A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)
This paper presents a stylistic analysis of two poems of well-known poets of the English literature, namely; E.E. Cummings and the Irish noble laureate Seamus Heaney. The researcher's attempt here is to approach Cummings’s poem “maggie and milly and molly and may” and Heaney’s “A Kite for Aibhín” from the stylistics’ point of view. The paper also analyzes the poems using the tools of linguistics with a view to make their meaning explicit.
It is worth noting that stylistics as a scientific discipline is really beneficial to those who are teaching and studyi
... Show MoreIn this paper, the asymptotic behavior of all solutions of impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term was investigated. Some sufficient conditions were obtained to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were given for the main results.
In this paper the definition of fuzzy anti-normed linear spaces and its basic properties are used to prove some properties of a finite dimensional fuzzy anti-normed linear space.
A comparative study was carried out on ecological and genetical adaptation of three Iraqi
freshwater snails, Physa acuta, Melanopsis buccinoidea and Melanoides tuberculata, in
respect to acute toxicity of heavy metals (Zn, Cd and Hg). Longevity are used as poisoning
tolerance criterion. LT 50 and LT 100 were determined for the studied snails at (0.5, 1, 5, and
10 ppm), for the three metals. Results indicated that Physa acuta had a higher tolerance than
Melanopsis buccinoidea and Melanoides tuberculata, which was the lower one. Previous
exposure to heavy metals in the original habitat was affecting on experimental tolerance and
no relationships of physical and chemical factors (total hardness, temperature, D. O. and
In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.
Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking f
... Show MoreThis study was conducted in a lath house, Dept of Hort. and Landscape, College of Agricultural Engineering Sciences, Univ. During the 2021 growing season, Baghdad will investigate the influence of organic and Biological fertilizers on three Citrus rootstocks' growth and leaf mineral content. The first factor is the addition of liquid organic fertilizers Vit-Org (O) at three levels without addition (O0), soil addition at 10 ml.L-1 (O10) and soil addition at 20 ml.L-1 (O20). The second factor is the addition of nitrogen-fixing bacteria without addition (N1), add 30 ml.Transplant-1 of Azotobacter chroococcum (N2) and add 30 ml.Transplant-1 of Azospirillum brasilemse (N3). The third factor is three citrus rootstocks: sour orange (R1), R
... Show MoreA three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the p
... Show MoreIn this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.
In this paper, we present some numerical methods for solving systems of linear FredholmVolterra integral equations of the second kind. These methods namely are the Repeated Trapezoidal Method (RTM) and the Repeated Simpson's 1/3 Method (RSM). Also some numerical examples are presented to show the efficiency and the accuracy of the presented work.