Open Access Original Research Article

On the Response to Distributed Loads of Elastic Isotropic Rectangular Plate Moving with Varying Velocities

Sunday Tunbosun Oni, Oluwatoyin Kehinde Ogunbamike

Journal of Advances in Mathematics and Computer Science, Page 1-25
DOI: 10.9734/JAMCS/2018/42037

The dynamic behaviour of a simply supported rectangular plate moving with non-uniform velocities is investigated in this paper. The inertia and gravity effects of the moving load are taken into consideration. In order to solve the governing fourth order partial differential equation, a technique based on two-dimensional finite Fourier sine integral transformations, modification of Struble’s asymptotic technique and Fresnel sine and Fresnel cosine identities were used.

The closed form solutions are obtained and numerical analyses in plotted curves are presented. The results show that as the foundation stiffness K and other structural parameters increases, the response amplitude of the simply supported rectangular plate resting on Pasternak foundation decreases. It is also shown that for fixed  value of foundation stiffness K, axial force N, shear modulus G and rotatory inertia correction factor R0, the transverse deflections of the rectangular plate under the action of moving distributed masses are higher than those when only force effects of the moving load is considered. This implies that resonance is reached earlier in moving partially distributed mass problem than in moving distributed force problem.

Open Access Original Research Article

A Bioconvection Model for Squeezing Flow between Parallel Plates Containing Gyrotactic Microorganisms with Impact of Thermal Radiation and Heat Generation/Absorption

Syed Asif Hussain, Sher Muhammad, Gohar Ali, Syed Inayat Ali Shah, Mohammad Ishaq, Zahir Shah, Hameed Khan, Mohammad Tahir, Muhammad Naeem

Journal of Advances in Mathematics and Computer Science, Page 1-22
DOI: 10.9734/JAMCS/2018/41767

The aim of present paper is to investigate the bioconvection squeezing nanofluid flow between two parallel plates’ channels. One of the plates is stretched and the other is fixed. In this study water is considered as a base fluid because microorganisms can survive only in water. The significant influences of thermophoresis and Brownian motion have also been taken in nanofluid model. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (non-dimensional bioconvection flow model) of ordinary differential equations with the help of feasible non-dimensional variables. The acquired nonlinear system has been solved via homotopy analysis method (HAM). The convergence of the method has been shown numerically. Also, influence of various parameters has been discussed for the non-dimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. The variation of the Skin friction, Nusselt number, Sherwood number and their effects on the velocity, concentration, temperature and the density motile microorganism profiles are examined. Furthermore, for comprehension the physical presentation of the embedded parameters, such as unsteady squeezing parameter, Thermal radiation parameter, Peclet number, Thermophoresis parameter, Levis number, Prandtl number, Schmidt number and Brownian motion are plotted and discussed graphically. At the end, we make some concluding remarks in the light of this article.

Open Access Original Research Article

Recursively-Defined Combinatorial Functions: The Case of Binomial and Multinomial Coefficients and Probabilities

Ali Muhammad Ali Rushdi, Mohamed AbdulRahman Al-Amoudi

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2018/42137

This paper studies a prominent class of recursively-defined combinatorial functions, namely, the binomial and multinomial coefficients and probabilities. The paper reviews the basic notions and mathematical definitions of these four functions. Subsequently, it characterizes each of these functions via a recursive relation that is valid over a certain two-dimensional or multi-dimensional region and is supplemented with certain boundary conditions. Visual interpretations of these characterizations are given in terms of regular acyclic signal flow graphs. The graph for the binomial coefficients resembles a Pascal Triangle, while that for trinomial or multinomial coefficients looks like a Pascal Pyramid, Tetrahedron, or Hyper-Pyramid. Each of the four functions is computed using both its conventional and recursive definitions. Moreover, the recursive structures of the binomial coefficient and the corresponding probability are utilized in an iterative scheme, which is substantially more efficient than the conventional or recursive evaluation. Analogous iterative evaluations of the multinomial coefficient and probability can be constructed similarly. Applications to the reliability evaluation for two-valued and multi-valued k-out-of-n systems are also pointed out.

Open Access Original Research Article

The Boundaries of Infinity and the Dance of c at the Hybrid Dynamic Vision in Engineering Physics

Md. Abdul Hakim

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/JAMCS/2018/40596

The speed of light c and its momentum in spite of its rest mass is in great triumph at the helm of galore hotch potch to the mathematical physicists in worldwide business of applied physics. There is an abundance of different dancing to the theoretical physicist to curb these panics in different theoretical and laboratory setup in applied physics. The intent of this study is to see the light of riding anchor in view of making a dot over these clouds to escape these dilemmas in applied physics. This study can reveal the open secret in choosing the astrophysical parent equation (x) along with its sister concern equations (xi) and (xii) in the route ahead of inventing the boundaries of the infinity in the equations (xi) and (xii) where c = ∞ is the prime concern of the applied mathematicians. Analyses on the equations  (x), (xi), (xii) and (xiii) have given vent at the disposal of God particles at the 3rd eye on equation (x) and (xiii) directs the astrophysical Mendelism devoted to understanding the God particle in mathematical astrophysics. An all out physical and applied mathematical planning and policies ahead of searching the God’s phenotypic aliving is in galore need dealing in the Arshi, the eye of knowledge at equation (xiii) in theoretical mathematics to carry the day in spiritual physics bearing a remembrance to the VTSP in the study.

Open Access Original Research Article

Optimum Location of Emergency Services for Weighted Callers

Emad El-Din H. Hassan

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2018/41996

This paper is an approach for introducing a mathematical treatment of the problem of finding the optimum location(s) of the emergency service centers concerning the case in which the callers for the service have different degrees of importance (weights) leading to present appropriate algorithm needed to solve it. In the end of the paper we introduce a numerical example to illustrate the steps of the algorithm.