Asian Research Journal of Mathematics

Maximum Linear Forest of Graphs Resulting from Some Binary Operations

2023-07-25T13:52:37+00:00

For a connected nontrivial graph G, the maximum linear forest of G is the linear forest having maximum number of edges. The number of edges in a maximum linear forest is denoted by \(\ell\)`(G). In this paper we determine the maximum linear forest of the join and union of nontrivial connected graphs G and H , denoted by G + H and G \(\cup\) H , respectively.

Mathematical Modeling of Plants, Herbivore and Natural Enemies of Herbivores Interaction with Harvesting

2023-08-01T11:00:36+00:00

Plant-herbivore-natural enemies of herbivores interaction is one of the basic interactions that drives of the ecosystem yields. In this interaction, plants are the primary food source for herbivores while natural enemies of herbivores depends on herbivores for food and on plants for shelter. Harvesting of every species which is common in many habitat may affect the population densities of the species and even the entire ecosystem. Therefore, conservation and maintenance of the harvested species is critical for ecosystem balance. In this paper, a model of plant-herbivore-natural enemies interactions with the constant effort harvesting of every species was developed and analyzed. The positive invariant set, the conditions of existence and locally asymptotically, stability of the equilibria were determined using the stability theory of ordinary differential equations. The results shows that the species being harvested would become extinct if harvesting effort exceeded a threshold value for the given population. While maintaining the coexistence of populations in the ecosystem requires sensible harvesting practices. Therefore, it is fair to choose a reasonable harvesting effort to allow all species to coexist in order to govern the species’ dynamic behavior. The insights of the solutions of this study are of great essence to ecologists and policy developers in environmental conservation. The authorities to pay attention to the minimum number required based on the area coverage in deciding when to harvest and also be cautious to the amount and effort of harvesting in view of conserving the species and the environment.

Pointwise Clique-Safe Domination in the Complement and Complementary Prism of Special Families of Graphs

2023-08-05T12:57:20+00:00

Let G = (V (G), E(G)) be any finite, undirected, simple graph. The maximun size of a clique containing a vertex \(\mathit{x}\) \(\in\) V (G) is called the clique centrality of \(\mathit{x}\) , denoted by \(\omega\)_G(\(\mathit{x}\)) . A set D \(\subseteq\) V (G) is said to be a pointwise clique-safe dominating set of G if for every vertex \(\mathit{y}\) \(\in\) D^c there exists a vertex \(\mathit{x}\) \(\in\) D such that \(\mathit{xy}\) \(\in\) E (G) where \(\omega\)_{\(\small\langle\)D}_{\(\small\rangle\)G}(\(\mathit{x}\)) \(\ge\) \(\omega\)_{\(\small\langle\)D^c\(\small\rangle\)G}(\(\mathit{y}\)) . The smallest obtainable cardinality of a pointwise clique-safe dominating set of G is called the pointwise clique-safe domination number of G, denoted by \(\gamma\)_{\(\mathit{pcs}\)} (G) . This study aims to generate some properties of the parameter and to characterize the minimum pointwise cliquesafe dominating sets of the complement of some special families of graphs as well as their complementary prism.

Cosmic Ray Detector Using Geiger Tubes and Coincident Pulses

2023-08-07T07:06:57+00:00

Cosmic Rays (CRs) are extreme strength particles resigning from outside the Earth and transported through space. These atoms can considerably impact human fitness, aviation and photo electric suppliers. A high energy radiation from space indicator is a tool that detects and measures the force of limitless beams. In this project, one can build a high energy radiation from space indicator utilizing two Geiger Muller tubes, Lead sheets, a stiff frame, a Microcontroller and a Protractor to regulate the frame at certain angle. At different altitudes, at different temperatures, at different humidities, we can identify and record CRs. A portable Muon Detector project that incorporates two Geiger Tubes enclosed within a lead sheet for detecting CRs. The system utilizes a coincidence circuit login to enhance the detection accuracy and reduce false positive rates. Additionally, the device is equipped with sensors to collect data on Temperature, Humidity, Latitude, Longitude and Atmospheric Pressure. The combination of these features provides a comprehensive and versatile solution for studying Muons and their interactions with the surrounding environment.

Rationality Proof of Newton's Method for Finding Quadratic Trinomial Factors of Univariate Integer Coefficient Polynomials

2023-08-08T10:07:41+00:00

The method of finding quadratic trinomial factors for univariate integer coefficient polynomials, proposed by the famous mathematician Isaac Newton in his mathematical monograph Arithmetica Universalis, is novel and concise, and has attracted the attention of mathematicians such as Leibniz and Bernoulli. However, no proof of this method has been given so far. This paper provides an in-depth analysis of this method and proves it with mathematical reasoning.Therefore, Newton's method of finding quadratic factors for univariate integer coefficient polynomials is reasonable, validate, and universal.

Exchange Rate Pass-through Dynamics: VAR Evidence for Kenya

2023-08-10T13:24:07+00:00

A VAR framework with exogenous variable is considered to analyse the exchange rate pass-through dynamics in Kenya. Monthly time series data from January 2006 to December 2022 is used. Six endogenous variables namely; US dollar exchange rate, broad money supply, total import, 20 Nairobi stock exchange share index, consumer price index and 91 days treasury bond rate sourced from the central bank of Kenya were considered. Global food price index and oil prices per barrel sourced from statista and Murban Adnoc respectively are the exogenous variables. Unit root test is first performed to test for stationary in line with VAR assumptions. Oil price and total import are the only stationary variables, while the other variables are of integrated order 1. Secondly, a VARX (2,0) is estimated, which is statistically significant at 5% level. Thirdly, Granger causality test is performed, that provide evidence of causality for 20 Nairobi stock exchange share index, consumer price index and broad money supply with respect to other endogenous variables. In addition, VARX(2,0) is converted to MA(2) to develop US dollars impulse response function. There exist high level of volatility for all variables. Finally, a forecast error variance decomposition following Cholesky decomposition shows significant proportion of variance explained by other variables respectively. Kenya’s policy makers need to build strong framework for monetary policy and exchange rate control measures in safeguarding the performance of macroeconomic indicators.

Fuzzy Fixed Point Theorems in Normal Cone Metric Space

2023-08-12T13:24:47+00:00

In this paper, we proved a few fuzzy fixed point theorems in whole regular cone metric spaces, which can be the generalization of a few current consequences within side the literature.

Computing Y-index of Different Corona Products of Graphs

2023-08-21T09:22:38+00:00

The Y-index of a graph is defined by the sum of four of degrees of the vertices of a graph. Among the all topological indices the Zagreb indices have been used more considerably than any other topological indices in chemical literature. The concept of Corona Product is a recent inclusion to mathematical vocabulary. One of the most significant graph operations is the corona product of several generic and specific graphs, which is one of the most well-known graph products. In this study, we derive some explicit formulations of several corona product types, including subdivision-vertex corona, subdivision-edge corona, subdivision-vertex neighborhood corona, subdivision-edge neighborhood corona, and vertex-edge corona of two graphs.

Analytical Solution of Hyperbolic Tangent Fluid's Peristaltic Flow in an Inclined Channel: Hall Effect's Impact

2023-08-22T11:37:21+00:00

Aim: In our study, we investigated, based on the premise of a long wavelength, how Hall's theory affected the peristaltic pumping of a fluid with a hyperbolic tangent within an inclined planar channel, and how both affected each other.

Study Design: Abstract, introduction, Statement, Analytical Solution, Results and Discussion, and conclusion.

Methodology: The intra-uterine fluid motion with tiny particles in a non-pregnant uterus is one of the many applications of the current physical problem, and this fluid motion condition is crucial for analysing the motion of the embryo in a uterus. Perturbation-oriented numerical research has been carried out in the current study to characterise the properties of velocity and axial pressure gradient in an inclined channel under Hall effect on the peristaltic flow of a Hyperbolic tangent because of these real-world applications. Under low Reynolds number and long-wavelength approximations, the current physical model yields the governing two-dimensional coupled nonlinear flow equations. For different values of the physical parameters, a suitable equation for the stream function is derived, and a regular perturbation scheme is used to produce the numerical solutions in terms of pressure rise and velocity. Weissenberg number, power-law index, Hall parameter, Hartmann number, and amplitude ratio relationships are examined in graphs along with their effects on the axial pressure gradient and time-averaged volume flow rate. According to the findings of this study, whereas the axial pressure gradient and time-averaged flow rate in the pumping region enhance with rising values of the Weissenberg, Hartmann, Reynolds, angle of inclination, and amplitude ratio, they diminish with enhances in the power-law index, Hall parameter, and Froude number. Hyperbolic tangent fluid has been discovered to require less pumping than Newtonian fluid.

Properties and Characterizations of Norm-Attainable Operators in Compact and Self-Adjoint Settings

2023-08-24T11:32:41+00:00

In this research paper, we investigate the properties and characterizations of norm-attainable operators in the context of compactness and self-adjointness. We present a series of propositions, a lemma, a theorem, and a corollary that shed light on the nature of these operators and provide insights into their behavior in various settings. Our results contribute to the understanding of norm-attainable operators and their implications in functional analysis.

A Theoretical Study on Correlation Analysis Between Eccentricity of VL-index and the Physical Properties of Alkanes

2023-08-24T13:19:16+00:00

Topological indices are mathematical techniques used to mathematically correlate the relationship between the chemical structure and various physical attributes, chemical reactivity, or biological activity. In this research studies, the interaction of various chemical compounds(alkanes), their structures, and the eccentricity of the VL-Index., using the First and Second Zagreb, and reformulated First Zagreb indices, we investigate the \(\xi\)VL index may be considered as an useful tool in predicting the physical properties of lower alkanes.

Connections between Anti-Excedance and Excedance on the \(\Gamma\)1-non Deranged Permutations

2023-08-26T04:23:47+00:00

In this paper, we investigated anti-excedance statistics in \(\Gamma\)₁-non deranged permutations, the permutation which fixes the first element in the permutations. This was accomplished by employing prime integers p \(\ge\) 5 in various calculations using this approach. The anti-excedance on \(\Gamma\)₁- non deranged permutations is redefined in this study. The recursive formula for the anti-excedance number and excedance number is generated, we also show that anti-excedance tops sum for any \(\omega\)_{\(\mathit{i}\)}^-1\(\in\)G_p^\(\Gamma\)1is equal to the excedance tops sum of \(\omega\)_{\(\mathit{i}\)} \(\in\)G_p^\(\Gamma\)1 . Similarly, we observed those anti-excedance bottoms sum for any \(\omega\)_{\(\mathit{i}\)}^-1\(\in\)G_p^\(\Gamma\)1 is equal to the excedance bottoms sum of \(\omega\)_{\(\mathit{i}\)} \(\in\)G_p^\(\Gamma\)1 other properties were also observed.

On Some New Properties for the Gamma Functions

2023-08-28T08:33:27+00:00

In this paper will be presented some new properties in form of the inequalities related to gamma function, product of two gamma functions and some of them will be presented in the form of infinite series and limit where are included the Euler number and the Euler-Mascheroni constant.

A New Estimator of Shannon Entropy with Application to Goodness-of-Fit Test to Normal Distribution

2023-08-28T11:45:15+00:00

In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \(\mathit{f}\)(\(\mathit{x}\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.

Some Characterizations of Whole Edge Domination in Bipolar Fuzzy Graphs

2023-08-29T13:18:47+00:00

In this paper, Some bounds, theorems and results on whole edge domination number in bipolar fuzzy graph are established with support of some examples. The concepts of perfect, complete perfect and semi-perfect whole edge domination in bipolar fuzzy graph are discussed and investigated with some of their properties and also results on perfect contributed via the support of some examples.

Some Properties and Inequalities for a Two-Parameter Generalization of the Incomplete Exponential Integral Function

2023-08-30T13:36:43+00:00

Motivated by the p-analogue of the exponential integral function [1], we introduce a two-parameter generalization of the Incomplete Exponential Integral function. By using the classical H¨older’s and Young’s inequalities, among other analytical techniques, we establish some new inequalities involving the generalized function.

Norm-Attainable Polynomials: Characterizations and Properties in Orthogonal Polynomial Families

2023-08-31T11:40:34+00:00

Norm-attainable polynomials play a crucial role in various mathematical contexts. This research paper investigates the characterizations and properties of norm-attainable polynomials in different orthogonal polynomial families. We explore their behavior, convexity, and positive definiteness. Additionally, we establish their norm-attainability in specific intervals for various weight functions. The findings contribute to a deeper understanding of norm-attainable polynomials and their applications in approximation theory and mathematical modeling.

Some New Optimal Bounds for Wallis Ratio

2023-08-31T11:55:24+00:00

Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.

On Heterodox Non-KL Generalized Divergence Metric with Characteristics in Fuzzy Environment

2023-09-05T10:14:50+00:00

In this paper, we suggest a novel divergence metric on a fuzzy set. Some scholars have used the fuzzy set extension and one that integrated with other theories. Axioms are proven in order to demonstrate the viability of measure. We create a way about decision-making criteria using the suggested measure and provide a workable method. We discuss the divergence metric metric for fuzzy sets in this post. The discussed properties of the proposed proposal. Multicriteria decision making is a very useful technique with a wide range of applications in the real world.

Minimum Transversal Eccentric Dominating Energy of Graphs

2023-09-19T07:50:57+00:00

For a graph G, the minimum transversal eccentric dominating energy \(\mathbb{E}\)_{\(\mathit{ted}\)} (G) is the sum of the eigenvalues obtained from the minimum transversal eccentric dominating \(\mathit{n}\) x \(\mathit{n}\) matrix \(\mathbb{M}\)_{\(\mathit{ted}\)} (G) = (\(\mathit{m}\)_{\(\mathit{ij}\)}). In this paper \(\mathbb{E}\)_{\(\mathit{ted}\)} (G) of some standard graphs are computed. Properties, upper and lower bounds for \(\mathbb{E}\)_{\(\mathit{ted}\)} (G) are established.

On the Modeling of Causative and Dependence Relationship of Cancers based on Gender and Cumulative Incidence

2023-09-19T11:06:54+00:00

Objectives: The goal of our study was to model the causative relationship and dependence of morbidity, mortality, and cumulative incidence with respect to GLOBOCAN 2020 age standardized world estimates for female and male malignancies using two adjustable parameters having physical significance.

Methods: The GLOBOCAN age standardized world estimates for patients for the year 2020 were used in this investigation. For the purposes of analyzing descriptive and analytical data, Kaleidagraph and Origin Software were employed. Bivariate empirical cross- correlation and dependency analyses were used to model how the variables were related to one another. The ratio of new cases to fatalities was calculated using equations comparing the stages of various malignancies.

Results: In this work, the use of a two-state parameter resulted in the estimation of the optimal solution. The results demonstrated a non-linear correlation with a progressive increase when the cumulative risk of cancer death for each sex was examined separately versus the global cumulative risk of cancer mortality for both sexes. Males experienced the increase more dramatically than females. This finding suggests that the global male-to-female population ratio is not the only factor contributing to cumulative risk.

Conclusion: South-Eastern Asia, out of all the regions of the world examined in this study, reached its inflection point at (16.23, 14.87). This generates the baseline and standard against which the overall risk of other countries can be measured. The global cumulative risk, which was estimated at 21.50 for females and 17.94 for males, respectively, dropped at this inflection point.

Periodic Oscillation of the Solutions for a Parkinson's Disease Model

2023-09-22T12:06:07+00:00

In this paper, the oscillation of the solutions for a Parkinson's disease model with multiple delays is discussed. By linearizing the system at the equilibrium point and analyzing the instability of the linearized system, some sufficient conditions to guarantee the existence of periodic oscillation of the solutions for a delayed Parkinson's disease system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate our theoretical prediction.

Orthogonal Polynomials and Operator Convergence in Hilbert Spaces: Norm-Attainability, Uniform Boundedness, and Compactness

2023-09-25T12:25:03+00:00

This research paper investigates the convergence properties of operators constructed from orthogonal polynomials in the context of Hilbert spaces. The study establishes norm-attainability and explores the uniform boundedness of these operators, extending the analysis to include complex-valued orthogonal polynomials. Additionally, the paper uncovers connections between operator compactness and the convergence behaviors of orthogonal polynomial operators, revealing how sequences of these operators converge weakly to both identity and zero operators. These results advance our understanding of the intricate interplay between algebraic and analytical properties in Hilbert spaces, contributing to fields such as functional analysis and approximation theory. The research sheds new light on the fundamental connections underlying the behavior of operators defined by orthogonal polynomials in diverse Hilbert space settings.

Some Common Fuzzy Fixed Point Theorems on G - Metric Space

2023-09-27T10:51:24+00:00

The motive of this paper is to give a few not unusual place constant factor theorems in G-Metric spaces, with the aid of using the perception of Common restrict with inside the variety belongings and to illustrate appropriate examples. These outcomes make bigger and generalizes numerous widely known outcomes with inside the literature.

Norm-Attainable Operators and Polynomials: Theory, Characterization, and Applications in Optimization and Functional Analysis

2023-09-26T04:48:22+00:00

This research paper offers a comprehensive investigation into the concept of norm-attainability in Banach and Hilbert spaces. It establishes that norm-attainable operators exist if and only if the target space is a Banach space and that norm-attainable polynomials are inherently linear. In convex optimization scenarios, norm-attainable polynomials lead to unique global optima. The paper explores the norm of norm-attainable operators, revealing its connection to supremum norms. In Hilbert spaces, norm-attainable operators are self-adjoint. Additionally, it shows that in finite-dimensional spaces, all bounded linear operators are norm-attainable. The research also examines extremal polynomials and their relationship with derivative roots, characterizes optimal solutions in norm-attainable operator contexts, and explores equivalence between norm-attainable operators through invertible operators. In inner product spaces, norm-attainable polynomials are identified as constant. Lastly, it highlights the association between norm-attainable operators and convex optimization problems, where solutions lie on the unit ball's boundary. This paper offers a unified perspective with significant implications for functional analysis, operator theory, and optimization in various mathematical and scientific domains.