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.

Background : The hepatopulmonary syndrome (HPS) is defined as the triad of liver disease, arterial deoxygenation, and pulmonary vascular dilatation. The reported prevalence of HPS in cirrhotic patients varies between 5% -17.5%.Objective : To estimate the prevalence of hepatopulmonary syndrome among patients with chronic liver disease and portal hypertension and to study the correlation between HPS and the severity of liver disease.Patients and methods : Thirty patients were studied for the presence of HPS using transthoracic contrast echocardiography for detection of pulmonary vasodilatation. Arterial oxygen saturation (SaO2) was determined in erect and supine position using a pulse oximeter , (SaO2 ≤ 92 % in supine position and/or a d

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

1-(4-amino-3-(benzo[d]thiazol-2-yldiazenyl)phenyl)ethanone has been synthezied by reaction the diazonium salt of 2-aminobenzothiazole with 4-aminoacetophenone. Specroscopic studies ( FTIR,UV-Vis, 1H and 13CNMR) and microelemental analysis (C.H.N.S.O) are use to identified of the azo ligand. Metal chelates of some transition metals were performed as well depicted. Complexes were identified using atomic absorption of flame, elemental analysis, infrared and UV-Vis spectral process as well conductivity and magnetic quantifications. Nature of compounds produced have been studied followed the mole ratio and continuous contrast methods, Beer's law followed during a concentration scope (1×10-4 - 3×10-4 mol/L). height molar absorbtivity of compoun

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 Purpose of this research is a comparison between two types of multivariate GARCH models BEKK and DVECH to forecast using financial time series which are the series of daily Iraqi dinar exchange rate with dollar, the global daily of Oil price with dollar and the global daily of gold price with dollar for the period from 01/01/2014 till 01/01/2016.The estimation, testing and forecasting process has been computed through the program RATS. Three time series have been transferred to the three asset returns to get the Stationarity, some tests were conducted including Ljung- Box, Multivariate Q and Multivariate ARCH to Returns Series and Residuals Series for both models with comparison between the estimation and for

   Infection with Trichomonas vaginalis and its relation to some diseases have lately had much attention.  The objective of this study was to assess the infection rate of T. vaginalis and its relation to pelvic inflammatory diseases, infertility, and vaginosis. The study also assessed some demographic, clinical, and immunological parameters in women infected with T. vaginalis. The study included 160 non-pregnant married women who attended some private clinics and public hospitals in Baghdad from October 2020 to February 2021. All participants had symptoms of vaginal discharge only or vaginal discharge with lower abdominal pain. The participants were divided into an infertility group (n = 61) and fertility group (n = 99). The participant