In this paper, the oscillatory properties and asymptotic behaviour of a third-order three-dimensional neutral system are discussed.  Some sufficient conditions are obtained to ensure that all bounded positive solutions of the system are oscillatory or non-oscillatory.  On the other hand, the non-oscillatory solutions either converge or diverge when  goes to infinity. A special technique is adopted to include all possible cases. The obtained results include illustrative examples.

DFT (3-21G, 6-31G and 6-311G/ B3LYP) and Semi-empirical PM3 methods were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) of the Tri-rings layer (6,0) Zigzag single wall carbon nanotube (SWCNT) at their equilibrium geometries which was found to have D6h symmetry point group with C-C bond alternation in all tube rings.as well as mono ring layer. Assignments of the modes of vibration were done depending on the pictures of their modes applying by Gaussian 03 program. The whole relations for the vibration modes were also done including (CH stretching, CC stretching, deformation in plane of the molecule (δCH, δring and δCCC), deformation out of plane of the molecule (CH and

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

The article presents the synthesis and liquid crystalline properties of some of new bent and linear core compounds containing a 1,3,4-oxadiazole, piperazine and thiazolidin-4-one rings as a central core. The new synthesized compounds were characterized by elemental analysis and FTIR, ¹HNMR and mass spectroscopy). The liquid crystalline properties were studied by polarized optical microscopy and differential scanning calorimetry. All Schiff bases compounds with 1,3,4-oxadiazole and piprzaine ring in central core presented liquid crystalline properties. The liquid crystallinity of compounds containing 1,3,4-oxadiazole and thiazolidin-4-one rings as a central core were found depending on the type of terminal substituents.

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

Maximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e