Abstract: This study used positivist quantitative approach to examine the mathematical concepts acquisition of- KS4 (14-16) Special Education Needs (SENs) students within the school sector education in England. The research is based on a pilot study and the design is completely holistic in its approach with mixing methodologies. The study combines the qualitative and quantitative methods of approach in gathering formative data for the design process. Although, the approach could best be described as a mix method, fundamentally with a strong positivist paradigm, hence my earlier understanding of the differentiation of the students, student – teacher body and the various elements of indicators that is being measured which will require an attenuated description of individual research subjects. The design process involves four phases with five key stages which are; literature review and document analysis, the survey, interview, and observation; then finally the analysis of data set. The research identified the need for triangulation with Reid-s phases of data management providing scaffold for the study. The study clearly identified the ideological and philosophical aspects of educational research design for the study of mathematics by the special education needs (SENs) students in England using the virtual learning environment (VLE) platform.
Abstract: We examine the maximum theorem by Berge from the
point of view of Bishop style constructive mathematics. We will show
an approximate version of the maximum theorem and the maximum
theorem for functions with sequentially locally at most one maximum.
Abstract: The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.
Abstract: In this paper, we give an overview of an online elearning
tool which has been developed for kids aged from nine to
eleven years old in Mauritius for the self-study of Mathematics in
order to prepare them for the CPE examination. The software does
not intend to render obsolete the existing pedagogical approaches.
Nowadays, the teaching-learning process is mainly focused towards
the class-room model. Moreover, most of the e-learning platforms
that exist are simply static ways of delivering resources using the
internet. There is nearly no interaction between the learner and the
tool. Our application will enable students to practice exercises online
and also work out sample examination papers. Another interesting
feature is that the kid will not have to wait for someone to correct the
work as the correction will be done online and on the spot. Additional
feedback is also provided for some exercises.
Abstract: The notions of intuitionistic fuzzy h-ideal and normal
intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some
of the basic properties of these ideals are investigated. Cartesian
product of intuitionistic fuzzy h-ideals is also defined. Finally a
characterization of intuitionistic fuzzy h-ideals in terms of fuzzy
relations is obtained.
Abstract: Cognitive Science appeared about 40 years ago,
subsequent to the challenge of the Artificial Intelligence, as common
territory for several scientific disciplines such as: IT, mathematics,
psychology, neurology, philosophy, sociology, and linguistics. The
new born science was justified by the complexity of the problems
related to the human knowledge on one hand, and on the other by the
fact that none of the above mentioned sciences could explain alone
the mental phenomena. Based on the data supplied by the
experimental sciences such as psychology or neurology, models of
the human mind operation are built in the cognition science. These
models are implemented in computer programs and/or electronic
circuits (specific to the artificial intelligence) – cognitive systems –
whose competences and performances are compared to the human
ones, leading to the psychology and neurology data reinterpretation,
respectively to the construction of new models. During these
processes if psychology provides the experimental basis, philosophy
and mathematics provides the abstraction level utterly necessary for
the intermission of the mentioned sciences.
The ongoing general problematic of the cognitive approach
provides two important types of approach: the computational one,
starting from the idea that the mental phenomenon can be reduced to
1 and 0 type calculus operations, and the connection one that
considers the thinking products as being a result of the interaction
between all the composing (included) systems. In the field of
psychology measurements in the computational register use classical
inquiries and psychometrical tests, generally based on calculus
methods. Deeming things from both sides that are representing the
cognitive science, we can notice a gap in psychological product
measurement possibilities, regarded from the connectionist
perspective, that requires the unitary understanding of the quality –
quantity whole. In such approach measurement by calculus proves to
be inefficient. Our researches, deployed for longer than 20 years,
lead to the conclusion that measuring by forms properly fits to the
connectionism laws and principles.
Abstract: This study adopted previous fault patterns, results of
detection analysis, historical records and data, and experts-
experiences to establish fuzzy principles and estimate the failure
probability index of components of a power transformer. Considering
that actual parameters and limiting conditions of parameters may
differ, this study used the standard data of IEC, IEEE, and CIGRE as
condition parameters. According to the characteristics of each
condition parameter, relative degradation was introduced to reflect the
degree of influence of the factors on the transformer condition. The
method of fuzzy mathematics was adopted to determine the
subordinate function of the transformer condition. The calculation
used the Matlab Fuzzy Tool Box to select the condition parameters of
coil winding, iron core, bushing, OLTC, insulating oil and other
auxiliary components and factors (e.g., load records, performance
history, and maintenance records) of the transformer to establish the
fuzzy principles. Examples were presented to support the rationality
and effectiveness of the evaluation method of power transformer
performance conditions, as based on fuzzy comprehensive evaluation.
Abstract: The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.
Abstract: In this research paper we have presented control
architecture for robotic arm movement and trajectory planning using
Fuzzy Logic (FL) and Genetic Algorithms (GAs). This architecture is
used to compensate the uncertainties like; movement, friction and
settling time in robotic arm movement. The genetic algorithms and
fuzzy logic is used to meet the objective of optimal control
movement of robotic arm. This proposed technique represents a
general model for redundant structures and may extend to other
structures. Results show optimal angular movement of joints as result
of evolutionary process. This technique has edge over the other
techniques as minimum mathematics complexity used.