Combinatorial methods in differential algebra

This thesis studies various aspects of differential algebra, from fundamental concepts to practical computations. A characteristic feature of this work is the use of combinatorial techniques, which offer a unique and original perspective on the subject matter. First, we establish the connection between the n-jet space of the fat point defined by xm and the stable set polytope of a perfect graph. We prove that the dimension of the coordinate ring of the scheme defined by polynomial arcs of degree less than or equal to n is a polynomial in m of degree n + 1. This is based on Zobnin’s result which states that the set {x^m} is a differential Gr ̈obner basis for its differential ideal. We generalize this statement to the case of two independent variables and link the dimensions in this case to some triangulations of the p × q rectangle, where the pair (p, q) now plays the role of n. Second, we study the arc space of the fat point x^m on a line from the point of view of filtration by finite-dimensional differential algebras. We prove that the generating series of the dimensions of these differential algebras is m/(1 -mt) . Based on this we propose a definition of the multiplicity of a solution of an algebraic differential equation as the growth of the dimensions of these differential algebras. This generalizes the concept of the multiplicity of an ideal in a polynomial ring. Furthermore, we determine a full description of the set of standard monomials of the differential ideal generated by x^m. This description proves a conjecture by Afsharijoo concerning a new version of the Roger-Ramanujan identities. Every homogeneous linear system of partial differential equations with constant coef- ficients can be encoded by a submodule of the ring of polynomials. We develop practical methods for computing the space of solutions to these PDEs. These spaces are typically infinite dimensional, and we use the Ehrenpreis–Palamodov Theorem for finite encoding. We apply this finite encoding to the solutions of the PDEs associated with the arc spaces of a double point. We prove that these vector spaces are spanned by determinants of some special Wronskians, and we relate them to differentially homogeneous polynomials. Finally, we introduce D-algebraic functions: they are solutions to algebraic differential equations. We study closure properties of these functions. We present practical algorithms and their implementations for carrying out arithmetic operations on D-algebraic functions. This amounts to solving elimination problems for differential ideals

Influence of Industrial, Agricultural and Sewage Water Discharges on Eutrophication of Quttina Lake

The influence of human activities on water quality of Quttina lake (an important water resource in the middle region of Syria), has been evaluated and correlated with pollution source situated at lake banks; namely, phosphate fertilizer factory, agriculture and wastewater drainages. Surface and deep water samples from different sites in the lake have been collected and analyzed during the period of April to October 2009 to study the effects of pollution sources on Quttina lake eutrophication. Water quality parameters include temperature, pH, EC, Dissolved Oxygen (DO), Chemical Oxygen Demand (COD), Biological Oxygen Demand (BOD), ammonium, phosphate and nitrates ions, total nitrogen and total phosphorous. The results have shown that these parameters varied from one site to another, where the highest concentrations were found to be in those sites close to phosphate factory discharges and in the northern part of the lake. Moreover, seasonal variations in pollution parameters were clear, especially for ammonium, phosphate and nitrates ions in addition to oxygen parameters (DO, COD and BOD). Moreover, mean total phosphorus concentration in Quttina lake surface water varied between 0.51 mg/l and 2.2 mg/1, where the highest values were found to be near the phosphate fertilizer factory discharges in addition to sites close to wastewater and agriculture runoffs situated at the western side of the lake. In addition, N:P ratio varied between 1.1 and 22.9 during the sampling period; the natural ratio being 16:1. On the other hand, the parameter distribution with depth in two sites has been studied. The results have shown that there are no clear differences between the deep and surface samples, and this is due to lake shallow depth and water flow. Furthermore, positive relationships have been found between total phosphors and nitrogen and oxygen indicators (BOD and COD), which indicates the increase of organic pollution and the algal bloom

Rangeland degradation assessment using remote sensing and vegetation species.

Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.The degradation of rangeland grass is currently one of the most serious environmental problems in South Africa. Increaser and decreaser grass species have been used as indicators to evaluate rangeland condition. Therefore, classifying these species and monitoring their relative abundance is an important step for sustainable rangelands management. Traditional methods (e.g. wheel point technique) have been used in classifying increaser and decreaser species over small geographic areas. These methods are regarded as being costly and time-consuming, because grasslands usually cover large expanses that are situated in isolated and inaccessible areas. In this regard, remote sensing techniques offer a practical and economical means for quantifying rangeland degradation over large areas. Remote sensing is capable of providing rapid, relatively inexpensive, and near-real-time data that could be used for classifying and monitoring species. This study advocates the development of techniques based on remote sensing to classify four dominant increaser species associated with rangeland degradation namely: Hyparrhenia hirta, Eragrostis curvula, Sporobolus africanus and Aristida diffusa in Okhombe communal rangeland, KwaZulu-Natal, South Africa. To our knowledge, no attempt has yet been made to discriminate and characterize the landscape using these species as indicators of the different levels of rangeland degradation using remote sensing. The first part of the thesis reviewed the problem of rangeland degradation in South Africa, the use of remote sensing (multispectral and hyperspectral) and their challenges and opportunities in mapping rangeland degradation using different indicators. The concept of decreaser and increaser species and how it can be used to map rangeland degradation was discussed. The second part of this study focused on exploring the relationship between vegetation species (increaser and decreaser species) and different levels of rangeland degradation. Results showed that, there is significant relationship between the abundance and distribution of different vegetation species and rangeland condition. The third part of the study aimed to investigate the potential use of hyperspectral remote sensing in discriminating between four increaser species using the raw field spectroscopy data and discriminant analysis as a classifier. The results indicate that the spectroscopic approach used in this study has a strong potential to discriminate among increaser species. These positive results prompted the need to scale up the method to airborne remote sensing data characteristics for the purpose of possible mapping of rangeland species as indicators of degradation. We investigated whether canopy reflectance spectra resampled to AISA Eagle resolution and random forest as a classification algorithm could discriminate between four increaser species. Results showed that hyperspectral data assessed with the random forest algorithm has the potential to accurately discriminate species with best overall accuracy. Knowledge on reduced key wavelength regions and spectral band combinations for successful discrimination of increaser species was obtained. These wavelengths were evaluated using the new WorldView imagery containing unique and strategically positioned band settings. The study demonstrated the potential of WorldView-2 bands in classifying grass at species level with an overall accuracy of 82% which is only 5% less than an overall accuracy achieved by AISA Eagle hyperspectral data. Overall, the study has demonstrated the potential of remote sensing techniques to classify different increaser species representing levels of rangeland degradation. In this regard, we expect that the results of this study can be used to support up-to-date monitoring system for sustainable rangeland management

Needs Analysis of Engineering Students’ English Needs at the University of Tabuk

This study aimed to identify the English language needs of the engineering students at University of Tabuk in the academic year 2013/2014 in Saudi Arabia. More specifically, it attempted to address the following question:What are the English language needs of the engineering students at University of Tabuk in Saudi Arabia?The sample of the study consisted of one hundred and fifty four students, twelve teachers from the University of Tabuk. A questionnaire was developed by the researcher and addressed to the students and teachers. The findings of the study revealed that there are some real special English language needs and interests of students in engineering faculty at the University of Tabuk. These needs motivate students to learn and build their self –confidence towards the learning process.It is recommended that curriculum designers make use of the resulting identifying these needs and to conduct similar studies for other specializations in Saudi Arabia and further afield. Keywords: ESP: English for specific purposes, Communicative Needs Processor, needs analysi

Related Named Entities Classification in the Economic-Financial Context

The present work uses the Bidirectional Encoder Representations from Transformers(BERT) to process a sentence and its entities and indicate whether two named entities present in a sentence are related or not, constituting a binary classification problem. It was developed for the Portuguese language, considering the financial domain and exploring deep linguistic representations to identify a relation between entities without using other lexical-semantic resources. The results of the experiments show an accuracy of 86% of the predictions.FCT CEECIND/01997/2017, UIDB/00057/202