The normal state of high temperature oxide superconductor

Looking back on the experiments about the normal state of the high temperature superconductor (HTS), the authors point out nine important experimental results. On the basis of these results, the authors have argued that the two-dimension, two-subsystem Hamiltonian is the appropriate starting point for describing the normal state of HTS. By this Hamiltonian, using the decoupling approximation of Green’s function method by Kaga through numerical calculations, the authors have obtained the temperature dependent pseudogap in the density of states (DOS), which is consistent qualitatively with the experimental results by angle-resolved photoemission spectroscopy (ARPES). Theoretically, this Hamiltonian has the superconducting order parameter of d + s symmetry with d-wave as the main component, which is consistent with experiments. Further, the quantum electronic liquid in HTS is a near Fermi liquid in which there is coexistence of the delocalized states and nearly localized states, and there is finite probability for the nearly localized carriers to form the nearly localized carrier pairs at any finite temperature.     

A comparative approach to the economic modelling of a large-scale wave power scheme

Conversion of marine energy sources, including ocean waves and tidal currents, into electricity is a rapidly developing industry. Although many technologies have been proposed and some have generated electricity at full scale, it is difficult to predict which technology will be economic at large scales of installation. Several studies have been conducted which estimate the cost of electricity on the basis of schematic designs. However, each study represents a best estimate of the future cost based on current design details and direct comparison between the results of these studies is not straightforward. A methodology for directly comparing different wave energy concepts and potential locations would be beneficial to aid investment decisions. In this study we describe how the established data envelopment analysis technique could be employed for this purpose. The developed model is employed to rank the efficacy with which several types of conceptual and prototype wave energy conversion technologies generate electricity from the wave energy resource available at UK and US sites.     

A nonstationary model of firespreading

A nonstationary (dynamical) model of the fire-spreading process is proposed in connection with firebreak designs, fire fighting policies and contingency for the people affected. The model is derived as a Stefan problem with the aid of the law of conservation of energy; firebrand-spotting and wind-blown effects are neglected. Also, the numerical examples of a laboratory scale fire are given; the results agree well, in the order of magnitude, with the experimental data reported. The stationary model is also derived from the dynamical model by use of Galilei's transformation and it is shown that a solution of the dynamical model approaches with time to a solution of the stationary model.     

Evaluation of high energy natural neutrino experiments

The directional intensities of neutrinos of various types produced in the decay of cosmic ray secondaries in the earth’s atmosphere have been estimated. The calculated energy spectra are believed to be uncertain by <20% for neutrino energies up to 100 GeV. Using these fluxes and making various assumptions about the behaviour of neutrino cross-section with energy, the energy spectra of neutrino-induced muons at large depths underground have been calculated. It is shown that a cross-section increasing only linearly with energy up to ～ 100 GeV. would account only for about one-fifth of the preliminary counting rate observed in a recent underground experiment. A more rapid increase in cross-section is indicated somewhere between 10 GeV. and 100 GeV. and this is shown to be quantitatively consistent with the existence of a charged intermediate boson of mass 2 GeV. ～ M_w < 5 GeV. (However see the note added in proof.) The question of detecting high energy neutrino signals from extra-terrestrial sources is briefly discussed.     

New maximum entropy-based algorithm for structural design optimization

A new algorithm based on nonlinear transformation is proposed to improve the classical maximum entropy method and solve practical problems of reliability analysis. There are three steps in the new algorithm. Firstly, the performance function of reliability analysis is normalized, dividing by its value when each input is the mean value of the corresponding random variable. Then the nonlinear transformation of such normalized performance function is completed by using a monotonic nonlinear function with an adjustable parameter. Finally, the predictions of probability density function and/or the failure probability in reliability analysis are achieved by looking the result of transformation as a new form of performance function in the classical procedure of maximum entropy method in which the statistic moments are given through the univariate dimension reduction method. In the proposed method, the uncontrollable error of integration on the infinite interval is removed by transforming it into a bounded one. Three typical nonlinear transformation functions are studied and compared in the numerical examples. Comparing with results from Monte Carlo simulation, it is found that a proper choice of the adjustable parameter can lead to a better result of the prediction of failure probability. It is confirmed in the examples that result from the proposed method with the arctangent transformation function is better than the other transformation functions. The error of prediction of failure probability is controllable if the adjustable parameter is chosen in a given interval, but the suggested value of the adjustable parameter can only be given empirically.     

Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

An evaluation was made of the mathematical and economic basis for conversion processes in the LEAP energy-economy model. Conversion processes are the main modelling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. The study arose out of questions about the uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity for factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioural features of the original model, is proposed to resolve these discrepancies.     

Poisson polyhedra in high dimensions

The zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated, as the space dimension tends to infinity. The model includes the zero cell of stationary and isotropic Poisson hyperplane tessellations as well as the typical cell of a stationary Poisson Voronoi tessellation as special cases. It is shown that asymptotically in the space dimension, with overwhelming probability these cells satisfy the hyperplane conjecture, if the distance exponent and the intensity parameter are suitably chosen dimension-dependent functions. Also the high dimensional limits of the mean number of faces are explored and the asymptotic behaviour of an isoperimetric ratio is analysed. In the background are new identities linking the f-vector of the zero cell to certain dual intrinsic volumes.     

变形色散水波方程的Auto-Backlund变换、多孤子解和有理分式解

利用未知数变换并借助Ｍａｔｈｅｍａｔｉｃａ软件,给出了变形色散水波方程的Ａｕｔｏ－Ｂａｅｃｋｌｕｎｄ变换以及它与热传导方程和线性方程之间的Ｄａｒｂｏｕｘ变换。进而用此变换,获得了变形色散水波方程的多孤子解,有理分式解及其他精确解。这种思路也适用于其它的非线性方程。     

An improved high order moment-based saddlepoint approximation method for reliability analysis

Moment-based methods use only statistical moments of random variables for reliability analysis. The cumulative distribution function (CDF) or probability density function (PDF) of a performance function can be constructed from the perspective of the first few statistical moments, and the failure probability can be evaluated accordingly. However, existing moment-based methods may lead to large errors or instability. As such, the present paper focuses on the high order moment method for higher accuracy of reliability estimation by combining the common saddlepoint approximation technique, and an improved high order moment-based saddlepoint approximation (SPA) method for reliability analysis is presented. The approximated cumulant generating function (CGF) and the CDF of the performance function in terms of its first four statistical-moments are constructed. The developed method can be used for reliability evaluation of uncertain structures follow any types of distribution. Several numerical examples are given to demonstrate the efficacy and accuracy of the proposed method. Comparisons of the new method and several existing high order moment methods are also made on the reliability assessment.     

2D semiclassical model for high harmonic generation from gas

The electron behavior in laser field is described in detail. Based on the ID semiclassical model, a2D semiclassical model is proposed analytically using 3D DC-tunneling ionization theory. Lots of harmonic features are explained by this model, including the analytical demonstration of the maximum electron energy 3.17U _p Finally, some experimental phenomena such as the increase of the cutoff harmonic energy with the decrease of pulse duration and the “anomalous” fluctuations in the cutoff region are explained by this model.     

Development of an energy-emission model using fuzzy sets

In searching for cost-efficient strategies to reduce emissions from energy conversion, most western countries use energy-emission models. In these models, the whole energy conversion chain and possible future options for energy supply and emission reduction are mapped into a network of energy flows. Total discounted cost of energy supply and emission reduction is minimized under the restriction of maximum allowed emissions of SO₂, NO _x , or CO₂. The present paper extends one of these models to allow for fuzzy parameters. Such an extension appears to be useful when the data situation is weak. In this paper, a fuzzy linear program is developed, which has been applied to an energy-emission model of Lithuania.     

New Potentialities in Producing Composites Reinforced with High-Strength High-Modulus Polyethylene Fibers

A concept of physical and chemical stages of interaction between the matrix and reinforcing fibers during the production of composite materials is introduced. A strong bond between these constituents is formed at the stage of chemical interaction, which is characterized by a certain value of activation energy. The activation energy of such an interaction for high-strength high-modulus polyethylene fibers used for reinforcing composites is estimated. Based on these estimates, conditions for fiber activation with cold plasma are found. The application of plasma-activated polyethylene fibers for reinforcing an epoxy matrix allows one to produce light-weight composites with high physicomechanical indices. The failure mode of such composites points to a high strength of the bond between the fibers and matrix. The data on treating the fiber surface with cold plasma above the activation energy of chemical interaction may be utilized to create new types of organic composites from other kinds of organic fibers and matrices.     

基于区制转换的股市泡沫动态监测模型

提出了两阶段区制转换模型,考虑了在两个时区之间的随机转换和退出泡沫时期的概率,使用序贯贝叶斯学习方法实时估计模型状态和参数。模拟试验表明,相比现有的其他方法,两阶段区制转换模型对于检测泡沫来说具有更好的效力。实证检验证实了模型的优势,并且得到一个重要的结论是2008年之后的A股市场的泡沫化程度较低。本文模型可以为机构投资者和监管部门动态监测股票市场可能存在的价格泡沫现象提供一些启示。     

A logarithmic Hardy inequality

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy. This inequality differs from standard logarithmic Sobolev inequalities in the sense that the measure is neither Lebesgue's measure nor a probability measure. All terms are scale invariant. After an Emden-Fowler transformation, the inequality can be rewritten as an optimal inequality of logarithmic Sobolev type on the cylinder. Explicit expressions of the sharp constant, as well as minimizers, are established in the radial case. However, when no symmetry is imposed, the sharp constants are not achieved by radial functions, in some range of the parameters.     

Couette-Taylor流的力学机理与能量转换

同轴圆筒间Couette-Taylor流问题是典型的旋转流动问题,它是层流到湍流过渡的范例,国内外众多学者对其进行了深入的研究.该文探讨Couette-Taylor流问题的力学机理与能量转换,通过将Couette-Taylor流三模混沌系统转换成Kolmogorov形系统,把系统的力矩分为四种类型:惯性力矩,内力矩,耗散力矩和外力矩.通过不同力矩的结合分析和研究了Couette-Taylor流产生混沌的关键因素和物理意义.研究了哈密顿能量,动能和势能之间的相互转换.讨论了能量与雷诺数之间的关系.研究表明四种力矩的耦合是产生混沌的必要条件,而且只有耗散力矩和驱动力矩(外力矩)相匹配时,系统才能产生混沌,其中任何三种力矩耦合均不可能产生混沌.圆筒旋转产生的外力矩供给系统能量,能量增长导致流动失稳,从而产生泰勒漩涡和混沌,进而得出了Couette-Taylor流的能量转换和物理意义.引进Casimir函数分析系统的动力学行为和能量转换,并估计混沌吸引子的界.Casimir函数反映了能量转换和轨道与平衡点间的距离,数值结果仿真出它们之间的关系.     

色散长波方程的Darboux变换及多孤子解

根据色散长波方程的可积性,首先借助符号计算构造出该方程的Lax对,接着构建一个包含多参数的Darboux变换,通过应用Darboux变换,得到色散长波方程的2N-孤子解,最后通过图像研究了孤子解的性质,这些解和图像可能对解释色散长波方程所描述的水波现象有所帮助.     

Tractable stochastic analysis in high dimensions via robust optimization

Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional options, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks, (b) designing multi-item, multi-bidder auctions with budget constraints, and (c) pricing multi-dimensional options.     

The mathematical beliefs and behavior of high school students: Insights from a longitudinal study

There is a documented need for more research on the mathematical beliefs of students below college. In particular, there is a need for more studies on how the mathematical beliefs of these students impact their mathematical behavior in challenging mathematical tasks. This study examines the beliefs on mathematical learning of five high school students and the students’ mathematical behavior in a challenging probability task. The students were participants in an after-school, classroom-based, longitudinal study on students’ development of mathematical ideas funded by the United States National Science Foundation. The results show that particular educational experiences can alter results from previous studies on the mathematical beliefs and behavior of students below college, some of which have been used to justify non-reform pedagogical approaches in mathematics classrooms. Implications for classroom practice and ideas for future research are discussed.     

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer–Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations.     

Search for high dimensional integrable models

The possible high dimensional integrable models are studied in three different aspects: (i) starting from a strong symmetry operator of a known (1+1) -dimensional integrable model, we can construct a type of (n+1)-dimensional integrable models, high dimensional breaking soliton equations; (ii) from every concrete realization of the generalized Virasoro algebra, we can get many high dimensional integrable models in the meaning that the models possess generalized Virasoro symmetry algebra; (iii) starting from the Schwartz equations which possess conformal invariance, we can also get various high dimensional integrable models in the meaning that they possess Painlevé property. Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.