Abstract: High cost of fossil fuels and intensifying installations of alternate energy generation sources are intimidating main challenges in power systems. Making accurate load forecasting an important and challenging task for optimal energy planning and management at both distribution and generation side. There are many techniques to forecast load but each technique comes with its own limitation and requires data to accurately predict the forecast load. Artificial Neural Network (ANN) is one such technique to efficiently forecast the load. Comparison between two different ranges of input datasets has been applied to dynamic ANN technique using MATLAB Neural Network Toolbox. It has been observed that selection of input data on training of a network has significant effects on forecasted results. Day-wise input data forecasted the load accurately as compared to year-wise input data. The forecasted load is then distributed among the six generators by using the linear programming to get the optimal point of generation. The algorithm is then verified by comparing the results of each generator with their respective generation limits.
Abstract: The research follows a systematic approach to optimize the parameters for parts machined by turning and milling processes. The quality characteristic chosen is surface roughness since the surface finish plays an important role for parts that require surface contact. A tapered cylindrical surface is designed as a test specimen for the research. The material chosen for machining is aluminum alloy 6061 due to its wide variety of industrial and engineering applications. HAAS VF-2 TR computer numerical control (CNC) vertical machining center is used for milling and HAAS ST-20 CNC machine is used for turning in this research. Taguchi analysis is used to optimize the surface roughness of the machined parts. The L9 Orthogonal Array is designed for four controllable factors with three different levels each, resulting in 18 experimental runs. Signal to Noise (S/N) Ratio is calculated for achieving the specific target value of 75 ± 15 µin. The controllable parameters chosen for turning process are feed rate, depth of cut, coolant flow and finish cut and for milling process are feed rate, spindle speed, step over and coolant flow. The uncontrollable factors are tool geometry for turning process and tool material for milling process. Hypothesis testing is conducted to study the significance of different uncontrollable factors on the surface roughnesses. The optimal parameter settings were identified from the Taguchi analysis and the process capability Cp and the process capability index Cpk were improved from 1.76 and 0.02 to 3.70 and 2.10 respectively for turning process and from 0.87 and 0.19 to 3.85 and 2.70 respectively for the milling process. The surface roughnesses were improved from 60.17 µin to 68.50 µin, reducing the defect rate from 52.39% to 0% for the turning process and from 93.18 µin to 79.49 µin, reducing the defect rate from 71.23% to 0% for the milling process. The purpose of this study is to efficiently utilize the Taguchi design analysis to improve the surface roughness.
Abstract: We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in Lq space to infinite in non-Lq space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.
Abstract: The goal of this project is to investigate constant
properties (called the Liouville-type Problem) for a p-stable map
as a local or global minimum of a p-energy functional where
the domain is a Euclidean space and the target space is a
closed half-ellipsoid. The First and Second Variation Formulas
for a p-energy functional has been applied in the Calculus
Variation Method as computation techniques. Stokes’ Theorem,
Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and
the Bochner Formula as estimation techniques have been used to
estimate the lower bound and the upper bound of the derived
p-Harmonic Stability Inequality. One challenging point in this project
is to construct a family of variation maps such that the images
of variation maps must be guaranteed in a closed half-ellipsoid.
The other challenging point is to find a contradiction between the
lower bound and the upper bound in an analysis of p-Harmonic
Stability Inequality when a p-energy minimizing map is not constant.
Therefore, the possibility of a non-constant p-energy minimizing
map has been ruled out and the constant property for a p-energy
minimizing map has been obtained. Our research finding is to explore
the constant property for a p-stable map from a Euclidean space into
a closed half-ellipsoid in a certain range of p. The certain range of
p is determined by the dimension values of a Euclidean space (the
domain) and an ellipsoid (the target space). The certain range of p
is also bounded by the curvature values on an ellipsoid (that is, the
ratio of the longest axis to the shortest axis). Regarding Liouville-type
results for a p-stable map, our research finding on an ellipsoid is a
generalization of mathematicians’ results on a sphere. Our result is
also an extension of mathematicians’ Liouville-type results from a
special ellipsoid with only one parameter to any ellipsoid with (n+1)
parameters in the general setting.
Abstract: Regarding heavy video game players for boys and super online chat lovers for girls as a symbolic phrase in the current adolescent culture, this project of data analysis verifies the displacement effect on deteriorating mathematics performance. To evaluate correlation or regression coefficients between a factor of playing video games or chatting online and mathematics performance compared with other factors, we use multivariate analysis technique and take gender difference into account. We find the most important reason for the negative sign of the displacement effect on mathematics performance due to students’ poor academic background. Statistical analysis methods in this project could be applied to study internet users’ academic performance from the high school education to the college education.
Abstract: The main aim of this research is to investigate a novel technique for implementing a more natural and intelligent conversation system. Conversation systems are designed to converse like a human as much as their intelligent allows. Sometimes, we can think that they are the embodiment of Turing-s vision. It usually to return a predetermined answer in a predetermined order, but conversations abound with uncertainties of various kinds. This research will focus on an integrated natural language processing approach. This approach includes an integrated knowledge-base construction module, a conversation understanding and generator module, and a state manager module. We discuss effectiveness of this approach based on an experiment.