The Hamilton-Jacobi equation revisited

A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

Phase space methods and the Hamilton-Jacobi form of dynamics

A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.

Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

迎风紧致格式求解Hamilton-Jacobi方程

基于Hamilton-Jaeobi(H-J)方程和双曲型守恒律之间的关系,将三阶和五阶迎风紧致格式推广应用于求解H-J方程,建立了高精度的H-J方程求解方法.给出了一维和二维典型数值算例的计算结果,其中包括一个平面激波作用下的Richtmyer-Meshkov界面不稳定性问题.数值试验表明,在解的光滑区域该方法具有高精度,而在导数不连续的不光滑区域也获得了比较好的分辨效果.相比于同阶精度的WENO格式,本方法具有更小的数值耗散,从而有利于多尺度复杂流动的模拟中H-J方程的求解.

非平整运动海底上n层流动中波浪传播的Hamilton逼近

在海洋水域，界面波对大尺度变化流的作用是一种典型的分层流动现象。考虑一不可压缩、无黏的分层势流运动，建立了一个在非平整运动海底上的n层流体演化系统，并对其进行了Hamilton描述。每层流体具有各自的常密度、均匀流水平速度，其厚度由未扰动和扰动部分构成。相对于顶层流体的自由表面，刚性、运动的海底具有一般地形变化特征。在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件（包含各层交界面上张力效应）后，对该分层动力系统进行了Hamilton构造，即给出其正则方程和其下述的正则变量：各交界面位移和各交界面上的动量势密度差。

Preliminary observations on the availability of Tor tor (Hamilton) fry in the River Narmada near Hoshangabad, Madhya Pradesh

Collection of mahseer (Tor tor) fry during December to January from three centres of the river Narmada near Hoshangabad, (Joshipur ghat, Dungerwada ghat and Kherra ghat) using a special type of fry collection net is described. The physical features and physico-chemical conditions of the collection sites are also dealt with.

A note on the calorific values of a freshwater teleost, Labeo gonius (Hamilton)

Forty specimens of Labeo gonius (Ham) were analysed for protein, carbohydrate and fat values. The calorific value was calculated by multiplying the value of protein and carbohydrate with the energy factor 4.1 and for fat by 9.3. The average calorific values of fish for protein, carbohydrate and fat were 72.16, 9.55 and 11.90 cal/100 g respectively suggesting that the fishes are highly nutritious.

Determination of ubiquinone and tocopherol in heart, liver and muscle tissues of fresh water fish, Rohu (Labeo rohita, Hamilton)

The liver, heart and muscle tissues of Rohu, (Labeo rohita, Hamilton) were examined for their ubiquinone (UQ) and tocopherol contents. These three tissues contained respectively 11.60, 3.94 and 0.19 mg of ubiquinone and 10.16, 5.32 and 3.58 mg of tocopherol per 100 g. The 4% (V/V) of diethyl ether (EE) in light petroleum ether (PE) fractions of all three tissues on paper chromatographic separation gave spots having the same Rf value as standard ubiquinone-50 (UQ 10). Both the 4% and 6% (V/V) diethyl ether in light petroleum ether fraction of liver, heart and muscle tissues gave a single spot with the same Rf value as α – tocopherol.

Predation by Channa striatus (Bloch) on Rana tigrina (Daudin), Puntius gonionotus (Bleekeer) and Labeo rohita (Hamilton) in the laboratory

The growth performance of a predatory snakehead, Channa striatus was tested by supplying tadpoles of Rana tigrina and fingerlings of Puntius gonionotus and Labeo rohita as prey for a period of 21 days in aquaria. Prey consumption by C. striatus was significantly different (P<0.05) for different prey used (T1 - R. tigrina, T2 - P. gonionotus, T3 - L. rohita). Tadpoles of R. tigrina were preferred by the predator (C. striatus) over P. gonionotus and L. rohita although tadpole is nutritionally inferior to each of P. gonionotus and L. rohita. Each predator rayed on 50-330 mg per day per g of their body weight. Fish preyed on tadpoles also showed the highest growth. Significant difference in weight gain was found between T1 and T2 and also between T1 and T3 but no difference was found between T2 and T3. Food conversion ratio (FCR) was found to be lowest in treatment T3 followed by the treatments T2 and T1 respectively.

A histological study of the spermatogenesis in Ompok pabda (Hamilton-Buchanan 1822)

The present study deals with the histological analysis of testicular development in Ompok pabda. For the study, male gonads were collected month wise from January to September at Freshwater Station, BFRI, Mymensingh. From the analysis, 4 stages of sperm formation, namely, spermatogonia, spermatocytes, spermatids and spermatozoa, were distinguished. The percent distribution of spermatozoa was highest in July (about 92%). Maximum GSI value was 1.129±0.271 found in July. By analyzing the histology of spermatogenesis it was established that this species breeds once in a year.