Browsing by Author "Cancan, Murat"

Now showing 1 - 20 of 137

Algorithm for Computing Differential Char Sets Efficiently
(Taru Publications, 2020) Cancan, Murat; Afzal, Farkhanda; Maqbool, Ayesha; Afzal, Deeba
In order to triangularize differential polynomial sets and systems, we can use char sets method by Ritt and Wu. This method uses differential pseudo division for elimination of variables successively. In this paper, we have proved that Differential Pseudo division can be replaced by important reductions for computing differential char sets. An algorithm is presented for computing the differential char sets efficiently. This algorithmic scheme has been executed with precise admissible differential reductions. Primary results demonstrate that this new algorithm accomplishes better results than char set algorithm that are based on differential Pseudo division.
Analysis of Fractional Stochastic Evolution Equations by Using Hilfer Derivative of Finite Approximate Controllability
(Amer inst Mathematical Sciences-aims, 2023) Moumen, Abdelkader; Shafqat, Ramsha; Alsinai, Ammar; Boulares, Hamid; Cancan, Murat; Jeelani, Mdi Begum
The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstratedusing an example.
Base Polynomials for Degree and Distance Based Topological Invariants of N-Bilinear Straight Pentachain
(Taylor & Francis Ltd, 2021) Nizami, Abdul Rauf; Shabbir, Khurram; Sardar, Muhammad Shoaib; Qasim, Muhammad; Cancan, Murat; Ediz, Suleyman
Degree and distance-based graph polynomials are important not only as graph invariants but also for their applications in physics, chemistry, and pharmacy. The present paper is concerned with the Hosoya and Schultz polynomials of n-bilinear straight pentachain. It was observed that computing these polynomials directly by definitions is extremely difficult. Thus, we follow the divide and conquer rule and introduce the idea of base polynomials. We actually split the vertices into disjoint classes and then wrote the number of paths in terms of polynomials for each class, which ultimately serve as bases for Hosoya and Schultz polynomials. We also recover some indices from these polynomials. Finally, we give an example to show how these polynomials actually work.
Bounds on Partition Dimension of Peterson Graphs
(Taylor & Francis Ltd, 2021) Khalaf, Abdul Jalil M.; Nadeem, Muhammad Faisal; Azeem, Muhammasd; Cancan, Murat; Farahani, Mohammad Reza
The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (theta(1), theta(2), ..., theta(t)}. A vertex eta is an element of V(P), and r(eta vertical bar theta) = {d(eta, theta(1)), d(eta, theta(2)), ...., d(eta, theta(t))} be a l - tuple distances, where r(eta vertical bar theta) is the representation of a vertex eta with respect to set theta. If r(eta vertical bar theta) of eta is unique, for every pair of vertices, then theta is the resolving partition set of V(P). The minimum number l in the resolving partition set theta is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, P-lambda,P-lambda-1 and proved that these families have bounded partition dimension.
Calculating the Topological Indices of Starphene Graph Via M-Polynomial Approach
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Sattar, Sumera; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat
Chemical graph theory is related to the structure of different chemical compounds. A chemical graph represents the molecule of the substance. Chemical graph theory provides the connection between the real number and the different physical, chemical, and biological properties of the chemical species. By implementing the mathematical tools, a chemical graph is converted into a real number. This number can have the predicating ability about the properties of the molecule. In this article, we find some topological indices via M-polynomial for the Starphene graph.
Certain Types of Minimum Covering Estrada Index of Graphs
(World Scientific Publ Co Pte Ltd, 2023) Shooshtari, Hajar; Atapour, Maryam; Cancan, Murat
Let G be a simple, finite, undirected graph with n vertices. The main purpose of this paper introduces the concepts of the minimum covering Gutman Estrada index, the minimum covering Seidel Estrada index, the minimum covering distance Estrada index, the minimum covering Randic Estrada index, the minimum covering Harary Estrada index, and the minimum covering color Estrada index of a graph. First, we compute the new concepts for some of the graphs, such as cocktail party, star, crown, complete and complete bipartite. Moreover, we establish upper and lower bounds for the new concepts.
Characteristic Sets Verses Generalized Characteristic Sets
(Taru Publications, 2021) Afzal, Farkhanda; Akram, Safia; Ashiq, Muhammad; Afzal, Deeba; Cancan, Murat; Ediz, Suleyman
The notion of characteristic sets that was developed by Ritt and Wu has been turned into an usual tool for study of set/systems of polynomial equations, algebraic as well as differential equations. By constructing a characteristic sets, one can triangularize an arbitrary set/system of any type of polynomials. It ensures that it can be decomposed into triangular form of a particular set/system. In this manuscript, a comparison of characteristic sets defined by Ritt-Wu's differential is provided with the generalized characteristic sets defined by author in [5]. Comparison shows that this scheme performs better than earlier method.
Characterizations of Chemical Networks Entropies by K-Banhatii Topological Indices
(Mdpi, 2023) Ghani, Muhammad Usman; Campena, Francis Joseph H.; Ali, Shahbaz; Dehraj, Sanaullah; Cancan, Murat; Alharbi, Fahad M.; Galal, Ahmed M.
Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. We explain the basic applications of distance-based entropy to chemical phenomena. These applications include signal processing, structural studies on crystals, molecular ensembles, and quantifying the chemical and electrical structures of molecules. In this study, we examine the characterisation of polyphenylenes and boron (B-12) using a line of symmetry. Our ability to quickly ascertain the valences of each atom, and the total number of atom bonds is made possible by the symmetrical chemical structures of polyphenylenes and boron B-12. By constructing these structures with degree-based indices, namely the K Banhatti indices, ReZG(1)-index, ReZG(2)-index, and ReZG(3)-index, we are able to determine their respective entropies.
Closed Formulas of Topological Properties for Remdesivir (C27h35n6o8p)
(Sami Publishing Co-spc, 2021) Hussain, Sabir; Alsinai, Ammar; Afzal, Deeba; Maqbool, Ayesha; Afzal, Farkhanda; Cancan, Murat
Coronavirus is able to cause illnesses ranging from the common flu to severe respiratory disease. Today there is great competition among researchers and physcisians to cure COVID-19. Remdesivir is being studied for the COVID-19 treatment In this article, we presented the topological analysis of remdesivir with the help of M-polynomial. Proofs of the closed form of some topological indices via M-polynomial are also included in this article. [GRAPHICS] .
A Comparative Analysis of Consensus Protocols for Dealing Power Theft Issue in Pakistan
(Taru Publications, 2021) Maqbool, Ayesha; Sattar, Sumera; Naheed, Amna; Khalid, Sana; Rana, Tauseef; Afzal, Farkhanda; Cancan, Murat
Power is considered as a boon for life, lifeline of a country's economy; a key instrument for the socio-economic evolution of any country. Pakistan faces the issue of power theft that worsens the economy of utilities. The purpose of research is to modernize Pakistan's power sector with the usage of Blockchain. Research is based on a comparative analysis of proof of stake (POS) and proof of authority (POA) consensus protocols for the power theft issue for small, medium, or large scales of consumers; results showing automated and pre-selected processing time of transactions running on different nodes of POS and POA along. By comparative analysis of POS and POA; it is shown that the performance of Blockchain remains unaffected by the consensus protocol. To further strengthen the findings the statistical analysis data is carried out to establish the uniqueness of sampled data. The result establishes that Blockchain performs equally well for different architectures of the proposed architecture. The consensus protocol helps in achieving a suitable governing style with no effect on Blockchain performance.
Compilaton of Artificial Intelligence-Supported Studies: an Example of Mathematics Education
(2024) Aladağ, Yusuf Ziya; Cancan, Murat
Bu araştırmada 2020-2024 yılları arasında Google Akademi ve Ulakbim Merkezi'nde yayımlanan yapay zekâ destekli çalışmaların derlenmesi: Matematik eğitimi örneği ile ilgili çalışmalar sistematik derleme yöntemi ile incelemek amaçlanmıştır. Araştırmada belirli kriterler doğrultusunda seçilmiş olan 35 çalışma analiz edilmiştir. Çalışmaların hazırlandığı yıllar, yöntemleri, örneklemi, örneklem büyüklüğü, veri toplama araçları, veri analiz teknikleri, amaçları ve sonuçları incelenmiştir. Veriler analiz edilirken nitel analiz yöntemlerinden biri olan betimsel analiz tercih edilmiştir. İnceleme sonucunda elde edilen veriler şekil, grafik ve tablolarla ile ifade edilmiştir. Araştırma sonucunda 2024 yılında çalışma sayısında artış yaşandığı görülmüştür. 2022 yılında ChatGPT yapay zekâ robotu ile çalışmaların artış yaşandığı görülmüştür. Çalışmalarda sıklıkla lise ve ortaokul kademeleri tercih edilmiştir. Araştırmacılar daha çok 1-50 grubu arası çalışma grubu ile çalışmıştır. Veri toplama araçlarından daha çok dokümanlar kullanılmıştır. Çalışmada yayınların amaç ve sonuçları incelenmiş ve tasnif edilmiştir. Araştırmada konu ile çalışma yapacak araştırmacılara, yapay zekanın matematik eğitimindeki eksikliklerine değinilmiş ve önerilerde bulunulmuştur.
Computation of Differential and Integral Operators Using M-Polynomials of Gold Crystal
(Cell Press, 2024) Khan, Abdul Rauf; Bhatti, Saad Amin; Imran, Muhammad; Tawfiq, Ferdous M. O.; Cancan, Murat; Hussain, Shahid
Gold is generally considered a noble metal since it is inherently inert in its bulk state. However, gold demonstrates reactivity when it is in its ionic state. The inherent inertness of bulk gold has resulted in its widespread recognition as a vital raw material in various biomedical processes. The applications of these technologies include drug delivery microchips, dental prostheses, reconstructive surgery, culinary additives, and cardiovascular stents. Gold can also exist in molecules or ions, particularly gold ions, which facilitates the production of gold nanomaterials. In this paper, we have computed differential and integral operators by using the M-Polynomial of gold crystals and by utilizing this polynomial, we have also computed eleven topological indices like 1st Zagreb, 2nd Zagreb, Hyper, Sigma, Second Modified, General Randic, General Reciprocal Randic, 3rd Redefined Zagreb, Symmetric Division Degree, Harmonic, Inverse Sum indices for the structure of Gold crystal.
Computation of Zagreb Polynomial and Indices for Silicate Network and Silicate Chain Network
(Wiley, 2023) Ghani, Muhammad Usman; Inc, Mustafa; Sultan, Faisal; Cancan, Murat; Houwe, Alphonse
The connection of Zagreb polynomials and Zagreb indices to chemical graph theory is a bifurcation of mathematical chemistry, which has had a crucial influence on the development of chemical sciences. Nowadays, the study of topological indices has become a vast effective research area in chemical graph theory. In this article, we add up eight different Zagreb polynomials for the Silicate Network and Silicate Chain Network. From these Zagreb polynomials, we catch up on degree-based Zagreb indices. We also provide a graphical representation of the outcome that describes the dependence of topological indices on the given parameters of polynomial structure.
Computational Analysis of New Degree-Based Descriptors of Zig-Zag Benzenoid System
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Zaman, Muhammad; Chaudhry, Faryal; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat
Chemical graph theory is one of the dominant branches in graph theory. In this paper, we compute the atom bond connectivity, geometric arithmetic, first K-Banhatti, second K-Banhatti, first K-hyper Banhatti, second K-hyper Banhatti, modified first K-Banhatti, modified second K-Banhatti and harmonic K-Banhatti index via M-polynomial of zig-zag Benzenoid system. We also elaborate the result with graphical representation.
Computational Techniques in Machine Learning, Fuzzy Systems, Image Processing and Signal Analysis
(Taru Publications, 2025) Farahani, Mohammad Reza; Alaeiyan, Mehdi; Ameen, Hayder Baqer; Zhang, Xiujun; Cancan, Murat; Afzal, Farkhanda
Computing Forgotten Topological Index of Extremal Cactus Chains
(Walter de Gruyter Gmbh, 2021) Cancan, Murat; Imran, Muhammad; Akhter, Shehnaz; Siddiqui, Muhammad Kamran; Hanif, Muhammad Farhan
The F-index is the whole of 3D squares of vertex degrees in a chart G. It as of late turned into the subject of a few investigates because of its extraordinary capability of uses. The point of this paper is to register the F-record of triangular prickly plant chain, square desert flora chains, 6-sided cactus restraints and polyomino restraints. In addition, we decided the extremal chains in the desert plant chains and polyomino fastens as for the F-index.
Computing M-Polynomial and Topological Indices of Tuhrc4 Molecular Graph
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat; Ciftci, Idris
Chemical graph theory has an important role in the development of chemical sciences. A graph is produced from certain molecular structure by means of applying several graphical operations. The local graph parameter is valency, which is defined for every vertex as the number associates with other vertices in a graph, for example an atom in a molecule. The demonstration of chemical networks and chemical compounds with the help of M-polynomials is a novel idea. The M-polynomial of different molecular structures help to compute several topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and clarifies its physical features, chemical reactivates and boiling activities. In this paper we computed M-Polynomial and topological indices of TUHRC4 Graph, then we recovered numerous topological indices using the M-polynomials.
Connecting Sio4 in Silicate and Silicate Chain Networks To Compute Kulli Temperature Indices
(Mdpi, 2022) Zhang, Ying-Fang; Ghani, Muhammad Usman; Sultan, Faisal; Inc, Mustafa; Cancan, Murat
A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network. Furthermore, a QSPR study of the key topological indices is provided, and it is demonstrated that these topological indices are substantially linked with the physicochemical features of COVID-19 medicines. This theoretical method to find the temperature indices may help chemists and others in the pharmaceutical industry forecast the properties of silicate networks and silicate chain networks before trying.
Construction of Petersen Graph Via Graph Product and Correlation of Topological Descriptors of Petersen Graph in Terms of Cyclic Graph C5
(Taylor & Francis Ltd, 2022) Waheed, Muhammad; Saleem, Umair; Cancan, Murat; Tas, Ziyattin; Alaeiyan, Mehdi; Farahani, Mohammad Reza
Graph product yields a new structure from two initial given structures. The computation of topological indices for these sophisticated structures using the graph product is a critical endeavor. Petersen graph is a structure which consists of ten vertices and fif teen edges. It is commonly used as a counter example to graph theory conjectures. In this paper, we generate simple Petersen graph by using graph product and then explicit expressions of the first and second Zagreb indices, forgotten topological index, first hyper and first reformulated Zagreb index, reduced second Zagreb index and Y-index of the Peterson graph in terms of cyclic graph C-5 are computed.
Degree Based Topological Indices of Tadpole Graph Via M-Polynomial
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat; Ciftci, Idris
Chemical graph theory has an important impact on the development of the chemical sciences. A chemical graph is a graph that is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with the M-polynomials is a revolution and the M-polynomial of different molecular structures contributes to evaluating many topological indices. In this paper we worked out M-Polynomial and topological indices of the tadpole graph, then we recovered numerous topological indices using the M-polynomials.