Table of Contents
Articles
by Nwawuru Francis
Int J Math Phys
2018,
1(1);
doi:
4 Views,
12 PDF Downloads
Let and be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented. 
Articles
by Narottam Singh Chauhan
Int J Math Phys
2018,
1(1);
doi:
27 Views,
35 PDF Downloads
The aim of present work is to obtain the approximate solution of fractional model for the electrical RL circuit by using quadratic Legendre multiwavelet method (QLMWM). The beauty of the paper is convergence theorem and mean square error analysis, which shows that our approximate solution converges very rapidly to the exact solution and the numerical solution is compared with the classical solution and Legendre wavelets method (LWM) solution, which is much closer to the exact solution. The fractional integration is described in the RiemannLiouville sense. The results are shows that the method is very effective and simple. In addition, using plotting tools, we compare approximate solutions of each equation with its classical solution and LWM .

Articles
by Abirov Rustam
Int J Math Phys
2018,
1(1);
doi:
5 Views,
14 PDF Downloads
Drucker’s Associated Law of yielding and gradient plasticity cannot always adequately reflect the processes of stressstrain state in deformable continua. Aim of this issue explains these effects via theory of complex loading processes by Ilyushin. 
Articles
Statistical mechanics of hard spheres: the scaled particle theory of the hard sphere fluid revisited
by Bruno Baeyens
Int J Math Phys
2018,
1(1);
doi:
12 Views,
13 PDF Downloads
The aim of this paper is to exhaust the possibilities offered by the scaled particle theory as far as possible and to confirm the reliability of the virial coefficients found in the literature, especially the estimated ones: B i for i > 11. In a previous article (J.Math.Phys.36,201,1995) a theoretical equation of state for the hard sphere fluid was derived making use of the ideas of the so called scaled particle theory which has been developed by Reiss et al.(J.Chem.Phys.31,369,1959). It contains two parameters which could be calculated. The equation of state agrees with the simulation data up to high densities, where the fluid is metastable. The derivation was besed on a generalized series expansion. The virial coefficients B 2 , B 3 and B 4 are exactly reproduced and B 5 , B 6 and B 7 to within small deviations, but the higher ones up to B 18 are systematically and significantly smaller than the values found in the literature. The scaled particle theory yields a number of equations of which only four were used. In this paper we make use of seven equations to calculate the compressibility factors of the fluid. They agree with the simulation data slightly better than those yielded by the old equation. Moreover, the differences between the calculated virial coefficients B i and those found in the literature up to B 18 are very small (less than 4 percent). 
Articles
by Chellapilla Kameswara Rao 1, Lokavarapu Bhaskara Rao 2
Int J Math Phys
2018,
1(1);
doi:
12 Views,
16 PDF Downloads
The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thinwalled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doublysymmetric thinwalled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter. 