一类描述混沌映射的符号动力系统

本文定义了符号空间上的拟移位映射,并用该类映射描述了Ｃａｎｔｏｒ集及平面Ｃａｎｔｏｒ集上的混沌映射,本文结果可看作Ｓｍａｌｅ马蹄模型的简化。     

异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

梯度折射率棒透镜的色差模型

本文提出一个梯度折射率棒透镜(GRIN－RodLens)的色差模型,并运用本模型合理地解释了在色差测量过程发现的各类色差现象.     

e~＋－Kr和e~＋－Xe弹性散射截面的模型势计算

用模型势方法计算了低能正电子与Ｋｒ、Ｘｅ原子弹性散射总截面与动量转移截面，并将本文的计算结果与理论计算及实验值作了比较。     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

Numerical analysis of a moving boundary problem in coastal hydrodynamics

A finite element model to tackle the moving boundary problem of wave run-up on moderately steep slopes is developed. The special aspects considered in this study are (1) the modification of shallow water equations to accommodate the effect of vertical accelerations and (2) the use of Lagrangian acceleration coupled with an element that adapts itself to the moving boundary closely. The pressure term in the one-dimensional momentum equation is derived using the Eulerian equation in the vertical direction. This takes care of the vertical accelerations which are significant during the motion of a wave on moderately steep slopes. The element near the boundary is allowed to change its dimension so that the fluid boundary is closely followed. Such a flexible element precludes the need for approximation of the variables with regard to the indefinite position of the boundary. This element is split into two when its dimension becomes unduly large compared to the unchanging elements. The need for such a splitting is shown by an examination of the entries in the global matrix. Results of water profile as a wave runs up a structure are given. A brief history of the work on similar problems is outlined.     

光纤陀螺数字闭环控制系统模型实验研究

数字闭环光纤陀螺的动态性能受控制系统设计的影响.根据光纤陀螺数字闭环检测过程,建立了控制系统的数学模型.为在全频带内对模型进行验证,提出了基于Faraday效应的光纤陀螺频率响应测试方法,对该测试方法与角振动台测试方法的等效性进行了分析.设计了频率响应测试系统,测试范围大于50 kHz,波形失真小于0.1%.实测了采用一阶积分控制算法的数字闭环光纤陀螺频率响应.实验结果表明模型误差小于8%.     

Characterization of a Pd-Fe bimetallic model catalyst

Small bimetallic Pd-Fe particles supported on a well ordered alumina film grown on NiAl (1 1 0) were studied focusing on the geometric, electronic, adsorption, as well as magnetic properties. The morphology, growth mode and surface composition were investigated by combining scanning tunneling microscopy (STM), temperature-programmed desorption (TPD) and infrared spectroscopy (IRAS) using CO as a probe molecule. Information on the electronic properties of the bimetallic systems was obtained by means of X-ray photoelectron spectroscopy (XPS). These measurements were amended by in situ ferromagnetic resonance spectroscopy to address the magnetic properties of the bimetallic particles. The subsequent deposition of the metals at 300 K varying the order of metal deposition resulted in two distinct bimetallic systems. Pd deposited on existing Fe particles forms a shell, however, FMR and XPS suggest that intermixing of Pd and Fe occurs to some extent. For the reverse order, a larger amount of Fe is required to coat Pd particles, due to the strong tendency of Pd to segregate to the surface of the particles.     

Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.     

The Design and Analysis of Benchmark Experiments

The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Cross-validation or resampling techniques are commonly used to derive point estimates of the performances which are compared to identify algorithms with good properties. For several benchmarking problems, test procedures taking the variability of those point estimates into account have been suggested. Most of the recently proposed inference procedures are based on special variance estimators for the cross-validated performance. We introduce a theoretical framework for inference problems in benchmark experiments and show that standard statistical test procedures can be used to test for differences in the performances. The theory is based on well-defined distributions of performance measures which can be compared with established tests. To demonstrate the usefulness in practice, the theoretical results are applied to regression and classification benchmark studies based on artificial and real world data.