For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio

Background: Postoperative pain is one of the main complications following impacted mandibular third molar (IMTM) surgery. Objectives: The aim of this study was to assess the effect of the local application of bupivacaine on reducing early postoperative pain following IMTM surgery. Material and methods: A prospective, single-blinded, randomized controlled study was conducted on 40 patients who had undergone the surgical removal of an IMTM under local anesthesia. In the study group (n = 20), absorbable gelatin sponge (AGS) soaked in 3 mL of 0.5% plain bupivacaine hydrochloride was locally applied in the post-extraction socket. In the control group (n = 20), AGS soaked in 3 mL of normal saline was used. Pain intensity was assessed using a pa

The study was carried out during the 2022 agricultural season in the greenhouses belonging to the-College of Agricultural-Al-Ramadi, the study aimed to investigate the efficacy of alcoholic extract of Solanum eleaegnifolium, potassium silicate and ungicide Previcur Energy in normal and nano formula to control downy mildew disease on cucumber crops caused by the fungus Pseudoperonospora cubensis. The results showed that the normal potassium silicate treatment completely prevented the disease during the length of the season, with an infection severity rate of 0.00%, compared to infection with artificial contamination of 45.90%, followed by the treatment of nano fungicide 4.60%. While the treatments of alcoholic extract and nano of nightshade

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

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 information required for construction quantities surveying is not only generated by various participants in different construction phases but also stored in different forms including graphics, text, tables, or various combinations of the three. To report a bill of quantities (BOQ), the project manager has to continuously excerpt information from various resources and record it on papers. Without adequate staff and time, this repetitive and tedious process is difficult for the project manager to handle properly and thus reduces the effectiveness and the accuracy of the quantities surveying process which creates problems during the design, tender, and construction supervision of construction projects for designers and contractors pract

Abstract

Agricultural Bank is an important source of funding Specialist His role in lending to farmers, it imposes a great job in providing the necessary head for any developmental process in the agricultural sector money. The ACB of ancient Iraqi banks, and that because of its importance to the advancement of the national economy and contribute to the development and regulation of the economic sector through the support and the assignment of the Iraqi agricultural sector in various agricultural activities because it is responsible

for the process of granting agricultural loans to farmers bank.

The aim of the internal control in the agricultural banks to

We report on using a CO₂ (10.6 µm) laser to debond the lithium disilicate veneers. Sixty-four sound human premolar teeth and 64 veneer specimens were used in the study. The zigzag movement via CO₂ laser handpiece along with an air-cooled jet to prevent temperature elevation above the necrosis temperature limit (5.5 C°) was applied. The optimal deboning irradiation time was super-fast, at about 5 seconds at 3 Watt CO₂ laser power. It is 20 times less than any previously published work for veneers debonding. The enamel beneath the debonded veneers has been assessed by atomic force microscopy (AFM) and shear stress technique as criteria for the easiness of debonding. The

The current study aimed to ascertain the levels of matrix metalloproteinase-12 (MMP-12) and Lysyl oxidase (LOX) in osteoporosis patients and their correlation with alkaline phosphatase (ALP), magnesium (Mg), vitamin D (Vit D), calcium (Ca), phosphorus (P), and T-score %. 110 participants recruited from Baghdad Teaching Hospital, Iraq, were enrolled in this study from November 2019 to March 2020). The participants were divided into two groups: Group 1 comprised 60 osteoporotic women and group 2 consisted of 50 healthy women. (MMP and LOX) were estimated using a quantitative enzyme-linked immunosorbent assay (ELISA. The results showed significant differences in serum LOX, age, ALP, Mg, and T-score %, while no significant differences i