In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Objective: Breast cancer is regarded as a deadly disease in women causing lots of mortalities. Early diagnosis of breast cancer with appropriate tumor biomarkers may facilitate early treatment of the disease, thus reducing the mortality rate. The purpose of the current study is to improve early diagnosis of breast by proposing a two-stage classification of breast tumor biomarkers fora sample of Iraqi women.

Methods: In this study, a two-stage classification system is proposed and tested with four machine learning classifiers. In the first stage, breast features (demographic, blood and salivary-based attributes) are classified into normal or abnormal cases, while in the second stage the abnormal breast cases are

In this paper, a mathematical model consisting of the two harmful
phytoplankton interacting with a herbivorous zooplankton is proposed and studied.
The existence of all possible equilibrium points is carried out. The dynamical
behaviors of the model system around biologically feasible equilibrium points are
studied. Suitable Lyapunov functions are used to construct the basins of attractions
of those points. Conditions for which the proposed model persists are established.
The occurrence of local bifurcation and a Hopf bifurcation are investigated. Finally,
to confirm our obtained analytical results and specify the vital parameters, numerical
simulations are used for a hypothetical set of parameter values.

Conducted two trials separate plants Defla first two seasons, 1998 and 1999 to test the susceptibility Altgveria three varieties including Azharha colored white and pink Qati and pink Qtmr and second seasons 1999 and 2000, two types color Azhaarhama white and pink Qati treated mind half-timbered two types of Alaoxinat IBA and NAA and three concentrations as well as repeatersAdhrt results low Almaah rooting

Ameloblastic fibroma is a rare benign tumor usually affects the first two decades of life. The neoplasm is more predominant in mandibular molar-premolar region and rarely affects the maxilla. In this report, we present a couple of Ameloblastic fibroma cases, affecting boys at their 1st decade. The lesions were presented as swellings of their maxilla, which is atypical location. Radiographic images showed well-defined radiolucency containing areas of radio-opacities and impacted teeth. Differential diagnosis was established as cystic/neoplastic conditions. The lesions were incised and histopathologically diagnosed as Ameloblastic fibroma, since they were composed of immature odontogenic mesenchymal and epithelial cells showing different c

There are many different methods for analysis of two-way reinforced concrete slabs. The most efficient methods depend on using certain factors given in different codes of reinforced concrete design. The other ways of analysis of two-way slabs are the direct design method and the equivalent frame method. But these methods usually need a long time for analysis of the slabs.

In this paper, a new simple method has been developed to analyze the two-way slabs by using simple empirical formulae, and the results of final analysis of some examples have been compared with other different methods given in different codes of practice.

The comparison proof that this simple proposed method gives good results and it can be used in analy

     In this article, we introduce a two-component generalization for a new generalization type of the short pulse equation was recently found by Hone and his collaborators. The coupled of nonlinear equations is analyzed from the viewpoint of Lie’s method of a continuous group of point transformations. Our results show the symmetries that the system of nonlinear equations can admit, as well as the admitting of the three-dimensional Lie algebra. Moreover, the Lie brackets for the independent vectors field are presented. Similarity reduction for the system is also discussed.