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Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction
Mashadi,
Chitra Valentika,
Sri Gemawati
Issue:
Volume 3, Issue 2, April 2017
Pages:
54-57
Received:
25 October 2016
Accepted:
12 January 2017
Published:
9 February 2017
Abstract: In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.
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Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations
Fadugba Sunday Emmanuel,
Falodun Bidemi Olumide
Issue:
Volume 3, Issue 2, April 2017
Pages:
58-63
Received:
27 October 2016
Accepted:
16 January 2017
Published:
9 February 2017
Abstract: In this paper, a new one-step scheme was developed for the solution of initial value problems of first order in ordinary differential equations. In its development a combination of interpolating function and Taylor series were used. The method was used for the solution of initial value problems emanated from real life situations. The numerical results showed that the new scheme is consistent, robust and efficient.
Abstract: In this paper, a new one-step scheme was developed for the solution of initial value problems of first order in ordinary differential equations. In its development a combination of interpolating function and Taylor series were used. The method was used for the solution of initial value problems emanated from real life situations. The numerical resu...
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Dot Products and Matrix Properties of 4×4 Strongly Magic Squares
Neeradha. C. K.,
V. Madhukar Mallayya
Issue:
Volume 3, Issue 2, April 2017
Pages:
64-69
Received:
4 November 2016
Accepted:
27 December 2016
Published:
13 February 2017
Abstract: Magic squares have been known in India from very early times. The renowned mathematician Ramanujan had immense contributions in the field of Magic Squares. A magic square is a square array of numbers where the rows, columns, diagonals and co-diagonals add up to the same number. The paper discuss about a well-known class of magic squares; the strongly magic square. The strongly magic square is a magic square with a stronger property that the sum of the entries of the sub-squares taken without any gaps between the rows or columns is also the magic constant. In this paper a generic definition for Strongly Magic Squares is given. The matrix properties of 4×4 strongly magic squares dot products and different properties of eigen values and eigen vectors are discussed in detail.
Abstract: Magic squares have been known in India from very early times. The renowned mathematician Ramanujan had immense contributions in the field of Magic Squares. A magic square is a square array of numbers where the rows, columns, diagonals and co-diagonals add up to the same number. The paper discuss about a well-known class of magic squares; the strong...
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Near Ground Path Loss Prediction for UMTS 2100 MHz Frequency Band Over Propagating Over a Smooth-Earth Terrain
Umesi Cosmos Nnanyerem,
Ozuomba Simeon,
Afolayan J. Jimoh
Issue:
Volume 3, Issue 2, April 2017
Pages:
70-76
Received:
25 October 2016
Accepted:
17 January 2017
Published:
16 February 2017
Abstract: In this paper, path loss prediction for near ground propagation of third generation (3G)-based Universal Mobile Telecommunications System (UMTS) network signal in the 2100 MHz frequency band over a smooth-earth terrain is presented. Particularly, the attenuation due to diffraction is estimated based on ITU-R Recommendation P.526-13 for diffraction over smooth earth. Furthermore, the total pathloss is determined using the Blomquist empirical model which combined free-space loss, plane-earth loss and the diffraction loss over smooth earth. In the study, two drive tests are conducted for the UMTS 2100 MHz frequency band in suburban area of Uyo. The Blomquist empirical model was tuned with respect to the first drive test pathloss dataset. The results show that with the training data (first drive test data), the untuned Blomquist empirical model has RMSE=10.21344 dB, Prediction Accuracy = 89.92%, minimum Prediction error = 9.02 dB and maximum Prediction error = -34.05 dB. Also, with the training data, the optimized Blomquist empirical model has RMSE=1.625388dB, Prediction Accuracy = 98.48%, minimum Prediction error = 5.34 dB and maximum Prediction error = -5.40 dB. Furthermore, with the cross validation data (second drive test data), the optimized Blomquist empirical model has RMSE=1.831368 dB, Prediction Accuracy = 98.24%, minimum Prediction error = 5.25 dB and maximum Prediction error = -6.15 dB. The results show that for the given terrain under study, the tuned or optimized Blomquist empirical model can effectively predict the pathloss for the UMTS network signal in the 2100 MHz frequency band.
Abstract: In this paper, path loss prediction for near ground propagation of third generation (3G)-based Universal Mobile Telecommunications System (UMTS) network signal in the 2100 MHz frequency band over a smooth-earth terrain is presented. Particularly, the attenuation due to diffraction is estimated based on ITU-R Recommendation P.526-13 for diffraction ...
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Optimization of Vegetable Planting and Allocation
Xie Siqi,
Chong Yangjing,
Sun Wenyuan
Issue:
Volume 3, Issue 2, April 2017
Pages:
77-81
Received:
29 December 2016
Accepted:
12 January 2017
Published:
27 February 2017
Abstract: In this paper, we aiming at question about vegetable planting. First we use the method of line segment superposition to calculate the minimum distance between 8 vegetable planting bases and 35 sales points’ and every route must through traffic junction. After we get the shortest distance, we change the conditions and establish the relationship between the planting base supply and the demand of each point of sale. According to the above relationship to write lingo program, and get optimal allocation scheme from direct allocation. Then we change the procedure and get the optimal allocation schemes between expanding the planting area and ensuring the vegetable species two circumstance.
Abstract: In this paper, we aiming at question about vegetable planting. First we use the method of line segment superposition to calculate the minimum distance between 8 vegetable planting bases and 35 sales points’ and every route must through traffic junction. After we get the shortest distance, we change the conditions and establish the relationship betw...
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Combinatorial Structures to Construct Simple Games and Molecules
Issue:
Volume 3, Issue 2, April 2017
Pages:
82-87
Received:
28 October 2016
Accepted:
12 January 2017
Published:
2 March 2017
Abstract: We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-) heuristics algorithms and parallel programming, among others.
Abstract: We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to mo...
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Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population
Issue:
Volume 3, Issue 2, April 2017
Pages:
88-93
Received:
20 January 2017
Accepted:
13 February 2017
Published:
2 March 2017
Abstract: More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.
Abstract: More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in th...
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Tuning and Cross Validation of Blomquist-Ladell Model for Pathloss Prediction in the GSM 900 Mhz Frequency Band
Njoku Chukwudi Aloziem,
Ozuomba Simeon,
Afolayan J. Jimoh
Issue:
Volume 3, Issue 2, April 2017
Pages:
94-99
Received:
25 October 2016
Accepted:
23 December 2016
Published:
18 April 2017
Abstract: In this paper, Blomquist-Ladell model is tuned and used for the prediction of total pathloss for GSM signal in the 900 MHz band. The model combined free-space loss, excess plane-earth loss and tunable multiple knife-edge diffraction loss to give the total loss. Pathloss data captured from two drive test conducted in Uyo suburban area are used in the study. The first drive test dataset are used to tune the Blomquist-Ladell model, particularly to select the value of the statistical terrain diffraction loss that minimizes the root mean square error (RMSE) of the model prediction. The tuned Blomquist-Ladell model is then cross validated with the second drive test dataset. The results show that the Blomquist-Ladell model performed very well; with the training data (first drive test dataset) the model has RMSE of 2.935598 dB and Prediction Accuracy of 98.16323% and in the cross validation data (the second drive test dataset) the model has RMSE of 3.398141dB and Prediction Accuracy of 97.82251%. In both cases, the RMSE is below 3.5 dB which is below the acceptable maximum value of 7dB for such pathloss prediction model.
Abstract: In this paper, Blomquist-Ladell model is tuned and used for the prediction of total pathloss for GSM signal in the 900 MHz band. The model combined free-space loss, excess plane-earth loss and tunable multiple knife-edge diffraction loss to give the total loss. Pathloss data captured from two drive test conducted in Uyo suburban area are used in th...
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