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Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts
Issue:
Volume 3, Issue 4, August 2015
Pages:
169-173
Received:
30 November 2014
Accepted:
6 February 2015
Published:
14 June 2015
Abstract: Historically, a contrived trisected line was used to trisect any other line, using the principle of projection. This is in essence about relationship and its accomplishment is about working backwards. Loosely speaking, any angle comprises two connecting lines. Attempts at trisecting any angle, which is dividing it into three equal parts, failed. In this paper any angle is defined as a unique pair of arc and chord of sector of a circle irrespective of arc radius. Two theorems viz. Equal arcs have equal central angles and equal chords have equal central angles are combined to establish a unique relationship between a pair of arc-chord and its composite of three identical pairs of arc-chord, thereby revealing a CYCLIC TRAPEZIUM, where the base defines the angle, and each equal edge defines each of the equal trisected parts of this angle. For a range of angles between 0o and 360o, this relationship is expressed as Lorna Graph, which becomes the practical tool for trisection of any angle, using the working backwards approach. This approach is extended to division of any angle into any number of equal parts.
Abstract: Historically, a contrived trisected line was used to trisect any other line, using the principle of projection. This is in essence about relationship and its accomplishment is about working backwards. Loosely speaking, any angle comprises two connecting lines. Attempts at trisecting any angle, which is dividing it into three equal parts, failed. In...
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Study on the Decline Analysis of Oil Well Stimulation Rule Based on Matlab-m
Xie Congjiao,
Guan Zhenliang,
Luo Guoping,
Zhou Hong
Issue:
Volume 3, Issue 4, August 2015
Pages:
174-178
Received:
16 May 2015
Accepted:
29 June 2015
Published:
9 July 2015
Abstract: Well Stimulation and machinery extraction are two main methods which the engineer of oil production and related industry used to increase production .The purpose is to enhance the oil field final recovery ratio though speeds up the production rate of the petroleum fluid, especially for old oil field development. A set of methods which be suitable for the high water content maturing field about predicting output of well stimulation used in Xiaermen oilfield and providing the foundation of the oil field natural decline regular pattern. Then, a decline-analysis model is derived based on reservoir characteristic parameters and used to analyze natural decline rates for the Xiaermen oilfield developed by waterflooding. Formation factor and remaining oil saturation are included in this model, which reveals non-linear relationships between natural decline rates and the production time. We applied the model to the oil-production data from different blocks in the Xiaermen oilfield and found non-linear relationships between natural decline rates and production time as foreseen by the model, especially at the high water cut period. The results showed that the analytical model could match the natural decline rate data satisfactorily. It was also found there are non-linear relationships between oil incrementals for water flooding step stimulation and step time which different laws with permeability, net pay, and remaining oil saturation and structure place of reservoir in limit period. Decline analysis can be used to predict different oil wells production nature decline rule. Furthermore, we made computer programming in Matlab-m language to calculate the natural decline rate with any time, which made it much easier and practical to predict the future decline rate. Finally, the analytical model was compared with conventional models.
Abstract: Well Stimulation and machinery extraction are two main methods which the engineer of oil production and related industry used to increase production .The purpose is to enhance the oil field final recovery ratio though speeds up the production rate of the petroleum fluid, especially for old oil field development. A set of methods which be suitable f...
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Higher Order Sylster’s Equation on Measure Chains-Controllability and Observability
Issue:
Volume 3, Issue 4, August 2015
Pages:
179-184
Received:
17 June 2015
Accepted:
2 July 2015
Published:
15 July 2015
Abstract: In this article we derive the solution of higher order Sylster’s type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster’s type differential system on measure chains is established.
Abstract: In this article we derive the solution of higher order Sylster’s type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster’s type differential system on measur...
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A Study on (Q,L)-Fuzzy Normal Subsemiring of a Semiring
S. Sampathu,
S. Anita Shanthi,
A. Praveen Prakash
Issue:
Volume 3, Issue 4, August 2015
Pages:
185-188
Received:
6 May 2015
Accepted:
9 June 2015
Published:
17 July 2015
Abstract: In this paper, we introduce the concept of (Q,L)-fuzzy normal subsemirings of a semiring and establish some results on these. We also made an attempt to study the properties of (Q,L)-fuzzy normal subsemirings of semiring under homomorphism and anti-homomorphism , and study the main theorem for this. We shall also give new results on this subject.
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Crisp Function of Integral Nonlinaer Equation of the Second Kind over the Fuzzy Interval with Application
Issue:
Volume 3, Issue 4, August 2015
Pages:
189-200
Received:
27 June 2015
Accepted:
8 July 2015
Published:
18 July 2015
Abstract: In this paper, the basic principle and definitions for nonlinear integral equation of a crisp function over a fuzzy interval have been discussed. a numerical technique method and some algorithm for solving non-linear of crisp valued function over fuzzy interval using the domain and range partitions of the membership functions of the fuzzy interval . the numerical solution of the crisp function over the fuzzy interval using the LR-type representation of fuzzy interval. Some numerical examples are prepared to show the efficiency and accuracy of the methods.
Abstract: In this paper, the basic principle and definitions for nonlinear integral equation of a crisp function over a fuzzy interval have been discussed. a numerical technique method and some algorithm for solving non-linear of crisp valued function over fuzzy interval using the domain and range partitions of the membership functions of the fuzzy interval ...
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Application of Neural Network Model in an Epidemiological Study
Renhao Jin,
Fang Yan,
Jie Zhu
Issue:
Volume 3, Issue 4, August 2015
Pages:
201-205
Received:
19 July 2015
Accepted:
24 July 2015
Published:
1 August 2015
Abstract: This paper use the neural network model to an epidemiological study, i.e. bovine tuberculosis (bTB) occurrence in cattle herds, together with well-established risk factors in the area known as West Wicklow, in the east of Ireland. The binary target variable is whether the herd is in the restricted status, which is defined by whether any bTB reactor is detected in the herd. To estimate the parameters and prevent over-fitting in neural network model fitting, the observations are divided into three part of Training data set, Validation data set, and Test data set. By analysis on the lift charts on test data set, the fitted neural network model can be used to enhance practice efficiency.
Abstract: This paper use the neural network model to an epidemiological study, i.e. bovine tuberculosis (bTB) occurrence in cattle herds, together with well-established risk factors in the area known as West Wicklow, in the east of Ireland. The binary target variable is whether the herd is in the restricted status, which is defined by whether any bTB reactor...
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