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.

PVA, Starch/PVA, and Starch/PVA/sugar samples of different
concentrations (10, 20, 30 and 40 % wt/wt) were prepared by casting
method. DSC analysis was carried; the results showed only one glass
transition temperature (Tg) for the samples involved, which suggest
that starch/PVA and starch/PVA/sugar blends are miscible. The
miscibility is attributed to the hydrogen bonds between PVA and
starch. This is in a good agreement with (FTIR) results. Tg and Tm
decrease with starch and sugar content compared with that for
(PVA). Systematic decrease in ultimate strength, due to starch and
sugar ratio increase, is attributed to (PVA), which has more hydroxyl
groups that made its ultimate strength higher than that for

The experimental study showed the use of closed cavity wall (the thickness of the cavity 5cm) made a percentage reduction in the cooling load caused by heat gain from the wall by (21.5 %) compared with the conventional wall. also the thermal resistance of the closed cavity was an average (0.2 m².^oC/W).

The experimental results of the study showed that the use of closed cavity wall reduced the average temperature of the inner surface of the wall during the day, and that the reduction was an average (0.45 ^oC)  when compared with the conventional wall , as well as the use of closed cavity wall reduced the temperature difference range of the inner surface of the wall during the day, and that the

In this paper, investigates the biosynthesis of gold nanoparticles (AuNPs) by biochemical method using Myrtus communis leaves extract as reducing agent and Chloroauric acid (HAuCl4) as precursors. X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and FTIR were used in addition to UV-visible spectroscopy (UV) in order to characterize the AuNPs. The biosynthesized AuNPs exhibited inhibitory effects on alpha amylase and alkaline phosphatase in sera of patient with type 2 Diabetes Miletus and the sera of healthy control subjects; the inhibition percentage with alpha amylase was 72 % and 45 % for patient and control group respectively. Oral consent obtained from the most of patients and healthy subjects before them being under

Background: the primary objective for many researches carried out in dental implantology was to reduce the period needed for functional implant loading, simvastatin (cholesterol lowering medication) had many pleiotropic effects, one of which was increasing bone density around titanium implants (1) and subsequently establishing faster osseointegrated dental implants (2,3). This study aims to reduce the period of time needed to establish secondary stability of dental implant measured in ISQ (Implant Stability Quotient) by investigating the effect of orally administered simvastatin on bone. Materials and methods: simvastatin tablets (40mg/day for three months) were administered orally for 11 healthy women aged (40-51) years old who received 1

been taken at room temperature down to liquid nitrogen temperature (77K). Polar and nonpolar solvents have been used to study the solvent effect on the absorption and fluorescence spectra of solute molecules. Some of the spectroscopic parameters have been determined as functions of solvent polarity and temperature. The results indicate that the band width FWHM increases with increasing the solvent polarity and temperature, while the peak emission cross section decreases with increasing of solvent polarity and decreases with increasing the temperatures. Clear vibrational structure spectra of benzoanthracene molecules have been observed in Nonane and Hexane solvents at 77K.

Background: Apicoectomy and retrograde filling is indicated when conventional endodontic treatment is impossible or failed to achieve apical seal. The aim of this study was to evaluate the effect of ER: YAG laser on apical microleakage. Materials and Methods: Sixty extracted single-rooted teeth were used in this study. The roots were divided into six groups. Group 1: apicoectomy by fissure bur, and apical cavities prepared by round bur, then cavities were filled with MTA. Group 2: the roots preparations and fillings were the same as group 1, then the apical areas were treated by Er:YAG Laser. Group 3: apicoectomy by fissure bur, and apical cavities prepared by ultrasound retrotip and cavities were filled with MTA. Group 4: the roots prepara

In this paper, SiO2 nanoparticles thin films were synthesised at different PH values of solution by sol gel method at fixed temperature (25oC) and molar ratio (R =H2O/precursor) of (Tetra Ethyl Ortho Silicate) TEOS as precursor at (R=1). The structure and optical properties of the thin films have been investigated. All thin films were tested by using X-RAY diffraction. All X-RAY spectrum can be indexed as monoclinic structure with strong crystalline (110) plane. The morphological properties of the prepared films were studied by SEM. The results indicate that all films are in nano scale and the particle size around (19-62) nm .The size of silica particles increases with increasing PH value of solution where both the rate of hydrolysis and

The Karolinka earth-fill dam was constructed between 1977 and 1984 on the Stanovnice river above the town of Karolinka in the region of Vsetínsko in Czech Republic. Because of leakage on the downstream dam face due to technological indiscipline when filling dam layers during the dam construction stage, there were some steps to improve state dam safety. The final rehabilitation is to construct the diaphragm walls from self-hardening cement-bentonite suspension along the length of the dam. In addition to connecting the gallery and abutment (2 × 25 m long) by using jet piles. The article presents numerical modeling of safety factor evaluation associated with the state of the dam body and foundation; before, and after seal

Background: Relapse of previously moved teeth, is major clinical problem in orthodontics with respect to the goals of successful treatment. This study investigated the effect of orthodontic relapse on the proliferation of fibroblast and epithelial rests of Malassez cells in periodontal ligament of rat molars. Materials and Methods: Sixteen ten-week- old male Wister rats were randomly divided into four groups composed of four animals each: Group I received no orthodontic force (control). In both Group II and Group III, uniform standardized expansive springs were used for moving the maxillary first molars buccally for periods of one and three weeks respectively. The spring initially generated an average expansive force of 20 g on each side.