Papers by Dr. Shatha A.Salman
Journal of applied sciences and nanotechnology, Sep 30, 2023
Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in ... more Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in various sectors of mathematics and science. The chromatic polynomial is a type of polynomial that has valuable and attractive qualities. Ehrhart's polynomials and chromatic analysis are two essential techniques for graph analysis. They both provide insight into the graph's structure but in different ways. The relationship between chromatic and Ehrhart polynomials is an area of active research that has implications for graph theory, combinatorial, and other fields. By understanding the relationship between these two polynomials, one can better understand the structure of graphs and how they interact. This can help us to solve complex problems in our lives more efficiently and effectively. This work gives the relationship between these two essential polynomials and the proof of theorems, and an application related to these works, the model Physical Cell ID (PCID), was discussed.
Journal of Al-Qadisiyah for Computer Science and Mathematics
Scholars have recently become interested in the importance of the reflexive and Birkhoff polytope... more Scholars have recently become interested in the importance of the reflexive and Birkhoff polytopes in a variety of applications in our daily lives. Unanswered queries and educated guesses abound in reflexive polytopes. We use the free sum and product for reflexives polytopes, as well as the product for two Birkhoff polytopes, and the proven theorem to get specific unimodality results. The computations are acquired via algorithms.
Engineering and Technology Journal
Engineering and Technology Journal
A polytope plays a central role in different areas of mathematics. It is used quite heavily in ap... more A polytope plays a central role in different areas of mathematics. It is used quite heavily in applied fields of mathematics, such as medical imaging and robotics, geometric modeling. A polytope has many users in modern science such as computer graphics, optimization, and search engine. It is intended for a broad audience of mathematically inclined. Therefore in this paper, we shall take a polytope with one kind of application, which is known as a Stasheff polytope. it has been applied in: moduli spaces, Erhart polynomial, physics-chemistry, and Hopf algebras. In this paper, a finite graph G with tubing is taken, the nodes of the graph are reduce to points in and the convex hull for them are simplex, permutahedron and associahedron (Stasheff polytope ) are studied. Also, a fan graph to the painted tree is also taken and reduces its nodes to points in . The converse of this result is also given with different examples to consult our results.
DOAJ (DOAJ: Directory of Open Access Journals), 2022
2020 1st. Information Technology To Enhance e-learning and Other Application (IT-ELA, 2020
The term of Ehrhart tensor polynomials is a natural popularization of the Ehrhart polynomial of l... more The term of Ehrhart tensor polynomials is a natural popularization of the Ehrhart polynomial of lattice polytopes which is a much more used in different applications. As our fundamental instrument, we present $\mathrm{h}^{\mathrm{r}}$-tensor polynomials which expand the idea of the Ehrhart $\mathrm{h}*$-polynomial for a polytope, and networks. It also examines their coefficients for positive semi definiteness rather than the standard $\mathrm{h}*-$ polynomial. This paper gives the proof of two theorems that compute the coefficients of the Ehrhart Tensor polynomials (h3 and $\mathrm{h}^{4}$). The positivity for these coefficients is also proved. Some applications on the Ehrhart tensor polynomials are given.
2017 International Conference on Current Research in Computer Science and Information Technology (ICCIT), 2017
In remote sensing applications, a solid angle has a wide appearing, therefore it's important ... more In remote sensing applications, a solid angle has a wide appearing, therefore it's important to know what it means. The solid angle subtended by a surface S is characterized as the surface range of a unit circle secured by the surface's projection onto the circle. Solid angle is effectively, an observer that can be used as a measure of how big an object looks to be. The paper is aimed to find the solid angle polynomials for a polytope of dimension d where it is proved in a main theorem. Some applications of these polynomials are presented to show it's important.
2017 International Conference on Current Research in Computer Science and Information Technology (ICCIT), 2017
Algebra is one of the important fields of mathematics. It concerns in the study and manipulates o... more Algebra is one of the important fields of mathematics. It concerns in the study and manipulates of mathematical symbols. It also concerns with study of abstractions such as groups, rings and fields. Ring theory is the most attractive category of algebra in the area of cryptography. Recently, many algebraic cryptosystem protocols based on non-commutative algebraic structures such as; authentication, key exchange, and encryption-decryption processes are adopted. In this paper, we employ the algebraic structure called nil Armendariz (NA) rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is implemented and illustrated through numerical example, and its soundness and completeness are proved.
Solid State Technology, 2020
In this research a composite material consisting of unsaturated polyester (UPE)resin reinforced ... more In this research a composite material consisting of unsaturated polyester (UPE)resin reinforced by mullite particles with different weight ratios (0, 20, 40, and 60wt%) was prepared. The samples were studied for the effect of adding mullite on the electrical and mechanical properties of the composite. The composite material was prepared by a hand lay-up molding method. The results showed that the electrical properties (the real and imaginary dielectric constants) increased after reinforcement with the addition of mullite content but reduced with increasing frequency, whereas electrical conductivity reduced with increasing frequency and mullite content. The mechanical properties (tensile strength and hardness) increased after reinforcement with an increasing mullite content. Keywords:Unsaturated polyester, Mullite, Dielectric constant, Tangent loss, Hand lay- Up molding.
2017 Second Al-Sadiq International Conference on Multidisciplinary in IT and Communication Science and Applications (AIC-MITCSA), 2017
Fourier transform is a principal analysis tool which has been found to be especially useful for p... more Fourier transform is a principal analysis tool which has been found to be especially useful for problem simplification in many fields of scientific endeavor. This paper is aimed to find the Fourier transform of the indictor function for a real closed polytope P of dimension d where it is proved in a main theorem. Some applications of Fourier transform are presented to show it's important.
Iraqi journal of science, 2019
As of late, humankind has experienced radiation issues either computerized tomography (CT) or X-r... more As of late, humankind has experienced radiation issues either computerized tomography (CT) or X-rays. In this investigation, we endeavor to limit the effect of examination hardware. To do this the medical image is cropping (cut and zoom) then represented the vascular network as a graph such that each contraction as the vertices and the vessel represented as an edges, the area of the coagulation was processed already, in the current search the shortest distance to reach to the place of the blood vessel clot is computed
uotechnology.edu.iq
The Randomness is one of the basic criterions to measure Key Generator Efficiency. The key genera... more The Randomness is one of the basic criterions to measure Key Generator Efficiency. The key generator depends basically on Linear FeedBack Shift Register which is considered as one of the basic units of Stream Cipher Systems. In this paper, the frequency postulate of Randomness criteria is calculated theoretically for non-linear key generator before it be implemented or constructed (software or hardware), this procedure save time and costs. Two non-linear key generators are chosen to apply the theoretical studies; these key generators are the Product and Brüer.
Engineering and Technology Journal
In recent years, the uses of high dimensional appear in a large and a lot of applications appear ... more In recent years, the uses of high dimensional appear in a large and a lot of applications appear within it. So, we study these applications and take one of them that play a central role in the factoring of prime number which is an application especially in cryptography. Our main purpose is to introduce another procedure which make the operation of computing the factoring of N = p.q as more easy as the direct computation fast, therefore, an approach is working on for finding the number of integral points(lattice points) make benefit from the concept of the Tutte polynomial and its application on integral points of a polytope. Polytopes which are taken are the Platonic solid, and a map is making between a ball and a polytope in four dimensions, then discusses the relation between the numbers of integral points of them from dimension one to n dimension. We found a relation between the radiuses of the ball, the edge of the cube which is one of the Platonic solid and the dimension together with Pascal triangle, the rhombic dodecahedron, octahedron, and icosahedrons are also taken.
Indonesian Journal of Electrical Engineering and Computer Science, 2020
A lot of side effects accusers which the humans have suffered from a scan either by CT phrases, r... more A lot of side effects accusers which the humans have suffered from a scan either by CT phrases, rays and magnetic resonance. Different methods were used to eliminate these affects depends on segmentation of vascular networks then represents it as a graph, where the intersection of the vessel as a vertex and the line between them as an edge. The place of the clot can be found by representing the weight of each edge as the amount of the blood in the vessel. Sign the place; if the amount is less than the normal flux that represents thrombosis. An algorithm in a graph theory is used to find the minimum distance, if more than one thrombosis exists to reach the nearest one and sign it alternately.
Journal of Al-Qadisiyah for Computer Science and Mathematics
Transportation polytopes of non- negative m × n matrices compose of two vectors: a and b which ro... more Transportation polytopes of non- negative m × n matrices compose of two vectors: a and b which row sums are equal to fixed constant and column sums are equal to different constant. The transportation polytopes are denoted by T (a, b) and these two vectors are called margins. An open problem that the 2-way transportation polytopes are Hamiltonian is proved in this paper with application of optimization.
Indonesian Journal of Electrical Engineering and Computer Science, 2020
The article describes new algorithms for water retention using magic square, based on the propert... more The article describes new algorithms for water retention using magic square, based on the properties of magic square which is defined as an n n matrix with positive entries enabling to pouring amounts of water over the magic square and measuring the amount of water that does not leak out of the square. The new method effectiveness evaluation is confirmed by the calculation in many applications; one of them is water retention.
Al-Mustansiriyah Journal of Science, 2019
Magic squares is n×n matrix with positive integer entries as well as the sum of rows, columnsand ... more Magic squares is n×n matrix with positive integer entries as well as the sum of rows, columnsand mains diagonal have the same magic constant, one of the most oldest magic square wasdiscovered in china. In this paper the history of magic square is displayed and some definitionof its kind is given the prove of two theorems about properties of magic square is introduced.
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Papers by Dr. Shatha A.Salman