In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

This research includes the synthesis of some new different heterocyclic derivatives of 5-Bromoisatin. New sulfonylamide, diazine, oxazole, thiazole and 1,2,3-triazole derivatives of 5-Bromoisatin have been synthesized. The synthesis process started by the reaction of 5-Bromoisatin with different reagents to obtain schiff bases of 5-Bromoisatin intermediate compounds(1, 8, 19) by using glacial acetic acid as a catalyst in three routes. The first route, 5-Bromoisatin reacted with p-aminosulfonylchloride to product compound(1), then converted to sulfonyl amide derivatives(2-7) by the reaction of compound(1) with different substituted primary aromatic amine in absolute ethanol. The second route includes the reaction of 5-Bromoisatin rea

Rudimentary non-communicating functional uterine horn with unicornuate uterus, originating from anomalous embryological development of one Mullerian duct, is prone to different complications either at the gynecological or obstetrical level such as chronic pelvic pain, hematometra, subfertility and decreased quality of life. This unique case report presents a 14-year-old female with a history of severe chronic pelvic pain. She was diagnosed with Familial Mediterranean Fever (FMF) and had an appendectomy for suspected appendicitis within the symptoms’ interval. Ultrasound showed a right 5*6 cm right complex cystic mass assuming ovarian in place. She underwent a suspected endometrioma cystectomy operation and was diagnosed with left unico

The aim of the study was to evaluate the efficacy of diode laser (λ=940 nm) in the management of gingival hyperpigmentation compared to the conventional bur method. Materials and methods: Eighteen patients with gingival hyperpigmentation were selected for the study with an age between 12-37 years old. The site of treatment was the upper gingiva using diode laser for the right half and the conventional method for the left half. All patients were re-evaluated after the following intervals: 3 days, 7 days, 1 month and 6 months post-operation. Pain and functions were re-evaluated in each visit for a period of 1 day, 3 days and 1 week post-operation. Laser parameters included 1.5 W in continuous mode with an initiated tip (400 μm) placed in

In an attempt to disposal from nuclear waste which threats our health and environments. Therefore we have to find appropriate method to immobilize nuclear waste. So, in this research the nuclear waste (Strontium hydroxide) was immobilized by Carbon nanotubes (CNTs).  The Nd-YAG laser with wave length 1064 nm, energy 750 mJ and 100 pulses used to prepare CNTs. After that adding Sr(HO)₂ powder to the CNTs colloidal in calculated rate to get homogenous mixing of CNTs-Sr(OH)_2. The Sr(HO)₂ absorbs carbon dioxide from the air to form strontium carbonate so, the  new solution is CNTs-SrCO₃. To dry solution putting three drops from the new solution on the glass slides. To investigate the radi

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd 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

  Many production companies suffers from big losses because of  high production cost and low profits for several reasons, including raw materials high prices and no taxes impose on imported goods also consumer protection law deactivation and national product and customs law, so most of consumers buy imported goods because it is characterized by modern specifications and low prices.

  The production company also suffers from uncertainty in the cost, volume of production, sales, and availability of raw materials and workers number because they vary according to the seasons of the year.

  I had adopted in this research fuzzy linear program model with fuzzy figures

The δ-mixing ratios have been calculated for several γ-transitions in 90Mo using the 𝛔 𝐉 method. The results are compared with other references the agreement is found to be very good .this confirms the validity of the 𝛔 𝐉 method as a tool for analyzing the angular distribution of γ-ray. Key word: population parameter, γ-ray transition, 𝛔 𝐉 method, multiple mixing ratios.