Möbius-like groups of homeomorphisms of the circle

A group G → Homeo_+(S^1) is a Möbius-like group if every element of G is conjugate in Homeo(S^1) to a Mobius transformation. Our main result is: given a Mobus like like group G which has at least one global fixed point, G is conjugate in Homeo(S^1) to a Möbius group if and only if the limit set of G is all of S^1 . Moreover, we prove that if the limit set of G is not SI, then after identifying some closed subintervals of S^1 to points, the induced action of G is conjugate to an action of a Möbius group.

We also show that the above result does not hold in the case when G has no global fixed points. Namely, we construct examples of Möbius-like groups with limit set equal to S^1, but these groups cannot be conjugated to Möbius groups.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

Note on the size groups of prawns landed by shrimp trawls of four different cod end meshes

A study on the different size groups of prawns caught by four shrimp trawls having different cod-end meshes was made by the author. The results indicate that small sized prawns of mean length 77.15 mm were captured by the net having 23.38 mm cod-end at 5-6 fathoms depth, medium prawns of mean length 105.22 mm was caught in 25.21 mm and 19.88 mm cod-end at 8 fathoms depth and big sized prawns of mean length 117.98 mm were caught in 21.29 mm cod-end. Further the relation of length on breadth of prawn is worked out to be : Bp=0.15 Lp - 1.50 where Bp and Lp are breadth and length respectively.

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.

Determination of biological characteristics and blood groups of hilsa shad (Tenualosa ilisha) in the north of Persian Gulf (Bushehr coastal waters)

Hilsa shad, Tenuolosa ilisha, belongs to Clupeidae family and Alsinae subfamily is an euryhaline pelagic and anadromous species living in marine and freshwater waters. Regarding to study the biological characteristics of this species, this study was carried out in the Northern Persian Gulf within Bushehr province waters during years 2006-7. A total of 344 specimens were collected and transported to the laboratory for further different biological measurements consist of: reproduction (GSI, fecundity, maturity stages), feeding (stomach contents, food preference ...), aging; 58 morphometric and ٧ meristic measurements. The results indicate that minimum, maximum and mean body weight are 203, 953 and 481.35±147.64 g, respectively and this values for total length are 26.5, 45.1 and 35.99±3.98 cm. For food regimes, the most abundant phytoplankton foods belong to Bacillariophyta (83.74٪) and zooplanktons of Arthropoda (51٪). The mean RLG was measured about 1.53±0.22 and the mean feeding intensity was about 51.79±38.13. Also, the aging of studied fishes showed that they have 2 to 4 years and most of the samples had 2+ years. The reproduction studies showed that Indian shad is a batch spawner species. The average gonadosomatic index (GSI) is 1.64±1.382 and the main spawning season was determined for April-May.

PATTERNS OF SPATIAL-DISPERSION, LOCOMOTION AND FORAGING BEHAVIOR IN 3 GROUPS OF THE YUNNAN SNUB-NOSED LANGUR (RHINOPITHECUS-BIETI)

Aspects of the behaviour of three groups of Yunnan snub-nosed langurs, Rhinopithecus bieti, were observed over the course of three field seasons from 1986 to 1988. The major findings of the study were: (1) The habitats of R. bieti were mainly at heights of 3,600-4,150 m above sea level. (2) Groups were very large, with group sizes ranging from more than 100 to 269 individuals. (3) Spatial dispersion densities ranged from about 27 to 106 m2/individual during sleeping and resting, to feeding dispersions as large as 5,000-15,000 m2. (4) The locomotor repertoire of R. bieti consisted largely of walking, jumping and climbing. On very rare occasions, semibrachiation was observed, but true brachiation was never observed. The locomotor repertoires of juveniles were more diverse than those of subadults or adults. (5) Communication consisted mainly of eye-to-eye contact accompanied by murmurs; while loud calls were heard only rarely. (6) Groups moved between sleeping and feeding sites in single file. It is concluded that R. bieti is a mainly terrestrial species.

Flipped physics

This paper defines flipped learning and then examines its practical implementation in AS and A2 level physics classes, that is, classes for 16-18 year olds. The effect of this teaching style on student learning behaviour and its impact on test results are evaluated. The paper recounts the difficulties of implementing it and evaluates student preferences. It concludes with comments about this teaching style's appropriateness for various groups of students and identifies those for whom it is not suitable. A list of useful websites is included. © 2013 IOP Publishing Ltd.

Molecular evidence for the monophyly of East Asian groups of Cyprinidae (Teleostei : Cypriniformes) derived from the nuclear recombination activating gene 2 sequences

The family Cyprinidae is one of the largest families of fishes in the world and a well-known component of the East Asian freshwater fish fauna. However, the phylogenetic relationships among cyprinids are still poorly understood despite much effort paid on the cyprinid molecular phylogenetics. Original nucleotide sequence data of the nuclear recombination activating gene 2 were collected from 109 cyprinid species and four non-cyprinid cypriniform outgroup taxa and used to infer the cyprinid phylogenetic relationships and to estimate node divergence times. Phylogenetic reconstructions using maximum parsimony, maximum likelihood, and Bayesian analysis retrieved the same clades, only branching order within these clades varied slightly between trees. Although the morphological diversity is remarkable, the endemic cyprinid taxa in East Asia emerged as a monophyletic clade referred to as Xenocypridini. The monophyly for the subfamilies including Cyprininae and Leuciscinae, as well as the tribes including Labeonini, Gobionini, Acheilognathini, and Leuciscini, was also well resolved with high nodal support. Analysis of the RAG2 gene supported the following cyprinid molecular phylogeny: the Danioninae is the most basal subfamily within the family Cyprinidae and the Cyprininae is the sister group of the Leuciscinae. The divergence times were estimated for the nodes corresponding to the principal clades within the Cyprinidae. The family Cyprinidae appears to have originated in the mid-Eocene in Asia, with the cladogenic event of the key basal group Danioninae occurring in the early Oligocene (about 31-30 MYA), and the origins of the two subfamilies, Cyprininae and Leuciscinae, occurring in the mid-Oligocene (around 26 MYA). (c) 2006 Elsevier Inc. All rights reserved.

北京中小学生创造性思维的发展以及十三年前后之比较

This study investigated the major characteristics of creative thinking development for the school children in Beijing with paper/pencil tests. The “Creative Thinking Test” was executed. The representative samples were two groups of students who came from the classes in 3rd-grade to 12th-grade of normal schools in Beijing. The classes were selected at random, one grade one class. One group is composed of 387 students (218 males, 169 females) in 1993, the other is composed of 420 students (181 males, 239 females) in 2006. According to the data analysis, the major characteristics and the changes over the 13 years of the development of creative thinking for student were explored and discussed. 1) The development trends of three types of creative thinking were all flexuous increase with grade moving up. The mean score of elementary school students was the lowest. And scores of junior high school students and senior high school students were significant higher than elementary school students’. 2) The most rapid increase occurred from the 5th grade to 6th grade. 3) Slumps occurred in the 7th grade in PNE curve and also in the 9th and 12th grades in TPC curves. There was no slump in FGA curve. 4) The girl’s scores in PNE and TPC tests were significant better than boys’. No obvious gender difference was found in FGA test. 5) The scores of three creative thinking tests in 2006 were all better than those in 1993. Separately, the scores of FGA and TPC tests in 2006 were significant higher than the corresponding scores in 1993, and no significant difference was found in two PNE tests. 6) There was no significant difference in the maximum scores of the three creative thinking tests between 2006 and 1993. 7) The most rapid developing period of three types of creative thinking in 2006 were the 5th grade and the 6th grade. The same period in 1993 was from the 7th grade to 9th grade. 8) In 1993, there is no significant gender difference for each creative thinking test. In 2006, PNE and TPC results had remarkable gender difference that girls were higher than boys. No significant gender difference was found in FGA tests.