Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Effectiveness of coir geotextiles in soil moisture conservation

Among the diversified use of coir geotextiles, its use as a protective covering to improve crop productivity and to reduce weed problem assumes to be much significant. An experiment has been conducted at Kumbazha, in Pathanamthitta district, Kerala, India to evaluate the different types of coir geotextiles and polythene as soil mulch. The treatments include different mulching materials like natural needled felt, black needled felt, rubberized coir, black polythene and transparent polythene along with a control plot (no mulch). The experiment was laid out in Completely Randomized Design with six replications. The test crops used were bhindi (var. Salkeerthi) and pineapple (var. Mauritius). The study reveals that with bhindi crop growth parameters like plant height, leaf number and lateral spread were increased by mulching with rubberized coir and transparent polythene. These two mulches caused early flowering and increased fruit yield. Coir materials as mulch recorded a yield increase ranging from 67 to 196%. Observations also reveal that weeds were not grown in plots mulched with black polythene, transparent polythene and rubberized coir. Rubberized coir as mulch enhanced the fruit yield in the case of pineapple, which is followed by natural needled felt and transparent polythene. Black polythene resisted weed growth up to 7MAP, whereas rubberized coir and transparent polythene suppressed weeds up to 8MAP. Though the weeds were grown in other treatments the weeds count was significantly lower than that of control plot. Mulching with transparent polythene enhanced the soil temperature whereas rubberized coir lowered soil temperature. More over all mulched treatments had a favourable influence in increasing soil moisture. Observing the biodegradability and eco-friendly nature of coir it could be inferred that rubberized coir can serve as good mulch for bhindi and pineapple with minimum weed problem

The protective and attractive covering of a vegetated embankment using coir geotextiles

This paper presents the results of a field experiment conducted in Kerala, South India, to test the effectiveness of coir geotextiles for embankment protection. The results reveal that treatment with geotextile in combination with grass is an effective eco-hydrological measure to protect steep slopes from erosion. In the context of sustainable watershed management, coir is a cheap and locally available material that can be used to strengthen traditional earthen bunds or protect the banks of village ponds from erosion. Particularly in developing countries, where coir is abundantly available and textiles can be produced by small-scale industry, this is an attractive alternative for conventional methods. This paper analyses the performance of coir geotextile in different treatments with respect to soil moisture content, protection against erosion and biomass production

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Algorithms for Tamagawa Number Conjectures

In dieser Arbeit werden Algorithmen zur Untersuchung der äquivarianten Tamagawazahlvermutung von Burns und Flach entwickelt. Zunächst werden Algorithmen angegeben mit denen die lokale Fundamentalklasse, die globale Fundamentalklasse und Tates kanonische Klasse berechnet werden können. Dies ermöglicht unter anderem Berechnungen in Brauergruppen von Zahlkörpererweiterungen. Anschließend werden diese Algorithmen auf die Tamagawazahlvermutung angewendet. Die Epsilonkonstantenvermutung kann dadurch für alle Galoiserweiterungen L|K bewiesen werden, bei denen L in einer Galoiserweiterung E|Q vom Grad kleiner gleich 15 eingebettet werden kann. Für die Tamagawazahlvermutung an der Stelle 1 wird ein Algorithmus angegeben, der die Vermutung für ein gegebenes Fallbeispiel L|Q numerischen verifizieren kann. Im Spezialfall, dass alle Charaktere rational oder abelsch sind, kann dieser Algorithmus die Vermutung für L|Q sogar beweisen.

Biologische Funktionsanalyse und Identifizierung neuer Substrate der Methyltransferase Dnmt2

Obwohl die DNA Methyltransferase 2 (Dnmt2) hoch konserviert ist und zu der am weitesten verbreiteten eukaryotischen MTase-Familie gehört, ist ihre biologische Funktion nach wie vor unklar. Nachdem lange Zeit keine DNA Methylierungsaktivität nachgewiesen werden konnte, wurde vor einigen Jahren über geringe Mengen an 5-Methylcytosin (5mC) in Retroelementen der “Dnmt2-only”-Organismen D. melanogaster, D. discoideum und E. histolytica berichtet (Kunert et al. 2003; Fisher et al. 2004; Kuhlmann et al. 2005; Phalke et al. 2009). Als kurze Zeit später robuste Methylierung der tRNAAsp durch humane Dnmt2 gezeigt wurde (Goll et al. 2006), wurde zunächst eine Dualspezifität des Enzyms vorgeschlagen (Jeltsch et al. 2006). Neuere Daten zum 5mC-Status verschiedener „Dnmt2-only“-Organismen bilden Anlass für kontroverse Diskussionen über Ausmaß und Bedeutung der DNA Methyltransferaseaktivität von Dnmt2 (Schaefer et al. 2010a; Krauss et al. 2011). Die vorliegende Arbeit konzentriert sich auf die Identifizierung neuer RNA Substrate des Dnmt2-Homologs DnmA aus D. discoideum sowie die biologische Bedeutung der tRNA-Methylierung durch Dnmt2. Wie in anderen Organismen beschrieben, fungiert auch DnmA als tRNAAsp(GUC) MTase in vitro und in vivo. Zusätzlich konnte in vitro tRNAGlu(UUC) als neues Substrat der Dnmt2-Homologe aus D. discoideum und dem Menschen identifiziert werden. In einem Kooperationsprojekt wurde außerdem auch tRNAAsp-Methylierungsaktivität für das Dnmt2-Homolog aus S. pombe (Pmt1) nachgewiesen. Crosslink-RNA-Immunopräzipitationen (RNA-CLIP) mit anschließender Next-Generation-Sequenzierung der mit DnmA assoziierten RNAs zeigen, dass DnmA mit tRNA Fragmenten interagiert, die sich vom Anticodonloop bis in den T-loop erstrecken. Neben der tRNAAsp(GUC) und tRNAGlu(UUC/CUC) sind Fragmente der tRNAGly(GCC) verstärkt angereichert. Inwiefern diese Fragmente eine biologische Funktion haben oder spezifische Degradationsprodukte darstellen, ist noch ungeklärt. Interessanterweise sind von einigen tRNAs wenige Sequenzen von antisense-Fragmenten in den RNA-CLIP Daten zu finden, die etwas kürzer, jedoch exakt komplementär zu den genannten sense-Fragmenten sind. Besonders stark sind diese Fragmente der tRNAGlu(UUC) vertreten. In einem weiteren RNA-CLIP Experiment wurden U-snRNAs, snoRNA und intergenische Sequenzen mit DnmA angereichert. Bei nachfolgenden in vitro Methylierungsstudien konnte ausschließlich die U2-snRNA als potentielles Nicht-tRNA-Substrat der hDnmt2 und DnmA identifiziert werden. Da tRNA Modifikationen im Anticodonloop die Codonerkennung beeinflussen können, wurde ein System etabliert um die Translationseffizienz eines GFP-Reportergens in Wildtyp- und dnmAKO-Zellen zu messen. In D. discoideum wird das Aspartat-Codon GAU ca. zehnmal häufiger genutzt als das GAC Codon, allerdings ist nur eine tRNAAsp(GUC) im Genom der Amöbe kodiert. Aus diesem Grund wurde zusätzlich die Frage adressiert, inwiefern die DnmA-abhängige Methylierung dieser tRNA das „Wobbling“ beeinflusst. Dazu wurde dem Reportergen jeweils eine (GAU)5- und (GAC)5-Leadersequenz vorgeschaltet. Entgegen der Annahme wurde der (GAC)5-Leader in beiden Stämmen etwas effizienter translatiert. Insgesamt zeigte der dnmAKO-Stamm eine leicht erhöhte Translationseffizienz der Reportergene. Vergleichende Analysen zur Aufnahme von Fremd-DNA zeigten signifikant reduzierte Transformationseffizienzen mit einem integrierenden Plasmid in dnmAKO-Zellen. Ein weiterer dnmAKO-Stamm zeigte diesen Effekt jedoch nicht, wobei bei derselben Mutante eine deutlich reduzierte Aufnahme eines extrachromosomalen Plasmids zu verzeichnen war. Untersuchungen zum Einfluss von DnmA auf die Regulation des Retroelements skipper ergaben keinen Zusammenhang zwischen der Generierung kleiner RNAs und der erhöhten Transkription des Retrotransposons in dnmAKO-Zellen (Kuhlmann et al. 2005). Durch Kompensationsversuche sowie Experimente mit einer weiteren dnmAKO-Mutante konnte die Mobilisierung des Retrotransposons nicht eindeutig als DnmA-Funktion eingeordnet werden. In einem weiteren Projekt wurden die Bindung des m5C-bindenden Proteins EhMLBP aus E. histolytica an DNA mittels Rasterkraftmikroskopie abgebildet (Lavi et al. 2006). Neben vermutlich unspezifischen Endbindungsereignissen konnte eine bevorzugte Bindungsstelle des Proteins an LINE DNA (long intersperesed nuclear element) identifiziert werden. Möglicherweise fällt diese mit einem von zwei A/T-reichen Bereichen der LINE DNA zusammen, von denen vermutet wird, dass diese für die Bindung von EhMLBP an DNA von Bedeutung sind. Insgesamt bestätigen die Ergebnisse dieser Arbeit die tRNAAsp Methylierungsaktivität als konservierte Dnmt2-Funktion. Darüber hinaus erweitern sie das Substratspektrum der Dnmt2-Methyltransferasen im Bereich der tRNA. Außerdem wird erstmals ein potentielles Nicht-tRNA Substrat vorgeschlagen. Zusätzlich geben neu entdeckte Phänotypen Hinweise auf vielfältige zelluläre Dnmt2-Funktionen.

Status and Potential of Smallholder Livestock Production Systems in Xishuangbanna, southern P.R. China

With Chinas rapid economic development during the last decades, the national demand for livestock products has quadrupled within the last 20 years. Most of that increase in demand has been answered by subsidized industrialized production systems, while million of smallholders, which still provide the larger share of livestock products in the country, have been neglected. Fostering those systems would help China to lower its strong urban migration streams, enhance the livelihood of poorer rural population and provide environmentally save livestock products which have a good chance to satisfy customers demand for ecological food. Despite their importance, China’s smallholder livestock keepers have not yet gained appropriate attention from governmental authorities and researchers. However, profound analysis of those systems is required so that adequate support can lead to a better resource utilization and productivity in the sector. To this aim, this pilot study analyzes smallholder livestock production systems in Xishuangbanna, located in southern China. The area is bordered by Lao and Myanmar and geographically counts as tropical region. Its climate is characterized by dry and temperate winters and hot summers with monsoon rains from May to October. While the regionis plain, at about 500 m asl above sea level in the south, outliers of the Himalaya mountains reach out into the north of Xishuangbanna, where the highest peak reaches 2400 m asl. Except of one larger city, Jinghong, Xishuangbanna mainly is covered by tropical rainforest, areas under agricultural cultivation and villages. The major income is generated through inner-Chinese tourism and agricultural production. Intensive rubber plantations are distinctive for the lowland plains while small-scaled traditional farms are scattered in the mountane regions. In order to determine the current state and possible future chances of smallholder livestock production in that region, this study analyzed the current status of the smallholder livestock sector in the Naban River National Nature Reserve (NRNNR), an area which is largely representative for the whole prefecture. It covers an area of about 50square kilometer and reaches from 470 up to 2400 m asl. About 5500 habitants of different ethnic origin are situated in 24 villages. All data have been collected between October 2007 and May 2010. Three major objectives have been addressed in the study: 1. Classifying existing pig production systems and exploring respective pathways for development 2. Quantifying the performance of pig breeding systemsto identify bottlenecks for production 3. Analyzing past and current buffalo utilization to determine the chances and opportunities of buffalo keeping in the future In order to classify the different pig production s ystems, a baseline survey (n=204, stratified cluster sampling) was carried out to gain data about livestock species, numbers, management practices, cultivated plant species and field sizes as well associo-economic characteristics. Sampling included two clusters at village level (altitude, ethnic affiliation), resulting in 13 clusters of which 13-17 farms were interviewed respectively. Categorical Principal Component Analysis (CatPCA) and a two-step clustering algorithm have been applied to identify determining farm characteristics and assort recorded households into classes of livestock production types. The variables keep_sow_yes/no, TLU_pig, TLU_buffalo, size_of_corn_fields, altitude_class, size_of_tea_plantationand size_of_rubber_fieldhave been found to be major determinants for the characterization of the recorded farms. All farms have extensive or semi-intensive livestock production, pigs and buffaloes are predominant livestock species while chicken and aquaculture are available but play subordinate roles for livelihoods. All pig raisers rely on a single local breed, which is known as Small Ear Pig (SMEP) in the region. Three major production systemshave been identified: Livestock-corn based LB; 41%), rubber based (RB; 39%) and pig based (PB;20%) systems. RB farms earn high income from rubber and fatten 1.9 ±1.80 pigs per household (HH), often using purchased pig feed at markets. PB farms own similar sized rubber plantations and raise 4.7 ±2.77 pigs per HH, with fodder mainly being cultivated and collected in theforest. LB farms grow corn, rice and tea and keep 4.6 ±3.32 pigs per HH, also fed with collected and cultivated fodder. Only 29% of all pigs were marketed (LB: 20%; RB: 42%; PB: 25%), average annual mortality was 4.0 ±4.52 pigs per farm (LB: 4.6 ±3.68; RB: 1.9 ±2.14; PB: 7.1 ±10.82). Pig feed mainly consists of banana pseudo stem, corn and rice hives and is prepared in batches about two to three times per week. Such fodder might be sufficient in energy content but lacks appropriate content of protein. Pigs therefore suffer from malnutrition, which becomes most critical in the time before harvest season around October. Farmers reported high occurrences of gastrointestinal parasites in carcasses and often pig stables were wet and filled with manure. Deficits in nutritional and hygienic management are major limits for development and should be the first issues addressed to improve productivity. SME pork was found to be known and referred by local customers in town and by richer lowland farmers. However, high prices and lacking availability of SME pork at local wet-markets were the reasons which limited purchase. If major management constraints are overcome, pig breeders (PB and LB farms) could increase the share of marketed pigs for town markets and provide fatteners to richer RB farmers. RB farmers are interested in fattening pigs for home consumption but do not show any motivation for commercial pig raising. To determine the productivity of input factors in pig production, eproductive performance, feed quality and quantity as well as weight development of pigs under current management were recorded. The data collection included a progeny history survey covering 184 sows and 437 farrows, bi-weekly weighing of 114 pigs during a 16-months time-span on 21 farms (10 LB and 11 PB) as well as the daily recording of feed quality and quantity given to a defined number of pigs on the same 21 farms. Feed samples of all recorded ingredients were analyzed for their respective nutrient content. Since no literature values on thedigestibility of banana pseudo stem – which is a major ingredient of traditional pig feed in NRNNR – were found, a cross-sectional digestibility trial with 2x4 pigs has been conducted on a station in the research area. With the aid of PRY Herd Life Model, all data have been utilized to determine thesystems’ current (Status Quo = SQ) output and the productivity of the input factor “feed” in terms of saleable life weight per kg DM feed intake and monetary value of output per kg DM feed intake.Two improvement scenarios were simulated, assuming 1) that farmers adopt a culling managementthat generates the highest output per unit input (Scenario 1; SC I) and 2) that through improved feeding, selected parameters of reproduction are improved by 30% (SC II). Daily weight gain averaged 55 ± 56 g per day between day 200 and 600. The average feed energy content of traditional feed mix was 14.92 MJ ME. Age at first farrowing averaged 14.5 ± 4.34 months, subsequent inter-farrowing interval was 11.4 ± 2.73 months. Littersize was 5.8 piglets and weaning age was 4.3 ± 0.99 months. 18% of piglets died before weaning. Simulating pig production at actualstatus, it has been show that monetary returns on inputs (ROI) is negative (1:0.67), but improved (1:1.2) when culling management was optimized so that highest output is gained per unit feed input. If in addition better feeding, controlled mating and better resale prices at fixed dates were simulated, ROI further increased to 1:2.45, 1:2.69, 1:2.7 and 1:3.15 for four respective grower groups. Those findings show the potential of pork production, if basic measures of improvement are applied. Futureexploration of the environment, including climate, market-season and culture is required before implementing the recommended measures to ensure a sustainable development of a more effective and resource conserving pork production in the future. The two studies have shown that the production of local SME pigs plays an important role in traditional farms in NRNNR but basic constraints are limiting their productivity. However, relatively easy approaches are sufficient for reaching a notable improvement. Also there is a demand for more SME pork on local markets and, if basic constraints have been overcome, pig farmers could turn into more commercial producers and provide pork to local markets. By that, environmentally safe meat can be offered to sensitive consumers while farmers increase their income and lower the risk of external shocks through a more diverse income generating strategy. Buffaloes have been found to be the second important livestock species on NRNNR farms. While they have been a core resource of mixed smallholderfarms in the past, the expansion of rubber tree plantations and agricultural mechanization are reasons for decreased swamp buffalo numbers today. The third study seeks to predict future utilization of buffaloes on different farm types in NRNNR by analyzing the dynamics of its buffalo population and land use changes over time and calculating labor which is required for keeping buffaloes in view of the traction power which can be utilized for field preparation. The use of buffaloes for field work and the recent development of the egional buffalo population were analyzed through interviews with 184 farmers in 2007/2008 and discussions with 62 buffalo keepers in 2009. While pig based farms (PB; n=37) have abandoned buffalo keeping, 11% of the rubber based farms (RB; n=71) and 100% of the livestock-corn based farms (LB; n=76) kept buffaloes in 2008. Herd size was 2.5 ±1.80 (n=84) buffaloes in early 2008 and 2.2 ±1.69 (n=62) in 2009. Field work on own land was the main reason forkeeping buffaloes (87.3%), but lending work buffaloes to neighbors (79.0%) was also important. Other purposes were transport of goods (16.1%), buffalo trade (11.3%) and meat consumption(6.4%). Buffalo care required 6.2 ±3.00 working hours daily, while annual working time of abuffalo was 294 ±216.6 hours. The area ploughed with buffaloes remained constant during the past 10 years despite an expansion of land cropped per farm. Further rapid replacement of buffaloes by tractors is expected in the near future. While the work economy is drastically improved by the use of tractors, buffaloes still can provide cheap work force and serve as buffer for economic shocks on poorer farms. Especially poor farms, which lack alternative assets that could quickly be liquidizedin times of urgent need for cash, should not abandon buffalo keeping. Livestock has been found to be a major part of small mixed farms in NRNNR. The general productivity was low in both analyzed species, buffaloes and pigs. Productivity of pigs can be improved through basic adjustments in feeding, reproductive and hygienic management, and with external support pig production could further be commercialized to provide pork and weaners to local markets and fattening farms. Buffalo production is relatively time intensive, and only will be of importance in the future to very poor farms and such farms that cultivate very small terraces on steep slopes. These should be encouraged to further keep buffaloes. With such measures, livestock production in NRNNR has good chances to stay competitive in the future.

Analysis of the relationship between the number of citations and the quality evaluated by experts in psychology journals

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