International Journal of Mathematics And its Applications

Dynamics of Tsallis Holographic Dark Energy Interaction in a Bianchi Type-V Universe with a Constant Deceleration Parameter

2024-03-27T13:31:44+00:00

In this study, we explore a universe characterized by Anisotropic and Homogeneous Bianchi Type-V geometry, filled with both Dark Matter (DM) and Dark Energy (DE) within the framework of General Theory of Relativity. We introduce an interaction between DM and DE, incorporating Tsallis generalized entropy. The field equations are solved using the constant deceleration parameter proposed by Berman (1983). The Equation of State (EoS) parameter of Tsallis Holographic Dark Energy (THDE) elucidates the current accelerated expansion of the universe, exhibiting Phantom-like and approaching $\Lambda {CDM}$. Additionally, we calculate the EoS parameter, Anisotropy Parameter, Deceleration Parameter, and Total Energy Density parameter. Our results align well with observational data.

Applications on Laplace Transforms, Elzaki Transforms and Sumdu Transforms Using Initial and Boundary Conditions

2024-04-30T15:47:09+00:00

The Laplace transform, Elzaki transform, and Sumudu transform methods are used in this paper to solve initial value problems directly without having to convert them to ordinary differential equations. One of the three methods can be used to solve initial value problems using these transformation techniques. By applying the relevant transform to the governing equation and initial conditions, initial value problems can be addressed using the Laplace, Elzaki, and Sumudu transform methods. By doing this, problems can be solved without having to convert them to ODE form. Transforming the initial value problems directly leads to solutions being obtained in one of the three proposed approaches: Laplace, Elzaki, or Sumudu. The added complexity of transforming problems to ODEs before using transforms to find solutions is avoided by this reformulation.

Few Integrals Involving H-function Of One Variable

2024-03-14T15:18:04+00:00

This paper contains eight integrals involving H-function of one variable with proper conditions of validity. The special cases for G-functions have also been obtained.

Common Fixed Point Theorem for a New Type of $F-$Contraction in $b-$Metric Spaces

2024-03-27T13:23:53+00:00

In this paper, firstly, we introduce the notion of contraction of $F-$type function and the concept of $\alpha _{s} -$orbital admissible mapping. Secondly, we establish a fixed point theorem for this type contraction in the setting of complete $b-$metric spaces and substantiate our theoretical findings with a supportive example. This approach not only broadens the spectrum of fixed point theory but also demonstrates the practical applicability of our results in the analysis of $b-$metric spaces.

Ethnomathematical Ideas in Dhakiya Weaving in Tharu Community

2024-02-26T02:25:07+00:00

The indigenous people Tharu have a distinctive culture and way of life. While performing daily tasks, they practice their own mathematical concepts and thinking. The study of mathematical ideas and skills that are common within a population but are often not included in the formal curriculum is known as ethnomathematics. This study intends to reveal the secret ethnomathematical expertise and knowledge used in Tharu community Dhakiya weaving. The observation and documentation analysis approach were utilized in this study's data collection to attain its objectives. Under the photograph of the Dhakiya is redrewn to better illustrate the art and designs of the Dhakiya weaving techniques. Emic ethnomodeling is used to look at the mathematical ideas weaved within Dhakiya. The findings indicated that intricate mathematical ideas and concepts like the center of a circle, radius and diameter of a circle, concentric circles, concepts of, circumference of a circle, sequence, symmetry, and other geometric shapes are demonstrated in the weaving of Dhakiya in the Tharu community.

L-valued Intuitionistic L-fuzzy Generalised Lattice Ordered Groups of the Type 3

2024-05-20T17:21:58+00:00

A generalised lattice ordered group (gl-group) is a system in which the underlying set is a generalised lattice as well as a group. This article deals with the concept of L-valued intuitionistic L-fuzzy gl-subgroup of the type 3 (IFgl-subgroup of type 3) of a gl-group. Introduced the concept L-valued intuitionistic L-fuzzy gl-subgroup of the type 3 (IFgl-subgroup of type 3) of a gl-group and characterized by the level subsets and discussed some equivalent conditions. Finally proved that intersection of any family of L-valued intuitionistic L-fuzzy gl-subgroups of the type 3 (IFgl-subgroups of type 3) of a gl-group is again an IFgl-subgroup of type 3.

Multiplicative Neutrosophic Metric Space and Fixed point Result for Multiplicative Neutrosophic Contraction on MNMS

2024-03-27T13:26:56+00:00

M. Kiri\c{s}ci, N. Simsek, M. Akyigit [21] have established fixed point result for neutrosophic banach contraction. The aim of this paper is to put the notion of multiplicative netrosophic metric space, to define topology on MNMS and to prove a fixed point theorem for a multiplicative neutrosophic contraction mapping.

Absolute Mean Graceful Labeling of Disjoint Union of Some Graphs

2024-01-13T16:10:44+00:00

In this paper, we prove that the disjoint union of cycle and complete bipartite graph, jewel graph and sunlet graph, cycle and alternate helm, jewel graph and complete bipartite graph, swastik graph and path, and gear graph and sunlet graph are absolute mean graceful graphs.

Perfect 2-colorings of 4-regular Circulant Graphs

2024-05-02T14:50:32+00:00

In this study, we determine the perfect 2-colorings of $Ci_{2n}(1,n-1)$, a class of 4-regular circulant graphs with even order. We determine the parameter matrices that result to these perfect 2-colorings.

Bessel Polynomials Through Linear Algebra

2024-02-14T17:08:53+00:00

In the present note, Bessel polynomials are obtained through linear algebra methods. A matrix corresponding to the Bessel differential operator is found and its eigenvalues are obtained. The elements of the eigenvector obtained correspond to the Bessel polynomials.

A Study of Appell Function of Two Variables Using Hurwitz - Lerch Zeta Function of Two Variables

2024-02-05T14:04:18+00:00

Firstly, the Appell's Hypergeometric Function of two variables $F_{2}[a, b_{1}, b_{2};c_{1},c_{2};x_{1},x_{2}]$ is introduced using Hurwitz-Lerch Zeta Function of two variables $\phi_{a_1,a_2,b_1,b_2;c_1c_2} (x_1, x_2, s, p)$. Then several integral representations and differential formula are investigated for this function $F_{2}[a, b_{1},b_{2};c_{1},c_{2};x_{1},x_{2}]$. The function $F_{2}[a,b_{1},b_{2};c_{1},c_{2};x_{1},x_{2}]$ that we have introduced \& defined here has also been represented in term of generalized Hypergeometric Function ${}_{p}F_{q}$. To strengthen our main results, we have also considered some important special cases.