A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple technique. Illustrative examples use MathCad software to deal with upper and lower-bound solutions to fuzzy problems. The method provides a reliable way to ensure that an exact solution is approximated. Also, figures and tables show the potential of the method.
This research presents a new study in reactive distillation by using consecutive reaction: the saponification reaction of diethyl adipate (DA) with sodium hydroxide solution .
The effect of three parameters were studied through a design of experiments applying 23 factorial design . These parameters were : the mole ratio of DA to NaOH solution (0.1 and 1) , NaOH solution concentration (3 N and 8 N) , and batch time (1.5 hr. and 3.5 hr.) . The conversion of DA to sodium monoethyladipate(SMA)(intermediate product) was the effect of these parameters which was detected . Also , the percentage purity of the intermediate product was recorded . The results showed that increasing mole ratio of DA to NaOHsolutio
... Show MoreCorrosion rate tests were carried out on carbon steel under concentration cells conditions of oxygen and sodium chloride. The effect of aeration in one compartment on the corrosion rate of both coupled metals was determined. In addition, the effects of time and temperatures on the corrosion rate of both coupled metals and galvanic currents between them were investigated. Corrosion potentials for the whole range of operating conditions under concentration cell conditions were also studied. The results showed that under aeration condition, the formation of concentration cell caused a considerable corrosion rate of the Carbon steel specimens coupled in different concentrations of O2 and NaCl due to the galvanic effect
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The research aims to measure, assess and evaluate the efficiency of the directorates of Anbar Municipalities by using the Data Envelopment Analysis method (DEA). This is because the municipality sector is consider an important sector and has a direct contact with the citizen’s life. Provides essential services to citizens. The researcher used a case study method, and the sources of information collection based on data were monthly reports, the research population is represented by the Directorate of Anbar Municipalities, and the research sample consists of 7 municipalities which are different in terms of category and size of different types. The most important conclusion reached by the research i
... Show MoreThe present study aimed at identifying the effectiveness of Macaton method in improving some sensory and cognitive skills in autistic children. In order to achieve the aims of the study, the researcher used the experimental method. The present study sample was (10) children whose ages ranged between (7-10) years and were diagnosed medically with autism disorder. The researcher randomly selected the sample and divided it into two groups: the first group consisted of (5) children representing the experimental group, and (5) children representing the control group after extracting the equivalence between the two groups in terms of age, intelligence, economic and social level and the degree of communication. The program was implemented for t
... Show MoreCoagulation - flocculation are basic chemical engineering method in the treatment of metal-bearing industrial wastewater because it removes colloidal particles, some soluble compounds and very fine solid suspensions initially present in the wastewater by destabilization and formation of flocs. This research was conducted to study the feasibility of using natural coagulant such as okra and mallow and chemical coagulant such as alum for removing Cu and increase the removal efficiency and reduce the turbidity of treated water. Fourier transform Infrared (FTIR) was carried out for okra and mallow before and after coagulant to determine their type of functional groups. Carbonyl and hydroxyl functional groups on the surface of
... Show MoreIn this paper, the impact of magnetic force, rotation, and nonlinear heat radiation on the peristaltic flow of a hybrid bio -nanofluids through a symmetric channel are investigated. Under the assumption of a low Reynolds number and a long wavelength, the exact solution of the expression for stream function, velocity, heat transfer coefficient, induced magnetic field, magnetic force, and temperature are obtained by using the Adomian decomposition method. The findings show that the magnetic force contours improve when the magnitude of the Hartmann number M is high and decreases when rotation increases. Lastly, the effects of essential parameters that appear in the problem are analyzed through a graph. Plotting all figures is done using the
... Show MoreEmploying phase-change materials (PCM) is considered a very efficient and cost-effective option for addressing the mismatch between the energy supply and the demand. The high storage density, little temperature degradation, and ease of material processing register the PCM as a key candidate for the thermal energy storage system. However, the sluggish response rates during their melting and solidification processes limit their applications and consequently require the inclusion of heat transfer enhancers. This research aims to investigate the potential enhancement of circular fins on intensifying the PCM thermal response in a vertical triple-tube casing. Fin arrays of non-uniform dimensions and distinct distribution patterns were des
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