Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

  This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

Back ground: This in vitro study was carried out to investigate the effect of post space regions (coronal, middle and apical), Time and the mode of polymerization (dual, self-cured) of the cements used on the bond strength between translucent fiber post and root dentin by using push-out test. Materials and Methods: Forty eight extracted mandibular first premolars (single root) were instrumented with ProTaper Universal system files (for hand use) and obturated with gutta percha for ProTaper and AH26® root canal sealer following the manufacturer instructions, after 24 hours post space was prepared using FRC postec® plus drills no.3 creating 8 mm depth post space. The prepared samples were randomly divided into two main groups (24 samples ea

Background: The purpose of this study is to compare the color changes between the bonded middle third and the unbonded gingival and incisal thirds, fallowing fixed orthodontic treatment Material and method: The color parameter l, a, b has been recorded for each thirds in upper anterior teeth by mean of easy shad device. The has been calculated for gingival, middle and incisal thirds for the upper anterior teeth in 34 patient, 17 males and 17femals, those subject undergone fixed orthodontic treatment Results: The in middle bonded third is highly significant higher than that in incise and gingival thirds p<0.01 because the middle third isn’t expose to oral fluid and dental brushing since it covered by the bracket. Also there

Background: The aim of this study is to evaluate the color change ∆E of the dental enamel following treatment with 2 kinds of protector (icon infiltrant, clinpro varnish) before fixed orthodontic treatment to avoid the possible white spot lesions. Materials and Methods: Fifty four subjects treated with fixed appliances were divided into 3 groups: the 1st group was control, while the 2nd and 3rd groups were treated with icon infiltrant and clinpro varnish before bonding procedure, respectively. Color parameters (L,a,b) were recorded for the middle and gingival thirds before and after bonding procedure to get the ∆E of each group. Results: One-way ANOVA test showed a non-significant difference in ∆E between the 3 groups a

In linear regression, an outlier is an observation with large residual.  In other words, it is an observation whose dependent-variable value is unusual given its values on the predictor variables. An outlier observation may indicate a data entry error or other problem.

An observation with an extreme value on a predictor variable is a point with high leverage. Leverage is a measure of how far an independent variable deviates from its mean. These leverage points can have an effect on the estimate of regression coefficients.

Robust estimation for regression parameters deals with cases that have very high leverage, and cases that are outliers. Robust estimation is essentially a