论文分析了数学素养的内涵、构成要素以及其行为表现,比较了传统的课堂教学与数学素养视域下的课堂教学的不同,概括出数学素养视域下的课堂教学的三个主要特征:一是重视培养观念成分数学素养中的整体观素养,加强知识结构的系统性,引导学生从整体性上认识数学的内容;二是重视知识成分数学素养中的关联性和策略性知识教学,加强数学的思想性教学和数学思维的培养;三是重视精神成分的数学素养中的文化价值,加强数学教育的育人性.论文以此为指导,对正项级数的比值审敛法的课堂教学进行了教学设计,突出了该次教学内容中蕴含的化归和类比数学思想方法以及辩证思维的设计,收到了满意的教学效果.

To compute torpedo shooting parameters for a straight running target with non-constant velocity, a general method for computing torpedo shooting parameter for a target with predictable trajectory is presented. For easy under-standing and application, the torpedo trajectory is expressedin form of subsection increment, and a computation model of shooting parameter is established. Compared with the method for shooting a target with constant velocity, the pro-posed method needs to solve a system of nonlinear equations with two unknowns. For an ideal acoustic homing target, the numerical solution ofa differential equation is used to compute the target state, and Newton iteration is adopted to compute the numerical solution of the system of binary equations. Numerical experiment indicates that this method can compute shooting parameter rapidly and accurately.

文中提出将目标运动要素解算结果进行图形表达的概念,对于等速直航目标,以声速有限的单站纯方位方法估计其运动要素,并以计算机绘制出最近若干个目标位置点估计、目标速度估计、目标方位观测误差均方差估计,以此表达运动要素解算结果的稳定性,便于决策者直观理解及提高采用目标运动要素的效率.同时发现,可以用目标方位观测误差均方差估计的性质判断目标可能的机动,以此作为重置解算的基础,用以更好地为鱼雷作战应用提供参考.

As the difficulty of torpedo twice turn angle parameter solving under predetermined encountering situation,we constructed a model of torpedo and target targeting point meeting model considering the con-dition of underway time after first turn angle to adjust the “first meeting”position before the movement of second turn angle,and gave an iterative solving method of this problem.Finally it gave a simulation for the model and the result proved the validity of the method and met the need of torpedo twice turn angle param-eter solving.

To predict the trajectory of acoustic homing torpedo fastly,the distance and bearing relative to this ship for specified time were taken as the torpedo motion factors,and the trajectory was parameterized to the solution of differential equations taking the factors as initial value. The result demonstrates that the analytic solution is equivalent to an algebraic equation, and this transformed algebraic-equation can be calculated using standard Newton method. A detection model of active sonar with the separation of sending and receiving point was established by considering sound speed influence. Based on the observation value of distance and azimuth,a relatively superior criterion named trajectory fitting for solving the motion factor was constructed. The fast calculation was realized for estimating the ideal acoustic homing trajectory under the conditions of small samples. Simulation results show that the torpedo trajectory predicted by this method can meet the parameters calculation for firing anti-torpedo torpedo.

In order to improve the probability of wake homing torpedoes in hitting the target,using the method of mathematical analysis,we studied the trajectory of wake homing torpedo during the closing stage. By calculating and analyzing the fire triangle,we obtained the unique solution of the advance angle. By analyzing the corner shooting model of volley sector neutral,we gave the method of using the model and the calculation formula of modifying the model. By analyzing the firing order of torpedo salvo,calculating ray flare angle and the rotation degree,we calculated the torpedoes shooting parameters. All the works pro-vides more accurate calculating data for guidance section.

为了更方便地研究鱼雷、水面舰船等武器或装备的平面运动规律,运用复数的指数表示,在相应坐标系下对它们的运动规律进行描述,得到任意时刻的轨迹方程,从而利用复数的运算性质和数学分析的方法进行分析,不仅能简单明确的描述问题,又能很大程度地省去了直角坐标系下繁琐的运算过程,还可以直接在MATLAB环境实现相关的结果,从而为平面运动规律问题的研究提供了的更为方便的工具和方法,尤其是对解决有关转角运动的问题意义更大.

By calculation the methods for calculating fire parameters of straight running torpedo parallel salvo can not satisfy that each torpedo encounter the head and end of the target without error. And it is proved that torpedo parallel salvo can not satisfy this property. The mode of firing twice independently which aims at the head and end of the ship and the mode of firing twice independently which always aims at the observation point are taken into account. Problems such as the simplicity of fire organization method,calculation of the parameters and jamming of two torpedoes are described quantitatively. The two modes above are compared with parallel salvo on probability index. Numerical tests find that under some condition there is little difference of these modes if the error is larger. And if the error becomes small,it seems that the former parallel salvo method should not be used.

To compute the parameters of two-time turn angle shooting of a torpedo for predetermined encountering situ-ation, a general model satisfying the requirements of different shooting modes is constructed by considering possible special trajectory and torpedo velocity change. The formulas for Newton iteration algorithm are given. The correctness of the proposed model and algorithm is validated by numerical experiment, and the results indicate that the model and algorithm can satisfy the computation requirements of the shooting parameters for straight running, acoustic homing, wake homing, salvo, target selection, etc.

In order to exert operational effectiveness for torpedo,this paper bring forward the conception of sub-launched torpedo favorableness meeting situation,points out that torpedoes of every homing method need second turning angle firing when first turning angle firing can't satisfy torpedo to approach and find the target with favored meeting situation.The key point of second turning angle firing—how to choose the second turning point is emphasized systemic research,based on giving out the second turning angle firing occasion and count model used in submarine torpedo weapon system.The paper imposts choosing method of the distance between the second turning point and given meeting point based on torpedo homing detected distance,so to make the choose of second turning point have more rationality and pertinence,and can be suitable for all kinds of torpedoes which include straight running torpedo.

Based on experiments of software and hardware, this paper presents several problems and solutions for Graphic Processing Unit(GPU) parallel computing in Matlab, mainly including operating system, GPU device and their driver, data parallel computing using GPU, compile timeout, restricts of programming, synchronously using several GPU devices, etc. It is concluded that the data parallel computing method using GPU in Matlab is simple and cost-efficient, and it can significantly improve the computing speed.

Aiming at the arithmetic of observing target which has uniform course and velocity,using target motion factor and average sound velocity to be the parameters for estimated,the analytic formulas to compute gradient vector and Hessian matrix for the nonlinear least square objective function are given.Based on these formulas,it can construct the arithmetic and program realization for estimating target motion factor.Some numerical experiments indicate that the trust region arithmetic and Levenberg-Marquardt arithmetic have almost the same computational accuracy to lsqnonlin which is a Matlab function used specially for solving nonlinear least square problem.

Through the description of straightforward shooting of a straight running torpedo,the random error and some concepts of hitting problem are studied,and the difference between success probabilities based on true value and observed value of target movement element is pointed out.For objective probability,two analytic methods of computing probability are proposed based on the first order or second order approximation of the function of random error vector.According to a theorem about the formulas to compute the mean value,variance and eigenfunction of a common second order function of normal distributed random vector,an analytic method with the second order approximation is given.Results show that the two analytic methods have high precision,and the first order approximation method is better than the second order one in the case of computing the objective hitting probability of torpedo straightforward shooting.

Based on the idea of combining arith and figure,this paper uses the element method and the shape graph coordinate formula to deduce a calculating formula for the volume of ring rotating object and gives the application.

For researching observation of motion factor of target which has uniform course and velocity,considering effect of sound travel time in sea water,a analytic formula to compute observable target bearing is established.Basing on assumption that the average sound velocity is a finite constant,it is proved that the target motion factor is generally observable although the observation station does not move.Under the Assumption that the bearing observation errors are independent identically distributed normal random errors with mean zero,it is proved that the estimator giving by least square of bearing observation error is maximum likelihood estimator.Emulational experiments indicate that this method improved notably degree of observability on classical method when observation station move in turning and straight.

Based on the analysis of relative bearings error range in the scope of acoustic homing torpedo,the optimization model is established according to the definition of optimized lead angle.In addition,the capture probability of acoustic homing torpedo is simulant calculated.The simulation results show that the numerical solution of the optimization model is correct.

The straight running attack is a classic torpedo attacking,and the hit probability distribution is very important basis for commanders' tactical decision.Considering different measuring errors,the paper put forward the analytic formula on the hit probability of the straight running torpedo and parallel calculates the formula making use of CUDA and finally get the omni bearing map of hit probability distribution about straight running torpedo.At the same time display the map in the real-time speed.

Battle effect and attack decisions use generally probabilities to describe the indetermination problems,however probabilities are separated into subjective and objective,for explaining the dissimilarity,by a imaginary straight forward shooting problem,consider only the err of target movement velocity,this paper discussed the essence about known a exact value or a observed value.The conclusion enunciate that,when deal with the successful probabilities of shooting,it is necessity to explain clearly the essence and function of that probabilities.The probability computed based on observed value is subjective,and could be used for the support of decision making.And the decision making precision based on subjective probability depend quite on the precision of transcendental knowledge which is about the exact value of the observed variable and used for computing that subjective probability.

通过对概念的诠释,从职业的视角加深对任职教育的理解;通过对教学改革认识的提高,在任职教育的大体系中加大改革力度,加速推进任职教育的深入发展。

The mathematical model for solving the factors of target motion with two bearings plus two known factors is also used for solving the factors of target motion with three bearings plus known speed,but the amount of calculating is very large.And the formula is fussy.The graphic method of solving the factors of target motion with three bearings plus known speed is studied,and an algorithm is proposed in this paper.Using this algorithm,the factors of target motion can be solved correctly.The amount of calculating is smaller.So the algorithm is more efficient.