South East Asian J. of Mathematics and Mathematical Sciences

FAMILY OF CONGRUENCES FOR (2, β) REGULAR BIPARTITION TRIPLES

V. Puneeth, Anirban Roy — Fri, 30 Dec 2022 00:00:00 +0100

Though congruences have their limitations, they have significant impor- tance in the field of number theory and helps in proving many interesting results. Thus, this article has adopted the technique and properties of congruences to iden- tify and prove a set of congruent properties for integer partition. The partition of a positive integer is a way of expressing the number as a sum of positive in- tegers. One such partitions known as regular bipartition triple are discussed in this article. New congruences modulo even integers and modulo prime (p 5) powers are derived for (2, β) regular bipartition triples. Also infinite families of congruences modulo 2 for some (2, β) regular bipartition triples are derived. The theorems stated in this article are proved using the q series notation and some of the prominent results such as Euler’s pentagonal number theorem and Jacobi’s triple product identities. There are certain lemmas which are derived using these results that help in proving the major results of this article.

ON THE SOLUTION OF A CLASS OF EXPONENTIAL DIOPHANTINE EQUATIONS

Mridul Dutta, Padma Bhushan Borah — Fri, 30 Dec 2022 00:00:00 +0100

In this note, we show that for n = 4N + 3, N N 0 , the expo- nential Diophantine equation n^x + 24^y = z² has exactly two solutions if n + 1 or equivalently N + 1 is an square. When N + 1 = m², the solutions are given by (0, 1, 5) and (1, 0, 2m). Otherwise it has a unique solution (0, 1, 5) in non-negative integers. Finally, we leave an open problem to explore.

HOMOMORPHISM AND ANTI-HOMOMORPHISM OF SPHERICAL CUBIC BI-IDEALS OF GAMMA NEAR-RINGS

V. Chinnadurai, V. Shakila — Fri, 30 Dec 2022 00:00:00 +0100

The purpose of the article is to study about homomorphism and anti- homomorphism of spherical cubic bi-ideals of Gamma near-rings R₁ and R₂. If φ : R₁ −→ R₂ be a gamma homomorphism and (C U _s1 , R₁), (C U _s2 , R₂) are spher- ical cubic bi-ideals of gamma near-rings R₁ and R₂.Then the image (φ(C U _s1 ), R₂) and pre-image (φ⁻¹(C U _s ), R₁) are also spherical cubic bi-ideals of gamma near- rings R₂ and R₁. If φ : R₁ −→ R₂ be an epimorphism of gamma near-rings R₁and R₂ and (C U _s , R₂) is a SCS of R₂ such that (φ⁻¹(C U _s ), R₁) is a SCBI of 2 2 R₁, then (C U _s2 , R₂) is a SCBI of R₂.

M − N ANTI HOMOMORPHISM OF AN M − N FUZZY SOFT SUBGROUPS AND ITS LEVEL M − N SUBGROUPS

M. Kaliraja, S. Rumenaka — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we have discussed the concept of M N anti homomor- phism of fuzzy soft subgroups, then we define the M N anti level subsets of a fuzzy soft subgroup and its some elementary properties are also discussed.

CERTAIN COEFFICIENT INEQUALITIES FOR THE CLASSES OF q-STARLIKE AND q-CONVEX FUNCTIONS

Murli Manohar Gour, Sunil . Joshi, Sunil Dutt Purohit — Fri, 30 Dec 2022 00:00:00 +0100

In this paper we determine certain coefficient inequalities for the classes of q-starlike and q-convex function and find the sufficient conditions for generalized Bessel function to belonging in these classes.

EXTENDED GENERALIZED τ -GAUSS’ HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATIONS

Bharti Chauhan, Prakriti Rai — Fri, 30 Dec 2022 00:00:00 +0100

In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

ON SOME NEW GENERATING FUNCTIONS OF HYPERGEOMETRIC POLYNOMIALS

Chaudhary Wali Mohammad, Jahan Ara — Fri, 30 Dec 2022 00:00:00 +0100

This paper contains mainly three theorems involving Kampe´ de Fe´riet’s function F ⁽²⁾ and expressed in terms of single and double Laplace and Beta inte- grals. The theorems, in turn, yield, as special cases, a number of linear, bilin- ear and bilateral generating functions of generalized polynomials of Rice, Jacobi polynomials, Ultraspherical, Generalized Laguerre, Bedient polynomials and other polynomials hypergeometric in nature. One variable special cases of generalized polynomials are useful in several applied problems.

CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF (p, q)-EXTENDED τ -HYPERGEOMETRIC FUNCTION

Mamta Gupta, Kanak Modi, Naveen Jha, Mukesh Sharma — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we established certain image formulas of the (p, q)–extended τ hypergeometric function R^{τ p ,q}(a, b; c; z) by employing Marichev-Sigo-Maeda(M-S-M) fractional integration and differentation Corresponding special cases for the Saigo’s, Riemann-Liouville and Erdelyi-Kober fractional integral and differ- ential operators are also deduced which are earlier obtained by Solanki et al. [23]. Further certain integral transforms of the (p, q)–extended τ hypergeometric function R^τ(a, b; c; z) are established. All the results are represented in terms of the Hadamard product of the (p, q)–extended τ hypergeometric function R^τ(a, b; c; z) and the Fox-Wright function.

AN SVIQR EPIDEMIC MODEL FOR COVID-19

Fri, 30 Dec 2022 00:00:00 +0100

We have proposed an SVIQR epidemic model for COVID-19 with vac- cination in this research. Some fundamental characteristics such as positivity of the solution, boundedness and invariance of the model are analyzed. Expressions for disease-free equilibrium (DFE) and endemic equilibrium (EE) points with certain criteria for existence are derived. Rigorous analysis of the model reveals that as- sociated DFE is locally asymptotically stable whenever the effective reproduction number is less than one. Also, the EE point is stable whenever certain restric- tions are satisfied. Sensitivity analysis is performed to identify key parameters that significantly affect the effective reproduction number. Analytical results are illustrated using parameter values and the results are analyzed using numerical simulation which suggests that the disease will eventually die out, particularly if the control measures are implemented above a specified level for a sustained period of time.

SOME PROPERTIES OF FRACTIONAL HARTLEY TRANSFORM

Swati Nikam, B. Surendranath Reddy, Vasant Gaikwad — Fri, 30 Dec 2022 00:00:00 +0100

This paper is motivated by the ideas of fractional Fourier transform and Hartley transform. Looking towards the practicality and demanding attention of fractional Hartley transform we take keen interest into it. In this paper, we deal with inverse theorem of FRHT and some important properties of fractional Hartley transform like exponential rule, multiplication rule, transform of derivative and derivative of transform, which play a very crucial role in the development of fractional Hartley transform.

EXISTENCE AND UNIQUENESS OF FIXED POINT FOR NEW CONTRACTIONS IN RECTANGULAR b-METRIC SPACES

Jayesh Tiwari, Dileep Kumar Sharma — Fri, 30 Dec 2022 00:00:00 +0100

In this article, we give some new examples of rectangular b-metric spaces which are neither rectangular metric space nor metric space. After that we prove existence and uniqueness of new fixed points for some new contractions in rectangular b-metric spaces. Then we validate these results with suitable, appro- priate and innovative examples.

CERTAIN SUBCLASS OF BI-UNIVALENT FUNCTIONS RELATED TO HORADAM POLYNOMIALS ASSOCIATED WITH q-DERIVATIVE

P. Nandini, S. Latha — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, by making use of q-derivative, we define a new subclass of analytic and bi-univalent functions related to Horadam polynomials. For func- tions belonging to this class, we derive coefficient inequalities and the Fekete-Szego¨ inequalities. We also provide relevant connections of our results with those consid- ered in earlier investigations

ON RECURRENT LIGHTLIKE HYPERSURFACE OF KENMOTSU MANIFOLD

Sushil Shukla — Fri, 30 Dec 2022 00:00:00 +0100

The object of present paper is to study the properties of recurrent lightlike hypersurfaces of Kenmotsu manifold with (l, m)−type connection.

ON SUBMANIFOLDS OF A MANIFOLD ADMITTING fa(2ν + 3, −1) - STRUCTURE

Jai Pratap Singh, Kripa Sindhu Prasad — Fri, 30 Dec 2022 00:00:00 +0100

Psomopoulou defined and studied the Invariant submanifolds of a man- ifold with f (2ν + 3, 1)-structure. In this paper f_a(2ν + 3, 1) structure has been defined and submanifolds, of a manifold with such a structure have been studied. Some interesting results have been stated and proved in this paper.

CARTAN SPACES WITH SLOPE METRIC UNDER h-METRICAL d-CONNECTION

Madeeha Muneer, Avdhesh Kumar, A. K. Shrivastav — Fri, 30 Dec 2022 00:00:00 +0100

This paper studies Cartan space with Matsumoto metric or slope met- ric under the effect of h-metrical d-connection. Then we deduce the conditions under which the Cartan space with slope metric becomes locally Minkowski and conformally flat.

EQUIVALENT STRUCTURES ON N (κ) MANIFOLD ADMITTING GENERALIZED TANAKA WEBSTER CONNECTION

Shweta Naik, H. G. Nagaraja — Fri, 30 Dec 2022 00:00:00 +0100

The main objective of the present paper is to study the equivalence of semi-symmetric and pseudo-symmetric conditions imposing on different curvature tensors in N (κ) manifolds admitting generalized Tanaka Webster ( ˜) connection. Classification is done according as expression of Ricci tensor and scalar curvature with respect to ∇˜. Finally an example is given.

Nnc δ-OPEN SETS

A. Vadivel, C. John Sundar — Fri, 30 Dec 2022 00:00:00 +0100

A new strong forms of sets called N -neutrosophic crisp δ-open sets and N -neutrosophic crisp δ-closed sets in N -neutrosophic crisp topological space are introduced in this article. Also, discuss their properties and examples are related to N -neutrosophic crisp δ open sets along with their near sets in N -neutrosophic crisp topological spaces.

REMARKS ON WEAK FORM OF NANO DERIVED SETS

B. Tamilarasan, Lellis Thivagar, Carmel Richard, G. Kabin Antony — Fri, 30 Dec 2022 00:00:00 +0100

This paper aims to introduce the concept of nano α- derived set and study the characteristics of nano α- derived set. Further, we investigate the different forms of nano α- derived set using lower and upper approximation.

COMPLETENESS IN MULTI METRIC SPACES

Sujoy Das — Fri, 30 Dec 2022 00:00:00 +0100

In the present paper a notion of convergence in multi metric space is presented. Complete multi metric space is introduced and some properties are studied. Cantor’s intersection theorem and Banach’s fixed point theorem are es- tablished in multi set settings.

MULTIPLICATION AND TRANSLATION OF CUBIC β−IDEALS

P. Muralikrishna, R. Vinodkumar, G. Palani — Fri, 30 Dec 2022 00:00:00 +0100

Cubic set is a structure with two components which has been applied in the conditions of β ideals. This paper presents the notion of cubic fuzzy β ideal of a β algebra. In addition that, the notion of cubic (a, b)-translation, cubic µ- multiplication were presented. Further, some engrossing results of cubic β ideals with the combination of multiplication and translation were investigated.

SCHULTZ INDICES AND THEIR POLYNOMIALS OF MYCIELSKIAN GRAPHS

Lavanya E., M. A. Sriraj, Bhagyashri R. Doddamani — Fri, 30 Dec 2022 00:00:00 +0100

Topological indices are studied extensively due to its vibrant applica- bility in the field of chemical graph theory. These connectivity indices(topological indices) is a numerical value resulting in an unequivocal process based on the struc- ture of graph. Numerous topological indices are classified based on their distance and degree. The Schultz and modified Schultz indices considered in this paper have been expansively studied by various authors on different types of graphs. In this paper, we established the results on Schultz, modified Schultz indices and their polynomials for mycielskian graphs.

COMPUTATION OF WIENER INDEX, RECIPROCAL WIENER INDEX AND PERIPHERAL WIENER INDEX USING ADJACENCY MATRIX

R. Rajendra, P. Siva Kota Reddy, M. Prabhavathi — Fri, 30 Dec 2022 00:00:00 +0100

In this short paper, we establish formulae to compute Wiener index, reciprocal Wiener index and peripheral Wiener index of graphs using adjacency matrix. Further, we present algorithms for the same

QSPR ANALYSIS OF CERTAIN ANTI-HIV DRUGS

Ishita Sarkar, Manjunath Nanjappa — Fri, 30 Dec 2022 00:00:00 +0100

A broad spectrum of advanced medications appears yearly following the accelerated evolution of the chemical and pharmaceutical industry. In this paper, various degree-based and neighborhood degree sum-based topological indices of some anti-HIV drugs are explored applying the M-polynomial and NM-polynomial formulations. Moreover, QSPR analysis is carried out for the topological indices with regard to the physico-chemical properties of the anti-HIV drugs. The activity of nucleoside and non-nucleoside reverse transcriptase inhibitors is implemented as in drug configuration to manifest the significance of topological indices in the medicinal world. The procured outcomes affirm that topological indices being stud- ied reflect effective correlation in accordance to physical and chemical properties of the anti-HIV drugs and consequently can assist in development of advanced and promising pharmaceutical for HIV medication.

SOMBOR INDEX OF EDGE CORONA PRODUCT OF SOME CLASSES OF GRAPHS

Hemalatha R., K. Somasundaram — Fri, 30 Dec 2022 00:00:00 +0100

The operations of graphs spread their wings in designing complex net- work structures in various engineering domains. Graph indices, popularly termed topological indices are computed on the basis of distance or degree. The boundless part of graph indices has its foot print in network centrality and the robustness of complex networks. The goal of this paper is to provide a complete expression for the Sombor index of edge corona product of few classes of graphs.

ON THE S3-MAGIC GRAPHS

Anusha C., Anil Kumar V. — Fri, 30 Dec 2022 00:00:00 +0100

Let G = (V (G), E(G)) be a finite (p, q) graph and let (A, ∗) be a finite non-abelain group with identity element 1. Let f : E(G) → N_q = {1, 2, . . . , q} and let g : E(G) → A \ {1} be two edge labelings of G such that f is bijective. Using these two labelings f and g we can define another edge labeling l : E(G) → N_q × A \ {1} by l(e) := (f (e), g(e)) for all e ∈ E(G). Define a relation ≤ on the range of l by: (f (e), g(e)) ≤ (f (e^j), g(e^j)) if and only if f (e) ≤ f (e^j). This relation ≤ is a partial order on the range of l. Let {(f (e₁), g(e₁)), (f (e₂), g(e₂)), . . . , (f (e_k), g(e_k))} be a chain in the range of l. We define a product of the elements of this chain as follows: k (f (e_i), g(e_i)) := ((((g(e₁) ∗ g(e₂)) ∗ g(e₃)) ∗ · · · ) ∗ g(e_k). i=1 Let u ∈ V and let N ^∗(u) be the set of all edges incident with u. Note that the restriction of l on N ^∗(u) is a chain, say (f (e₁), g(e₁)) ≤ (f (e₂), g(e₂)) ≤ · · · ≤ (f (e_n), g(e_n)). We define n l^∗(u) := (f (e_i), g(e_i)). i=1 If l^∗(u) is a constant, say a for all u V (G), we say that the graph G is A - magic. The map l^∗ is called an A -magic labeling of G and the corresponding constant a is called the magic constant. In this paper, we consider the permutation group S₃ and investigate graphs that are S₃-magic.

ON METRIC DIMENSION OF BOOLEAN GRAPH BG1(G)

Sameerali C. P., Sameena K. — Fri, 30 Dec 2022 00:00:00 +0100

Let G be a simple graph with vertex set V and edge set E. BG,NINC,Kq (G), known as boolean graph of G-first kind,simply denoted by BG₁(G) is defined as the graph with vertex set V E and two vertices are adjacent if and only if they correspond to adjacent vertices in G or to a vertex and an edge in G such that the edge is not incident with the vertex. In this paper we give a bound for metric dimension of BG₁(G) and also find expression for metric dimension of boolean graphs of Complete graphs and Star graphs. Finally, an algorithm for finding the metric dimension of BG₁(G) is established.

ANTIPODAL DOMINATION NUMBER OF GRAPHS

Kokilambal . — Fri, 30 Dec 2022 00:00:00 +0100

A dominating set S V is said to be an Antipodal Dominating Set(ADS) of a connected graph G if there exist vertices x, y S such that d(x, y) = diam(G). The minimum cardinality of an ADS is called the Antipodal Domination Number(ADN), and is denoted by γ_ap(G). In this paper, we determined the antipodal domination number for various graph prod- ucts, bound for antipodal domination and characterize the graphs with γ_ap(G) = 2.

VERTEX-EDGE NEIGHBORHOOD PRIME LABELING IN THE CONTEXT OF CORONA PRODUCT

N. P. Shrimali, A. K. Rathod — Fri, 30 Dec 2022 00:00:00 +0100

Let G be a graph with vertex set V (G) and edge set E(G). For u ∈ V (G), N_V (u) = {w ∈ V (G)|uw ∈ E(G)} and N_E(u) = {e ∈ E(G)|e = uv, for some {| ∈ } { | ∈ } v ∈ V (G)}. A bijective function f : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G) ∪ E(G)|} is said to be a vertex-edge neighborhood prime labeling, if for u ∈ V (G) with deg(u) = 1, gcd {f (w), f (uw)|w ∈ N_V (u)} = 1 ; for u ∈ V (G) with deg(u) > 1, gcd f (w) w N_V (u) = 1 and gcd f (e) e N_E(u) = 1. A graph which admits a vertex-edge neighborhood prime labeling is called a vertex-edge neighborhood prime graph. In this paper we prove K_m,n Ⓢ K₁, W_n Ⓢ K₁, H_n Ⓢ K₁, F_n Ⓢ K₁ and S(K_1,n) Ⓢ K₁ are vertex-edge neighborhood prime graphs.

DETOUR PEBBLING ON CARTESIAN PRODUCT GRAPHS

Lourdusamy ., S. Saratha Nellainayaki — Fri, 30 Dec 2022 00:00:00 +0100

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles on an adjacent vertex. The t - pebbling number of G is the smallest number, f_t(G) such that from any distribution of f_t(G) pebbles, it is possible to move t pebbles to any specified target vertex by a sequence of pebbling moves. The detour pebbling number of a graph f ^∗(G) is the smallest number such that from any distribution of f ^∗(G) pebbles, it is possible to move a pebbles to any specified target vertex by a sequence of pebbling moves using a detour path. In this paper, we find the detour pebbling number for some Cartesian product graphs and also the detour t - pebbling number for those cartesian product graphs.

DOUBLE ROMAN DOMINATION NUMBER OF MIDDLE GRAPH

Shailaja S. Shirkol, Pavitra P. Kumbargoudra, Meenal M. Kaliwal — Fri, 30 Dec 2022 00:00:00 +0100

For any graph G(V, E), a function f : V (G) 0, 1, 2, 3 is called Double Roman dominating function (DRDF) if the following properties holds, If f (v) = 0, then there exist two vertices v₁, v₂ ∈ N (v) for which f (v₁) = f (v₂) = 2 or there exist one vertex u ∈ N (v) for which f (u) = 3.∈ If f (v) = 1, then there exist one vertex u N (v) for which f (u) = 2 or Σ f (u) = 3. The weight of DRDF is the value w(f ) = v∈V (G) f (v). The minimum weight among all double Roman dominating function is called double Roman domination number and is denoted by γ_dR(G). In this article we initiated research on double Roman domination number for middle graphs. We established lower and upper bounds and also we characterize the double Roman domination number of middle graphs. Later we calculated numerical value of double Roman domination number of middle graph of path, cycle, star, double star and friendship graphs.

MATHEMATICAL STUDY OF PULMONARY AND INTRAVENOUS ADMINISTRATION OF OXYGEN IN BIOLOGICAL TISSUES UNDER HYPOXIA CONDITIONS

Ahsan Ul Haq Lone, M. A. Khanday, Saqib Mubarak — Fri, 30 Dec 2022 00:00:00 +0100

Mathematical modelling of oxygen transport in biological tissues played a great role and provides optimal results for advanced biomedical and biophysical research. Conventionally, oxygen is administered to hypoxic patients through pul- monary route. A mathematical model has been proposed to establish an alternative route for oxygen supply, whereby oxygen is administered directly into the target tis- sue bypassing the lung compartment. Our study aims at evaluating the feasibility of the novel approach using compartment modelling. The model is represented by a system of first order ordinary differential equations and their solution by Cramer’s rule and Laplace transform method. The concentration profiles of oxygen through pulmonary and intravenous routes were estimated in the arterial blood and tissue compartments at different flow rates; and with respect to initial oxygen concen- tration in the lung compartment and in the injected solution. Our results are in agreement with those arrived at by Lin Gui and Jing Liu (2006) [4]. The method offers a promising alternative to the conventional approach for clinical rescue of hypoxic patients, more so in emergency situations.

ANALYSIS OF TUMOR-IMMUNE RESPONSE MODEL BY USING CONFORMABLE FRACTIONAL ORDER DERIVATIVE

Ausif Padder, Rimpi Pal, Afroz ., Ayub Khan — Fri, 30 Dec 2022 00:00:00 +0100

In this research paper, the authors propose a generalized three-dimensional fractional order tumor-immune response model. The generalization of the model is made by introducing interleukin-2 (IL₂) cell population as the third variable in the proposed system. The study of the proposed model is performed by using a new concept of fractional-order derivatives called as conformable fractional-order derivative. The authors aim to study, analyze, and compare the dynamical be- havior of both the three-dimensional fractional order model and the conformable fractional order version of the proposed model. The stability analysis is done for both versions of the model at the biologically feasible equilibrium points. To vali- date the theoretical results numerically, numerical simulation is performed by using a piecewise constant approximation process.

ACCELERATING COSMOLOGICAL MODELS WITH VARIABLE G AND Λ-TERM IN GENERAL RELATIVITY

Vinod Kumar Bhardwaj, Ajay Singh — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we have presented a new class of accelerating universe models with variable cosmological term Λ(t) and gravitational constant G(t) in the framework of general relativity. To get exact solution of Einstein’s field equations for homogeneous and anisotropic Bianchi type-V space-time, a time varying de- celeration parameters is considered as q = 1 + ^nα , where n, α are constants. The present model shows a point type singularity at origin. The results establish the quintessence like behavior of model initially, and approaches to ΛCDM model ultimately. Some geometrical and physical properties of the models have been evidenced, and conferred to derive the validity of models with respect to recent astrophysical observations. Stability of the model has been discussed through the means of Om(z) diagnostic and state-finder analysis.

TRANSIT ISOMORPHISM AND ITS STUDY ON OCTANE ISOMERS

Reshmi K. M. , Raji Pilakkat — Tue, 07 Feb 2023 00:00:00 +0100

Having defined and studied, the transit index and transit decomposition of a connected graph, we introduce the concept of transit isomorphism. In this paper we discuss the transit isomorphism between certain graphs and its line graphs. Construction of transit isomorphic graphs is also dealt with. Finally we discuss how transit isomorphism relates to chemical properties of octane isomers.

A STUDY OF AN UNDIRECTED GRAPH ON A FINITE SUBSET OF NATURAL NUMBERS

Ivy Chakrabarty , Joseph Varghese Kureethara, Mukti Acharya — Fri, 30 Dec 2022 00:00:00 +0100

Let $G_{n}=(V,E)$ be an undirected simple graph, whose vertex set comprises of the natural numbers which are less than $n$ but not relatively prime to $n$ and two distinct vertices $u,v \in V$ are adjacent if and only if $\gcd(u,v)>1$. Connectedness, completeness, minimum degree, maximum degree, independence number, domination number and Eulerian property of the graph $G_n$ are studied in this paper.