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 Nuclear structure of 110-116Cd isotopes was studied theoretically in the framework of the interacting boson model of IBM-l and IBM-2. The properties of the lowest mixed symmetry states such as the 1+, 2+ and 3+ levels produced by the IBM-2 model in the vibrational-limit U(5) of Cd - isotopes are studied in details. This analysis shows that the character of mixed symmetry of 2+ is shared between and states in 110-114Cd – isotopes, the large shar goes to s, while in isotope, the state is declared as a mixed symmetry state without sharing. This identification is confirmed by the percentage of F-spin contribution. The electromagnetic properties of E2 and Ml operators were investigated and the results were analyzed. Various

Money matters exert a considerable influence on man’s life-style, social
rank and his relationship with other people. This paper aims at exploring the impact
of money matters on the characters’ inner feelings, social status, and personal
relationships in Muriel Spark’s modern novel The Ballad Of Peckham Rye. This
paper aspires to show that Spark’s subtle portrayal of characters reveals the
dominance of money matters over human and social relationships.
Muriel Spark ( 1918-2006) is a modern Scottish novelist whose wit and
detached sense of humour has brought her prolific body of both popular and critical
acclaim. Spark is interested not in building suspense but in exploring the moral
significance of the

The study included general survey of some districts of Iraq in order to determinate new distribution areas for 33 species of the genus salvia L. ,new collections obtained , new locations for many species recorded. Observed specimens in most Iraqi herbaria were studies and identified. ,the flowering period were also studied

The study included general survey of some districts of Iraq in order to determinate new distribution areas for 33 species of the genus salvia L. ,new collections obtained , new locations for many species recorded. Observed specimens in most Iraqi herbaria were studies and identified. ,the flowering period were also studied

The process of digital transformation is considered one of the most influential matters in circulation at the present time, as it seeks to integrate computer-based technologies into the public services provided by companies or institutions. To achieve digital transformation, basics and points must be established, while relying on a set of employee skills and involving customers in developing this process. Today, all governments are seeking electronic transformation by converting all public services into digital, where changes in cybersecurity must be taken into account, which constitutes a large part of the priorities of nations and companies. The vulnerability to cyberspace, the development of technologies and devices, and the use

The chamomile is one of the most important medicinal plants recommended for treatment of asthma and some respiratory system diseases. This research was designed to research the effects of aqueous extract of chamomillarecutita on histological structure of Diaphragm of albino mice. The study included 40 male albino mice Musmusculus, their age ranged from (5-7) weeks.The mices were divided randomly to 5 groups and oral administered with 1 ml every day for 10 days:- First Group G1: consider as control group and treated with normal saline,Second Group G2: was treated with aqueous extract of chamomile with concentration of 3 gm /100 ml D.W, Third Group G3: was treated with aqueous extract of chamomile with concentration of 5 gm /100 ml D.W.Fourth

Background: The aim of this in vitro study was to evaluate and compare the effect of preheating microleakage among three different filler size composites which include Filtek^tm Z250 micro hybrid, Z250^xt Nano hybrid and nanocomposite Z350^xt.  in Class II cavity preparation .

Materials and methods: sixty maxillary first premolars were prepared with class II cavities. Samples were divided into three groups according to material used    group A (FiltekZ250 micro hybrid). Group B(Z250^xt Nano hybrid). Group C (nanocomposite Z350^xt)and each group divided into two subgroups of ten teeth according to temperature of  composite: