关于Diophantine方程的解

对于正整数a ,设S(a)是Smarandache函数。证明了 :方程S(1·2 ) +S(2·3) +… +S(x(x +1) ) =S(x(x +1) (x +2 ) /3)仅有正整数解x =1。     

AN EVALUATION OF SAS/GRAPH SOFTWARE FOR COMPUTER CARTOGRAPHY1

The SAS® computer software system, widely used and respected for its capabilities in statistical analysis and data base management, now includes a new set of graphic and cartographic procedures called SAS GRAPH?. We have used these cartographic procedures in research on mapping ethno-cultural census data from metropolitan areas in Ontario and in undergraduate and graduate courses in computer cartography. On the basis of that experience, we describe and evaluate SAS/GRAPH'S cartographic capabilities and illustrate with maps drawn by various devices.     

台湾海峡西岸重力场变化梯度场图像分析

讨论了应用曲面拟合技术和利用离散的重力观测点的重力变化对特定研究区的重力场变化进行数值模拟以获取该区重力变化空间梯度场图像的具体方法;并应用该方法获得了2004年3月福建安溪3.6级地震前的重力变化空间梯度场图像,发现空间梯度场图像能清晰地反映出地震前重力场群体性变化的差异性;利用此方法对2005年6月~2006年3月间台湾海峡西岸重力场变化进行数值模拟,获得其空间梯度场图像。     

西洋东大港水道流速垂线分布研究

对辐射沙洲海域东大港4#站位连续2个潮周期的流速测量资料进行了分析、研究,拟合给出了流速垂线分布关系,并根据实际测量资料确定了该站位6个水层的浑水水流尾流函数项表达式。这些表达式表明浑水水流尾流函数是相对深度和摩阻速度的函数。探讨分析了尾流函数的空间分布和潮周期过程。非恒定流的水流尾流函数项的准确表达,对于揭示含沙水流流速结构及水、沙相影响作用规律将起到启发和推动作用。     

Robust adaptive control of underactuated ships on a linear course with comfort

This paper addresses an important problem in ship control application—the robust stabilization of underactuated ships on a linear course with comfort. Specifically, we develop a multivariable controller to stabilize ocean surface ships without a sway actuator on a linear course and to reduce roll and pitch simultaneously. The controller adapts to unknown parameters of the ship and constant environmental disturbances induced by wave, ocean current and wind. It is also robust to time-varying environmental disturbances, time-varying change in ship parameters and other motions of the ship such as surge and heave. The roll and pitch can be made arbitrarily small while the heading angle and sway are kept to be in reasonably small bounds. The controller development is based on Lyapunov’s direct method and backstepping technique. A Lipschitz continuous projection algorithm is used to update the estimate of the unknown parameters to avoid the parameters’ drift due to time-varying environmental disturbances. Simulations on a full-scale catamaran illustrate the effectiveness of our proposed controller.     

Vertical variations of wave-induced radiation stress tensor

INTRODUcrIONThe concept of radiation stress was deve1oPed by tonguet--Higgins and Stewart (1964 ),who intreduced the definition of radiation stress as the excess mornentum due to the presence ofwaves, on the basis of time-averaged laws of Newtonian fluid mechanics and the assmption ofa unifOrm velocity distribution over depth. Subequently, the theory has been applied success-fully in the investigation of phenomena such as wave set-up and set--down (Bowen et al.,l968), longshore currents …     

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.     

Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach

Computational Fluid Dynamic (CFD) based on Reynolds Averaged Navier–Stokes equation is used for determining the transverse hydrodynamic damping force and moment coefficients that are needed in the maneuverability study of marine vehicles. Computations are performed for two geometrical shapes representing typical AUVs presently in use. Results are compared with available data on similar geometries and from some of the available semi-empirical relations. It is found that the CFD predictions compares reasonable well with these results. In particular, the CFD predictions of forces and moments are found to be nonlinear with respect to the transverse velocity, and therefore both linear and nonlinear coefficients can be derived. A discussion on the sources of the component forces reveal that the total force and moment variations should in fact be nonlinear.     

晚中生代─新生代南海周缘地块运动与南海演化

报道了由华南几个盆地的古地磁数据综合而得的反映该区白垩纪以来古纬度变化曲线，结合Ｓｃｈｍｉｄｔｋｅ等（１９９０）发表的加里曼丹１５０Ｍａ以来的古地磁数据，表明华南与加里曼丹在４０Ｍａ前具有大致相同的古纬度变化史，差异仅出现在距今３０Ｍａ前后和１０Ｍａ以来。若此趋势可靠，则可作出下列推断：（１）南海的扩张只能发生在距今３０Ｍａ附近或１０Ｍａ以后华南与加里曼丹反向运动时期；距今３０Ｍａ的扩张已被广为接受；（２）华南与加里曼丹之向可能存在的古南海只能在９１Ｍａ之前存在；（３）南海演化可能存在两期扩张。南海的拟合可通过沿３５００ｍ等深线的先道时针旋转、后北向平移两个步骤完成。这与Ｈａｙａｓｈｉｄａ等（１９９１）提出的日本海张开与扩张模式很相似，提示东亚边缘海的形成和演化可能具有同样的机制。华南距今５０Ｍａ以来的古纬度变化与Ｔａｐｐｏｎｎｉｅｒ（１９８２）的传播挤出构造模式所预期的基本吻合，表明距今５０Ｍａ以来华南古纬度变化的运动学机制可用Ｔａｐｐｏｎｎｉｅｒ模式作解释。     

浅述多元数据处理的一种简化拟合形式及算法剖析

在实际工程试验与研究中 ,多元数据处理经常遇到 ,根据 Weierstrass定理 ,采用多项式拟合是一种常见的数据处理方法。对于多元多项式的系数求解问题 ,可以归结为超定方程组的求解问题。该文以超定方程组的 SVD求解算法为核心 ,阐述了在工程实际中关于多元数据处理的一种应用方法 ,并尝试给出多元多项式拟合的一种简化方法