Mathematical model of anisotropy of magnetic susceptibility (AMS)

Magnetic susceptibility of natural rocks and ores is important in many applications. In a few rock types magnetic susceptibility is independent of the direction in which a weak magnetic field is applied. Such rocks are magnetically isotropic. In most rock types, however, the magnitude of magnetic susceptibility in a constant weak field depends on the orientation of the magnetic field applied. Such rocks are magnetically anisotropic and such directional variation in magnetic susceptibility with these rocks is termed as anisotropy of magnetic susceptibility (AMS). Although attempts have been made on describing AMS using mathematical models, there is still a need to present a more consistent and united mathematical process for AMS. This paper presents a united AMS model by rationalizing the existing pieces of different AMS models through a consistent approach. A few examples of AMS from some types of natural rocks and ores are also presented to substantiate this united AMS model

Adaptive potential field data processing in spatial domain

Potential field data contain unwanted noises due to many variable factors during the data acquisition. A common approach to minimise these noises is to smooth the data using various approaches. Traditionally, data smoothing is carried out using separate programs based on different mathematical models. The adaptive spatial data processing system (ASDPS) provides a new way in processing potential field data in spatial domain. ASDPS not only can be implemented as a unique user interface for either selecting an implemented method or defining a new method without recoding and recompilation, but also supports parallel processing in a multithreaded computing environment. This paper presents applications of ASDPS to gravity and magnetic data processing for both reducing the survey noises contained in the original data and carrying out easy data transformations for different purposes

Modelling textural anisotropy of magnetic susceptibility of banded iron formations

Anisotropy of magnetic susceptibility (AMS) of banded iron formations (BIFs) is characterized by high anisotropy and well-developed bedding-parallel magnetic foliation. Since most previous studies were focused on palaeomagneism of BIFs and BIF-derived iron ores, little effort has been made to further understand this special type of AMS for BIFs. A detailed theoretical analysis, incorporating with the previous experimental data, is made to understand the formative mechanism of this special anisotropy for BIFs. The good consistence between the theoretical and experimental results demonstrates that this type of anisotropy is likely caused by the layered structure of BIFs, and thus verifies the term of textural anisotropy for BIFs. Theoretical analysis also shows that in the negligence of the inter-layer magnetic action BIF’s apparent anisotropy increases with an increase in intrinsic susceptibility of magnetic layers, but decreases with an increase in length-to- diameter ratio of the magnetic layer

Incorporating statistical and neural network approaches for student course satisfaction analysis and prediction

Student’s perception on course satisfaction through student surveys has become more influential in institutional operations because their experience in study may affect not only the prospective student’s decision in choosing the institution for their tertiary education, but also the retention of existing students. Student course satisfaction is a multivariate nonlinear problem. Neural network (NN) techniques have been successfully applied to approximating nonlinear functions in many disciplines, but there has been little information available in applying NN to the modelling of student course satisfaction. In this paper, based on the student survey results collected from 43 courses in 11 semesters from 2002 to 2007, statistical analysis and NN techniques are incorporated for establishing some dynamic models for analysing and predicting student course satisfaction. The factors identified from this process also allow new strategies to be drawn for improving course satisfaction in the future. This study shows that both the number of students (NS) enrolled to a course and the high distinction (HD) rate in final grading are the two most influential factors to student course satisfaction. The three-layer multilayer perceptron (MLP) models outperform the linear regressions in predicting student course satisfaction, with the best outcome being achieved by combining both NS and HD as the input to the networks

A regression algorithm for rock magnetic data mining

The correlation between magnetic susceptibility and the content of magnetite is important in interpretation of magnetic anomalies, and understanding the basic magnetic behaviour of rocks in rock magnetism study. A few correlations were proposed in the 1950s-1960s and have been widely used. In the last a few decades, the adoption of new technologies in chemical analysis and magnetic measurements have led to the acquisition of more new rock magnetic data in a format different from the data obtained before. There is a need to establish new correlations between the susceptibility and magnetite content in rocks using the collection of data from both current and previous studies. The statistical analysis used in the previous studies was predominantly focused on seeking a sole linear or power correlation between susceptibility and magnetite content. This is because each study used the data collected from a confined area where the magnetite content in rocks was naturally concentrated within a certain range. Multiple correlations may be determined for different ranges of magnetite content if a database consisting of the data from various regions is used for the statistical analysis. In this study, data mining technique is introduced to rock magnetic data analysis. A data mining algorithm is designed to carry out data selection, pre-processing, transformation, and data analysis for rock magnetic data. This algorithm is able to search for linear, power, logarithmic, and exponential correlations that may exist between susceptibility and magnetite content contained in rocks. This algorithm is tested using a new magnetic database constructed by collecting the datasets from the previous studies. The results from this data mining process are then interpreted incorporating with the relevant knowledge in rock magnetism. Although strong linear, power, logarithmic, and exponential correlations are all revealed by this algorithm, only the power and exponential correlations are considered useful for different ranges of magnetite content in rock magnetism study

Advanced mathematics for engineering and applied sciences

This book was written as a designated textbook for university students studying engineering and some areas of applied sciences to continue knowledge building in mathematics after successfully completing a course in elementary calculcus and is designed to be delivered over one semester of 12-13 teaching weeks

Local position classification for pattern discovery in multivariate sequential data

Traditional sequential data analysis largely depends on the magnitude of the data with the geometric features of individual data points sometimes being regarded as noise to such analysis. To explore whether these geometric features alone carry some useful information for a better understanding of hidden facts contained in the sequential data, a new method called local position classification (LPC) is proposed in this paper. LPC works on extracting local geometric features of individual data points. The correlated geometric features in different variants in the same sequential data are then classified into some LPC clusters for further interpretation. This semi-quantitative method is easy to use and also a simple tool to estimate possible correlation between two categories in the same series. To exclude the unrelated categories from LPC clusters, a selective correlation analysis (SCA) is combined with LPC so as to make both complement with each other. Analysis of email entries over a year in an Australian university demonstrated that LPC and its combination with SCA could become a new effective tool for discovering useful patterns contained in sequential data

Documentation centric approach for managing progressive software/information system development

One common difficulty for students to take their final-year project on software and/or information systems development is how to effectively execute a selected system development model so as to smoothly follow the processes throughout the project. The project supervisors must provide students with an appropriate guideline that is both understandable and executable by the students. Management centric and programming centric approaches have been widely adopted in guiding systems development. In this paper, a documentation centric approach is presented for guiding student projects on developing software and information systems. This approach is based on separate but yet linked phases. It aims to achieve the highest possible inheritance to and/or reusability for the next development phase. The case studies demonstrate that this approach is useful and effective in systems articulation and maximising reusability in progressive systems development. Failing to do so leads to abandonment of any further development due to insufficient supporting information inherited from the previous development

A statistical reasoning scheme for geochemical data mining and automatic anomaly identification and classification

Geochemical data processing aims to not only reduce the random and/or systematic errors resulted from the field survey and/or laboratory analysis, but also identify whether the data contain useful information indicating the existence of mineral concentrations, oil fields, and pollution sources in the survey area. The first task is usually achieved by using various smoothing approaches. However, how to determine the ‘best’ outcome from using many smoothing methods is still qualitative. The second task is made by comparing the data to some geochemical benchmarks. In this paper, a statistical reasoning scheme is proposed to determine the likely ‘best’ outcome among many smoothed datasets, and then this ‘best’ fitted dataset is used to determine anomalies in reference to different geochemical benchmarks. The proposed statistical selector quantifies the determination of smoothing for geochemical data. The anomaly classifiers proposed can identify and classify the potential geochemical anomalies contained in the data as background anomaly (BA), threshold anomaly (TA), reliable anomaly (RA), and local anomaly (LA) automatically

Flexible selection of output format for sets in Java collections : algorithms and their complexity and reusability

Set, a collection of distinct values, is widely used in many applications. There are three applicable set classes included in the Java Collections. TreeSet produces a sorted output in ascending order whereas HashSet provides an output with random order. LinkedHashSet, a subclass of HashSet, produces an output in insertion order, but does not support the sorted output. Three algorithms are proposed in this paper to modify the existing set classes in the Java Collections so that they can provide multiple output formats for users to select from. The algorithm at application-level does not change the current configurations of the set classes, but it offers little reusability. The algorithm at method level introduces an internal method for producing sorted output into the LinkedHashTable class, in addition to its default output in insertion order. This can be achieved without change to other configurations of the class. If this method is placed in the HashSet class, users can freely choose their preferred output format from random order, insertion order, or ascending order. The algorithm at class level proposes a new LinkedTreeSet class that is implemented using both a balanced BST and a doubly linked list. The basic operations of this class may be slightly slower than that in the TreeSet class