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 faujasite type Y zeolite catalyst was prepared from locally available kaolin. For prepared faujasite type NaY zeolite X-ray, FT-IR, BET pore volume and surface area, and silica/ alumina were determined. The Xray and FT-IR show the compatibility of prepared catalyst with the general structure of standard zeolite Y. BET test shows that the surface area and pore volume of prepared catalyst were 360 m2 /g and 0.39 cm3 /g respectively.
The prepared faujasite type NaY zeolite modified by exchanging sodium ion with ammonium ion using ammonium nitrate and then ammonium ion converted to hydrogen ion. The maximum sodium ion exchange with ammonium ion was 53.6%. The catalytic activity of prepared faujasite type NaY, NaNH4Y and NaHY zeolites
Abstract The purpose of this paper is to preparing small games for fifth graders. And to identify the impact of these small games in developing some concepts of traffic safety for fifth graders. The two researchers used the experimental method to solve the research problem, and the research community was identified with students. The fifth grade of primary school in the province of Baghdad and a sample was chosen from the private Baghdad Primary School, which numbered (60) male and female students. They were distributed equally into two groups by simple random method (experimental and control groups). As for the most important conclusions reached by the two researchers, it is the presence of an effect of small games in developing some conce
... Show MoreReactive Powder Concrete (RPC) is one of the most advanced recent high compressive strength concrete. This work explored the effects of using glass waste as a fractional replacement for fine aggregate in reactive powder concrete at levels of 0%, 25%, 50%, and 100%. Linear and mass attenuation coefficients have been calculated as a function of the sample's thickness and bremsstrahlung energy. These coefficients were obtained using energy selective scintillation response to bremsstrahlung having an energy ranging from (0.1-1.1) MeV. In addition, the half-value thickness of the samples prepared has been investigated. It was found that there is a reversal association between the attenuation coefficient and the energy of the bremsstrahlu
... Show MoreThe removal of turbidity from produced water by chemical coagulation/flocculation method using locally available coagulants was investigated. Aluminum sulfate (alum) is selected as a primary coagulant, while calcium hydroxide (lime) is used as a coagulant aid. The performance of these coagulants was studied through jar test by comparing turbidity removal at different coagulant/ coagulants aid ratio, coagulant dose, water pH, and sedimentation time. In addition, an attempt has been made to examine the relationship between turbidity (NTU) and total suspended solids (mg/L) on the same samples of produced water. The best conditions for turbidity removal can be obtained at 75% alum+25% lime coagulant at coagulant dose of 80 m
... Show MoreThis study was conducted in the botanical garden, Department of biology, College of Science/ Mustansiriyah University in from (15 February to 15 March, 2019) under the natural environmental conditions in the greenhouse in order to evaluate the effectiveness of parsley aqueous extract as a promoter for rooting. The study included the use of aqueous extract of a plant Parsley (Petroselinum crispum) extract was used in concentrations (1.25, 2.5 g / l), compare with IBA in concentration (100 mg / L) with dipping time 24 hour for all treatments. The cutting stems were included Rosmarinus officinalis, Nerium oleander, Olea europaea, Plumeria alba, Hibiscus rosa, Pelargonium graveolens, and Myrtus communis. The following measurements were
... Show MoreThe aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra without identity can be embedded into fuzzy normed algebra with identity and is an ideal in is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.
Abstract
The perpetuity of the Quranic discourse required being suitable for all ages.
Accordingly, the method of the Glorious Quran a pre request for the conscious
investigation and realization in order to detect the core of the texts, as the Quranic
discourse is considered a general address for the humanity as a whole. For this
reason, the progress of the concerned studies neceiated that it should cope with the
current development in the age requirements and its cultural changes within ages.
The texts of the Glorious Quran lightened the human reason as being the
Creator’s miracle for it is characterized by certain merits that makes it different from
poetry and prose. It is a unique texture in its rheto
... Show MoreThis work investigates the effect of the gas nitriding process on the surface layer microstructure and mechanical properties for steel 37, tool steel X155CrVMo12-1 and stainless steel 316L. Nitriding was conducted at a temperature of 550 °C for 2 hours during the first stage and at 750 °C for 4 hours during the second stage. SEM and X-ray diffraction tests were performed to evaluate the microstructural features and the major phases formed after surface treatment. SEM and X-ray diffraction tests were performed to assess the microstructural features and the primary phases formed after surface treatment. The new secondary precipitates were identified as γ′-Fe4N, ε (Fe2–3N), and α-Fe, exhibiting an uneven chain-like pattern wit
... Show MoreRadial density distribution function of one particle D(r1) was calculated for main orbital of carbon atom and carbon like ions (N+ and B- ) by using the Partitioning technique .The results presented for K and L shells for the Carbon atom and negative ion of Boron and positive ion for nitrogen ion . We observed that as atomic number increases the probability of existence of electrons near the nucleus increases and the maximum of the location r1 decreases. In this research the Hartree-fock wavefunctions have been computed using Mathcad computer software .