In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

The university course timetable problem (UCTP) is typically a combinatorial optimization problem. Manually achieving a useful timetable requires many days of effort, and the results are still unsatisfactory. unsatisfactory. Various states of art methods (heuristic, meta-heuristic) are used to satisfactorily solve UCTP. However, these approaches typically represent the instance-specific solutions. The hyper-heuristic framework adequately addresses this complex problem. This research proposed Particle Swarm Optimizer-based Hyper Heuristic (HH PSO) to solve UCTP efficiently. PSO is used as a higher-level method that selects low-level heuristics (LLH) sequence which further generates an optimal solution. The proposed a

         The varied thermal conductivity (insulation) of silica aerogel with heating for different pH has been investigated, it has been depended on ambient pressure drying method in the preparing silica aerogel samples, also six different pH of samples (1, 2, 3, 7, 8 and 9) were treated under five degree of heating with (50,100,150,200 and 250) ᴼC. This technique is important to test the carry-outs hydrophobic silica to temperature without high-quality material changes in the basic characteristics. The hot-wire technique is used in this work to examine the thermal conductivity, Fourier Transform Infrared Spectroscopy (FTIR) depended to characterize the bonds and their artificial by heating. Resu

 Verbs in German and Arabic are of two types: active and passive. Passive voice  is a grammatical voice construction that is found in many languages.  Out of grammatical perspective, each main verb has a form in the active and one in the passive known as a "genus verbi" (type of verb). In passive voice, both in German and in Arabic, the focus is on the action itself or on the result of the action; often the perpetrator is not mentioned. In German, to conjugate verbs in the passive voice, you must know the forms of werden (to become). German uses werden  + the past participle and states it at the end of a sentence. In Arabic,

An experimental investigation has been made to study the influence of using v-corrugated aluminum fin on heat transfer coefficient and heat dissipation in a heat sink. The geometry of fin is changed to investigate their performance. 27 circular perforations with 1 cm diameter were made. The holes designed into two ways, inline arrangement and staggered in the corrugated edges arrangement. The experiments were done in enclosure space under natural convection. Three different voltages supplied to the heat sink to study their effects on the fins performance. All the studied cases are compared with v-corrugated smooth solid fin. Each experiment was repeated two times to reduce the error and the data recorded after reaching t

Background. After tooth extraction, alveolar bone resorption is inevitable. This clinical phenomenon challenges dental surgeons aiming to restore esthetic and function. Alveolar ridge preservation can be applied to minimize dimensional changes with a new socket grafting material, an autogenous dentin graft, produced by mechanically and chemically processing natural teeth. This study assessed the safety and efficacy of using autogenous dentin biomaterial in alveolar ridge preservation. Materials and Methods. Patients with nonrestorable maxillary anterior teeth bounded by natural sound teeth were included in this study. After a detailed clinical and tomographic examination, eligibl