##### Indirect RBF for High-Order Integro-Differential Equations

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2015/19199

Two di erent approaches are applied to solve high-order integro-di erential equations (IDEs), based on Radial Basis Functions (RBF). The rst approach, which is called the direct approach (DRBF) is based on di erentiation, and considers the solution as a nite linear combination of RBFs. While the second, the indirect approach (IRBF), is based on integration and considers the highest order derivative of the solution as a nite linear combination of RBFs. The results of this study indicate that for low-order IDEs, both approaches are enough accurate, but for high-order IDEs, the IRBF solutions are more accurate than those of direct RBF. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

##### Distributional Schwarzschild Geometry from Non Smooth Regularization Via Horizon

Jaykov Foukzon

Journal of Advances in Mathematics and Computer Science, Page 1-28
DOI: 10.9734/BJMCS/2015/16961

In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear distributional geometry and Colombeau generalized functions it seems possible to show that the horizon singularity is not only a coordinate singularity without leaving Schwarzschild coordinates. However the Tolman formula for the total energy ET of a static and asymptotically flat spacetime,gives ET = m, as it should be.

##### Undecidability of the Criterion for Recognizing the Fibonacci Numbers

Alexander Bolotin

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/BJMCS/2015/19785

Assuming the conjecture that all effectively calculable functions must be Turing-machine computable, this paper demonstrates that the problem of recognizing Fibonacci numbers must be in general undecidable. This means that there is no algorithm, which in a finite number of steps can correctly decide whether a given positive integer z of arbitrarily large size belongs to the Fibonacci sequence.

##### Real-Time Volume Rendering of FCC Datasets Using Box-Splines on the Mobile Platforms

Aaliya Sarfaraz, Muhammad Shaban

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2015/19044

Visualizing volumetric datasets using real-time volume rendering technique involves a large number of interpolation operations that are computationally expensive. This situation used to restrict real-time volume rendering methods to be used only on high-end graphics workstations or special-purpose hardware. This paper presented a real-time direct volume rendering (DVR) implementation of face centered cubic (FCC) datasets with box-spline interpolation on mobile devices. The latest version of OpenGL ES (Open Graphics Library for Embedded System) (3.0) is used for implementation to leverage cutting-edge 3D graphics technology, and it shows interactive performance (2.40 frame per second (FPS)) for moderate-sized volume datasets (64×64×64).

Aims: To present a real-time direct volume rendering (DVR) implementation of face centered cubic (FCC) datasets with box-spline interpolation on mobile devices.

Study Design:  Study is based on research conducted in computer lab, University of Seoul, South Korea.

Place and Duration of Study: Computer Science Lab, Department of Computer Science, The graduate College, University of Seoul, South Korea, between June 2014 and April 2015.

Methodology: The latest version of OpenGL ES (Open Graphics Library for Embedded System) (3.0) is used for implementation to leverage cutting-edge 3D graphics technology, and it shows interactive performance (2.40 frame per second (FPS)) for moderate-sized volume datasets (64×64×64).

Results: In our implementation, we calculated the opacity using front–to-back composting whereby the viewing rays are traversed from the eye point into the volume. We also compared different volume sizes, having the same density.

Conclusion: We have presented a real-time volume rendering technique for FCC datasets on mobile devices that efficiently evaluate spline value. Our work has proven that mobile devices constitute a valid program to achieve interactive volume visualization, despite the fact that the rendering capabilities are concentrated in comparison to desktop solutions, due to their inherent autonomy limitations.

##### Solving three Level Quadratic Programming Problem with Stochastic Parameters in the Objective Functions

O. E. Emam, M. A. Abdel-Fattah, A. S. Ahmed

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2015/19962

This paper solves a stochastic three-level decision maker’s model. This approach uses stochastic parameters in the objective function to solve a three level quadratic programming problem. The probabilistic nature of the objective functions is converted to an equivalence deterministic one and then a fuzzy programming technique will be used in each level to optimize its problem separately; implementing tolerance membership concept is used to generate Pareto optimal solution for these problems. Finally, the main results developed will be clarified by a numerical example in this paper.

##### MOND Kinematics of n-Pendulums

Smita V. Nahatkar, Manisha Pund

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2015/19525

We generalized our earlier result (Nahatkar and Pund [6]) with regard to the motion of a simple pendulum in a plane.

##### Improving Adequacy in a Rule-Based English-to-Igala Automatic Translation System through Word Sense Disambiguation

Sani Felix Ayegba, O. E. Osuagwu

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2015/19994

Here, we describe a rule-based machine translation system that translates English sentences to the Igala language. This work was evaluated with respect to adequacy, a measure of the quantity of information existent in the original text that the translated text contains. It indicates whether the output is a correct translation of the original sentence in a sense that the right meaning is communicated. An analysis revealed that adequacy was poor for sentences that contain words that exhibit ambiguity. The errors originated from the fact that correct meanings of ambiguous words were not selected based on the context. A further study of the architecture of the translation system showed it has no built-in module for word sense disambiguation. This accounts for the poor adequacy. A word-sense model was developed and incorporated into the MT system to disambiguate sentences before passing it to the translator.  The model was implemented using JSP, a technology for building and deploying web applications in Java as the front end and MySQL as a backend. The model was tested on 100 previously translated sentences that contain ambiguous words. The level of adequacy increased from 32% to 68.2%.