In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

his analysis aims to establish Riemann-Liouville derivation andintegral operators regarding the recently suggested seven-parameter Mittag-Leffler function then investigates the corresponding special cases. In addition,certain notable results associated with those new operators have been dis-cussed

This paper presents a hybrid software copy protection scheme, the scheme is applied to
prevent illegal copying of software by produce a license key which is unique and easy to
generate. This work employs the uniqueness of identification of hard disk in personal
computer which can get by software to create a license key after treated with SHA-1 one way
hash function. Two mean measures are used to evaluate the proposed method, complexity
and processing time, SHA-1 can insure the high complexity to deny the hackers for produce
unauthorized copies, many experiments have been executed using different sizes of software
to calculate the consuming time. The measures show high complexity and short execution
time for propos

Background: The main drawback of soft lining materials was that they debonded from the denture base after a certain period of usage. Therefore, the purpose of this research was to determine the impact of oxygen and argon plasma treatment on the shear bonding strength of soft liners to two different kinds of denture base materials: conventional acrylic resin and high impact acrylic resin. Materials and Methods: Heat cure conventional and high impact acrylic blocks (40 for each group) were prepared. A soft liner connected the final test specimen of two blocks of each acrylic material. Shear bond strength (SBS) was assessed using universal testing machine. Additional blocks were also prepared for analyzing Vickers microhardness, contact ang

Background: Oral lichen planus (OLP) is a chronic immunologic disease. The etiology of OLP is unknown, viral antigens (for example EBV) have been proposed as etiologic agents. OLP may get transformation to malignancy so research on the presence of these in OLP lesions seems to be necessary. The aim of this study was to evaluate EBV expression immunohistochemically in OLP. Materials and Methods: Tissue specimens of 30 formalin fixed, paraffin-embedded tissue Blocks histologically diagnosed oral lichen planus was performed to evaluate EBV expression. Results: Expression of EBV was detected in epithelium of (46.6%) in the study samples in (OLP). no statistically significant correlation was found with clinical parameters except for a significan

Background: The aim of the present study is to evaluate the esthetic smile in sample of Iraqi adults and to assess the gender differences. Materials and Methods: 100 persons (50malesand 50 females had class I normal dental and skeletal selected for this study.Clinical examination and digital photograph with posed smile were performed for each individual. Six linear soft tissue parameters in each photograph using AutoCAD program 2011. Five visual and four quantitative evaluations of the smile were studied for eachsubject. The smile arch and index, buccal corridor spaces (BCSs) were studied.Descriptive statistics of the measurements were calculated. Independent student’s ttestswere used to evaluate the gender differences. Statistics: Desc

Aim: The study aimed to investigate the presence of the specific B1 gene T gondii in blood and milk samples from natural infected cattle and pregnant women (16-30 weeks) whose examination performed by the officers at the women's and children's Educational hospital in Al-Diwaniyah, Iraq. Materials and methods: A total of 150 serum samplings were collected analysed and scanned for Anti-T gondi antibodies (75 naturally-infected goats and 75 pregnant women with Toxoplasma). Polymerase chain reaction (PCR) was used to detect of B1(399pb) gene in 26 goat's blood samples and 7 samples from pregnant women. Results: A quick-test anti-cassette gondii results showed 26 positive samples of goats in a percentage of 34,666 percent, while a higher percent

Objectives: Dickkopf-1 (DKK-1) is WNT/b-catenin pathway antagonist which plays a detrimental role in the development of diabetic retinopathy (DR). This research aimed to assess serum DKK-1 levels in diabetic patients who have and have not developed DR and, compare them with the control subjects finding out whether we can use it as an indicator for DR early diagnosis and to find out which one of the widely used two groups of antidiabetic treatments had the greater effect on this biomarker and hence on the progression of DR. Methods: The study participants were divided into two subgroups: First, 70 patients (36 male, 34 female) with type 2 diabetes mellitus, among them 35 patients diagnosed with DR and 35 with no evidence of DR, and s