987.     

A feedback nash equilibrium solution for non–cooperative innovations in a stochastic differential game framework

In this paper, a stochastic model of non–cooperative technological innovations is developed. A feedback Sash equilibrium solution is obtained and the equilibrium innovation strategies are derived in explicit form. Several interesting properties of the equilibrium strategies are observed. On the one hand, an increase in the degree of competition in the industry, in the discount rate or in the state of technologyreduces innovation efforts. On the other hand, an increases the rate of degradation of the state of technology due to obsolescence results in an increase in innovation investment. While an increase in uncertainty reduces the expected present value of present and future discounted profits innovation efforts increase as uncertainty increases     

Electroelastic waves in polarizing media : Report to the fifth all-union congress on theoretical and applied mechanics. Alma-Ata, 27 May 1981

A system of equations is considered that describes a certain class of polarizing media in an electromagnetic field with both the spatial inhomogeneities and the relaxation processes of electrical polarization of the media taken into account. The nonlinear and the linearized theories are elucidated within the framework of the electrostatic approximation. Solutions are given for the equations considered in an electrostatic approximation, in the form of electroelastic waves. Without taking the relaxation of the electrical polarization into account, electorelastic waves were considered in piezoceramic media in /1/ and in ferroelectrics in /2/.     

On the generalized 2-D stochastic Ginzburg-Landau equation

This paper proves the existence and uniqueness of solutions in a Banach space for the generalized stochastic Ginzburg-Landau equation with a multiplicative noise in two spatial dimensions. The noise is white in time and correlated in spatial variables. The condition on the parameters is the same as in the deterministic case. The Banach contraction principle and stochastic estimates in Banach spaces are used as the main tool.     

“小麦发育后期茎秆抗倒性的数学模型”综述

2011年第8届全国研究生数学建模竞赛C题是一个农业生产中小麦倒伏问题,在给出3年原始测量数据的基础上要求建立小麦发育后期茎秆抗倒性的数学模型,内容包括小麦性状数据处理和弹性力学模型.综述为C题竞赛总结,含问题的提出、问题的解答与评阅情况、存在问题及研究建议.     

Stabilization by memory effects: Kirchhoff plate versus Euler–Bernoulli plate

In this paper we study the asymptotic behavior of solutions of a dissipative coupled system where we have interactions between a Kirchhoff plate and an Euler–Bernoulli plate. The dissipative mechanism is given by memory terms that act either collaboratively (in both equations) or unilaterally (in only one equation). We show that the solutions of this system decay to zero sometimes exponentially and other times polynomially. We found explicit decay rates that depend on the fractional exponents of the memory in each of the following cases: when the memory only acts in the Kirchhoff equation, or only in the Euler–Bernoulli equation, or in both. We also show that all decay rates found are the best. The results obtained are surprising for the following facts: in the collaborative case, the best decay rates of the system are given by the worst decay rates of the uncoupled equations, and in the unilateral case, we conclude that the memory effects in the Euler–Bernoulli equation dissipate the system more slowly than memory effects in the Kirchhoff equation.