In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Nanotechnology is a continually expanding field for its uses and applications in multiple areas i.e. medicine, science, and engineering. Biosynthesis is straightforward, less-toxicity, and cost-effective technology. TiO2 NPs biosynthesis has attained consideration in recent decades. In this study, probiotic bacteria were isolated from cow’s raw milk samples, and then were identified by using the Vitek2 system; as Leuconostoc spp. included Leuconostoc mesenteroides subsp. mesenteroides (Leu.1), Leuconostoc mesenteroides subsp. cremoris (Leu.4), and Leuconostoc pseudomesenteroides (Leu.14). All Leuconostoc spp. isolates showed an ability for TiO2 NPs bio-production, after being incubated at anaerobic conditions (30 o C/ 24 h) in DeM

A sensitive and selective method have been developed for the determination of palladium (II)and platinum (II) . A new reagent and two complexes have been prepared in ethanolic solutions .The method is based on the chelation of metal ions with 4-(4?- pyrazolon azo) resorcinol (APAR) to form intense color soluble products, that are stable and have a maximum absorption at 595 nm and at 463 nm and ?max of 1.11×10 4 and.1.35 ×104 Lmole-1cm-1 for Pd(II) Pt(II) respectively. A linear correlation of (1.4 – 0.2) and (3.2 -0.4 ) ppm for pd(II) pt(II) respectively .The stability constants , relative errors , a relative standard deviations for Pd(II) and Pt(II) were 0.40×105 , 0.4×104 L mol-1 ,0.34 - 0.21% and 2.4 – 0.91% respectively.

    Ferns are considered as important medical herbs. They produce a wide range of secondary metabolites that could be useful in treating different diseases. However, they still remain underexplored in medical aspects in Iraq. Hence, the purpose of this study was to identify alkaloids components in the methanol extracts of four fern species (Asplenium ceterach L., A. scolopendrium L., Cheilanthes pteridioides (Richard) C. Chr. from Malakan region in Erbil Governorate and Equisetum ramosissimum Desf. from Chemi Rezan in Sulaimaniyah Governorate,  of northen Iraq during March - June 2018. The research was conducted by using High performance liquid chromatography (H

This paper presents a vibration suppression control design of cantilever beam using two piezoelectric ‎patches. One patch was used as ‎an actuator element, while the other was used as a sensor. The controller design was designed via the balance realization reduction method to elect the reduced order model that is most controllable and observable. ‎the sliding mode observer was designed to estimate six states from the reduced order model but three states are only used in the control law. Estimating a number of states larger than that used is in order to increase the estimation accuracy. Moreover, the state ‎estimation error is proved bounded. An ‎optimal LQR controller is designed then using the ‎estimated states with the slid

Artemia fransiscana is one of the most important live food for commercial larval aquaculture. The aim of this study is to investigate the effects of 890 nm diode laser irradiation on Artemia capsulated cysts using (1-10) minutes exposure time, and 2.26x10-3 J/cm2 Fluence. The Artemia samples were obtained from two locations: Dyalaa and Basraa. After irradiation, hatching percentage (H %) and hatching efficiency(HE) of Artemia were measured after 24 and 48 hours of incubation. The results of the effect of laser light on the capsulated cysts from Dyalaa showed that the optimum dose for enhancing (H %) after 24 hours of incubation is using 10 minutes exposure time, while after 48 hours of incubation the (H %) enhancement can be achieved

Humans are exposed to nuclear radiations every day, and these radiations are both natural and artificial. When the body tissues are exposed to nuclear radiation, free radicals are formed, which are responsible for cancer development. In this research, silver nanoparticles were synthesized by electrical explosion wire method. Nanoparticles were added to deionized water that contained free radicals before and after exposure to gamma rays. The obtained results indicate that the silver nanoparticles have antioxidant potential through possessing free radical scavenging activity, as they can donate electron to free radicals and become neutralize. Then, these nanoparticles were injected to mice before and after their irradiation with gamma ray.

Modern automation robotics have replaced many human workers in industrial factories around the globe. The robotic arms are used for several manufacturing applications, and their responses required optimal control. In this paper, a robust approach of optimal position control for a DC motor in the robotic arm system is proposed. The general component of the automation system is first introduced. The mathematical model and the corresponding transfer functions of a DC motor in the robotic arm system are presented.  The investigations of using DC motor in the robotic arm system without controller lead to poor system performance. Therefore, the analysis and design of a Proportional plus Integration plus Divertive (PID) controller is illustrated.

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.