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.

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.

Jacobi forms and differential operators

We affirmatively answer a question due to S. Bocherer concerning the feasibility of removing one differential operator from the standard collection of m + 1 of them used to embed the space of Jacobi forms of weight 2 and index m into several pieces of elliptic modular forms. (C) 2014 Elsevier Inc. All rights reserved.

El Liber Sancti Jacobi y la sacralización universal de las reliquias compostelanas

Resumen: La leyenda franca del descubrimiento de los restos de Santiago plantea una serie de problemas que trascienden la historia del Camino en sí mismo. Desde hace más de quince años he trabajado sobre los vínculos culturales entre Hispania y Galia. Coincidí con la tesis de Rucquoi, sobre las rutas del saber y retrotraje su hipótesis de trabajo hasta el siglo VIII. En este artículo intento exponer mi hipótesis sobre la posible relación entre las reliquias compostelanas y la Sacralización del Imperio Alemán durante el reinado de Federico I Barbarroja.

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.

Effect of lykamin on growth and biochemical composition of long whiskered catfish, Mystus gulio (Hamilton) fingerlings under laboratory conditions

A growth trial was conducted to test the effect of Lykamin (dietary supplement) on growth, survival and feed conversion in Mystus gulio. Four isoproteic diets were formulated by incorporating the growth promoter, Lykamin at the levels of 0, 0.25, 0.50 and 0.75% diet. The crude protein content was 30% in each diet. The diets were fed to triplicate groups of catfish fingerlings twice daily at a level of 5% of the total body weight for 120 days. Regular fortnightly sampling was done to evaluate the growth performance of the experimental animals. Water quality parameters during the experimental period were maintained within the range suitable for catfish. The results showed better specific growth rate, weight gain, protein efficiency ratio and feed conversion ratio in the group which was given 0.75% Lykamin diet.

Food of two size-groups of the catfish Mystus giulio (Hamilton-Buchanan) in Vemblai canal, Vypeen Island

The stomach contents of two length-groups of the catfish Mystus gulio collected from Vemblai Canal in Vypeen Island (Kochi) were examined by frequency of occurrence and points methods. Analyses using standard indices proved difference in diet composition between the two size-groups.

Studies on the age and growth of Labeo calbasu (Hamilton) with an exploitation pattern from the Ganga River system, Uttar Pradesh (India)

Samples were collected to study the age and growth of Labeo calbasu (Hamilton) from the river Ghaghra (Guptarghat centre, Faizabad). The scales of L. calbasu have been used for age and growth studies in present paper. Study of the marginal rings on the scales of L. calbasu indicates their annual nature. The fish attained growth in 1st 18.7 cm, 2nd 27.8 cm, 3rd 35.7 cm, 4th 41.8 cm, 5th 46.9 cm, 6th 54.9 cm and 7th 57.4 cm years of the life. The growth rate was observed 18.7, 9.1, 7.9, 6.7, 5.1, 8.0 and 2.5 cm for 1st to 7th age classes respectively. The age groups 1+ to 4+ constituted 91.17% of the total exploited population and 8.83% of remaining age groups (5+ to 7+). The maximum exploited population was observed in 2+ age group with 33.68%. Overall exploitation pattern was systematic and a good indicator for heavy recruitment.

Studies on maturation, spawning, fecundity and sex ratio in Barbus (Puntius) sarana (Hamilton-Buchanan) from Lake Kolleru, Andhra Pradesh

Barbus sarana contains only one batch of mature ova in the mature ovaries to be spawned in one spawning act. It spawns during July-September. The fecundity ranges from 11,201 to 224,248 ova. There is a positive curvilinear correlation between total length and fecundity, the latter increasing with length at a rate of less than cube of length. The stock of this species from Lake Kolleru appears to be more fecund than that inhabiting Loni reservoir. The sex ratio indicates that females outnumber males in all months and in larger length groups. Females appear to reach a larger length than males.