Nutrient cycling and field-based partial nutrient balances in two mountain oases of Oman

Little is known about nutrient fluxes as a criterion to assess the sustainability of traditional irrigation agriculture in eastern Arabia. In this study GIS-based field research on terraced cropland and groves of date palm (Phoenix dactylifera L.) was conducted over 2 years in two mountain oases of northern Oman to determine their role as hypothesized sinks for nitrogen (N), phosphorus (P) and potassium (K). At Balad Seet 55% of the 385 fields received annual inputs of 100–500 kg N ha^-1 and 26% received 500–1400 kg N ha^-1. No N was applied to 19% of the fields which were under fallow. Phosphorus was applied annually at 1–90 kg ha^-1 on 46% of the fields, whereas 27% received 90–210 kg ha^-1. No K was applied to 27% of the fields, 32% received 1–300 kg K ha^-1, and the remaining fields received up to 1400 kg ha^-1. At Maqta N-inputs were 61–277 kg ha^-1 in palm groves and 112–225 kg ha^-1 in wheat (Triticum spp.) fields, respective P inputs were 9–40 and 14–29 kg ha^-1, and K inputs were 98–421 and 113–227 kg ha^-1. For cropland, partial oasis balances (comprising inputs of manure, mineral fertilizers, N2-fixation and irrigation water, and outputs of harvested products) were similar for both oases, with per hectare surpluses of 131 kg N, 37 kg P, and 84 kg K at Balad Seet and of 136 kg N, 16 kg P and 66 kg K at Maqta. This was despite the fact that N2-fixation by alfalfa (Medicago sativa L.), estimated at up to 480 kg ha^-1 yr^-1 with an average total dry matter of 22 t ha^-1, contributed to the cropland N-balance only at the former site. Respective palm grove surpluses, in contrast were with 303 kg N, 38 kg P, and 173 kg K ha^-1 much higher at Balad Seet than with 84 kg N, 14 kg P, and 91 kg K ha^-1 at Maqta. The data show that both oases presently are large sinks for nutrients. Potential gaseous and leaching losses could at least partly be controlled by a decrease in nutrient input intensity and careful incorporation of manure.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

Evaluating partial root-zone irrigation and mulching in okra (Abelmoschus esculentus L.) under a sub-humid tropical climate

The field experiments were conducted to compare the alternate partial root-zone irrigation (APRI) with and without black plastic mulch (BPM) with full root-zone irrigation (FRI) in furrow-irrigated okra (Abelmoschus esculentus L. Moench) at Bhubaneswar, India. APRI means that one of the two neighbouring furrows was alternately irrigated during consecutive watering. FRI was the conventional method where every furrow was irrigated during each watering. The used irrigation levels were 25% available soil moisture depletion (ASMD), 50% ASMD, and 75% ASMD. The plant growth and yield parameters were observed to be significantly (p < 0.05) higher with frequent irrigation (at 25% ASMD) under all irrigation strategies. However, APRI + BPM produced the maximum plant growth and yield using 22% and 56% less water over APRI without BPM and FRI, respectively. The highest pod yield (10025 kg ha^-1) was produced under APRI at 25% ASMD + BPM, which was statistically at par with the pod yield under APRI at 50% ASMD + BPM. Irrigation water use efficiency (IWUE), which indicates the pod yield per unit quantity of irrigation water, was estimated to be highest (12.3 kg m^-3) under APRI at 50% ASMD + BPM, followed by APRI at 25% ASMD + BPM. Moreover, the treatment APRI at 50% ASMD + BPM was found economically superior to other treatments, generating more net return (US $ 952 ha^-1) with higher benefit–cost ratio (1.70).

Molecular Beam Epitaxial Growth of III-V Semiconductor Nanostructures on Silicon Substrates

The main focus and concerns of this PhD thesis is the growth of III-V semiconductor nanostructures (Quantum dots (QDs) and quantum dashes) on silicon substrates using molecular beam epitaxy (MBE) technique. The investigation of influence of the major growth parameters on their basic properties (density, geometry, composition, size etc.) and the systematic characterization of their structural and optical properties are the core of the research work. The monolithic integration of III-V optoelectronic devices with silicon electronic circuits could bring enormous prospect for the existing semiconductor technology. Our challenging approach is to combine the superior passive optical properties of silicon with the superior optical emission properties of III-V material by reducing the amount of III-V materials to the very limit of the active region. Different heteroepitaxial integration approaches have been investigated to overcome the materials issues between III-V and Si. However, this include the self-assembled growth of InAs and InGaAs QDs in silicon and GaAx matrices directly on flat silicon substrate, sitecontrolled growth of (GaAs/In0,15Ga0,85As/GaAs) QDs on pre-patterned Si substrate and the direct growth of GaP on Si using migration enhanced epitaxy (MEE) and MBE growth modes. An efficient ex-situ-buffered HF (BHF) and in-situ surface cleaning sequence based on atomic hydrogen (AH) cleaning at 500 °C combined with thermal oxide desorption within a temperature range of 700-900 °C has been established. The removal of oxide desorption was confirmed by semicircular streaky reflection high energy electron diffraction (RHEED) patterns indicating a 2D smooth surface construction prior to the MBE growth. The evolution of size, density and shape of the QDs are ex-situ characterized by atomic-force microscopy (AFM) and transmission electron microscopy (TEM). The InAs QDs density is strongly increased from 108 to 1011 cm-2 at V/III ratios in the range of 15-35 (beam equivalent pressure values). InAs QD formations are not observed at temperatures of 500 °C and above. Growth experiments on (111) substrates show orientation dependent QD formation behaviour. A significant shape and size transition with elongated InAs quantum dots and dashes has been observed on (111) orientation and at higher Indium-growth rate of 0.3 ML/s. The 2D strain mapping derived from high-resolution TEM of InAs QDs embedded in silicon matrix confirmed semi-coherent and fully relaxed QDs embedded in defectfree silicon matrix. The strain relaxation is released by dislocation loops exclusively localized along the InAs/Si interfaces and partial dislocations with stacking faults inside the InAs clusters. The site controlled growth of GaAs/In0,15Ga0,85As/GaAs nanostructures has been demonstrated for the first time with 1 μm spacing and very low nominal deposition thicknesses, directly on pre-patterned Si without the use of SiO2 mask. Thin planar GaP layer was successfully grown through migration enhanced epitaxy (MEE) to initiate a planar GaP wetting layer at the polar/non-polar interface, which work as a virtual GaP substrate, for the GaP-MBE subsequently growth on the GaP-MEE layer with total thickness of 50 nm. The best root mean square (RMS) roughness value was as good as 1.3 nm. However, these results are highly encouraging for the realization of III-V optical devices on silicon for potential applications.

A Compilation Strategy for Numerical Programs Based on Partial Evaluation

This work demonstrates how partial evaluation can be put to practical use in the domain of high-performance numerical computation. I have developed a technique for performing partial evaluation by using placeholders to propagate intermediate results. For an important class of numerical programs, a compiler based on this technique improves performance by an order of magnitude over conventional compilation techniques. I show that by eliminating inherently sequential data-structure references, partial evaluation exposes the low-level parallelism inherent in a computation. I have implemented several parallel scheduling and analysis programs that study the tradeoffs involved in the design of an architecture that can effectively utilize this parallelism. I present these results using the 9- body gravitational attraction problem as an example.

Geometry and Photometry in 3D Visual Recognition

The report addresses the problem of visual recognition under two sources of variability: geometric and photometric. The geometric deals with the relation between 3D objects and their views under orthographic and perspective projection. The photometric deals with the relation between 3D matte objects and their images under changing illumination conditions. Taken together, an alignment-based method is presented for recognizing objects viewed from arbitrary viewing positions and illuminated by arbitrary settings of light sources.

Exploiting the Parallelism Exposed by Partial Evaluation

We describe the key role played by partial evaluation in the Supercomputing Toolkit, a parallel computing system for scientific applications that effectively exploits the vast amount of parallelism exposed by partial evaluation. The Supercomputing Toolkit parallel processor and its associated partial evaluation-based compiler have been used extensively by scientists at MIT, and have made possible recent results in astrophysics showing that the motion of the planets in our solar system is chaotically unstable.

Application of the european customer satisfaction index to postal services. Structural equation models versus partial least squars

Customer satisfaction and retention are key issues for organizations in today’s competitive market place. As such, much research and revenue has been invested in developing accurate ways of assessing consumer satisfaction at both the macro (national) and micro (organizational) level, facilitating comparisons in performance both within and between industries. Since the instigation of the national customer satisfaction indices (CSI), partial least squares (PLS) has been used to estimate the CSI models in preference to structural equation models (SEM) because they do not rely on strict assumptions about the data. However, this choice was based upon some misconceptions about the use of SEM’s and does not take into consideration more recent advances in SEM, including estimation methods that are robust to non-normality and missing data. In this paper, both SEM and PLS approaches were compared by evaluating perceptions of the Isle of Man Post Office Products and Customer service using a CSI format. The new robust SEM procedures were found to be advantageous over PLS. Product quality was found to be the only driver of customer satisfaction, while image and satisfaction were the only predictors of loyalty, thus arguing for the specificity of postal services

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materials represent a composition of mineralogies or solute species. Minerals are composed of structured relationships between cations and anions which, through atomic and molecular forces, keep the elements bound in specific configurations. The chemical compositions of minerals have specific relationships that are governed by these molecular controls. In the case of olivine, there is a well-defined relationship between Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition and other significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linear relationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe), which is typically described but poorly illustrated in the simplex. The present contribution corresponds to ongoing research, which attempts to relate stoichiometry and geochemical data using compositional geometry. We describe here the approach by which stoichiometric relationships based on mineralogical constraints can be accounted for in the space of simplicial coordinates using olivines as an example. Further examples for other mineral types (plagioclases and more complex minerals such as clays) are needed. Issues that remain to be dealt with include the reduction of a bulk chemical composition of a rock comprised of several minerals from which appropriate balances can be used to describe the composition in a realistic mineralogical framework. The overall objective of our research is to answer the question: In the cases where the mineralogy is unknown, are there suitable proxies that can be substituted? Kew words: Aitchison geometry, balances, mineral composition, oxides

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

Partial disjoint path for multi-layer protection in GMPLS networks

In this paper, different recovery methods applied at different network layers and time scales are used in order to enhance the network reliability. Each layer deploys its own fault management methods. However, current recovery methods are applied to only a specific layer. New protection schemes, based on the proposed partial disjoint path algorithm, are defined in order to avoid protection duplications in a multi-layer scenario. The new protection schemes also encompass shared segment backup computation and shared risk link group identification. A complete set of experiments proves the efficiency of the proposed methods in relation with previous ones, in terms of resources used to protect the network, the failure recovery time and the request rejection ratio

Partial Diff pdf

Exam questions and solutions in PDF

MA17xexam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files