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Volume 6, December
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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.

Math. Comput. Appl., Volume 6, Issue 2 (August 2001) – 8 articles , Pages 85-154

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Article
A Relation between Prime Numbers and Twin Prime Numbers
Math. Comput. Appl. 2001, 6(2), 153-154; https://doi.org/10.3390/mca6020153 - 01 Aug 2001
Viewed by 664
Abstract
Every mathematician has been concerned with prime numbers, and has metwith mysterious surprises about them. Besides intuition, using empirical methods has an important role to findrelations between prime numbers. A relation between any prime numberand any twin prime number has been obtained. Full article
Article
Linear Transverse Vibrations of a Simply Supported Beam Carrying Concentrated Masses
Math. Comput. Appl. 2001, 6(2), 147-152; https://doi.org/10.3390/mca6020147 - 01 Aug 2001
Cited by 8 | Viewed by 640
Article
On the Integral Invariants of a Time-Like Ruled Surface
Math. Comput. Appl. 2001, 6(2), 137-145; https://doi.org/10.3390/mca6020137 - 01 Aug 2001
Cited by 4 | Viewed by 770
Abstract
In this study, we discuss the dual Lorentzian spherical motions and calculate the real integral invariants of a closed time-like ruled surfaces in \(R_1^3\). Then, we define the dual angle of pitch of a closed time-like ruled surface, and give a relation between [...] Read more.
In this study, we discuss the dual Lorentzian spherical motions and calculate the real integral invariants of a closed time-like ruled surfaces in \(R_1^3\). Then, we define the dual angle of pitch of a closed time-like ruled surface, and give a relation between the dual Steiner vector of the dual spherical motion and dual angle of pitch of the time­like ruled surface. Finally, we obtain a relation between the dual angle of pitch and the real integral invariants of time-like ruled surface. Full article
Article
An Analytical Elastic-Plastic Stress Analysis for a Steel Fibre Reinforced Thermoplastic Composite Beam Subjected to Thermal Loading
Math. Comput. Appl. 2001, 6(2), 123-136; https://doi.org/10.3390/mca6020123 - 01 Aug 2001
Viewed by 690
Abstract
This paper is concerned with a thermal elastic-plastic stress analysis on a steel fibre reinforced thermoplastic matrix composite beam fixed at its to ends. Temperature varying linearly is chosen at the upper and lower surfaces to be zero and T0, respectively. [...] Read more.
This paper is concerned with a thermal elastic-plastic stress analysis on a steel fibre reinforced thermoplastic matrix composite beam fixed at its to ends. Temperature varying linearly is chosen at the upper and lower surfaces to be zero and T0, respectively. The solution is performed at 0, 60, 75 and 90° orientation angles. Plastic yielding does not occur at 30 and 45° orientation angles. It is found that the intensity of the residual stress component of σx and the equivalent plastic strain are maximum at the lower surface of the beam. The intensity of the residual stress is maximum at 0° orientation angle. The intensity of the equivalent plastic strain is found to be the greatest at 60° orientation angle. Full article
Article
Fredholm-Volterra Integral Equation with Potential Kernel
Math. Comput. Appl. 2001, 6(2), 113-122; https://doi.org/10.3390/mca6020113 - 01 Aug 2001
Cited by 1 | Viewed by 884
Abstract
A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω) × C(O, T), Ω = {(x, y) \(\in\) Ω : \(\sqrt{{x^2}+{y^2}}\) ≤ a, z = 0} and T [...] Read more.
A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω) × C(O, T), Ω = {(x, y) \(\in\) Ω : \(\sqrt{{x^2}+{y^2}}\) ≤ a, z = 0} and T < ∞. The kernel of the Fredholm integral term is considered in the generalized potential form belongs to the class C ([Ω] × [Ω]), while the kernel of Volterra integral term is a positive and continuous function belongs to the class C[0,T). Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established from the wok. Full article
Article
The Effect of the Galileo Invariance Pairing on the 1- States in Spherical Nuclei
Math. Comput. Appl. 2001, 6(2), 103-111; https://doi.org/10.3390/mca6020103 - 01 Aug 2001
Cited by 2 | Viewed by 711
Abstract
Experimentally investigation low lying 1- excitations in heavy nuclei plays important role in modern nuclear structure physics. In particular the measurements of the El strength in the region Ex ≤ 3 MeV may shed some light on the mechanism by means [...] Read more.
Experimentally investigation low lying 1- excitations in heavy nuclei plays important role in modern nuclear structure physics. In particular the measurements of the El strength in the region Ex ≤ 3 MeV may shed some light on the mechanism by means of which isospin symmetry or Galilean invariance of pairing is broken in nuclei. In our search we investigate the characteristics of 1- states for Te, Ba, Ce isotopes in translational invariance GDR model including Galilean invariance pairing. Our calculations show that integrated cross sections is sensitive to restoration broken Galilean invariance of pairing. This restoration does not influence the positions of the low lying 1- states, but changes its El strengths. In spite of restoration Galilean invariance of pairing it is impossible to carry out to the experimental results with spherical structure of nuclei which have been examined. Full article
Article
The Importance of Mesh Modeling in the Calculation of Stress Intensity Factor
Math. Comput. Appl. 2001, 6(2), 97-101; https://doi.org/10.3390/mca6020097 - 01 Aug 2001
Viewed by 703
Abstract
In this paper, stress intensity factor (SIF) of an infinite plate with a center notched hole is calculated by means of finite element method (FEM) using both triangular quadratic element (TQE) and triangular quarter point element (TQPE) (Fig. 2). The FE analyses are [...] Read more.
In this paper, stress intensity factor (SIF) of an infinite plate with a center notched hole is calculated by means of finite element method (FEM) using both triangular quadratic element (TQE) and triangular quarter point element (TQPE) (Fig. 2). The FE analyses are performed using Ansys5.4 program code. SIF also is calculated from linear elastic fracture mechanics. The obtained results are compared to each other and it is found that the results from the TQPE are closer to exact solution. Full article
Article
Wavelet-Neural Network Model for Automatic Traffic Incident Detection
Math. Comput. Appl. 2001, 6(2), 85-96; https://doi.org/10.3390/mca6020085 - 01 Aug 2001
Cited by 11 | Viewed by 681
Abstract
The problem of traffic incident detection can be viewed as a pattern recognition problem. Neural networks are known to solve pattern recognition problems effectively, especially when there is no mathematical model. The computational complexity of neural network algorithms, however, increases exponentially with an [...] Read more.
The problem of traffic incident detection can be viewed as a pattern recognition problem. Neural networks are known to solve pattern recognition problems effectively, especially when there is no mathematical model. The computational complexity of neural network algorithms, however, increases exponentially with an increase in the size of the network. Furthermore, with an increase in the size of the network, the size of the training set has to be increased exponentially in order to achieve the same level of accuracy. To overcome this double exponential complexity a hybrid feature extraction algorithm and neural network architecture is created specifically for automatic detection of traffic incidents. The upsteam and downstream traffic data are first filtered by the discrete wavelet transform. Then, a linear discriminant network is used for feature extraction. Finally, the adaptive conjugate gradient learning algorithm of Adeli and Hung is used to train the network. Full article
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