The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
The study tagged: (The aesthetics of balance and its relationship to the design of the body of the industrial product) discussed the role of balance in the design of industrial products of different shapes, colors and sizes, as well as their function. Based on the research problem that was determined by the following question: What is the relationship between balance and the design of the body of the industrial product? The aim of the research is to: reveal the statement of the effectiveness of the balance in the design of the industrial product body.
The study was defined in four chapters: in the first chapter, a problem, the importance, and the aim of the research were presented. The second chapter contained the theoretical framewor
In this investigation, Rayleigh–Ritz method is used to calculate the natural frequencies of rectangular isotropic and laminated symmetric and anti-symmetric cross and angle ply composite plate with general elastic supports along its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be applied to various boundary conditions. Several numerical examples are studied to demonstrate the accuracy and convergence of the current s
... Show MoreCollagen triple helix repeat containing-1 (CTHRC1) is an essential marker for Rheumatoid Arthritis (RA), but its relationship with pro-inflammatory, anti-inflammatory, and inflammatory markers has been scantily covered in extant literature. To evaluate the level of CTHRC1 protein in the sera of 100 RA patients and 25 control and compare levels of tumour necrosis factor alpha (TNF-α), interleukin 10 (IL-10), RA disease activity (DAS28), and inflammatory factors. Higher significant serum levels of CTHRC1 (29.367 ng/ml), TNF-α (63.488 pg/ml), and IL-10 (67.1 pg/ml) were found in patient sera as compared to that in control sera (CTHRC1 = 15.732 ng/ml, TNF-α = 33.788 pg/ml, and IL-10 = 25.122 pg/ml). There was no significant correlation be
... Show MoreAn efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT
... Show MoreCurrent numerical research was devoted to investigating the effect of castellated steel beams without and with strengthening. The composite concrete asymmetrical double hot rolled steel channels bolted back to back to obtain a built-up I-shape form are used in this study. The top half part of the steel is smaller than the bottom half part, and the two parts were connected by bolting and welding. The ABAQUS/2019 program employed the same length and conditions of loading for four models: The first model is the reference without castellated and strengthening; the second model was castellated without strengthened; the third model was castellated and strengthened with reactive powder concrete encased in the
... Show MoreThe utilization and incorporation of glass fiber-reinforced plastics (GFRP) in structural applications and architectural constructions are progressively gaining prominence. Therefore, this paper experimentally and numerically investigates the use of GFRP I-beams in conjunction with concrete slabs to form composite beams. The experimental design incorporated 2600 mm long GFRP I-beams which were connected compositely to concrete slabs with a 500 mm width and 80 mm thickness. The concrete slabs are categorized into two groups: concrete slabs cast using normal-strength concrete (NSC), and concrete slabs prepared using high-strength concrete (HSC). Various parameters like the type of concrete (normal and high-strength concrete), type of
... Show MoreBackground: Pyogenic granuloma is a hyperplastic benign tumor. The most common intra-oral site is marginal gingiva. It is often occurred in the second decade of life, it has a strong tendency to recur after simple excision.
The aim of study: to evaluate the therapeutic advantages of diode laser (810-980 nm) in intraoral Pyogenic granuloma management.
Materials and method: A total of 28 patients (14 men and 14 females) were enrolled in this study and had their pyogenic granuloma surgically removed using a diode laser. All of the patients were given local anesthetic and went through the identical surgical procedure (cartridge containing 1 percent lidocaine with epinephrine 1:
... Show MoreBackground: Trauma to the anterior teeth is a common injury in young children. Themaxillary incisors being the most affected. Although root fractures are rare, theydo occur and were previously and often considered hopeless and were extracted.The time between the injury and the initiation of treatment, level of the fractureline, and stage of root development are some criteria to be considered whenchoosing a treatment approach for a complicated tooth fracture. This case reportdescribes the management of a traumatized immature maxillary central incisorwith Elise class IV fracture with vertical oblique subgingival fracture of the root.Materials and method: Apexification was carried out using biodentine followed byremoval of the fracture
... Show MoreIn this study, Zinc oxide nanostructures were synthesized via a hydrothermal method by using zinc nitrate hexahydrate and sodium hydroxide as a precursor. Three different annealing temperatures were used to study their effect on ZnO NSs properties. The synthesized nanostructure was characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), Atomic force microscope (AFM), and Fourier Transform Infrared Spectroscopy (FTIR). Their optical properties were studied by using UV -visible spectroscopy. The XRD analysis confirms that all ZnO nanostructures have the hexagonal wurtzite structure with average crystallite size within the range of (30.59 - 34
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