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.

Nuclear emission rates for nucleon-induced reactions are theoretically calculated based on the one-component exciton model that uses state density with non-Equidistance Spacing Model (non-ESM). Fair comparison is made from different state density values that assumed various degrees of approximation formulae, beside the zeroth-order formula corresponding to the ESM. Calculations were made for 96Mo nucleus subjected to (N,N) reaction at Emax=50 MeV. The results showed that the non-ESM treatment for the state density will significantly improve the emission rates calculated for various exciton configurations. Three terms might suffice a proper calculation, but the results kept changing even for ten terms. However, five terms is found to give

Rock engineers widely use the uniaxial compressive strength (UCS) of rocks in designing
surface and underground structures. The procedure for measuring this rock strength has been
standardized by both the International Society for Rock Mechanics (ISRM) and American Society
for Testing and Materials (ASTM), Akram and Bakar(2007).
In this paper, an experimental study was performed to correlate of Point Load Index ( Is(50))
and Pulse Wave Velocity (Vp) to the Unconfined Compressive Strength (UCS) of Rocks. The effect
of several parameters was studied. Point load test, Unconfined Compressive Strength (UCS) and
Pulse Wave Velocity (Vp) were used for testing several rock samples with different diameters.
The predicted e

An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

This paper provides an attempt for modeling rate of penetration (ROP) for an Iraqi oil field with aid of mud logging data. Data of Umm Radhuma formation was selected for this modeling. These data include weight on bit, rotary speed, flow rate and mud density. A statistical approach was applied on these data for improving rate of penetration modeling. As result, an empirical linear ROP model has been developed with good fitness when compared with actual data. Also, a nonlinear regression analysis of different forms was attempted, and the results showed that the power model has good predicting capability with respect to other forms.

In this paper, chip and powder copper are used as reinforcing phase in polyester matrix to form composites. Mechanical properties such as flexural strength and impact test of polymer reinforcement copper (powder and chip) were done, the maximum flexural strength for the polymer reinforcement with copper (powder and chip) are (85.13 Mpa) and (50.08 Mpa) respectively was obtained, while the maximum observation energy of the impact test for the polymer reinforcement with copper (powder and chip) are (0.85 J) and (0.4 J) respectively  

Objective: The study aimed to assess the postoperative nurses' intervention for the patients with laparoscopic
cholecystectomy and to determine the relationship between Nurses' interventions and their demographic
characteristics.
Methodology: Quantitative design (a descriptive study) was started from 20th November 2012 up to 1st
September 2013. Non-probability (purposive sample) of (50) nurses, who were working in surgical wards, were
selected from Baghdad teaching hospitals (Baghdad Teaching Hospital, Digestives System and Liver Teaching
Hospital, AL-Kindy Teaching Hospital, and AL-Kadhimiyia Teaching Hospita). The data were collected through
the use of a constructed questionnaire, which consisted of two parts; the

Objective(s): assessment of  the health follow up and weight control for women with osteoporosis and find out the relationship between their health follow up and weight control and their socio-demographic characteristics.

Methodology: A descriptive study was conducted on women with osteoporosis for the period of September, 26^th 2020 to Jun, 20th 2021. Non- probability (convenient) sample of (70) women with osteoporosis selected from (5) Private Clinics for Joints and Fractures in Baqubah City. A questionnaire was designed though extensive review of literatures and it consists of three parts: the first part includes women’s socio demographic characteristics, the second part inclu