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.

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

Current search aims to identify the creative thinking of the kindergarten teachers and
solving professional problems among kindergarten teachers skills, and whether the level of
creative thinking in solving professional problems, according on marital status years of
service academic achievement of teachers as well as to identify the correlation between the
two variables the current sample consisted of (300) teachers to achieve the objectives of the
stndy , the researcher used two measures, one to measure creative thinking and the other to
measure the solution to the problems of professional kindergarten teachers skills. It has been
shown. validity and reliability of the two measures. The present stndy aims to identif

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.

Periodontitis is one of the most prevalent bacterial diseases affecting man with up to 90% of the global population affected. Its severe form can lead to the tooth loss in 10-15% of the population worldwide. The disease is caused by a dysbiosis of the local microbiota and one organism that contributes to this alteration in the bacterial population is Prophyromonas gingivalis. This organism possesses a range of virulence factors that appear to contribute to its growth and survival at a periodontal site amongst which is its ability to invade oral epithelial cells. Such an invasion strategy provides a means of evasion of host defence mechanisms, persistence at a site and the opportunity for dissemination to other sites in the mouth. However, p

The aims of this research is to investigate : The nature of academic specialization of the officials of Baghdad University Presidency , Level of job performance of the officials of Baghdad University Presidency through job performance appraisal form per year , Differences in the levels of job performance of the officials of Baghdad university presidency , according to the variables (sex , academic specialization , the current work , the duration between the date of graduation and the date of appointment , service duration) , The relationship of academic specialization of the officials of Baghdad university presidencywith their job performance . The researcher has followed the analytical descriptive mode to achieve the aims of this resear

       Staphylococcus aureus is a common pathogenic agent due to its ability to cause various types of infections, ranging from mild skin infections to sever systemic diseases. One of the most virulence factors of this bacterium is its ability to from biofilms on solid surfaces by anchoring the planktonic cells and by producing a protective layer of extra polymeric substances. Biofilm formation is controlled through many genes. The most important ones are icaA and icaD. Dentures are prosthetic devices that are made of different materials to replace lost teeth. The aim of this study is to examine the ability of different types of denture materials to support the biofilm formation of S. aureus at phenotypic level by detecting ba

In the present work, the ternary compound MgxZn7-x O7Wurtzoid with variable Zn and Mg contents was analyzed using density functional theory with B3LYP 6-311G**basis set. The electronic and vibrational properties of MgxZn7-xO7 wurtzoids, were investigated, including energy gaps, bond lengths, spectral properties, such like infrared spectra and Raman. IR and Raman spectra were compared with experimental longitudinal optical modes frequency results. The theoretical results agree well with experiments and previous data. It has been found that the energy gap is increasing with the increased Mg concentration, and that the longitudinal optical position exposes a UV shift movement with an increase in the concentration.