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.

 A mixture model is used to model data that come from more than one component. In recent years, it became an effective tool in drawing inferences about the complex data that we might come across in real life. Moreover, it can represent a tremendous confirmatory tool in classification observations based on similarities amongst them. In this paper, several mixture regression-based methods were conducted under the assumption that the data come from a finite number of components. A comparison of these methods has been made according to their results in estimating component parameters. Also, observation membership has been inferred and assessed for these methods. The results showed that the flexible mixture model outperformed the

Abortion is categorized as the termination of conception caused by the failure or removal of the embryo from the uterus before the conclusion of pregnancy. Microorganisms and genetic factors are two of the many factors associated with abortion. Cytomegalovirus is a widespread congenital virus infection pathogen that affects a wide variety of people. The prothrombin gene is one of the essential causes that trigger blood clotting and the function of abortion women, therefore the aim of the study is to detect and associate Cytomegalovirus and prothrombin gene mutation (Gene ID: 14061 in NCBI) with abortion through genetic and immunological methods. Five ml of whole blood was collected from an intravenous puncture and divided into two tubes,

Objective: to evaluate body image and depression symptoms of children with precocious puberty, and find out association between children`s sociodemographic characteristics and their body image and depression signs. Methodology: A cross sectional study, sample of (80) child from both gender, > 7 years were included due to their ability to express their own feeling, diagnosed with precocious puberty, attending out-patient endocrine clinics at pediatric hospitals in Baghdad city. Data collected, during the period from May to November 2018. Consent form has taken from children and their guardians to participate in study. Child body image scale (CBIS) was used to evaluate children body satisfaction (1) and Mood and feeling questionnaire (M

A novel series of mixed-ligand complexes of the type, [ML1(L2)3]Clx [M= Cr(III), Fe(III), Co(II),Ni(II), Cu(II), Cd(II) and Hg(II), n = 2, 3], was synthesized using Schiff base (HL1) as main ligand, nicotinamide (L2) as secondary ligand, and the corresponding metal ions in 1:3:1 molar ratio. The main ligand, HL1 was prepared by the interaction of ampicillin drug and 4-chlorobenzophenone. The synthesized mixed ligand complexes were characterized by elemental analysis, UV-Vis, FT-IR,1H-NMR,13C-NMR and TG/DTG studies. In the mixed-ligand complexes, the Schiff base ligand, HL1 showed coordination to the central metal ion in tridentate manner via azomethine nitrogen, β-lactam ring oxygen and deprotonated carboxylic oxygen atoms, whereas the sec

The electron correlation for inter-shells (1s 2p), (1s 3p) and (1s 3d) was described by the inter-particle radial distribution function f(r12). It was evaluated for Li-atom in the different excited states (1s2 2p), (1s2 3p) and (1s2 3d) using Hartree-Fock approximation (HF). The inter particle expectation values for these shells were also evaluated. The calculations were performed using Mathcad 14 program.

The use of Bayesian approach has the promise of features indicative of regression analysis model classification tree to take advantage of the above information by, and ensemble trees for explanatory variables are all together and at every stage on the other. In addition to obtaining the subsequent information at each node in the construction of these classification tree. Although bayesian estimates is generally accurate, but it seems that the logistic model is still a good competitor in the field of binary responses through its flexibility and mathematical representation. So is the use of three research methods data processing is carried out, namely: logistic model, and model classification regression tree, and bayesian regression tree mode

This research includes the study of dual data models with mixed random parameters, which contain two types of parameters, the first is random and the other is fixed. For the random parameter, it is obtained as a result of differences in the marginal tendencies of the cross sections, and for the fixed parameter, it is obtained as a result of differences in fixed limits, and random errors for each section. Accidental bearing the characteristic of heterogeneity of variance in addition to the presence of serial correlation of the first degree, and the main objective in this research is the use of efficient methods commensurate with the paired data in the case of small samples, and to achieve this goal, the feasible general least squa

In this research weights, which are used, are estimated using General Least Square Estimation to estimate simple linear regression parameters when the depended variable, which is used, consists of two classes attributes variable (for Heteroscedastic problem) depending on Sequential Bayesian Approach instead of the Classical approach used before, Bayes approach provides the mechanism of tackling observations one by one in a sequential way, i .e each new observation will add a new piece of information for estimating the parameter of probability estimation of certain phenomenon of Bernoulli trials who research the depended variable in simple regression  linear equation. in addition to the information deduced from the past exper

The consensus algorithm is the core mechanism of blockchain and is used to ensure data consistency among blockchain nodes. The PBFT consensus algorithm is widely used in alliance chains because it is resistant to Byzantine errors. However, the present PBFT (Practical Byzantine Fault Tolerance) still has issues with master node selection that is random and complicated communication. The IBFT consensus technique, which is enhanced, is proposed in this study and is based on node trust value and BLS (Boneh-Lynn-Shacham) aggregate signature. In IBFT, multi-level indicators are used to calculate the trust value of each node, and some nodes are selected to take part in network consensus as a result of this calculation. The master node is chosen