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.

One of the most important virulence factors in Pseudomonas aeruginosa is biofilm formation, as it works as a barrier for entering antibiotics into the bacterial cell. Different environmental and nutritional conditions were used to optimize biofilm formation using microtitre plate assay by P. aeruginosa. The low nutrient level of the medium represented by tryptic soy broth (TSB) was better in biofilm formation than the high nutrient level of the medium with Luria Broth (LB). The optimized condition for biofilm production at room temperature (25 °C) is better than at host temperature (37 °C). Moreover, the staining with 0.1% crystal violet and reading the biofilm with wavelength 360 are considered essential factors in

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

Aim: surface modification of titanium using fiber laser 1064 nm to enhance the bond strength to resin cement. Material and Methods: thirty titanium discs of 0.6 cm x 0.3 cm (diameter and thickness respectively) were categorized after preparation into three groups (n=10) as follows: control group with no surface treatment and two test groups were treated with fiber laser after estimation the appropriate parameters in the pilot study which are 81 ns pulse duration, 30,000 Hz frequency, 50 µm spot size and 10,000 mm/s scanning speed and different average power values (10 W and 20 W) depending on the tested group. Titanium discs surface characterization was performed by scanning electron microscope (SEM), a

Nano TiO₂ thin films on glass substrates were prepared at a constant temperature of (373 K) and base vacuum (10_-3 mbar), by pulsed laser deposition (PLD) using Nd:YAG laser at 1064 nm wavelength. The effects of different laser energies between (700-1000)mJ on the properties of TiO₂ films was investigated. TiO₂ thin films were characterized by X-ray diffraction (XRD) measurements have shown that the polycrystalline TiO₂ prepared at laser energy 1000 mJ. Preparation also includes optical transmittance and absorption measurements as well as measuring the uniformity of the surface of these films. Optimum parameters have been identified for the growth of high-quality TiO₂ films

Results showed that the optimum conditions for production of inulunase from isolate Kluyveromyces marxianus AY2 by submerged culture could be achieved by using inulin as carbon source at a concentration of 2% with mixture of yeast extract and ammonium sulphate in a ratio of 1:1 in a concentration of 1% at initial pH 5.5 after incubation for 42 hours at 30ºC.

The present study was conducted to determine the optimum conditions required for lipase enzyme activity extracted from germinated sunflower seeds, including temperature, pH, agitation, time of incubation, enzyme concentration, substrate type, and concentrations of mineral salts and EDTA. Optimum pH, temperature and time of incubation required for lipase stability were also determined. The results showede optimum lipase activity (3.251U/ml) wasund at 30 ÌŠC and pH 7 after 20 minutes of incubation when using 1 ml lipase enzyme with 0.02 ml of CaCl2 (10 mM) at 100 rpm of agitation and in the presence of olive oil as the substrate for enzyme reaction. EDTA appeared to have inhibitory effects, while Ca+2 and Mg+2 have stimulatory effec

This paper presents the effect of Cr doping on the optical and structural properties of TiO2 films synthesized by sol-gel and deposited by the dip- coating technique. The characteristics of pure and Cr-doped TiO2 were studied by absorption and X-ray diffraction measurement. The spectrum of UV absorption of TiO2 chromium concentrations indicates a red shift; therefore, the energy gap decreases with increased doping. The minimum value of energy gap (2.5 eV) is found at concentration of 4 %. XRD measurements show that the anatase phase is shown for all thin films. Surface morphology measurement by atomic force microscope (AFM) showed that the roughness of thin films decrease with doping and has a minimum value with 4 wt % doping ratio.

Background:In this study,TiO2 layer was thermally grown as a diffusion barrier on CP Ti substrate prior to electrophoretic deposition of HA coatings, to improve the coating’s compatibility also macro and micro pores in nano Hydroxyapatite dual coatings were created and their effect on the bond strength between the bone and implant was evaluated. Materials and methods: Electrophoretic Deposition technique (EPD) was used to obtain coatings for each one of four types of Hydroxyapatite(HA)on CP Ti screws (micro HA, nano HA, dual nano HA with micro pores, dual nano HA with macro pores) where carbon particles used as fugitive material to be removed by thermal treatment to create porosity.For examination of the changes occurred on the subs