http://eiris.it/ojs/index.php/ratiomathematica/issue/feedRatio Mathematica2024-01-05T07:33:01+01:00Fabrizio Maturofabmatu@gmail.comOpen Journal Systems<p><strong>RATIO MATHEMATICA - JOURNAL OF MATHEMATICS, STATISTICS, AND APPLICATIONS</strong></p><p>Ratio Mathematica is a historical journal of Mathematics and Statistics that has been publishing scientific articles for more than thirty years. Ratio Mathematica, founded by Prof. Franco Eugeni, was born in 1990 in Pescara, a city located in the Abruzzo region of Italy. Since the first years of activity, the journal has always been characterized by a strong internationalization.</p><p>Ratio Mathematica is an open-access journal that publishes an issue every six months (in June and December). The journal is interested in original research articles on theoretical and applied Mathematics and Statistics.</p><p>Only English-language publications are accepted. 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Any ellipses (... marks) shown in this report originate with the data source; they are NOT caused by subsequent processing in Publish or Perish.</p><p><br />Metrics</p><p>Reference date: 2024-01-02 08:14:04 +00100<br />Publication years: 1990-2024<br />Citation years: 34 (1990-2024)<br />Papers: 608<br />Citations: 1206<br />Citations/year: 35.47 (acc1=45, acc2=14, acc5=0, acc10=0, acc20=0)<br />Citations/paper: 1.98<br />Citations/author: 815.83<br />Papers/author: 379.03<br />Authors/paper: 1.88/2.0/2 (mean/median/mode)<br />Age-weighted citation rate: 128.69 (sqrt=11.34), 82.42/author<br />Hirsch h-index: 17 (a=4.17, m=0.50, 457 cites=37.9% coverage)<br />Egghe g-index: 23 (g/h=1.35, 552 cites=45.8% coverage)<br />PoP hI,norm: 13<br />PoP hI,annual: 0.38<br />Fassin hA-index: 3</p>http://eiris.it/ojs/index.php/ratiomathematica/article/view/851Attribute Reduction in Students Selection for a Merit Cum Means Based Scholarship Scheme using Basis in Nano Topological Spaces2023-12-30T22:02:41+01:00Kalarani Mkalasiva1922k10@gmail.comNithyakala Rnithyaeswar11@gmail.com<p>The objective of this paper is to identify the key attributes that have a significant impact on the merit cum means-based scholarship selection process, ensuring that the allocation of resources is fair and efficient. Scholarships aid students with limited resources in their pursuit of a college education. The complexity of selecting suitable candidates with multiple characteristics has made it harder to determine the essential factors for deciding whether or not an applicant is eligible. To reduce attributes, we use the concepts of basis, lower and upper approximations of Nano Topological Spaces to identify the most relevant traits that affect scholarship eligibility. By using a systematic approach, decision-making is minimized and resources are allocated more effectively. Administrators can ensure that scholarships reach deserving students in need by focusing on essential attributes. The research will help to improve scholarship awarding methods and increase inclusion and accessibility in higher education.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Kalarani M, Nithyakala Rhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/951Inventory model with preservation technology and exponential holding cost in fuzzy scenario2023-12-30T22:02:41+01:00Hemalatha Shunmugamshemalatha1974@gmail.comAnnadurai Karuppuchamydrkannadurai@gmail.com<p>Inventories are ubiquitous in the business sector. Since inventory is most frequently incurring expense, stock control is critical for an organization and it must be scrimping and saving in contemplation of function the merchandising fruitfully. In this paper, an inventory model for a deteriorating item under exponential holding cost with collaborative preservation technology investment under carbon policy is considered. Also, this study is developed in a fuzzy scenario by employing triangular fuzzy numbers. Signed distance method is utilized to enhance decision making and optimization. Further the convexity of the total cost function for both the crisp and the fuzzy case is established. The objective is to determine the optimal investment in preservation technology and the optimal cycle length so as to minimize the total cost. Moreover, some managerial results are obtained by using sensitivity analysis and graphical representation is also carried out. The applications of the proposed model is used in the fields of constructing machinery or heavy duty construction equipment, specific chemicals and processed food. </p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Hemalatha Shunmugam et al.http://eiris.it/ojs/index.php/ratiomathematica/article/view/956Topology via Graph Ideals2023-12-30T22:02:41+01:00P. Gnanchandrapgchandra07@gmail.comK. Lalithambigailalithambigaimsc@gmail.comThe study of ideal topological space has started since 1933 and till date it is being developed by several mathematicians. Various classes of open sets, different types of operators and exploration of elementary topological results in ideal topological spaces have been discussed in various research papers. Methods of generating topologies using various relations have been explored by many researchers. Many researchers explored the methods of inducing topologies via graphs. This paper, introduces the notions of graph ideals, graph local function and characterizes some of their properties. It also describes a method of generating a new graph topology on the vertex set of a graph from the graph adjacency topology using Kuratowski closure operator and depicts the nature of open sets with respect to the new topology. Further, it explores the condition for compatibility of the graph adjacency topology with graph ideal.2023-12-30T21:58:40+01:00Copyright (c) 2023 P. Gnanchandra, K. Lalithambigaihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/961W8 - Curvature Tensor in Generalized Sasakian Space Forms2023-12-30T22:02:41+01:00Gyanvendra Pratap Singhgpsingh.singh700@gmail.comR Rajanrajanvishwakarma497@gmail.comAnand Kumar Mishraaanandmishra1796@gmail.comPawan Prajapatipawanpra123@gmail.com<p>The generalized Sasakian-space-forms and their properties have been examined by various researchers such as Alegre and Carriazo [2008], Prakasha [2012], Sarkar and Akbar [2014], Shanmukha et al. [2018], Sarkar and Sen [2012], Rajan and Singh [2020] and Sarkar and Sen [2012]. Motivated by the results of these works, we have proposed the idea of the W8−curvature tensor in generalized Sasakian-space- forms. The main goal of this paper is to investigate the curvature properties of generalized Sasakian-space-forms that satisfy the conditions ξ − W8− flatness, ϕ − W8−semi-symmetric, W8 · Q = 0, W8 · R = 0 and to prove some interesting results.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Gyanvendra Pratap Singh, Rajan, Anand Kumar Mishra, Pawan Prajapatihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1092Approximation and moduli of continuity for a function belonging to Holder’s class Hα [0, 1) and solving Lane-Emden differential equation by Boubaker wavelet technique2023-12-30T22:02:41+01:00Swatantra Yadavswatantrayadavbhu@gmail.comShyam Lalshyam_lal@rediffmail.comIn this paper, Boubaker wavelet is considered. The Boubaker wavelets are orthonormal. The series of this wavelet is verified for the function f(t) = t. The convergence analysis of solution function of Lane-Emden differential equation has been studied. New Boubaker wavelet estimator E2 k,M(f) for the approximation of solution function f belong to H¨older’s class Hα[0, 1) of order 0 < α ≤ 1, has been devloped. Furthermore, the moduli of continuity of solution function of Lane-Emden differential equation has been introduced and it has been estimated for solution function f∈ Hα[0, 1) class. These estimator and moduli of continuity are new and best possible in wavelet analysis. Boubaker wavelet collocation method has been proposed to solve Lane-Emden differential equations with unkown Boubaker coefficients. In this process, Lane-Emden differential equations are reduced into a system of algebraic equations and these equations are solved by collocation method. Three Lane-Emden type equations are solved to demonstrate the applicability of the proposed method. The solutions obtained by the proposed method are compared with their exact solutions. The absolute errors are negligible. Thus,this shows that the method described in this paper is applicable and accurate.2023-12-30T21:58:40+01:00Copyright (c) 2023 Swatantra Yadav and Shyam Lalhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1095Group Fuzzy Languages and its Generalizations2023-12-30T22:02:41+01:00Archana Vasudevan Pillai Prasannarajesharchana09@gmail.comRamesh Kumar Pramesh.ker64@gmail.comPrakash G Narasimha Shenoiprakashgn1976@gmail.com<p>In fuzzy language theory, every monoid is the syntactic monoid of some fuzzy language. By using this result the properties of fuzzy language can be studied by the algebraic properties of the syntactic monoids. There are so many methods for studying fuzzy languages. We adopt the above method to analyze different class of fuzzy languages and also characterize certain varieties of fuzzy languages. In this paper we give the variety description of group fuzzy languages and also provide the Eilenberg variety theorem for the class of group fuzzy languages. Moreover we described a fuzzy language whose syntactic monoid is isomorphic to the group Zn.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 ARCHANA VASUDEVAN PILLAI PRASANNA, Ramesh Kumar P, Prakash G Narasimha Shenoihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1131Cactus Graphs with Cycle Blocks and Square Product Labeling2023-12-30T22:02:41+01:00Keerthi G. Mirajkarkeerthi.mirajkar@gmail.comPriyanka G. Sthavarmathpriyankasthavarmath1990@gmail.com<p>In many real world problems, cactus graphs were considered as models from both algorithmic and theoretical point of view and this graph is a subclass of planar graph and superclass of a tree. In this article, the study has been carried out on some cactus graphs with cycle blocks for obtaining results on square product labeling. </p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Keerthi G. Mirajkar et al.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1133Amalgamated rings with m-nil clean properties2023-12-30T22:02:41+01:00Vijayanand Venkatachalamvvijayanandmath@gmail.comSelvaraj Chelliahselvavlr@yahoo.com<p>In this paper, we study the transfer of the notion of $m$-nil clean (i.e., a ring in which every element is a sum of a nilpotent and an $m$-potent elements) to the amalgamarted rings. We also find many sufficient and necessary conditions for the $m$-nil clean property to the amalgamated rings.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Vijayanand Venkatachalam, Selvaraj Chelliahhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1134Fork-decomposition of strong product of graphs2023-12-30T22:02:41+01:00Samuel Issacrajsamuelissacraj@gmail.comPaulraj Josephprof.japulraj@gmail.comDecomposition of arbitrary graphs into subgraphs of small size is assuming importance in the literature. There are several studies on the isomorphic decomposition of graphs into paths, cycles, trees, stars, sunlet etc. Fork is a tree obtained by subdividing any edge of a star of size three exactly once. In this paper, we investigate the necessary and sufficient for the fork-decomposition of Strong product of graphs.2023-12-30T21:58:40+01:00Copyright (c) 2023 Samuel Issacraj, Paulraj Josephhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1136Results on Binary Soft Topological Spaces2023-12-30T22:02:41+01:00P. G. Patilpgpatil01@gmail.comAsha G. Adakiasha.adaki@kud.ac.in<p>The Baire space is used in the proof of results in many areas of analysis and geometry, including some of the fundamental theorems of functional analysis. The concept of Baire spaces has been studied extensively in general topology. Thangaraj and Anjalmose [35] studied Baire spaces in the context of fuzzy theory. In this paper, we discussed the notions of the binary soft nowhere dense, binary soft dense, binary soft Gδ-set, binary soft first and second category sets, binary soft Baire spaces. Many of their properties are revealed and different characterizations of each are given. In conclusion, we determined some conditions under which the subspace property of a Baire space is preserved.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 P. G. Patil, Asha G. Adakihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1139Deep Features and Clustering Based Keyframes Selection with Security2023-12-30T22:02:41+01:00Prachi Chauhan49422_prachichauhan@gbpuat-tech.ac.inHardwari Lal Mandoriadrmandori1@gmail.comAlok Negialok.negi@ddn.upes.ac.in<p>The digital world is developing more quickly than ever. Multimedia processing and distribution, however become vulnerable issues due to the enormous quantity and significance of vital information. Therefore, extensive technologies and algorithms are required for the safe transmission of messages, images, and video files. This paper proposes a secure framework by acute integration of video summarization and image encryption. Three parts comprise the proposed cryptosystem framework. The informative frames are first extracted using an efficient and lightweight technique that make use of the color histogram-clustering (RGB-HSV) approach's processing capabilities. Each frame of a video is represented by deep features, which are based on an enhanced pre-trained Inception-v3 network. After that summary is obtain using the K-means optimal clustering algorithm. The representative keyframes then extracted using the clusters highest possible entropy nodes. Experimental validation on two well-known standard datasets demonstrates the proposed methods superiority to numerous state-of-the-art approaches. Finally, the proposed framework performs an efficient image encryption and decryption algorithm by employing a general linear group function GL<sub>n</sub> (F). The analysis and testing outcomes prove the superiority of the proposed adaptive RSA.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Prachi Chauhan, Hardwari Lal Mandoria, Alok Negihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1140Products on Maximal Compact Frames2023-12-30T22:02:41+01:00Jayaprasad P. N.jayaprasadpn@gmail.com<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>In topological spaces, many topological properties such as separation properties, paracompactness etc. are preserved under the act of taking product of topological spaces. The well known Tychonoff theorem in topological spaces which states that product of compact spaces is compact. Many of these results can be extended to the “generalized topological spaces”, known as locales (frames). According to Tychonoff product theorem for locales, locale product(coproduct of frames) of compact locales (frames) is compact. In this paper, we examine whether the coproduct of maximal compact frames is maximal compact. We examine the case for a finite coproduct and for an arbitrary coproduct of maximal compact frames. Every subframe of a compact frame is compact but a sublocale need not be. We provide a characterization for a sublocale of a maximal compact frame to be a maximal compact sublocale.</p></div></div></div>2023-12-30T21:58:40+01:00Copyright (c) 2023 JAYAPRASAD P Nhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1144Feebly r-clean ring and feebly*-r-clean ring2023-12-31T08:31:02+01:00Saravanan Viswanathananalysissaravanan@gmail.com<p>In this article, we introduce the concept of feebly r-clean ring and feebly ∗-r-clean ring. A ring R is defined to be feebly r-clean, if every element a can be written as a = r + e − f, where u is a regular and e, f are orthogonal idempotents and A ∗ ring R is defined to be feebly ∗-r clean if every element a can be written as a = r + p − q, where r is regular element and p, q are orthogonal projections. Further we generalise this concept of feebly r-clean ring to feebly g(x)−r-clean ring, where g(x) ∈ C(R)[x] and C(R) is the centre of ring R.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Saravanan Viswanathanhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1152Optimization of fuzzy two-level production inventory system with persuasive exertion-reliant demand2023-12-30T22:02:41+01:00R Vithyadevivithyakrishnan26@gmail.comK Annaduraidrkannadurai@gmail.comDynamic manufacturing-inventory system’s intelligent production design develops a crucial problem in the business reactivity of indecisions. This investigation examines a two-level production system under fuzzy parameters and decision variables by implementing a pentagonal fuzzy quantity. As designed, the fuzzy system is defuzzified through the graded mean technique, and then the Kuhn-Tucker technique is utilised to obtain the optimum production size and shortage level. The effectual algorithms are established to project an intellectual industrial approach such as optimal production quantity, shortage level, trade group’s exertions, and then minimum integrated expected total cost. The evaluation of the proposed fuzzy system is primed to fit numerical examples compared to the crisp system. This suggested fuzzy system is likewise compared with a particular case of the prior model. Numerical illustrations and sensitiveness studies are delivered in the direction of exhibiting the applicability based on the offered procedure and the attained outcomes..2023-12-30T21:58:40+01:00Copyright (c) 2023 Vithyadevi Ramakrishnan, Annadurai Karuppuchamyhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1153Fuzzy dominator coloring on fuzzy soft graphs2023-12-30T22:02:41+01:00Jahir Hussain Rasheedhssn_jhr@yahoo.comAfya Farhanaafyafarhana@gmail.com<p>A fuzzy soft dominator colouring of a fuzzy soft graph $G^S$(T,V) is an appropriate fuzzy soft colouring such that every single vertex of $G^S$(T,V) dominate entire vertex of a colour group. In the present work, we initiate fuzzy dominator colouring on fuzzy soft path, fuzzy soft cycle, complete fuzzy soft graph, complete fuzzy soft bipartite graph and its fuzzy soft dominator chromatic number is presented as well as bounds for fuzzy soft dominator chromatic number on fuzzy soft graph is established.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Jahir Hussain Rasheed, Afya Farhanahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1155Non Deterministic Zero Divisor Graph2023-12-30T22:02:41+01:00Shakila Banushakimeeran10@gmail.comNaveena Selvarajnaveena94430@gmail.com<p>A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined. In other words, there may be multiple elements that can multiply with the given element to produce zero. This concept is typically encountered in non-commutative rings or algebras where the order of multiplication matters. In such structures, the existence of non-deterministic zero divisors can complicate calculations and lead to different results depending on the order of operations. In this paper, we examine that all the zerodivisor graphs are nondeterministic graph but the converse need not. We manifest the nondeterministic zero divisor graph is possible only with nonprimes. Hereby, we study about weighted graphs, Weiner index and golden ratio rule. Also we provide an algorithm for zero divisor graph of n parameters and thereby, explore the given graph is either deterministic or nondeterministic graph using python.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Banu and Selvarajhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1180Fuzzy soft set connected mappings2023-12-30T22:02:41+01:00Alpa Singh Rajputasr_sh@vignan.ac.inMahima Thakurmthakur@jecjabalpur.ac.inSamajh Singh Thakursamajh_singh@rediffmail.comIn this paper, the concepts of fuzzy soft connectedness between fuzzy soft sets and fuzzy soft set connected mappings in fuzzy soft topological spaces has been introduced. It is shown that a fuzzy soft topological space is fuzzy soft connected if and only if it is fuzzy soft connected between every pair of its nonempty fuzzy soft sets. Every fuzzy soft continuous mapping is fuzzy soft set-connected a counter example is given to show the converse may not be true. Several properties of fuzzy soft set-connected mappings in fuzzy soft topological spaces have been studied.2023-12-30T21:58:40+01:00Copyright (c) 2023 Alpa Singh Rajput, Mahima Thakur, Samajh Singh Thakurhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1189Anti-Adjacency Matrices of Certain Graphs Derived from Some Graph Operations2023-12-30T22:02:41+01:00Manju V Nmanjushaijulal@yahoo.comAthul T Bathultbacl@gmail.comSuresh Singh Ggsureshsingh65@gmail.comIf we go through the literature, one can find many matrices that are derived for a given simple graph. The one among them is the anti-adjacency matrix which is given as follows; The anti-adjacency matrix of a simple undirected graph $G$ with vertex set $V (G) \,= \,\{\,v_1,\,v_2,\\ \dots, v_n\}$ is an $n \times n$ matrix $B(G) = (b_{ij} )$, where $b_{ij} = 0$ if there exists an edge between $v_i$ and $v_j$ and $1$ otherwise. In this paper, we try to bring out an expression, which establishes a connection between the anti-adjacency matrices of the two graphs $G_1$ and $G_2$ and the anti-adjacency matrix of their tensor product, $G_1 \otimes G_2$. In addition, an expression for the anti-adjacency matrix of the disjunction of two graphs, $G_1\lor G_2$, is obtained in a similar way. Finally, we obtain an expression for the anti-adjacency matrix for the generalized tensor product and generalized disjunction of two graphs. Adjacency and anti-adjacency matrices are square matrices that are used to represent a finite graph in graph theory and computer science. The matrix elements show whether a pair of vertices in the graph are adjacent or not.2023-12-30T21:58:40+01:00Copyright (c) 2023 Manju V N, Athul T B, Suresh Singh Ghttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1193Commutative Medial Near Ring2023-12-30T22:02:41+01:00Dhivya Cdhivya.deepa7@gmail.comRadha Dradharavimaths@gmail.com<span>We deliberate a substructure of a near ring called mediality so as to create a new platform, on which many of the properties like commutativity, regular, idempotent and zero symmetric are applied with. It is shown that every medial near ring is commutative whenever cancellation law holds. Commutative medial near ring is left medial, right medial, reverse, reverse medial, reverse left medial and reverse right medial. It is proved that a non-trivial left medial regular near ring is reduced. Also, a structure theorem has been obtained.</span>2023-12-30T21:58:40+01:00Copyright (c) 2023 Dhivya C, Radha Dhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1200Application of m- polar soft fuzzy bi- partite graph in residence selection process2023-12-30T22:02:41+01:00S Ramkumarramkumarmat2015@gmail.comR Sridevidanushsairam@gmail.com<span>An $m-$polar fuzzy set and soft sets are two different tools for representing uncertainty and vagueness. An $m-$polar soft fuzzy set is a mapping from parameter set to the $m-$polar fuzzy subsets of the universe. An $m-$polar soft fuzzy set theory provides a parameterized point of view for uncertainty modeling and soft computing model. In this paper, we have introduced the notions of $m-$polar soft fuzzy bipartite graph, size and degree of $m-$polar soft fuzzy bi-partite graph as well as an investigation on buying of residence by considering various parameters. People, while buying residence, have many options. So, to choose the best one, they have to consider many parameters. $m-$polar soft fuzzy graph is one of the major areas of graph theory, which finds a solution to this problem</span>2023-12-30T21:58:40+01:00Copyright (c) 2023 Ramkumar and Sridevihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1201A perishable inventory optimization model for two commodities in multi-echelon system2023-12-30T22:02:41+01:00Prabaharan Kathiresanpharansouc@gmail.comBakthavachalam Rengarajanbakthaa@yahoo.com<p><span>In this article, we delve into the quest for an optimal solution within the realm of a practical inventory system, which serves as an integral component of a larger Multiechelon inventory system. Our study focuses on a warehouse (WH) that houses a single Distribution Center (DC) and a sole retailer (R) tasked with managing two distinct yet interconnected perishable products. This setup is modeled as a three-stage continuous review inventory system. At the retailer node, we implement an (s, S) inventory system, accommodating Poisson demand and exponentially distributed lead times. It’s important to note that the primary products are susceptible to perishing exclusively at the retailer node, characterized by a rate ζ, whereas the sub-products are non-perishable in nature. Deliveries to retailers occur in packs of Qi(= Si − si) units, originating from the distribution center (DC) with immediate replenishment capabilities sourced from the well-stocked warehouse (WH). Throughout our analysis, we rigorously maintain steady-state probability distributions and behavioral insights. Furthermore, we diligently collect and analyze performance measurements for the system under steady-state conditions. Our findings are showcased through numerical examples, shedding light on the practical implications of our inventory management approach.</span></p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Prabaharan Kathiresan, Bakthavachalam Rengarajanhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1204Nano δI-closed Sets in Nano Ideal Topological Spaces2023-12-30T22:02:41+01:00M.Karthigai Jothijothiperiyasamy05@gmail.comK Palanipalani@apcmcollege.ac.in<p>This article investigates the notion of N-δI-closed sets and its properties in ideal nano topological space using the closure operator Ncl<sub>δI</sub>(S)={xÎՍ/ Nint(Ncl<sup>*</sup>(W))∩ S ≠ ∅, for each WÎW<sub>N</sub>(x)}. We establish Ncl<sub>δI</sub>(S) is the intersection of all N-δI-closed supersets of S and Nint<sub>δI</sub>(S) is the union of all N-δI-open subsets of S in this space. Apart from that N-δI-closed sets occurs between the class of Nδ-closed sets and N-closed sets. Moreover, we explore the concepts of N-δI-interior, N-δI-Exterior, N-δI-Border, and N-δI-Frontier and discuss its properties.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 M.Karthigai Jothi, K Palanihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1206Weighted sharing of meromorphic functions concerning certain type of linear difference polynomials2023-12-30T22:02:41+01:00Megha M. Manakamemegha.manakame80@gmail.comHarina P Waghamoreharinapw@gmail.com<p>In this research article, with the help of Nevanlinna theory we study the uniqueness problems of transcendental meromorphic functions having finite order in the complex plane $\mathbb{C}$, of the form is given by $\phi^{n}(z)\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ and $\psi^{n}(z)\sum_{j=1}^{d}a_{j}\psi(z+c_{j})$ where $L(z,\phi)=\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ which share a non-zero polynomial $p(z)$ with finite weight. By considering the concept of weighted sharing introduced by I. Lahiri (Complex Variables and Elliptic equations,2001,241-253), we investigate difference polynomials for the cases $(0,2),(0,1),(0,0)$. Our new findings extends and generalizes some classical results of Sujoy Majumder\cite{m11}. Some examples have been exhibited which are relevant to the content of the paper.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Megha M. Manakame, Harina P Waghamorehttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1207Distance Based Topological Indices of Double graphs and Strong Double graphs2023-12-30T22:02:41+01:00Keerthi G. Mirajkarkeerthi.mirajkar@gmail.comShobha Rajashekhar Konnurshobhakonnur13@gmail.com<p>Topological index is a numerical representation of structure of graph. They are mainly classified as Distance and Degree based topological indices. In this article Distance based topological indices of Double graphs and Strong Double graphs are calculated. Let $G$ be a graph of order $n$ with the vertex set $ V(G)$ containing vertices $v_1,v_2,....,v_n$. Double graph of graph $G$ is constructed by taking two copies of G in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $ v_i$ and $v_j$ are adjacent in G. Strong Double graph is a double graph in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $i=j$. </p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Keerthi G. Mirajkar, Shobha Rajashekhar Konnurhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1211Results on Relatively Prime Domination Number of Vertex Switching of Some Graphs2023-12-30T22:02:41+01:00A Jancy Vinijancyvini@gmail.comC Jayasekaranjayacpkc@gmail.com<p>If a set S ⊆ V has at least two members and every pair of vertices u and v is such that (d(u), d(v)) = 1, then it is said to be a relatively prime dominating set. The relatively prime domination number, represented by γrpd(G), is the lowest cardinality of a relatively prime dominating set. The switching of a finite undirected graph by a subset is defined as the graph Gσ(V, E′), which is obtained from G by removing all edges between σ and its complement V − σ and adding as edges all non-edges between σ and V − σ. In this paper, we com-<br />pute the relatively prime domination number of vertex switching of cycle type graphs like David Star Graph, Helm Graph, Friendship Graph and Book Graph.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 A Jancy Vini, C Jayasekaranhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1221Stochastic Perishable Inventory System Analysis With Two Types Of Customers In The Supply Chain2023-12-30T22:02:41+01:00Virumandi Chellaiahvirumakodai@gmail.comBakthavachalam Rengarajanbakthaa@yahoo.com<div>In the supply chain model being examined in this study, there are two different client expectations. A warehouse, a single distribution centre, a single retailer, and the handling of a single perishable product make up the system. Retailer node (lower echelon) assumes a A(s, S) type inventory system with Poisson demand and exponentially dispersed lead times, and distribution centre assumes a (0, kQ) policy (middle echelon). Demands that happen during the times when there is no stock are taken to be lost sales. The merchandise is sent from the distribution centre to the stores in packs of Q(= S − s) items. It is believed that only the retailer nodes with rate γ experience item perishability. The upper echelon (warehouse) replaces the distribution center’s stock with exponentially distributed lead times due to its ample supply. Demands arrive at the retailer node in two categories: (i) normal customers; and (ii) priority customers, with arrival rates of α and β. It is possible to obtain the metrics of system performance as well as the steady state probability distribution of system states. The proposed paradigm is demonstrated with numerical examples.</div>2023-12-30T21:58:40+01:00Copyright (c) 2023 Virumandi CHELLAIAH and Bakthavachalam Rengarajanhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1224Compatible mappings and its variants satisfying generalized (ψ, φ)−weak contraction2023-12-30T22:02:41+01:00Kavita Latherkvtlather@gmail.comSanjay Kumardrsanjaykumar.math@dcrustm.orgRajesh Kumarrkdubaldhania@gmail.comNikita Kadiankadyannikita2@gmail.comBanach contraction principle behaves as a mathematical tool to solve various practical problems arising during mathematical formulation of many theoretical problems. In present work, the existence of a unique common fixed point for pairs of minimal commutative mappings is discussed, which satisfy a generalized (ψ, φ)−weak contraction involving cubic terms of distance functions. Examples are given in support of the obtained results and as an application the existence of solution of system of certain functional equations arising in dynamic programming is discussed.2023-12-30T21:58:40+01:00Copyright (c) 2023 kavita lather, sanjay kumar, rajesh kumar, nikita kadianhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1230Analytical solution of time-fractional N-dimensional Black-Scholes equation using LHPM2023-12-30T22:02:41+01:00Sanjay Ghevariyasj_ghevariya@spuvvn.eduCHETANBHAI PATELchetanbhai.patel@cvmu.edu.inA famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W. and Wiwattanapataphee B. obtained analytical solution of Black-Scholes equation with two assets in the Liouville-Caputo time-fractional derivative sense using Laplace homotopy perturbation method (LHPM). The aim of this paper is to derive solution of Liouville-Caputo time-fractional Black-Scholes equation with n assets using LHPM. Numerical results shows that our approach gives very accurate results and our formulas are quite close to the plain vanilla options.2023-12-30T21:58:40+01:00Copyright (c) 2023 Sanjay Ghevariya, CHETANBHAI PATELhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1236B-Gabor type frames in separable Hilbert spaces2023-12-30T22:02:41+01:00Thomas Jineeshjineeshthomas@gmail.comN M Madhavan Namboothirimadhavangck@gmail.comP N Jayaprasadjayaprasadpn@gmail.com<p>It is guaranteed that Gabor like structured frames do exist in any finite dimensional Hilbert space via an invertible map from l2(ZN) J Thomas and Nambudiri [2022]. Hence the question: whether it is possible to obtain structured class of frames in separable Hilbert spaces? is relevant. In this article we obtain a structured class of frames for separable Hilbert spaces which are generalizations of Gabor frames for L2(R) in their construction aspects. We call them as B-Gabor type frames and present a characterization of the frame operators associated with these frames when B is a unitary map. Some significant properties of the associated frame operators are discussed.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Thomas Jineesh, N M Madhavan Namboothiri, P N Jayaprasadhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1248Common fixed points of self-maps over the generalized cone b-metric spaces2024-01-01T07:05:38+01:00Mallikarjun Reddy Pagidipagidimallik@gmail.comThe main aim of this research paper is to establish the most generalized common fixed-point theorem for two self-maps that are commuting to each other under \mathbf{T}-Kannan type contractive condition over a generalized cone \mathbb{b}-metric spaces. The novelty of this research paper is to find a common fixed point of two weekly compatible self-maps over a generalized cone \mathbb{b}-metric spaces without assuming the normality condition of a cone. We illustrate our main result with a suitable example.2023-12-30T21:58:40+01:00Copyright (c) 2023 Mallikarjun Reddy Pagidihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1253Antimagic Labeling of Some Degree Splitting Graphs2023-12-30T22:02:41+01:00Chirag Barasarachirag.barasara@gmail.comPalak Prajapatipalakprajapati733@gmail.com<p>A graph with q edges is called antimagic if its edges can be labeled with 1, 2, 3, ..., q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. As Wang et al. [2012], proved that not all graphs are antimagic, it is interesting to investigate antimagic labeling of graph families. In this paper we discussed antimagic labeling of the larger graphs obtained using degree splitting operation on some known antimagic graphs. As discussed in Krishnaa [2016], antimagic labeling has many applications, our results will be used to expand the network on larger graphs.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Chirag Barasara, Palak Prajapatihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1270Non-deterministic-M-fuzzy Lattices2023-12-30T22:02:41+01:00Gireesan K.K.gireesankk@gcek.ac.inAnnie Sabitha Paulanniesabithapaul@gmail.comSabu Sebastiansabukannur@gmail.comGoran Trajakoviski and Tepavcevic´invented the L-fuzzy lattice in which a ´ bounded lattice is fuzzified using a complete lattice. Using a complete consistent distributive multilattice M, we broaden the concept of L-fuzzy lattice to Nd-M-fuzzy lattice in this study. We also introduce the idea of Nd-M-order relation on a set X. Additionally, we demonstrated that the equivalent condition for a Nd-M-fuzzy subset to be a Nd-M-fuzzy sublattice of a bounded lattice L.2023-12-30T21:58:40+01:00Copyright (c) 2023 GIREESAN K.K., Annie Sabitha Paul, Sabu Sebastianhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1288On Ideals in Partially Ordered Ternary Semigroups2023-12-30T22:02:41+01:00Dattatray Nabajirao Shindeshindednmaths@gmail.comMachchhindra T. Gophanemtg_maths@unishivaji.ac.in<p>The concept of ideals has been extensively studied through various algebraic structures such as near-rings, involution rings, regular rings, gamma-rings, semigroups, ordered semigroups, ternary semigroups<br />and ordered ternary semigroups. In this article, we have investigated some intriguing properties of ideals, bi-ideals and pseudo symmetric ideals in partially ordered ternary semigroup T. We establish conditions for (UV W] to be an ideal, bi-ideal and pseudo symmetric ideal of T, where U, V, W are non-empty subsets of T. We prove that the family P of all pseudo symmetric ideals of T forms a Moore family of subsets of T. We also prove that the collection P of all pseudo symmetric ideals of T is a Brouwerian lattice. Also we define a pseudo<br />symmetric partially ordered ternary semigroup.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Dattatray Nabajirao Shinde, Machchhindra T. Gophanehttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1289Relatively Prime Detour Domination Number of Some Switching Graphs2023-12-31T18:04:55+01:00C Jayasekaranjayacpkc@gmail.comL. G. Binojalgbinoja1994@gmail.comIn this paper, we introduce the concept of relatively prime detour domination number for switching graph. If a set S ⊆ V is a detour set, a dominating set with at least two elements, and has (deg(u), deg(v)) = 1 for each pair of vertices u and v, then it is said to be a relatively prime detour dominating set of a graph G. The relatively prime detour domination number of a graph G is known as γrpdn(G) and represents the lowest cardinality of a relatively prime detour dominating set. First, we explain the concept of a switching graph before producing some conclusions based on the switching graphs of helm, fan, complete, spider, and sunlet graphs that have relatively prime detour domination numbers.2023-12-30T21:58:40+01:00Copyright (c) 2023 C Jayasekaran et al.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1299Strongly*-2 Divisor Cordial Labeling of Cycle Related Graphs2024-01-02T14:38:40+01:00C. Jayasekaranjayacpkc@gmail.comV.G. Michael Florancemiclaelflorance@gmail.com<p>A strongly*-2 divisor cordial labeling of a graph G with the vertex set V (G) is a bijection a : V (G) → {1, 2, 3, ..., |V (G)|} such that each edge cd assigned the label 1 if the lower integal value of sum of a(c), a(d) and a(c)a(d) divided by 2 is odd and 0 if lower integal value of sum of a(c), a(d) and a(c)a(d) divided by 2 is even, then the number of edges labeled with 0 and the number of edges labeled with 1 differs by atmost 1 or |ea(0) − ea(1)| ≤ 1 where ea(0) denotes the number of edges labeled with 0 and ea(1) denotes the number of edges labeled with 1. A graph which admits a strongly*-2 divisor cordial labeling is called a srongly*-2 divisor cordial graph. In this paper, we prove that the wheel graph Wg and sunflower graph SFg are strongly*-2 divisor cordial graphs.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 C. Jayasekaran, V.G. Michael Florancehttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1310Inventory Model for Quadratic Demand and Deteriorating Items Following Weibull Distribution with Trade Credit Policy2023-12-30T22:02:41+01:00Khyati Singhcontact2khyati@gmail.comAshendra Kumar Saxenadrashendra.computers@tmu.ac.inIn this paper, an inventory model for deteriorating items following two parameter Weibull distribution with trade credit policy is developed, while demand is viewed as quadratic function of time. The supplier gives the retailer a trade credit period. Trade credit is a frequently used method of payment implemented by suppliers, and it generally leads to greater revenue and ultimately, higher income. The suggested inventory model seeks to calculate the ideal replenishment cycle duration in order to maximize the overall profit per unit of time. Shortages are permitted and partially backlogged. Two categories are applied to the mathematical model. Case I: When the payment to settle the account is made on or before the positive inventory. Case II: When the payment to settle the ac-count is made after the inventory reaches to zero. The model is illustrated through numerical experiments, sensitivity analysis, and graphical depiction.2023-12-30T21:58:40+01:00Copyright (c) 2023 Khyati Singh, Ashendra Kumar Saxenahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1315On Prime Index of a Graph2023-12-30T22:02:41+01:00Janani Rraseja3@gmail.comRamachandran Tyasrams@gmail.com<p>In prime labeling, vertices are labeled from 1 to n, with the condition that any two adjacent vertices have relatively prime labels. Coprime labeling maintains the same criterion as prime labeling with adjacent vertices using any set of distinct positive integers. Minimum coprime number prG, is the minimum value k for which G has coprime labeling. There are many graphs that do not possess prime labeling, and hence have coprime labeling. The primary purpose of this work is to change a coprime labeled graph into a prime graph by removing the minimum number of edges. Thus, the prime index ε(G) is the least number of edges to be removed from a coprime graph G to form a prime graph. In this study, the prime index of various graphs is determined. Also, an algorithmic way to determine the prime index of the complete graph is found.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Janani R and Ramachandran Thttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1353G-Supra and G-Infra space2023-12-30T22:02:42+01:00Sutha Devisuthadevi_ts240@anjaconline.orgEswari Keswarivvvc2017@gmail.com<p>The main idea of this paper is to generate supra and infra topologies from simple undirected graphs. For this, we have introduced two new operators namely supra and infra operators which are defined on the power set of the vertex set of a graph. Moreover, we have also proved that the supra operator satisfying Kuratowski’s closure axiom will yield a topology. Further it was extended to develop the concept of connectedness and separation axioms on G-supra and G-infra spaces.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Sutha Devi, Eswari Khttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1374Weaker forms of Contra Continuous Multifunctions2023-12-30T22:02:42+01:00Pallavi Mirajakarpsmirajakar@gmail.comRajeshwari K K.rajeshwaribhat10@yahoo.comSarika M. Patil Patilsarupatil@rediffmail.comT.D.Rayangoudar Rayanagoudarrgoudar1980@gmail.com<div>The purpose of this paper is to study αgs-continuous multifunctions. Some basic characterizations, preservation theorems and several properties concerning upper and lower αgs-continuous multifunctions are investigated.</div>2023-12-30T21:58:40+01:00Copyright (c) 2023 Pallavi Mirajakar, Rajeshwari K K., Sarika M. Patil Patil, T.D.Rayangoudar Rayanagoudarhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1384Monophonic Distance Laplacian Energy of Transformation Graphs Sn^++-,Sn^{+-+},Sn^{+++}2023-12-30T22:02:41+01:00Diana Rdianajino@gmail.comBinu Selin Tbinuselin@gmail.com<p>Let $G$ be a simple connected graph of order $n$, $v_{i}$ its vertex. Let $\delta^{L}_{1}, \delta^{L}_{2}, \ldots, \delta^{L}_{n}$ be the eigenvalues of the distance Laplacian matrix $D^{L}$ of $G$. The distance Laplacian energy is denoted by $LE_{D}(G)$. This motivated us to defined the new graph energy monophonic distance Laplacian energy of graphs. The eigenvalues of monophonic distance Laplacian matrix $M^{L}\left(G\right)$ are denoted by $\mu^{L}_{1}, \mu^{L}_{2}, \ldots, \mu^{L}_{n}$ and are said to be $M^{L}$- eigenvalues of $G$ and to form the $M^{L}$-spectrum of $G$, denoted by $Spec_{M^{L}}(G)$. Here $MT_{G}\left(v_{j}\right)$ is the $j^{th}$ row sum of monophonic distance matrix of $M(G)$ and $\mu^{L}_{1}\leq\mu^{L}_{2}\leq, \ldots, \leq\mu^{L}_{n}$ be the eigenvalues of the monophonic distance Laplacian matrix is $M^{L}(G)$. The monophonic distance Laplacian energy is defined as $LE_{M}(G)$. In this paper we computed the monophonic distance Laplacian energy of $S^{++-}_{n}$, $S^{+-+}_{n}$, $S^{+++}_{n}$ graphs based on its spectrum values.\</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Diana R, Binu Selin Thttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1397Restrained star edge coloring of graphs and its application in optimal & safe storage practices2023-12-30T22:02:42+01:00W. Evangeline Lydiaevangelinelydiaa@gmail.comJ. Vijaya Xavier Parthipanparthi68@rediffmail.com<p align="justify">In this paper we introduce the concept of restrained star edge coloring of graphs by restraining the conditions of the star coloring of graphs. The restrained star edge coloring of graphs is a path based graph coloring which is said to be proper if all the bichromatic subgraphs of the graph are in the form of a galaxy. The minimum requirement for this coloring is its restrained star chromatic index, denoted as χ'<sub>rs</sub>. This paper exclusively explains, the restrained star edge coloring of several families of graphs including path, cycle, wheel, etc., and provides the exact value of its respective restrained star chromatic index, χ'<sub>rs</sub> with the usage of appropriate illustrations. In addition to this, an application of this coloring in the optimal utilization of storage spaces and in ensuring safe storage practices is also briefly elaborated.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Evangeline Lydia. W, Vijaya Xavier Parthipan. Jhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/1399Short-time fourier transform based ensemble classifiers for detection of atrial fibrillation from ECG datasets2024-01-02T08:16:36+01:00Gowri Shankar Manivannanmshankar065@gmail.comKalaiyarasi Mkalaiyarasime@gmail.comHarikumar Rajaguruharikumarr@bitsathy.ac.inAtrial Fibrillation (Afib) is a common cardiac arrhythmia characterized by irregular and often rapid heart rate, leading to inefficient blood pumping from the atria. It increases the risk of stroke, heart failure, and other heart-related complications. Afib is often associated with symptoms like palpitations, shortness of breath, and fatigue. Diagnosis typically involves electrocardiography (ECG) to detect irregular electrical activity in the heart. Treatment options range from medication to procedures like catheter ablation, aimed at restoring normal heart rhythm and reducing associated risks. Soft computing methods can aid in automating the classification of cardiovascular diseases, assisting clinicians in diagnosing arrhythmias. In this research paper, ensemble classifiers are employed for the classification of Atrial Fibrillation based on ECG datasets. When utilizing the Catboost Classifier in conjunction with the STFT-based GEO implementation, the results indicate an average perfect classification rate of approximately 99%, an error rate of 1%, and a kappa coefficient of 0.9689% for detection of Afib.2023-12-30T21:58:40+01:00Copyright (c) 2023 Gowri Shankar Manivannan et al.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1417Polynomial Collocation Methods Based On Successive Integration Technique For Solving System Of Neutral Delay Differential Equations2024-01-05T07:33:01+01:00Kayelvizhi C.kayelchokkalingam1997@gmail.comEmimal Kanaga Pushpam A.emimal.ma@bhc.edu.in<p>This paper presents a new approach to using polynomials such as Hermite, Bernoulli,<br />Chebyshev, Fibonacci and Bessel to solve a system of linear and nonlinear neutral delay<br />differential equations. The proposed method is based on the truncated polynomial<br />expansion of the function together with collocation points and successive integration<br />techniques. This method reduces the given equation to system of non-linear equations<br />with unknown polynomial coefficients which can be easily calculated. The convergence<br />of the proposed method is discussed with several mild conditions. Numerical examples<br />are considered to demonstrate the efficiency of the method. The numerical results reveal<br />that the proposed new approach gives better results than other conventional methods. It<br />demonstrates the reliability and efficiency of this method for solving a system of linear<br />and nonlinear neutral delay differential equations.</p>2023-12-30T21:58:40+01:00Copyright (c) 2023 Kayelvizhi C. and Emimal Kanaga Pushpam A.