A complex number  is called an extended eigenvalue for an operator  on a Hilbert space H if there exists a nonzero operator  such that: such  is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward   and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.

Background: Elastomeric chains are used to generate force in many orthodontic procedures, but this force decays over time, which could affect tooth movement. This study aimed to study the force degradation of elastomeric chains. Data and Sources: An electronic search on Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, LILACS, and PubMed was made, only articles written in English were included, up to January 2022.Study selection: Fifty original articles, systematic reviews, and RCTs were selected. Conclusion: Tooth movement, salivary enzymes, alcohol-containing mouthwash, whitening mouthwash, and alkaline and strong acidic (pH <5.4) solutions all have a significant impact on elastomeric chain force degradation. T

Diabetes mellitus (DM) is a metabolic and hormonal disorder in which the body does not produce sufficient or respond ordinarily to insulin, leading to an increase in blood sugar (glucose) levels. This disordered has many side effects on body health, one of them being oral health. This study aimed to find these effects on several oral immune parameters included (IL6, CRP, and alpha-amylase) and the possible use of these parameters in the prediction of oral health and further risk sequel. A total of 91 specimens including 51 DM patients and 40 apparently healthy individuals were enrolled in this study which was carried out from November/2021 to February/2022. The results revealed that, abnormal increase of both IL6 and CRP in the saliva of

Secured multimedia data has grown in importance over the last few decades to safeguard multimedia content from unwanted users. Generally speaking, a number of methods have been employed to hide important visual data from eavesdroppers, one of which is chaotic encryption. This review article will examine chaotic encryption methods currently in use, highlighting their benefits and drawbacks in terms of their applicability for picture security.

After the persistence of the British policy of oppression and control over the American colonies and the attempts to obliterate the identity of their inhabitants, the colonies worked on moving forward towards achieving independence, and Virginia was the first to initiate the development of the new government frameworks, through George Mason in drafting the Virginia Bill of Rights in 1776, which expressed the philosophy of the era Enlightenment and independent revolutionary thought, which called for equality and natural rights for individuals and the need for a free popular government that works for the common good.

Improving the ability of asphalt pavement to survive the heavily repeated axle loads and weathering challenges in Iraq has been the subject of research for many years. The critical need for such data in the design and construction of more durable flexible pavement in bridge deck material is paramount. One of new possible steps is the epoxy asphalt concrete, which is classified as a superior asphalt concrete in roads and greatly imparts the level of design and construction. This paper describes a study on 40-50 penetration graded asphalt cement mixed with epoxy to produce asphalt concrete mixtures. The tests carried out are the Marshall properties, permanent deformation, flexural fatigue cracking and moisture damage. Epoxy asphalt mixes perf

The present work included new information about pollen of eighteen Spp. of Stachys  L. in Iraq ;showed their importance in diagnostsis.

Pollen shapes in equatorial view were ellipsoid in most spp .and spherical - subspherical ,  spherical - subprolate and  subprolate -

ellipsoid in others; while they were spherical - subspherical in polar

view . Pollen was tricolpate except St.iberica  M.B.georgica Rech.f. &

Ten. Which has tetracolpate and that was new for the genus.

The smallest pollen were seen in St.kotschyi  Boiss. & Hohen. but the biggest were in St.benthamiana Boiss.