Communications in Mathematics and Applications

Effect of Binary Hybrid Nanofluid Flow Between Parallel Plates With Applied Activation Energy

2024-05-25T05:51:49+00:00

This article examines the activation energy between two parallel plates consisting of MoS$_2$-GO-EO hybrid nanofluid. The nanoparticles, molybdenum disulphide (MoS$_2$) and graphene oxide (GO), are added to the base fluid, engine oil (EO). The influence of activation energy is also measured in this model. The finite difference method (FDM) is used to integrate the equations of motion, heat, and mass balance. The effects of important parameters such as activation energy, chemical reaction, temperature difference, random motion, and thermophoresis are discussed. The Nusselt number and skin friction are compared with available work to validate the numerical procedure. An enhanced Sherwood number is observed in Buongiorno's nanofluid model, while an elevated Nusselt number is seen with the hybrid nanofluid. Activation energy increases the profiles of temperature and concentration.

Certain Inequalities Involving Generalized Hyperbolic Sine and Cosine Functions

2024-03-20T04:52:30+00:00

In this article, we established generalizations of some inequalities involving generalized hyperbolic functions to establish several lower and upper bounds of known inequalities. The implanted results give the sharpness of inequalities.

Coupled Invariant Point Theorems in Bicomplex Parametric Partial Metric Space Amongst Dominate Function

2024-05-21T12:15:38+00:00

In this paper, bicomplex parametric partial metric space is discussed. The new contractive condition is discussed for coupled invariant point concerning self-mapping on the said spaces with particular conditions. We support our tracking down through models. Our outcomes sum up the common coupled invariant point in bicomplex valued parametric metric spaces by Saluja (Coupled fixed point results based on control function in complex partial metric spaces, Functional Analysis, Approximation and Computation 15(2) (2023), 1 – 15). Established results generalize previously known results for specified conditions.

On the Bihyperbolic $k$-Fibonacci Numbers

2024-02-14T18:02:29+00:00

In this paper, we extend the concept of bihyperbolic numbers to the $k$-Fibonacci numbers. We will find the main formulas that affect these numbers, such as the recurrence formulas and the sum of the first $n$ terms, as well as the identities of Binet, Catalan and d’Ocagne. We finish the study by finding the generating function of the bihyperbolic $k$-Fibonacci numbers.

Exploring Matroid Varieties: A Tropical Perspective on Combinatorial Structures and Intersection Products

2024-07-04T10:48:42+00:00

Matroid varieties give a wide range of tropicalizations and a complex way to understand their combinatorial structure when applied to classical linear spaces. In this paper, we delve into the intricate connections between matroid theory and tropical geometry, highlighting how matroid varieties inherit a natural fan structure that elegantly organises themselves based on the flats of the
matroid they stem from. This connection facilitates a seamless translation of matroid operations into the tropical realm, akin to speaking the same language in a different mathematical dialect. We focus on constructing an intersection product of cycles on matroid varieties, akin to understanding how loops interact within the landscape. By demonstrating the utility and consistency of this operation, we pave the way for further exploration and application in both matroid and tropical geometry.

Analyzing System Reliability Across Configurational Diversity and Component Variability: Insights From Reliability Block Diagrams and Event Space Method

2024-03-24T11:37:07+00:00

In this study, we systematically investigated the reliability of a complex system configured in multiple ways with diverse components, employing both Reliability Block Diagram and Event Space Method. Our approach involved evaluating component reliability in series and parallel arrangements, with a subsequent consolidation of these assessments. The primary aim was to set a benchmark for
quantifying system reliability across various configurations and conditions. The study outcomes are illustrated using graphs and tables, facilitating a comparative analysis of system reliability across diverse setups.

Stability of the Functional Equation Deriving From Quadratic Function in Banach Space

2023-12-25T17:01:58+00:00

In this manuscript, we introduce a quadratic functional equation of finite variable:
\begin{align}
\nonumber \sum\limits_{i=1}^m \phi \left(2v_i-\sum\limits_{1 \leq i \neq j}^m v_j\right)&=(m-7)\sum\limits_{1 \leq i <j \leq m} \phi (v_i+v_j)+\phi\left(\sum\limits_{i=1}^m v_i\right)\nonumber\\&\quad -(m^2-9m+5) \sum\limits_{i=1}^m \phi(v_i)
\end{align}
and examine its Hyers-Ulam stability of this functional equation in Banach space using direct and fixed point method.

Quadratic-Phase Hankel Transformation and Calderón’s Reproducing Formula

2024-06-21T13:05:21+00:00

In this paper, we have explored fundamental properties of the quadratic-phase Hankel transformation. Additionally, we have derived Calderón’s reproducing formula for quadratic-phase Hankel convolution based on the theory of the quadratic-phase Hankel transformation.

Some New Results in Extended Cone $b$-Metric Space

2024-02-15T09:20:50+00:00

The main aspect of this paper is to investigate some topological properties and Kannan-type contractions in extended cone b-metric spaces. Additionally, we have imposed some extra conditions such that a sequence in an extended cone b-metric space becomes a Cauchy sequence. Furthermore, in order to achieve new results the concept of asymptotic regularity has also been utilized.

On Super Heronian Mean Labeling of Some Subdivision Graphs

2023-01-06T00:21:31+00:00

Let $f:V(G) \rightarrow \{1, 2, \dots, p+q \}$ be an injective function, where $p=|V(G)|$ and $q=|E(G)|$. For a vertex labeling $f$ the induced edge labeling $f^*(e=uv)$ is defined by,
\[
f^*(e)= \left \lfloor {\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3}} \right \rfloor \ \text{or} \ \left \lceil\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3} \right \rceil.
\]
Then $f$ is called a super Heronian mean labeling if $\{f(V(G))\} \cup \{f(e): e \in E(G)\}=\{1, 2, 3, \dots, p+q\}$. A graph which admits super Heronian mean labeling is called super Heronian mean graph.

Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application

2024-02-29T08:16:38+00:00

In this paper, we consider generalized $\tau$-$\psi$-$\varphi$ weak contraction and generalized $\tau$-$\varphi$ weak contraction mappings in the setting of partial metric spaces and verify the existence of a fixed point on such spaces. Our results extend and strengthen various known results in this direction. We present an example showing the significance of our result. We also show that our result can be applied to the existence of solutions of a differential equation.

Monophonic Cover Pebbling Number of Standard and Algebraic Graphs

2024-03-06T04:55:51+00:00

Given a connected graph $G$ and a configuration $D$ of pebbles on the vertices of $G$, a pebbling transformation takes place by removing two pebbles from one vertex and placing one pebble on its adjacent vertex. A monophonic path is considered to be a longest chordless path between two vertices $u$ and $v$ which are not adjacent. A monophonic cover pebbling number, $\gamma_\mu(G)$, is a minimum number of pebbles required to cover all the vertices of $G$ with at least one pebble each on them after the transferring of pebbles by using monophonic paths. In this paper, we determine the monophonic cover pebbling number of cycles, square of cycles, shadow graph of cycles, complete graphs, Jahangir graphs, fan graphs, zero divisor graphs and unit graphs.

Applications of Binary Intuitionistic Fine Topological Spaces for Digital Plane

2024-03-29T13:44:48+00:00

In order to model computer images, digital spaces such as $Z^{2}$ are utilized and the link between the classical topological spaces such as $T_{1}, T_{1/2}, T_{0}$ spaces etc., and the digital spaces are studied by many authors to solve important connectivity problems, studying graphics, pattern recognition etc. In graph theoretical approach to solve connectivity contradictions 4 and 8 adjacencies serves as the basic. It is well known that key approaches to solve such problems are graph theoretic approach and topological approach. Traditional 4 and 8 adjacencies in a topology are considered in this article which aims to structure 4 and 8 adjacencies in a topology called binary intuitionistic fine topology $(\BI_fT)$. Initially 4 and 8 adjacencies-$\BI_fT$ are constructed and operators such as 4 and 8-$BI_fT$ interiors and closures are defined and their properties are discussed. Eventually, 4 and 8 connected-$\BI_f$-connected and non-connected points are defined and explained using example.

Two Versions of Quadratic-Phase Hankel Transformations of Random Order

2024-05-03T05:40:06+00:00

In this study, we have eliminated the restriction on the remaining parameters for the two versions of quadratic phase Hankel transformations (QPHT) with the aid of a new parameter. Furthermore, the QPHT of random order has been used to solve a few differential equations.

An Efficient Tri-Parametric Jarratt Family for Nonlinear Models Solution

2023-10-12T13:02:21+00:00

This paper offers an efficient and competitive tri-parametric family of iterative schemes for deciding nonlinear and systems of nonlinear models solution. The family has quartic-convergence order and is based on the composition of the Jarratt’s perturbed Newton method with a designed iterative function that involves rational approximation function of degree two in both its denominator and numerator. The new tri-parametric family is further extended to solving nonlinear models in n-dimensional form and its convergence investigation established to retain its quartic-convergence order. By varying the parameters in the family, enabled the rediscovery of many well established iterative schemes. The applicability and computational performance of some specified family examples, on some nonlinear models were also verified and results compared with some of known and established schemes that are also family members.

Estimation of Stock Price Using LSTM Algorithm and Sentiment Analysis

2024-02-17T20:35:47+00:00

Predicting price of the stock is a complex job and it is almost impossible to predict the exact amount of the stock. However, it’s possible to estimate future amount of the stock through searching at historical information. There are various machine learning models available with which stock price can be estimated. In this paper, initially a detailed survey is presented that is based on a comparison and examination of various deep learning algorithms for estimation of stock price. It includes Linear Regression, Support Vector Machine, Auto Regressive Integrated Moving Average, Convolutional Neural Network, Long Short-Term Memory, Artificial Neural network. It is observed that the LSTM algorithm has a better performance as compared to the others. In this work a univariate model is trained to estimate the price of the stock using LSTM model. To improve the results further a sentiment analysis based on twitter data is performed and a multivariate LSTM model is trained. The results presented in this work are based on three stocks Britannia, HDFC bank and Axis bank. The state-of-the-art natural language processing tool BERT are used to recognize the sentiments of text, and the long short term memory neural network (LSTM), which is good at analyzing time series data, is applied to forecast the stock price with stock historical transaction information and text sentiments The various performance parameters are also discussed in this paper. The analysis is performed based on changing number of epochs and it is observed that error percentage reduced with increasing number of epochs.

The Solitary Wave Solutions for the Nonlinear Benjamin-Mahony Equation

2023-11-20T05:35:21+00:00

The Benjamin-Bona-Mahony (BBM) equation is a nonlinear partial differential equation that describes the propagation of long waves in a shallow water channel. In this work, we present a comprehensive solution for the BBM equation using the Riccati-Bernoulli sub-ODE method. The method involves transforming the BBM equation into a Riccati equation, which is then further transformed into a Bernoulli equation. The Bernoulli equation is then solved analytically, and the solution is used to obtain the solution for the original BBM equation. Our results show that the Riccati-Bernoulli sub-ODE method provides an efficient and accurate solution for the BBM equation. The dfmethod can be extended to solve other nonlinear partial differential equations (NPDEs), making it a valuable tool for researchers in various fields.

Propagation of Waves in Thin Nanorod With the Effect of Thermal Field

2024-05-27T06:38:36+00:00

In this paper, thermal response for the propagation of waves in thin nanorod is studied with the Timoshenko beam theory. The important role for vibrational analysis of the rod and characteristics of the flexural waves is discussed. Numerical calculations are derived and the scattered relations between the wavenumber and wave velocities are computed.

An Integrated Framework for Inventory Management Considering Demand and Supply Uncertainties

2024-01-06T06:35:16+00:00

Due to uncertainties on both the demand and supply sides, managing inventories is the most critical and cost-effective challenge faced by supply chain managers in the supply chain network. While inventory management problems with uncertain demand and supply have been covered in the supply chain management literature for a long time, it is fair to say that no one approach can be applied universally across all scenarios. This paper presents an integrated inventory management framework considering non-linear optimization and multi-criteria decisionmaking tools. First, it presents a non-linear model to minimize the total inventory management cost at a centralized location (e.g., distribution center) by considering multiple inventory aggregation scenarios. A series of sensitivity analyses are conducted to examine the impact of demand and supply uncertainties on various key performance indicators related to inventory operations. Lastly, the best inventory aggregation model is selected by using a multi-criterion-based TOPSIS (Technique for order performance by similarity to ideal solution)) analysis.

Some Properties of $\epsilon$-Kenmotsu Manifolds With Quarter-Symmetric Non-Metric Connection

2024-02-20T12:31:20+00:00

The objective of this paper is to investigate the $\epsilon$-Kenmotsu manifolds with quartersymmetric non-metric connection. We have investigate an $\epsilon$-Kenmotsu manifolds admitting the quarter-symmetric non-metric connections satisfying certain conditions. We have further provided the equivalent conditions for Ricci soliton in an $\epsilon$-Kenmotsu manifolds to be shrinking or expanding with the quarter-symmetric non-metric connection. We have also investigated $\phi$-projectively flat, Quasiprojectively flat and some interesting results. Finally, we have given an example of 3-dimensional $\epsilon$-Kenmotsu manifolds with respect to quarter-symmetric non-metric connection.

On Average Hub Number of a Graph

2024-04-06T10:37:39+00:00

The idea of local and average hub numbers is explored as an expansion of the hub number in graphs, a connectivity measure that holds significance in transportation networks. In this analysis, we investigate the characterization of graphs by examining the local and average hub numbers and study them for graph classes namely trees and thorn graphs. Additionally, we determine the precise values of the average hub number for certain graph operations and discuss the bounds of Nordhaus-Gaddum type inequalities.

Some Fixed Point Theorems for Generalized $\alpha$-Admissible $Z$-Contraction via Simulation Function

2024-02-28T06:53:20+00:00

In this paper, we prove some fixed point theorems in metric-like space by using generalized $\alpha$-admissible mapping embedded in the simulation function. Our results generalize and extend several known results on literature.

Some Outcomes on Fuzzy Menger Space via Common Property (E.A) and Absorbing Maps

2022-12-22T14:27:16+00:00

The present idea of this paper is to generalize the result proved by Sing et al. (Fixed point results in Fuzzy Menger space, Journal of Applied Mathematics and Bioinformatics 5 (2015), 67 – 75) obtaining two results in fuzzy Menger space by employing absorbing maps, common property (E.A) and occasionally weakly compatible mappings. Moreover, these results are justified by suitable examples.

Applications of Linear Differential Operator on Varying Arguments

2024-05-19T13:03:27+00:00

In the present work, using Al-Oboudi operator and Carlson-Shaffer operator, we introduce a new Linear operator $\mathcal{AS}_{\lambda, q}^{\delta}$. The objective is to define the new subclasses of analytic functions $\mathcal{VS}_{\lambda,\delta}^{\alpha, \beta} (a,c,n; q)$, $\mathcal{VS}_{\lambda,\delta}^{\alpha}(a,c,n;q) $ using the above linear operator and for functions belonging to these classes we obtain coefficient estimates and many more related properties like extreme points, integral means, unified radii results etc.

Pseudosymmetric Almost $\alpha$-Cosymplectic $(\kappa,\mu,\nu)$-Spaces Admitting Einstein Solitons

2023-12-27T15:48:33+00:00

This paper attempts to characterize cases of an almost $\alpha$-cosymplectic $(\kappa,\mu,\nu)$-space admitting Einstein sloitons to be concircular Ricci pseudosymmetry, projective Ricci pseudosymmetry, $W_1$-curvature and the $W_2$-curvature Ricci pseudo symmetric.

Connected Certified Domination in Graphs: Properties and Algorithmic Aspects

2024-03-09T21:37:58+00:00

A certified dominating set $D$ of a graph $\Gamma=(V_\Gamma,E_\Gamma)$ denoted by $\gamma_{\mathit{cer}}$-set, is the subset of $V_\Gamma$ such that $|N(u)\cap(V_\Gamma-D)|$ is either $0$ or $2$, $\forall$ $u\in D$. A set $\mathcal{D}_c\subseteq V_\Gamma$ is called a connected certified dominating set $(\gamma_{\mathit{cer}}^c$-set$)$ if $\mathcal{D}_c$ is $\gamma_{\mathit{cer}}$-set and $\Gamma[\mathcal{D}_c]$ is connected. Also, if $\mathcal{D}_c$ has no proper subset, then it is a smallest $\gamma_{\mathit{cer}}^c$-set, and the cardinality of the smallest $\gamma_{\mathit{cer}}^c$-set is called as connected certified domination number (CCDN) of the graph $\Gamma$ represented by $\gamma_{\mathit{cer}}^c(\Gamma)$. In this article, we continue the study of connected certified domination. Herein, we classify graphs with larger values of CCDN and then we will study some properties of connected certified domination. Moreover, we will provide upper bounds and Nordhaus-Gaddum results for the CCDN. Additionally, we will prove that the connected certified domination problem is NP-complete for star convex bipartite graphs, comb convex bipartite graphs, and planar graphs.

Decomposition of Bipolar Pythagorean Fuzzy Matrices

2024-05-21T05:50:03+00:00

This paper presents novel findings on modal operators through the use of max-min composition, analyzing properties such as reflexivity, symmetry, transitivity, and idempotency related to necessity and possibility. It explores the necessary and sufficient conditions for transitive and $c$-transitive closure matrices using modal operators. Additionally, a new composition operator, labeled as `$\wedge_{m}$' is introduced and its algebraic properties are thoroughly discussed. The study also achieves a decomposition of a BPyFM utilizing the new composition operator and modal operators.

Properties of Modified Double Laplace Transforms and Special Functions

2024-06-04T18:17:19+00:00

This paper deals with new results on modified double Laplace transforms and special functions. Starting with basic definitions and results, we have obtained a modified double Laplace transform of unit step functions, and periodic functions and developed new theorems. Finally, we illustrate our results with examples.

Fixed Point Technique: Hyers-Ulam Stability Results Deriving From Cubic Mapping in Fuzzy Normed Spaces

2024-04-16T12:50:16+00:00

In this work, we introduce a novel finite-dimensional cubic functional equation
\begin{align*}
\phi\Bigg(\sum\limits_{a=1}^{l}a n_{a}\Bigg)&=\sum\limits_{1 \leq a < b < c \leq l}\phi(a n_{a}+b n_{b}+c n_{c})\\
&\quad +(3-l)\sum\limits_{1 \leq a < b \leq l}\phi(a n_{a}+b n_{b})\\
&\quad +\Bigg(\frac{(l^{2}-5l+6)}{2}\Bigg)\sum\limits_{a=0}^{l-1}(a+1)^{3}\phi(n_{a+1}),
\end{align*}
where $l \geq 4$ is an integer, and derive its general solution.\ The main purpose of this work is to examine the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by means of direct approach and fixed point approach.

A Markovian Queue With Feedback and Second Optional Working Vacation

2024-05-15T14:40:27+00:00

A Markovian queue with feedback and second optional working vacation is analysed in this study. Rather of fully suspending service during a vacation, the server operates with varying service times. After the completion of the regular working vacation, the server may opt for second optional working vacation. After getting the service the customer who is unsatisfied with incomplete, partial or unsatisfactory service may opt the feedback with probability ¯r or leave the system with the probability r.We use the matrix-geometric approach to find the essential and acceptable conditions for the system to be secure. After deriving the stationary probability distribution, various performance indicators are calculated. Some numerical examples are illustrated to show the model’s stability.

Series Solution of Fractional Differential Equations Describing Physical Systems

2024-05-14T07:19:14+00:00

The aim of this paper is to extend the iterative method based on the DGJM method of solving functional equations, to solve the fractional differential equations, where the order of derivative is taken in Caputo’s sense. The iterative procedure is explained and demonstrated by solving non-linear time fractional partial differential equations like Heat equation, Burger’s equation, Fokker Planck equation, Korteweg-de Vries (KdV) equation and Klien-Gordon equation. The scheme of iteration is also extended to solve the system of Drinfeld-Sokolov-Wilson equations and coupled Jaulent-Miodek equations. Graphs are used to depict the accuracy of the method and absolute errors between exact and approximate solutions are tabulated to ensure that the proposed scheme is both computationally intriguing and simple to implement.

Observations on Haüy Rhombic Dodecahedral Numbers with Some Special Numbers

2024-03-28T05:26:42+00:00

In this paper, the basic definition of Haüy rhombic dodecahedral numbers and nasty numbers are given. The Haüy rhombic dodecahedral number is taken into study and we prove this number is a combination of some special numbers. Also, we investigate about the relationships between the Haüy rhombic dodecahedral, stella octangula, hex number, centered tetrahedral and gnomonic numbers. For the clear understanding of the properties of special numbers we proved fifteen theorems. Sixteen special numbers are taken into consideration for this observation. The key points are given in the proof of the theorems.

Common Fixed Point Theorem for Three Self-maps in $G_{\mathit{JS}}$-Metric Space

2024-02-26T14:23:49+00:00

In this article, we prove a common fixed point theorem for three self-maps using the contractive modulus function in a recently emerged generalized metric space known as $G_{\mathit{JS}}$-metric space and verified its uniqueness. We illustrated the main theorem with an example.

Impacts of Fisheries Harvesting on Fish-Bird Model for the Salton Sea Region

2024-04-12T15:03:28+00:00

This study investigates the impact of fisheries harvesting on a Fish-bird model, focusing specifically on the presence of illnesses in fish and the consequential effects on bird populations. Tilapia fish, serving as the primary dietary source for pelican birds in the Salton Sea region, face the risk of overexploitation due to increased fishing activities. The study reveals that heightened harvesting rates can lead to the eventual extinction of bird species over time, highlighting the delicate balance between fishing sustainability and ecological preservation. The equilibrium and stability of the system are analyzed, with numerical simulations illustrating various dynamical behaviors such as chaotic attractors and quasi-periodic oscillations. The harvesting model considers the extraction of both susceptible and infected fish, demonstrating that an increase in the harvesting rate of susceptible fish poses a significant threat to bird populations. Conversely, while maintaining a constant harvesting rate of infected fish, the bird population remains viable even for varying levels of infected harvesting rates. Ultimately, the study underscores the importance of sustainable fishing practices, cautioning against the overexploitation of susceptible fish, which could lead to the extinction of birds in the Salton Sea region.

Domination Defect of Some Parameterized Families of Graphs

2022-07-10T11:22:59+00:00

In this paper, we study the concept of $k$-domination defect of a graph $G$ and investigate it for some parameterized families of graphs. We produce characterizations of the $\zeta_k$-sets of the path, cycle, centipede graph, sunlet graph, bi-star graph, crown graph, and complete bipartite graph, and then from these characterizations, the corresponding $k$-domination defects of the aforesaid graphs are determined.

The ScispaCy Clinical Term Extraction and Snomed CT Synonymy Elimination From Clinical Data For Clustering: A Novel Study

2024-11-20T10:26:35+00:00

A clinical document is a written or electronic record that encompasses details regarding a patient’s medical procedure, clinical trial, or test outcomes. Standard information mining approaches have challenges in clustering clinical documents due to their unstructured nature. This work introduced a new approach for grouping clinical documents to address problems related to synonymy,
abbreviation extension, and extraction of key features. The clinical document collection for coronary artery disease consists of 1304 records obtained from 296 patients. These records have been chosen for preprocessing with the aim of removing any irregularities. The scispaCy model extracts relevant information after a simple letter-matching algorithm identifies and extends abbreviations.
Furthermore, the features are examined using SNOMED CT ontology to eradicate medical terms that have similar meanings. The TF-IDF method is employed to convert the recovered features into vectors. The BERT model’s word embeddings were employed in this study to represent features. Nevertheless, the TF-IDF model surpasses the BERT model in performance. The clustering process utilises an enhanced k-means algorithm that incorporates the Red-Black Tree data structure. The recommended strategy was evaluated with several existing clustering algorithms in this study. It has been found that the proposed method produces clusters with higher scores for Normalised Mutual Information (NMI) and accuracy. Based on the results of this investigation, the model has the ability to detect
individuals with similar diseases and provide assistance to healthcare professionals.