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M_n – Polynomials of Some Special Graphs

 Let  be a connected graph with vertices set  and edges set . The ordinary distance between any two vertices of  is a mapping  from  into a nonnegative integer number such that  is the length of a shortest  path. The maximum distance between two subsets  and  of   is the maximum distance between any two vertices  and  such that  belong to  and  belong to . In this paper, we take a special case of maximum distance when  consists of one vertex and  consists of  vertices, . This distance is defined by: where  is the order of  a graph .

     In this paper, we defined  – polynomials based on the maximum distance between a vertex  in  and a subset  that has vertices of a vertex set of  and  – index. Also, we find  polynomials for some special graphs, such as: complete, complete bipartite, star, wheel, and fan graphs, in addition to  polynomials of path, cycle, and Jahangir graphs. Then we determine the indices of these distances.

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Publication Date
Wed Dec 04 2013
Journal Name
Proceedings Of Nuclei Of Seyfert Galaxies And Qsos - Central Engine & Conditions Of Star Formation — Pos(seyfert 2012)
Are Narrow Line Seyfert 1 galaxies a special class of Active Galactic Nuclei?

No. Due to their apparently extreme optical to X-ray properties, Narrow Line Seyfert 1s (NLSy1s) have been considered a special class of active galactic nuclei (AGN). Here, we summarize observational results from different groups to conclude that none of the characteristics that are typically used to define the NLSy1s as a distinct group – from the, nowadays called, Broad Line Seyfert 1s (BLSy1s) – is unique, nor ubiquitous of these particular sources, but shared by the whole Type 1 AGN. Historically, the NLSy1s have been distinguished from the BLSy1s by the narrow width of the broad Hb emission line. The upper limit on the full width at half maximum of this line is 2000kms−1 for NLSy1s, while in BLSy1s it can be of several thousands

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
Use special Erwa to determine the number of live bacteria in different models

Used in the study especially calibrated Erwa to determine the number of neighborhood or the Alayoshi number of bacteria in the count modeling and casting method dishes in addition to using the drop method yielded significant results for a match between the methods used ..

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Publication Date
Thu Dec 01 2022
Journal Name
Baghdad Science Journal
The Approximation of Weighted Hölder Functions by Fourier-Jacobi Polynomials to the Singular Sturm-Liouville Operator

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

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Publication Date
Wed Aug 30 2023
Journal Name
Iraqi Journal Of Science
Use Algebra of Group Action to Find Special Types of Caps in PG(3,13)

     Group action on the projective space PG(3,q)  is a method which can be used to construct some geometric objects for example cap. We constructed new caps in PG(3,13)  of degrees 2, 3, 4, 7,14 and sizes 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190. Then the incomplete caps are extended to complete caps. 

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Publication Date
Tue Nov 19 2024
Journal Name
Journal Of Physical Education
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Publication Date
Sun Oct 30 2022
Journal Name
Iraqi Journal Of Science
The Operator S(a,b;θ_x ) for the Polynomials Z_n (x,y,a,b;q)

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

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Publication Date
Mon Feb 20 2023
Journal Name
Pakistan Heart Journal
Special exercises for some physical, kinetic and electrical abilities accompanied by symmetrical electrical stimulation in the rehabilitation of the muscles of the legs for patients with simple hemiplegic cerebral palsy

The purpose of this paper is to identifying some of the physical, kinetic and electrical capabilities of the working muscles of patients with simple hemiplegic cerebral palsy, preparation of special exercises (rehabilitation and water) accompanied by symmetrical electrical stimulation in the rehabilitation of working muscles for patients with simple hemiplegic cerebral palsy, and identifying the effect of exercises, especially (rehabilitation and water), accompanied by symmetrical electrical stimulation, on some physical, kinetic and electrical capabilities in rehabilitating working muscles for patients with simple hemiplegic cerebral palsy. The researcher used the experimental approach with a one-group design with two pre and post-tests du

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Publication Date
Wed Jul 13 2016
Journal Name
International Journal Of Mathematics Trends And Technology
Designed Algorithms for Compute the Tenser Product of Representation for the Special Linear Groups

The main objective of this paper is to designed algorithms and implemented in the construction of the main program designated for the determination the tenser product of representation for the special linear group.

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Publication Date
Mon May 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Direct and Inverse Inequalities for Jackson Polynomials of 2-Periodic Bounded Measurable Functions in Locally Clobal Norms

Convergence prop erties of Jackson polynomials have been considered by Zugmund
[1,ch.X] in (1959) and J.Szbados [2], (p =ï‚¥) while in (1983) V.A.Popov and J.Szabados [3]
(1 ï‚£p ï‚£ ï‚¥) have proved a direct inequality for Jackson polynomials in L
p-sp ace of 2-periodic bounded Riemann integrable functions (f R) in terms of some modulus of
continuity .
In 1991 S.K.Jassim proved direct and inverse inequality for Jackson polynomials in
locally global norms (L
,p) of 2-p eriodic bounded measurable functions (f L) in terms of
suitable Peetre K-functional [4].
Now the aim of our paper is to proved direct and inverse inequalities for Jackson
polynomials

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Role of Audit Committees on Corporate Governance Effectiveness of Iraqi Special Banks (Filed Study)

Consistent with developments emerging environmental and canaccept by Iraq of the opportunities and challenges ahead in many fields,including economic areas, it requires the face of those developments andadaptation by adopting a lot of related concepts, including the concept ofcorporate governance and commitment to its principles, standards andmechanisms, especially those related to the formation of audit committeesand identify the tasks and duties entrusted to its members and terms oftheir independence as well as the rehabilitation of both scientific andpractical manner that is consistent with the interests of shareholders andother stakeholders in the companies, including banks, research sample, theresearch aims to shed light on the conc

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