This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

Abstract

  Bivariate time series modeling and forecasting have become a promising field of applied studies in recent times. For this purpose, the Linear Autoregressive Moving Average with exogenous variable ARMAX model is the most widely used technique over the past few years in modeling and forecasting this type of data. The most important assumptions of this model are linearity and homogenous for random error variance of the appropriate model. In practice, these two assumptions are often violated, so the Generalized Autoregressive Conditional Heteroscedasticity (ARCH) and (GARCH) with exogenous varia

This paper is concerned with introducing and studying the new approximation operators based on a finite family of d. g. 'swhich are the core concept in this paper. In addition, we study generalization of some Pawlak's concepts and we offer generalize the definition of accuracy measure of approximations by using a finite family of d. g. 's.

Nathaniel Hawthorne (1804-1864) has been widely known for his special interest in the female characters. In many of his novels, he narrates the conditions, values, and the institutions that surround and control the life of women, leading them to be victims. In “Rappaccini’s Daughter” (1844), the heroine, Beatrice is created to be victimized by her loved ones (her father and lover). This paper focuses on the term “victim,” it shows its aspects through the development of Beatrice’s character. The paper also studies a female character in the male-dominated society, to show the cruelty done to her, and how she is considered to be a second rate person, who is unable to live normally, or at least to save herself from dea

Historically, medicinal herbs have been utilized as an important origin of chemicals with particular therapeutic potentials, and they continue to be a great place to find new medication candidates. Parthenocissus quinquefolia L. is a member of the grape-growing family Vitaceae. It is indigenous to Central and North America. It is widely dispersed in Iraqi gardens and plant houses from north to south. Traditionally, it has many uses, like relieving constipation, treating jaundice, expectorant, emetic, and others. At the same time, its proven activities include antioxidant activity, antimicrobial, anti-diabetic, thrombin inhibitor effect, and medicine for treating eyelid eczema. Parthenocissus quinquefolia contains valuable phytochemicals lik

Background: Secretory Immunoglobulin A (SIgA) is a subclass of Immunoglobulin A (IgA), It is an antibody that plays an important role in mucosal immunity. It is the main immunoglobulin found in mucous secretions from mammary glands, tear glands and salivary glands, every pathologic process in the body involves the immune system, and periodontal inflammation is one of them and is not an exception. Material and methods: this study was consisted of 60 healthy male participants of an age ranged between (35-50) years old ; 25 of them with generalized moderate chronic periodontists(Clinical Attachment Loss equal to 3-4mm at ≥ 30% of the sites; 20 participants with plaque induced gingivitis and 15 participants had clinically healthy pe

Experimental investigation of the influence of inserting the metal foam to the solar chimney to induce natural ventilation are described and analyzed in this work. To carry out the experimental test, two identical solar chimneys (without insertion of metal foam and with insertion of metal foam) are designed and placed facing south with dimensions of length× width× air gap (2 m× 1 m× 0.2 m). Four incline angles are tested (20^o,30^o,45^o,60^o) for each chimney in Baghdad climate condition (33.3^o latitude, 44.4^o longitude) on October, November, December 2018. The solar chimney performance is investigated by experimentally recording absorber pl

This study examined the adsorption behavior of anionic dye (orange G) from aqueous solution onto the raw and activated a mixture of illite, kaolinite and chlorite clays from area of Zorbatiya (east of Iraq).The chemical treatment involved alkali and acid activation. The alkali activation obtained by treated the raw clay (RC) with 5M NaOH (ACSO) and the acid activation founded by treated it with 0.25M HCl (ACH) and 0.25M  (ACS). The thermal treatment carried out by calcination the produce activated clay at 750^oC for acid activation and 105^oC for alkali activation. Batch