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.

Background: Secretory Immunoglobulin A (SIgA) is a subclass of Immunoglobulin A (IgA), It is an antibody that plays an important role in mucosal immunity. It is the main immunoglobulin found in mucous secretions from mammary glands, tear glands and salivary glands, every pathologic process in the body involves the immune system, and periodontal inflammation is one of them and is not an exception. Material and methods: this study was consisted of 60 healthy male participants of an age ranged between (35-50) years old ; 25 of them with generalized moderate chronic periodontists(Clinical Attachment Loss equal to 3-4mm at ≥ 30% of the sites; 20 participants with plaque induced gingivitis and 15 participants had clinically healthy pe

Magnetic nanoparticles (MNPs) of iron oxide (Fe₃O₄) represent the most promising materials in many applications. MNPs have been synthesized by co-precipitation of ferric and ferrous ions in alkaline solution. Two methods of synthesis were conducted with different parameters, such as temperature (25 and 80 ̊C), adding a base to the reactants and the opposite process, and using nitrogen as an inert gas. The product of the first method (MNPs-1) and the second method (MNPs-2) were characterized by x-ray diffractometer (XRD), Zeta Potential, atomic force microscope (AFM) and scanning electron microscope (SEM). AFM results showed convergent particle size of (MNPs-1) and (MNPs-2) with (86.01) and (74.14)

A detailed experimental study was devoted to the anodic oxidation of oxalic acid using manganese dioxide rotating cylinder anode with the objective to evaluate in a systematic way the effect on the oxalic acid oxidation process of several relevant parameters, including the presence of sodium chloride, the current density (J), the rotation speed, the temperature, and the initial concentration of oxalic acid. Thin manganese dioxide film on graphite substrate has been prepared by electrochemical oxidation from MnSO4-H2SO4 electrolyte. The morphology of this electrode was investigated by XRD, SEM, EDS and AFM techniques. The results show that a firm γ-structure of MnO2 film on graphite rod can be obtained successfully. The results indicate tha

We explore the transform coefficients of fractal and exploit new method to improve the compression capabilities of these schemes. In most of the standard encoder/ decoder systems the quantization/ de-quantization managed as a separate step, here we introduce new way (method) to work (managed) simultaneously. Additional compression is achieved by this method with high image quality as you will see later.

The field of autonomous robotic systems has advanced tremendously in the last few years, allowing them to perform complicated tasks in various contexts. One of the most important and useful applications of guide robots is the support of the blind. The successful implementation of this study requires a more accurate and powerful self-localization system for guide robots in indoor environments. This paper proposes a self-localization system for guide robots.  To successfully implement this study, images were collected from the perspective of a robot inside a room, and a deep learning system such as a convolutional neural network (CNN) was used. An image-based self-localization guide robot image-classification system delivers a more accura

The book gives details about the healing power of love

The sol-gel route using an agar gel with calcium nitrate and phosphate solution as starting materials for producing hydroxyapatite (HAP). The product formed were needle like, zigzag and straight fibres. The fibrous products on sintering transformed into stoichiometric HAP with a biological Ca/P ratio of 1.67. The influences of pH, temperature, nature of base and phosphate solution on the growth of fibrous HAP were studied. The pH of the solution was found to greatly influence the growth rate and morphology of the resultant product. The optimum gel temperature was found to be 60oC and sintering temperature of 900oC for 1 hour. The crystalline, thermal, functional and morphological characteristics of the fibrous HAP were investigated.

Lignin has emerged as a promising asphalt binder modifier due to its sustainable and renewable nature, with the potential to improve flexible pavement performance. This study investigates the use of Soda Lignin Powder (SLP), derived from Pinus wood sawdust via alkaline treatment, as an asphalt modifier to enhance mixture durability. SLP was characterized using Fourier Transformation Infrared Spectroscopy (FTIR), X-ray Diffraction (XRD), and Scanning Electron Microscopy with Energy Dispersive X-ray Analysis (SEM/EDX), revealing significant changes in its chemical structure post-extraction. These analyses showed the presence of phenolic units, including hydroxyphenyl propane, syringyl, and guaiacyl units. The morphology of SLP was identified