In this paper we introduce the concept of generalized trees and compute the Hilbert series of their BINOMIAL EDGE IDEALs

We give upper bounds for the regularity of EDGE IDEAL of some classes of graphs in terms of invariants of graph. We introduce two numbers a’ (G) and n (G) depending on graph G and show that for a vertex decomposable graphG, reg (R/I (G)) £ min{a’ (G), n (G)} and for a shellable graph G, reg (R/I (G))£n (G). Moreover, it is shown that for a graphG, where Gc is a d-tree, we have pd (R/I (G)) =maxvÎV (G) {degG (v)}.

Let G be a simple, oriented connected graph with n vertices and m EDGEs. Let I (B) be the BINOMIAL IDEAL associated to the incidence matrix B of the graph G. Assume that IL is the lattice IDEAL associated to the rows of the matrix B. Also let Bi be a sub matrix of B after removing the i -th row. We introduce a graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =I (Bi) and I (Bi) =IL. After that we introduce another graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =IL. It is shown that the heights of I (B) and I (Bi) are equal to n - 1 and the dimensions of I (B) and I (Bi) are equal to m - n+1; then I (Bi) is a complete intersection IDEAL.

Aim: This study was designed to determine any profile changes and indentify the role of the most significant factors responsible for these changes.Materials and Methods: Cephalograms of 56 class II Division I patients (36 female and 18 male with mean age of 10 years) were used to analysis any changes in the perioral soft tissue profile before and after the treatment. A correlation analysis and multiple regression analysis (forward) revealed complex interaction between dentition, bony structures and soft tissues of the perioral area.Results: Retraction at the upper lip and increase in lower lip length in boys were more predictable than that of others. Significant soft tissue changes occured in response to orthodontic treatment, Upper lip retraction was shown to be related to the following factors: a- Retraction of upper incisal EDGEs during treatment, b-Retraction of Point A, c- Pretreatment upper sulcus thickness and d- Retraction of sulcus superior.Conclusion: A greater increase in lower lip length takes place with greater amount of maxillary incisa1 EDGE retraction during treatment and a greater amount of sulcus superior retraction.

In this paper, a new class of a weighted quadrature rule is represented as-------------------------------------------- where is a weight function, are interpolation nodes, are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as that and we obtain the explicit expressions of the coefficients using the q-BINOMIAL theorem. We give an error analysis for the introduced formula and finally we illustrate its application with some numerical examples.

In order to facilitate the interpretation of raw scores, they are usually converted to scale scores. In some cases, these conversions are a series of nonlinear transformations that can affect the conditional standard error of measurement throughout the scale of score. Therefore, the purpose of this study was to introduce methods for calculating the conditional standard error of measurement based on the strong true score theory. Furthermore, comparison of normalized and equipercentile nonlinear transformations on the raw scores of the academic achievements of the graduates of mathematical sciences in 2014 and their effect on conditional standard error of measurement was also conducted. So, in order to achieve these purposes, we used a sample of 3943 high school graduates of Mathematics and Physics in 2014 who had participated in national university entrance examination in 2015 randomly selected by National Organization of Educational Testing. The conditional standard error of measurement under these transformations was estimated based on the BINOMIAL procedure of Brennan and Lee (1999) and Chang (2006) method based on the beta-BINOMIAL distribution. The results of this study indicated that the conditional standard error of measurement of the Chang was smoother than BINOMIAL procedure, but in both methods the estimated errors are larger for middle points and smaller for extreme points. Additionally, the conditional standard errors of measurement of equipercentile were always less than normalized tranformation, so the equipercentile method found to be better than normalized transformation.

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The EDGE-tenacity Te(G) of a graph G was de ned as Te(G) = min F E(G) f j F j + (G 􀀀 F)! (G 􀀀 F) g where the minimum is taken over all EDGE cutset F of G. We de ne G-F to be the graph induced by the EDGEs of E(G)􀀀 F,  (G􀀀 F) is the number of EDGEs in the largest component of the graph induced by G-F and! (G 􀀀 F) is the number of components of G􀀀 F. A set F  E(G) is said to be a Te-set of G if Te(G) = jFj+ (G􀀀 F)! (G􀀀 F) Each component has at least one EDGE. In this paper we introduce a new invariant EDGE-tenacity, for graphs. it is another vulnerability measure. we present several properties and bounds on the EDGE-tenacity. we also compute the EDGE-tenacity of some classes of graphs.

Introduction: This study evaluated the degree of micro leakage of IDEAL Makoo and Tetric Flow composites using two dentin adhesives of Scotch Bond Multipurpose (SBMP) and Excite.Materials &Methods: 60 premolar teeth were divided in to four groups of 15. and class V cavity preparations were done in CEJ. Group 1 was rest orated with SBMP and IDEAL Makoo, Group II with SBMP and Tetric Flow, Group III with Excite and IDEAL Makoo, and Group IV with Excite and Tetric Flow. Stereomicroscope (X40) was used to evaluate and dye penetration in occlusal and gingival margins. Chi Square test, Pearson’s correlation test and Fishers exact test were used for data analysis (α= 0.05).Results: 1- The degree of leakage was not in correspondence to the type of composite.2- The degree of leakage was not in correspondence to the type of dentin adhesive.3- In four groups, the degree of leakage in gingival wall was significantly more than occlusal wall.Conclusion: Type of composite and dentin adhesive have no effect on degree of leakage. The important factor is the type of wall. It means that in class V restorations, gingival wall is always observed to have more micro leakage than occlusal wall.