In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

Na⁺/K⁺-ATPase is a prevalent enzyme that maintains the Na⁺ and K⁺ gradients across the cell membrane by transporting three Na⁺ out and two K⁺ into the cell, the aim of this study  is to provide detailed mechanistic insights, potentially with important effects on physiological regulation of active Na and K transport in tissues of Aerobic Thyroid Patient. Thyroid tissues were obtained from a 35 year old patients, the operation was carried out at the Al-Hadi Specialist Hospital in Samarra city, the sample was stored at -20^ºC until used. The purification protocol included Salt Precipitation, Ion Exchange Chromatography, Gel Filtration and E

In this research two algorithms are applied, the first is Fuzzy C Means (FCM) algorithm and the second is hard K means (HKM) algorithm to know which of them is better than the others these two algorithms are applied on a set of data collected  from the Ministry of Planning on the water turbidity of five areas in Baghdad to know which of these areas are less turbid in clear water to see which months during the year are less turbid in clear water in the specified area.

The research is aimed at investigating how the New York Times framed the war against ISIS in its news coverage and which news sources it adopted while reporting on this war.
‏ The research could be classified under descriptive researches. The survey methodology has been adopted and the content analysis has been used. The research sample consists of all the news stories the New York Times have published about the war against ISIS from 10/17/2016 to 4/16/2017 according to the comprehensive sampling method. The number of news stories that were analyzed was (155) news story. The research tool was (coding scheme).
The research has reached the following conclusions:
‏ 1. In its news coverage of the war against ISIS, the New York T

The study aimed to increase the biological value of white bean. The effect of different concentrations 0.01 ,0.02,0.03,and 0.04 M of sodium sulfite solutions for 1hr at 70 ºC on the trypsin inhibitors activity, protein isolate and protein solubility of complete and dehulling white bean flour were studied.Trypsin inhibitors activity were reduced by 42.97, 58.69, 68.59 and 69.58% in complete white bean flour at 0.01 ,0.02, 0.03, 0.04 M respectively, while the corresponding values were 50.43, 61.00, 75.61 and 85.66% respectively in dehulling white bean flour .Protein isolate value was 13.41% and protein solubility was 2.2% in control sample, Furthermore, the using of chemical treatment showed that protein isolate was reduced gradually and

This research include design and implementation of an Iraqi cities database using spatial data structure for storing data in two or more dimension called k-d tree .The proposed system should allow records to be inserted, deleted and searched by name or coordinate. All the programming of the proposed system written using Delphi ver. 7 and performed on personal computer (Intel core i3).

  The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs.         All of these arcs are incomplete.         The number of distinct (12,3)-arcs are six, two of them are complete.         There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete.         There exists one complete (15,3)-arc.
 

The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs. All of these arcs are incomplete. The number of distinct (12,3)-arcs are six, two of them are complete. There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete. There exists one complete (15,3)-arc.

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.