A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Destructive and non-destructive measurements of residual crop residue and phosphorus effects on growth and composition of herbaceous fallow species in the Sahel

Little is known about the residual effects of crop residue (CR) and phosphorus (P) application on the fallow vegetation following repeated cultivation of pearl millet [Pennisetum glaucum (L.) R. Br.] in the Sahel. The objective of this study, therefore, was (i) to measure residual effects of CR, mulched at annual rates of 0, 500, 1000 and 2000 kg CR ha^-1, broadcast P at 0 and 13 kg P ha^-1 and P placement at 0, 1, 3, 5 and 7 kg P ha^-1 on the herbaceous dry matter (HDM) 2 years after the end of the experiment and (ii) to test a remote sensing method for the quantitative estimation of HDM. Compared with unmulched plots, a doubling of HDM was measured in plots that had received at least 500 kg CR ha^-1. Previous broadcast P application led to HDM increases of 14% compared with unfertilised control plots, whereas no residual effects of P placement were detected. Crop residue and P treatments caused significant shifts in flora composition. Digital analysis of colour photographs taken of the fallow vegetation and the bare soil revealed that the number of normalised green band pixels averaged per plot was highly correlated with HDM (r=0.86) and that red band pixels were related to differences in soil surface crusting. Given the traditional use of fallow vegetation as fodder, the results strongly suggest that for the integrated farming systems of the West African Sahel, residual effects of soil amendments on the fallow vegetation should be included in any comprehensive analysis of treatment effects on the agro-pastoral system.

Effects of post-harvest treatments on the carbohydrate composition of yacon roots in the Peruvian Andes

Yacon (Smallanthus sonchifolius [Poepp. & Endl.] H. Robinson) is an under-exploited native root crop of the Andes, which stores oligofructans (fructo-oligosaccharides, FOS) as its main component of dry matter (DM). FOS are of increasing economic interest because of their low caloric value in human diets and bifidogenic benefits on colon health. Two on-farm experiments were conducted to: (i) determine the effect of shaded, short-term storage at 1990 and 2930 m a.s.l. in the Andean highlands; and (ii) address the effects of a traditional sunlight exposure (‘sunning’) on the carbohydrate composition in the DM of tuberous yacon roots. After a 6-day shade storage FOS concentrations were smaller at the lower (36–48% of DM) than at the higher altitude (39–58% of DM). After 12 days FOS concentrations were nearly equal at both sites (27–39% of DM). The concentration of free sugars (fructose, glucose, sucrose) increased accordingly from 29–34 to 48–52%. During the 6-day sunning experiment FOS concentrations decreased from 50–62 to 29–44% and free sugars increased from 29–34 to 45–51%. The results indicate that partial hydrolysis of oligofructans starts shortly after harvest. Storage in highland environments should wherever possible exploit the cooler temperatures at higher altitudes. Sunning of yacon’s tuberous roots effectively reduces much of the roots’ water content, in this experiment 40%, and thus allows energy to be saved if yacon is processed into dehydrated products.

Development and applications of density matrix functional theory of generalized Hubbard Models

In dieser Doktorarbeit wird eine akkurate Methode zur Bestimmung von Grundzustandseigenschaften stark korrelierter Elektronen im Rahmen von Gittermodellen entwickelt und angewandt. In der Dichtematrix-Funktional-Theorie (LDFT, vom englischen lattice density functional theory) ist die Ein-Teilchen-Dichtematrix γ die fundamentale Variable. Auf der Basis eines verallgemeinerten Hohenberg-Kohn-Theorems ergibt sich die Grundzustandsenergie Egs[γgs] = min° E[γ] durch die Minimierung des Energiefunktionals E[γ] bezüglich aller physikalischer bzw. repräsentativer γ. Das Energiefunktional kann in zwei Beiträge aufgeteilt werden: Das Funktional der kinetischen Energie T[γ], dessen lineare Abhängigkeit von γ genau bekannt ist, und das Funktional der Korrelationsenergie W[γ], dessen Abhängigkeit von γ nicht explizit bekannt ist. Das Auffinden präziser Näherungen für W[γ] stellt die tatsächliche Herausforderung dieser These dar. Einem Teil dieser Arbeit liegen vorausgegangene Studien zu Grunde, in denen eine Näherung des Funktionals W[γ] für das Hubbardmodell, basierend auf Skalierungshypothesen und exakten analytischen Ergebnissen für das Dimer, hergeleitet wird. Jedoch ist dieser Ansatz begrenzt auf spin-unabhängige und homogene Systeme. Um den Anwendungsbereich von LDFT zu erweitern, entwickeln wir drei verschiedene Ansätze zur Herleitung von W[γ], die das Studium von Systemen mit gebrochener Symmetrie ermöglichen. Zuerst wird das bisherige Skalierungsfunktional erweitert auf Systeme mit Ladungstransfer. Eine systematische Untersuchung der Abhängigkeit des Funktionals W[γ] von der Ladungsverteilung ergibt ähnliche Skalierungseigenschaften wie für den homogenen Fall. Daraufhin wird eine Erweiterung auf das Hubbardmodell auf bipartiten Gittern hergeleitet und an sowohl endlichen als auch unendlichen Systemen mit repulsiver und attraktiver Wechselwirkung angewandt. Die hohe Genauigkeit dieses Funktionals wird aufgezeigt. Es erweist sich jedoch als schwierig, diesen Ansatz auf komplexere Systeme zu übertragen, da bei der Berechnung von W[γ] das System als ganzes betrachtet wird. Um dieses Problem zu bewältigen, leiten wir eine weitere Näherung basierend auf lokalen Skalierungseigenschaften her. Dieses Funktional ist lokal bezüglich der Gitterplätze formuliert und ist daher anwendbar auf jede Art von geordneten oder ungeordneten Hamiltonoperatoren mit lokalen Wechselwirkungen. Als Anwendungen untersuchen wir den Metall-Isolator-Übergang sowohl im ionischen Hubbardmodell in einer und zwei Dimensionen als auch in eindimensionalen Hubbardketten mit nächsten und übernächsten Nachbarn. Schließlich entwickeln wir ein numerisches Verfahren zur Berechnung von W[γ], basierend auf exakten Diagonalisierungen eines effektiven Vielteilchen-Hamilton-Operators, welcher einen von einem effektiven Medium umgebenen Cluster beschreibt. Dieser effektive Hamiltonoperator hängt von der Dichtematrix γ ab und erlaubt die Herleitung von Näherungen an W[γ], dessen Qualität sich systematisch mit steigender Clustergröße verbessert. Die Formulierung ist spinabhängig und ermöglicht eine direkte Verallgemeinerung auf korrelierte Systeme mit mehreren Orbitalen, wie zum Beispiel auf den spd-Hamilton-Operator. Darüber hinaus berücksichtigt sie die Effekte kurzreichweitiger Ladungs- und Spinfluktuationen in dem Funktional. Für das Hubbardmodell wird die Genauigkeit der Methode durch Vergleich mit Bethe-Ansatz-Resultaten (1D) und Quanten-Monte-Carlo-Simulationen (2D) veranschaulicht. Zum Abschluss wird ein Ausblick auf relevante zukünftige Entwicklungen dieser Theorie gegeben.

Effects of dietary lipid source on growth, digestibility and tissue fatty acid composition of Heterobranchus longifilis fingerlings

One of the major problems facing aquaculture is the inadequate supply of fish oil mostly used for fish feed manufacturing. The continued growth in aquaculture production cannot depend on this finite feed resources, therefore, it is imperative that cheap and readily available substitutes that do not compromise fish growth and fillet quality be found. To achieve this, a 12-week feeding trial with Heterobranchus longifilis fed diets differing in lipid source was conducted. Diets were supplemented with 6% lipid as fish oil, soybean oil, palm oil, coconut oil, groundnut oil and melon seed oil. Triplicate groups of 20 H. longifilis were fed the experimental diets two times a day to apparent satiation, over 84 days. Growth, digestibility, and muscle fatty acid profile were measured to assess diet effects. At the end of the study, survival, feed intake and hepatosomatic index were similar for fish fed experimental diets. However, weight gain, SGR and FCR of fish fed soybean oil-based diet was significantly reduced. Apparent nutrient digestibility coefficients were significantly lower in fish fed soybean, coconut and groundnut oil-based diets. Fillet and hepatic fatty acid compositions differed and reflected the fatty acid compositions of the diets. Docosahexaenoic acid (22:6n-3), 20:5n-3 and 20:4n-6 were conserved in vegetable oils-based diets fed fish possibly due to synthesis of HUFA from 18:3n-3 and 18:4n-6. Palm oil diet was the least expensive, and had the best economic conversion ratio. The use of vegetable oils in the diets had positive effect on growth and fillet composition of H. longifilis.

Varying the dietary supply of C and N to manipulate the manure composition of water buffalo heifers in Oman

Optimizing the composition of manure has the potential to reduce nutrient losses to the environment and to increase crop yields. In this study the effect of dietary ratios of carbon (C) to nitrogen (N) and neutral detergent fibre (NDF) to soluble carbohydrates (SC) on faeces composition of water buffalo heifers was assessed. Two digestibility trials were conducted with 12 animals each, fed one control and four test diets composed to achieve (1) high C/N and high NDF/SC ratios (HH), (2) low C/N and low NDF/SC ratios (LL), (3) high C/N and low NDF/SC ratios (HL) and (4) low C/N and high NDF/SC (LH) ratios. Faecal C/N ratios were generally lower than dietary C/N ratios, but the reduction was especially large for high C/N ratio diets (HH=55 %, HL=51 %). Faecal N concentration was positively correlated (r^2 = 0.6; P < 0.001) with N intake, but the increase in faecal N was more pronounced for diets that supplied low amounts of N. Faecal NDF concentration was positively related to NDF intake (r^2 = 0.42; P < 0.001), as well as the faecal C/N ratio (r^2 = 0.3; P < 0.001). Results demonstrate that C/N ratio and NDF concentration of buffalo manure were affected by diet composition. Diets with high C/N ratio and low NDF/SC ratio are preferable with regard to manure quality, but may not satisfy the nutritional requirements of producing animals, since N concentration in these diets was low and fibre concentration simultaneously high.

Carcass composition of Venda indigenous scavenging chickens under village management

Four Venda indigenous scavenging (VIS) chickens (one young male and one young female of 10-16 weeks of age, a mature cockerel and a mature hen) were randomly purchased from each of six adjacent rural villages during three different seasons (autumn, winter and spring) to determine the meat yield and carcass chemical composition. A total of 72 chickens were slaughtered and feathers, head, neck, viscera, feet and lungs were removed. The live body weight, dressed carcass weight and also the mass of the breast without wings, thighs and drumsticks were recorded with bones and skin. The muscle tissues of the breast and both legs without tendons and fat were sampled for chemical analysis and were analysed for dry matter, ether extract, crude protein and ash. The carcass weight, dressing %, mass of the breast, mass of the thighs, mass of the drumsticks, breast yield, thighs yield and drumsticks yield of both grower and adult VIS chickens were not influenced by season. The crude protein of the grower chickens breast muscles and fat content of the adult chicken leg muscles differed with season. The meat from VIS chickens provided a constant nutrient (crude protein) supply throughout the year to the rural communities.