JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES

CONNECTION BETWEEN PARTIAL BELL POLYNOMIALS AND (q; q)k; PARTITION FUNCTION, AND CERTAIN q-HYPERGEOMETRIC SERIES

M. A. . Pathan, J. D. . Bulnes, J. . L´opez-Bonilla, Hemant . Kumar — Fri, 30 Dec 2022 00:00:00 +0100

We exhibit a relationship between q-shifted factorial, (q; q)n, and the incomplete exponential Bell polynomials and also evaluate several q-hypergeometric series using the q-version of Petkovsek-WilfZeilberger’s algorithm. Finally, we write the partition function p(n) in terms of Qm(k), the number of partitions of m using (possibly repeated) parts that do not exceed k.

EXPANDING THE LAURENT SERIES WITH ITS APPLICATIONS

Ganesh Prasad Adhikari — Fri, 30 Dec 2022 00:00:00 +0100

In Nepal, there are many mathematics subjects taught at university level. Among them, complex analysis is the most powerful. In complex analysis, the Laurent series expansion is a well-known subject because it may be used to find the residues of complex functions around their singularities. It turns out that computing the Laurent series of a function around its singularities is an effective way to calculate the integral of the function along any closed contour around the singularities as well as the residue of the function. Learning the Laurent series concepts can be difficult, and many students struggle to develop adequate understanding, reasoning, and problem-solving skills. Therefore, this article presents multiple practical examples where the Laurent series of a function is found and then utilized to compute the integral of the function over any closed contour around the singularities of the function, based on the theory of the Laurent series.

DIGITAL TIME: A FINITE FIELD, TF

G. . Manikandan, K. Srinivasa . Rao — Fri, 30 Dec 2022 00:00:00 +0100

Digital time was defined KSR-PP [2] with three two-digit positions as h2h1 : m2m1 : s2s1. It was identified with appropriate restricted place values on the hours (H), minutes (M) and seconds (S) shown to be 86400-element cyclic Time Group, TG. Here it is shown to be a finite time field, TF. A palindromic sequence of 119-elements and its sub-sequences are shown to be consequences of TF .

A MATHEMATICAL MODEL OF GLUCOSE HOMEOSTASIS IN CHAD CONTEXT

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

During these decades, mathematical modeling has become a key domain in science, especially in biomedical sciences. It allows for an experimental and rigorous approach. Thanks to mathematical modeling, the glucose-insulin system could be materialized, which is also theoretical, in order to analyze and interpret it and to predict the results. Many of the mathematical models of the glucose-insulin system have emerged in recent years. In literature, there are models that show the role of physical activity and response of mathematical model to glucose-insulin system dynamics. We propose the mathematical model of ordinary differential equations to investigate simple homeostasis generated by the dynamics of physiological parameters of the glucose-insulin system during physical activity for a healthy subject. Model parameters are estimated using a nonlinear optimization method generally based on inverse problems. The numerical simulations show that the proposed model is adaptable to the data collected in Chad and can be used to test glucose homeostasis for glucose-insulin system.

β-PREREGULAR SPACE IN FUZZY SETTING

Anjana . Bhattacharyya — Fri, 30 Dec 2022 00:00:00 +0100

In this paper a new type of fuzzy regular space is introduced and studied by introducing fuzzy β-preopen set, the class of which is strictly larger than that of fuzzy open set as well as fuzzy preopen set. Here we also introduce two new types of functions, viz., fuzzy β-precontinuous and fuzzy β-preirresolute functions. Lastly, the application of fuzzy β-precontinuous function on fuzzy β- preregular space is shown here.

LG-FUZZY PARTITION OF UNITY

Marzieh . Mostafavi — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we define LGc-fuzzy Euclidean topological space with countable basis, which L denotes a complete distributive lattice and we show that each LGc-fuzzy open covering of this space can be refined to an LGc-fuzzy open covering that is locally finite. We introduce C∞ LG-fuzzy manifold (X, Tc), with countable basis of LG-fuzzy open sets which X is an L-fuzzy subset of a crisp set M and T : LMX → L, is an L-gradation of openness on X. We prove that for any LG-fuzzy topological manifold (X,T), there exists an LG-fuzzy exhaustion. We prove LG-Urysohn lemma and also existence of LG-partitions of unity on every LG-fuzzy topological manifold.

FIXED POINT THEOREMS FOR θ-EXPANSIONS IN BRANCIARI METRIC SPACES

Priya . Shahi, Vishnu Narayan . Mishra — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we define θ-expansions on Branciari metric spaces by complementing the concept of θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014). Also, we present some new fixed point results for θ-expansion mappings on a Branciari metric space.

A FIXED POINT THEOREM ON ENRICHED (ψ, φλ)-WEAKLY CONTRACTIVE MAPS IN CONVEX METRIC SPACES

G. V. R. . Babu, Ch. Srinivasa . Rao, P. . Mounika — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we define enriched (ψ, φλ)-weakly contractive map in convex metric spaces where ψ is continuous on [0,+∞) and φλ is not continuous on [0,+∞) and prove the existence and uniqueness of fixed points of these maps in complete convex metric spaces. We provide an example in support of our result.

A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS

Shekhar . Suman, Raman Kumar Das — Fri, 30 Dec 2022 00:00:00 +0100

In this manuscript we denote by P ρ a sum over the non trivial zeros of Riemann zeta function (or over the zeros of Riemann’s xi function), where the zeros of multiplicity k are counted k times. We prove a result that the Riemann Hypothesis is true if and only if

NEW FUNCTIONAL RELATION FOR THE DILOGARITHM INVOLVING TWO VARIABLES

Jorge Luis Cimadevilla . Villacrota, M. P. . Chaudhary — Fri, 30 Dec 2022 00:00:00 +0100

We establish new functional relations for the dilogarithm involving two variables, which adhere the properties of Polylogarithm. We also considered several closely-related identities such as (for example) polylogarithm (also known as Jonqui`ere’s function), Euler dilogarithm function and Clausen’s function.

RELATIONS BETWEEN MOCK THETA FUNCTIONS AND COMBINATORIAL PARTITION IDENTITIES

M. P. . Chaudhary, Salem . Guiben, Kamel . Mazhouda — Fri, 30 Dec 2022 00:00:00 +0100

The main object of this paper is to present 6 new interrelationships between mock theta functions and combinatorial partition identities. The results presented in this paper are motivated by some recent works by M.P.Chaudhary [6].

SOME RESULTS IN CONNECTION WITH SUM AND PRODUCT THEOREMS RELATED TO GENERALIZED RELATIVE ORDER (α, β) AND GENERALIZED RELATIVE TYPE (α, β) OF ENTIRE FUNCTIONS IN THE UNIT DISC

Tanmay . Biswas, Chinmay . Biswas — Fri, 30 Dec 2022 00:00:00 +0100

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (α, β), generalized relative type (α, β) and generalized relative weak type (α, β) of entire functions in the unit disc D with respect to another entire function where α, β are continuous non-negative functions on (−∞,+∞).

COMPOSITION OF PATHWAY FRACTIONAL INTEGRAL OPERATOR ON PRODUCT OF SPECIAL FUNCTIONS

Harish . Nagar, Shristi . Mishra — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we study the pathway fractional integral operator colluded with composition of K-Struve function and extended Mittag-Leffler function. The obtained result is expressed in terms of generalized Wright hypergeometric function.

A NOTE ON ROGERS-RAMANUJAN-SLATER TYPE THETA FUNCTION IDENTITY

Jian . Cao, Sama . Arjika, M. P. . Chaudhary — Fri, 30 Dec 2022 00:00:00 +0100

In this paper, we research theta function identity involving Rogers– Ramanujan identity and establish a Rogers–Ramanujan–Slater type theta function identity related to G(q) and φ(q).

FRACTIONAL CALCULUS BETWEEN BANACH SPACES ALONG WITH OSTROWSKI AND GR¨USS TYPE INEQUALITIES

George A. . Anastassiou — Fri, 30 Dec 2022 00:00:00 +0100

Here we present a fractional calculus Caputo type for functions between Banach spaces. Left and right fractional derivatives are defined on a segment of a Banach space, then we expand. We apply the above to new Ostrowski and Gr¨uss type inequalities at very abstract level.

THE QUINTESSENTIAL NUMBER 24

K. Srinivasa . Rao, T. P. . Srinivasan, Satya Prakash Singh, Chandan Kumar Singh — Fri, 30 Dec 2022 00:00:00 +0100

In this article, the authors refer to the interesting nature and properties of the number 24 and its occurrence and relevance in different contexts and conjecture that it is the raison d’ˆetre for its occurrence in the definition of the τ -function of Ramanujan.