Communications in Mathematics and Applications

Weak Zero-Divisor Graphs of Finite Commutative Rings

2023-11-20T05:53:05+00:00

This paper introduces weak zero-divisor graphs of finite commutative rings. The concept of zero-divisor graphs over rings has been extensively investigated for decades. These graphs are constructed with the zero-divisors of rings as their vertex set. We define a weak zero-divisor graph as a graph whose vertex set consists of nonzero elements $u$ and $v$ of a ring $R$ and such that the vertices $u$ and $v$ are adjacent if and only if $(uv)^n=0$ for some positive integer $n$. This article will study parameters of weak zero-divisor graphs of commutative rings, including their diameter, their girth, their radius, their center, and their domination number. We also determine whether weak zero-divisor graphs of the ring of integers $\mathbb Z_m$ are Eulerian and Hamiltonian.

Two Novel With and Without Memory Multi-point Iterative methods for Solving Non-Linear Equations.

2023-09-27T15:37:46+00:00

In this work, we suggest two new iterative methods for finding simple roots of non-linear equations. The new methods are the modifications of the existing work proposed by Rafiullah and Jabeen [1]. The first method obtained is of fifth-order two-step with memory method while the second scheme is three-point eight-order optimal without memory method. First, we introduced Hermite interpolation polynomial to remove the first derivative. To preserve order, we converted it to with memory scheme by introducing self accelerated parameters without any new function evaluation. Furthermore, we introduced Gauss quadrature approach for the first derivative to achieve optimal eighth-order convergence. In particular, the efficiency index is increased from 1.4953 to 1.7099 and 1.5157 to 1.6817 for fifth-and eighth-orders respectively. We provided some real life application based problems including Kepler’s equation, Ocean Engineering problem, Planck’s radiation law, Blood rheology model and Charge between two parallel plates to confirm the validity and superiority of our proposed scheme. Another benefit of the proposed scheme is on the restriction of the Newton’s method that (ϕ ′(v) ̸= 0) can be eliminated close to the root.

EVEN INTENSITY AND IMPLEMENTATION OF FUZZY INTRINSIC EDGE -MAGIC GRAPHS

2023-09-18T09:40:53+00:00

A graph labelling is an assignment of integers to the vertices or edges, or both under certain restrictions. A fuzzy graph G is said to be intrinsic edge-magic if it satisfies the intrinsic edge-magic labelling with intrinsic constant for all . In this manuscript, we introduce the even intensity of intrinsic edge magic graph and the application of fuzzy intrinsic edge magic graph is illustrated with suitable example.

Some fixed point results on (α, β) − H − φ-contraction mappings in partial metric spaces with application

2023-11-09T09:53:23+00:00

In this paper, we introduce the notion of H−φ-contraction, generalized H−φ-contraction,
(α, β)−H −φ-contraction mappings and establish some fixed point results for such mappings
in the context of partial metric spaces. An example is presented to illustrate the validity of
the results. Further, the existence of the solution of nonlinear integral equation is discussed
as an application of the result.

Product Binary L-Cordial Labeling of Various Degree Splitting Graphs

2024-01-04T11:37:10+00:00

This study examines the probability of the degree splitting operation results from various graphs being product binary L-cordial Graphs. The graphs under investigation include the Path graph (Pn), Comb graph (Pn ⊙ k1), Double comb graph (Pn ⊙ 2k1), Cycle graph (Cn), Shell graph (Sn) and Ladder graph (Ln). The application of product binary L-cordial labeling demonstrates that these analyzed graphs exhibit characteristics of product binary L-cordial graphs.

A p-sum representation of the 1-jets of p-velocities

2024-03-29T07:20:51+00:00

The theory of jets provides a useful tool for various fields in mathematics, enabling the solution of higher-order differential equations and partial differential equations that model complex mechanical systems. This theory adopts a geometric approach to generalized mechanics and field theory. For instance, in Lagrangian particle mechanics, the formalism of higher-order jet bundles proves useful. Thus, the study of jets is not only beneficial to mathematics but also extends its applicability to other fields such as physics.

In this study, we approach jet bundles from a differential geometry perspective. Specifically, we use structure of the bundle of all 1-jets of maps from $\mathbb{R}^p$ to $M$ with source at 0. By employing normal coordinates on the manifold M, we demonstrate that this bundle is diffeomorphic to the p-Whitney sum of tangent bundles. Then we prove that this bundle carries a vector bundle structure. Using its vector bundle structure, the paper establishes the existence of the isomorphism for tangent bundles of $p^1$ velocities, and extends the previous result by proving that the vector bundle of 1-jets of p-velocities is isometric to p-sum of tangent bundles, even in cases where the base manifold does not carry a Banach structure.

Some properties of Kenmotsu manifolds admitting a new type of semi-symmetric non-metric connection.

2023-08-11T08:14:19+00:00

In this paper we study some properties of Kenmotsu manifolds admitting a semi-symmetric non-metric connection. Some curvature's properties of Kenmotsu manifolds that admits a semi-symmetric non-metric connection are obtained. Semi-symmetric, Ricci semi-symmetric and locally $\phi$-symmetric conditions for Kenmotsu manifolds with respect to semi-symmetric non-metric connection are also studied. It is proved that the manifold endowed with a semi-symmetric non-metric connection is regular. We obtain some conditions for semi-symmetric and Ricci semi-symmetric Kenmotsu manifolds endowed with semi-symmetric non-metric connection $\widetilde{\nabla}$. It is further observed that the Ricci soliton of data $(g,\xi,\Theta)$ are expanding and shrinking respectively for semi-symmetric and Ricci semi-symmetric Kenmotsu manifolds admitting a semi-symmetric non-metric connection.

An optimal solution to multi-goal fuzzy linear programming problems using elementary transformations

2023-09-06T08:57:57+00:00

This article explores how to solve multipurpose problems to obtain optimal solutions using fuzzy linear programming. Our goal is to minimize production and transportation costs by using the most basic transportation methods and comparing the results to conventional methods. We discuss the results of numerical examples and illustrate this method.

Soft n-Normed Linear Spaces: Generalizations and Extensions from Soft Normed Spaces

2023-09-24T14:56:00+00:00

This article presents the notion of soft 2-normed linear space (NDLS) and extends it to soft n-NDLS, providing a versatile framework beyond traditional soft NDLS and n-normed spaces (NDS). Established results in soft NDLS are adapted to soft n-NDLS, bolstered by practical examples.

A Novel Approach to Plithogenic Neutrosophic Hypersoft Rough Set and its Application to Decision Making Problem with Reference to Bakery Industry

2023-10-13T09:02:41+00:00

The neutrosophic set, Plithogenic Hypersoft set, and rough set are distinct mathematical models to deal with different types of uncertainties in data and information. In this paper, we advance the study of plithogenic neutrosophic hypersoft rough set by combining plithogenic neutrosophic hypersoft set with rough set. Using plithogenic neutrosophic hypersoft rough set and the correspondence between objects, we develop an algorithm to solve a decision making problem occurring in Bakery industry. Finally a real life example is solved using the algorithm developed.

A novel numerical scheme for time-fractional partial integro-differential equation of parabolic type

2023-11-26T05:31:07+00:00

This work is devoted to study numerical methods for time-fractional integro-differential equations. In order to compute the approximate solutions for highly non-linear or linear forms of various time-fractional integro-differential models, we apply the extended and more generalized finite difference methods. First order and second order spacial derivatives are approximated by the central difference. The integral terms and Capto fractional terms are approximated by the composite trapezoidal rule. Particularly we derive error estimation and stability analysis of the finite difference method for a Volterra type fractional differential equation. Illustrative examples are provided in support of the proposed methods with three distinct problems.

PREDICTION OF CARDIOVASCULAR DISEASE ON TRANSTHORACIC ECHOCARDIOGRAPHY DATA USING ARTIFICIAL NEURAL NETWORK

2024-02-12T10:22:19+00:00

According to World Bank Epidemiological modelling, India has the second highest rate of Cardiovascular Disease (CVD) mortality worldwide, at 2.5 million new cases occurring annually. Heart disorder is a condition that affects heart function. One of the main problems with heart conditions in estimating a person's risk of having insufficient blood supply to the heart. According to the World Health Statistics 2012 report, one in every three individuals in the world has high blood pressure, a condition that accounts for almost half of all fatalities from heart disease and stroke. Echocardiography is an ultrasound procedure that uses a projector to display moving images of the heart and is used to diagnose and assess a series of disorders. Authors have considered to analyse and review several recent research works on CVD and experimental models. The proposed retrospective experiment contained a total of 7304 patients Transesophageal echocardiography (TTE) records with no missing values were chosen for the research in that 1113 patients were diagnosed with Ischemic Heart disease (IHD) and 6191 normal patients were classified as the subject. 70% of patients data were used to train the Neural Network and the other 30% of patients data used to test the model. This research work estimates the efficiency of the Artificial Neural Network model to investigate the factors contributing significantly to enhancing the risk of IHD as well as accurately predict the overall risk using Machine learning software: WEKA 3.8.5. and SPSS modeler. The resulting model performance has a higher accuracy rate (97.0%) and this makes it a very vital techniques for cardiologists to screen patients at potential risk of developing the disease

RING IN WHICH EVERY ELEMENT IS SUM OF TWO 5-POTENTS

2023-07-05T13:04:03+00:00

In this paper we get the following results. Every element of a ring R is a sum of two
commuting 5-potents if and only if R =
R_1R_2R_3R_4, where R1/J(R_1) is Boolean and
U(R_1) is a group of exponent 4, R_2 is a subdirect product of Z_3's, R_3 is a subdirect product
of Z_5's and R_4 is a subdirect product of Z_{13}'s. Also if in a ring R every element is a sum of
two 5-potents and a nilpotent that commute with one another then R =
R_1 R_2 R_3 R_4
where R_1/J(R1) is Boolean and J(R_1) is nil, R_2
=
R_a R_b R_c where R_a = 0;R_c = 0 and
R_b/J(R_b) is a subdirect product of rings isomorphic to Z_3, M_2(Z_3) or F_9 with J(R_b) is nil,
R_3=J(R_3) is a subdirect product of Z_5's and J(R_3) is nil, R_4/J(R_4) is a subdirect product
of Z_{13}'s and J(R_4) is nil.

“$\mathbb{R}$-Complex Finsler spaces with generalized Kropina metric

2023-08-29T14:14:31+00:00

The study of $\mathbb{R}$-complex Finsler spaces with an $(\alpha, \beta)$-metric is a fundamental problem in Finsler geometry. In this paper, we introduce the concept of $\mathbb{R}$-complex Finsler spaces with a generalized Kropina metric given by $F = \frac{\alpha^{m+1}}{\beta^m}$. We derive explicit formulas for the fundamental metric tensor fields $g_{ij}$ and $g_{i\bar{j}}$, as well as their determinants and inverse tensor fields for this metric. Additionally, we discuss various properties of non-Hermitian $\mathbb{R}$-complex Finsler spaces with the aforementioned metric.

Super Restrained Domination in the Join of Some Graphs

2023-09-21T00:03:14+00:00

Survival signature approach for reliability evaluation of linear consecutive k-out-of-n : G system

2023-10-03T10:07:05+00:00

The present study concentrates on computing the reliability function for linear consecutive k-out-of-n : G system with independent and identically distributed components. For systems where 2k ≥ n, we establish a formulation for the system survival signature. This is subsequently utilized to find a non-recursive representation of system reliability. The attained closed-form representation of system reliability empowers us to easily evaluate the performance of higher-order consecutive systems. The system signature is also evaluated with the assistance of the survival signature. Additionally, a method for calculating the system hazard rate function in light of its components’ hazard rate functions is suggested. Both exponential and pareto distributions are considered in assessing the reliability function for such systems. A numerical example related to a quality control system provides a concrete illustration of the results achieved through the proposed method.

A novel approach to solve nonlinear higher order VFIDE using the Laplace transform and Adomian decomposition method

2023-11-11T06:19:17+00:00

This study explores the application of a novel approach called Laplace Discrete Modified Adomian Decomposition Method (LDMADM) to solve non-homogeneous higher-order nonlinear VFIDEs. LDMADM is an extension of the Laplace Modified Adomian Decomposition Method (LMADM) and combines it with quadrature integration criteria to improve accuracy. The proposed method is evaluated by comparing its results with exact solutions and calculating absolute error measurements. The study establishes the existence of unique solutions and presents experimental numerical findings that demonstrate the high accuracy and effectiveness of the LDMADM approach. This method offers a promising alternative to analytical approaches for solving higher-order nonlinear VFIDEs.

On Some Properties of the Degenerate Exponential Function

2024-01-04T18:02:42+00:00

In this paper, we study some limit properties and inequalities involving the degenerate exponential function. Utilizing analytical methods, we also obtain some monotonic properties involving the function.

On Neutrosophic implicative filters of BL-Algebra

2024-04-23T04:59:42+00:00

We put forward the ideas of the neutrosophic implicative and n-fold implicative filters of BL-algebras. Additionally, we demonstrate that every implicative filter, including the n-fold implicative filter, is a neutrosophic filter. Moreover, we obtain an extension property for the neutrosophic implication. We then look at some comparable circumstances for neutrosophic implicative filters.

Computational simulation and modelling of arterial drug delivery from half-embedded drug-eluting stents in single-layered homogeneous vessel wall

2023-08-15T07:23:05+00:00

The next-generation of drug therapics has started as a consequence of the invention of controlled-dose pharmaceutical delivery tools. More specifically, coronary angioplasty (CA) treatments often involve drug-eluting stents (DES$^s$) that eluting drug molecules. This mechanism decreases the in-stent restenosis with the help of releasing drugs from a thin polymer membrane covering into the coronary vessel tissue around it. Present day DES equipments, as the protective covering, biodurable polymers has been deployed, that, remains there forever until the drug has fully eluted from DES. In this present work, we investigated the aforementioned problems using a numerical simulation of vascular distribution of drugs as well as receptor binding mechanisms. Modelling is done for the intravascular drug delivery of a hydrophobic (like sirolimus or paclitaxel) drug from DES. The content of this paper discusses the effects of drug delivery from half-embedded circular drug-eluting stent struts. We introduce an elaborate mathematical approach based on axi-symmetry 2D layout, incorporates a two non-linear phases of drug binding namely specific and non-specific, and combines the impact of diffusion and advection, within the single-layered homogeneous vessel wall. The pharmaceutical delivery via five stent struts has been significantly strengthened in this framework. The free pharmaceuticals are moved using an unsteady covection-diffusion-reaction mechanism, even though the binding pharmaceuticals are being through an unsteady reaction-diffusion mechanism. The governing equations along with the initial and boundary conditions has been evaluated numerically using a finite-difference technique in staggered grids. The marker and cell (MAC) methodology has been employed to solved the model equations while taking into account the cylindrical system of polar coordinates. In this present assessment, our target is to visually illustrate the impact of the embedment of the stent on the drug release from stent and vessel drug distribution. According to the findings, it is indicate that the drug gradually binds to specific receptors and extracellular matrix sites until binding sites become saturated. Model simulations have improved our understanding of the potential influences of the different factors that may affect the effectiveness of drug administration. The created modelling allows for the modification of the model$'$s parameters for upcoming research on the development of PLGA-coated drug-eluting stents.

Perturbed MAP/PH risk model with possible delayed by-claims and a constant dividend barrier

2023-09-18T05:37:32+00:00

In this study we consider a perturbed risk model with MAP claim arrivals, PH claim sizes that incorporates possible by-claims and dividend barrier affected by a Brownian motion. The by-claims can occur along with the main claim, but their settlement is always delayed due to some necessary investigation. In order to analyze the model, we consider associated Markovian fluid models defined in the original timeline and an auxiliary timeline. We develop systems of second order integro-differential equations (I.D.E) for the Gerber-Shiu functions (GSF) of both the models without as well as with the barrier and solve them explicitly. Working on the same line we derive expressions for the Moment of the total dividends paid until ruin. Furthermore, a dividends-penalty identity is established. To showcase the effectiveness of the method, we numerically illustrate it using a two-phase model. Finally, we conduct a sensitive analysis by varying some of the parameters involved in the model.

A novel approximation on the solution of systems of ordinary differential equations

2023-09-26T15:31:56+00:00

In this paper, the initial-value problem for the system of first-order
differential equations is considered. To solve this problem, we construct a
fitted difference scheme using the finite difference method, which is based
on integral identities for the quadrature formula with integral term
remainder terms. Next, we prove first-order convergence for the method in
the discrete maximum norm. Although this scheme has the same rate of
convergence, it has more efficiency and accuracy compared to the classical
Euler scheme. Two test problems are solved by using the proposed method and
the classical Euler method, which confirm the theoretical findings. The
numerical results obtained from here show that the proposed method is
reliable, efficient, and accurate.

Niching Sparrow Search Algorithm for Solving Benchmark Problems, Speed Reducer Design, and Himmelblau’s Nonlinear Optimization Problem

2023-10-16T05:03:49+00:00

Metaheuristic algorithms are invented or modified in order to solve complex optimization
problems at the global level. With the development of technology, almost every domain such
as engineering, industrial, medical etcetera is facing the problem of optimization. In order to
solve these problems, a number of algorithms have been discovered. One of the most recent
optimization algorithms is the Sparrow Search Algorithm (SSA) which is famous for its good
optimal ability along with fast convergence, Although, the SSA has a lot of merits, it is still
facing numerous drawbacks namely falling into the local optima, steady convergence, etc.
Therefore, we have proposed Niching SSA (NSSA) by introducing the niching technique in
SSA for updating the position of followers and scouters. This NSSA has been tested on 18
benchmark functions, speed reducer design, and also on Himmelblau’s nonlinear optimization
problem. In this work, we have examined NSSA from various aspects like optimal value,
average mean for convergence accuracy, and the standard deviation for stability, and also
have drawn the convergence curves through Matlab to check the convergence rate. Moreover,
we have applied the Wilcoxon Signed rank test on NSSA. In all these aspects, computational
results reveal that the performance of NSSA is superior with respect to SSA, GWO, PSO,
and GSA.

A two server Poisson queue with state dependent hybrid service discipline with variant breakdown

2023-12-22T10:23:13+00:00

A Poisson queue with two servers and with system breakdown has been
considered in this paper. In addition, the servers are in homogeneous mode
upto serving of N customers. After which the servers changed to heterogeneous
mode. If the system is busy failure may occur to the system. As in the case
of service policy, in a similar way two different breakdown policies are assumed.
At the instant of breakdown, if there are N or less than N customers in the
system the system is completely shutdown. Otherwise, the servers provides service
with different service rates. The number of arrivals and the number of service
completions follows different Poisson distributions. The interbreakdown periods
follows negative exponential distributions. Immediately the repair process takes
place. The repair periods are random variables, follows negative exponential
distribution. This model is defined and the time independent solutions are
derived. Also some system performance measures are obtained. To show the
practical applicability of the model some numerical illustrations are provided.
The corresponding cost model is defined and analyzed.

Rough Decision Making of Facial Expression Detection

2024-02-21T04:10:26+00:00

This paper introduces a novel framework named Rough Decision Making which extends
the principles of Rough Set Theory. The mathematical model proposed consists of
a fuzzy interval-valued knowledge-based information system that includes a non-empty
finite universe of objects, a derived interval-valued fuzzy set of attributes, and a fuzzy
interval-valued set of decisions. To manage complexity, the roughness of decision-making
is introduced by defining Lower and Upper Rough Decisions for each object. Further
this model is implemented on a real-time affective image database RAF-DB for facial
expression detection. This approach is found to provide a comprehensive analysis of facial
expressions, demonstrating effective classification even in the presence of uncertainty.

On fixed point of monotone (α, β)− nonexpansive mappings in ordered hyperbolic metric spaces

2023-07-14T13:24:51+00:00

This paper is concerned with convergence and ∆− convergence of a sequence generated by Picard-Mann hybrid iteration scheme for monotone (α, β)− nonexpansive type mappings in ordered hyperbolic metric spaces along with some fixed point results. Here we also put an application in L1([0, 1]) space.

The Regular Domination Number of Some Special Graphs

2023-09-01T16:52:38+00:00

The purpose of this article is to illustrate the concept of regular domination on a variety of unique
graph types, including Complete graphs, Path graphs, Cycle graphs, Lollipop graphs, Barbell
graphs, Gear graphs, Petersen graphs, Helm graphs, Jellyfish graphs, Jewel graphs, and Complete
Bipartite graphs. We also determine the regular domination for specific operations, such as
the join of two graphs and the corona product of two graphs.

Rough Ideal Statistical Convergence via Generalized Difference Operators Intuitionistic Fuzzy Normed Spaces

2023-09-22T17:48:09+00:00

This study focuses on investigating the concept of rough ideal statistical convergence for generalized difference sequences in intuitionistic fuzzy normed spaces. We studied the algebraic and topological properties of rough ideal statistical limit points for generalized difference sequence. Apart from this, we also investigated rough ideal statistical cluster points, the relation between rough I-statistical limit points and rough I-statistical cluster points for generalized differnece sequence in intuitionistic fuzzy normed spaces.

Analysis of Speech Features for Gender Identification in Tai Language

2023-10-05T13:40:36+00:00

The vast number of information packed into the human speech signal makes analysis a tough undertaking. This intricacy is notably noticeable in tasks like speaker recognition, especially when it comes to gender distinction. In this paper, we address this issue by conducting a thorough examination of the effectiveness of various speech features, namely Pitch, Formant Frequency, MFCC (Mel Frequency Cepstral Coefficients), and Chroma, in the context of gender identification in the Tai Language, which is spoken by the Tai people of Assam. In this study, we use machine learning (SVM, KNN, Decision Tree, Neural Network) to analyze speech features (Pitch, Formant Frequency, MFCC, Chroma) for gender identification in the Tai language spoken by the Tai people of Assam. Our results show that MFCC consistently outperforms other features, delivering highest accuracy rates across all approaches. This demonstrates MFCC's ability to extract gender information from Tai Language speech signals, suggesting more accurate gender identification systems. Beyond gender identification, our study extends voice analysis in linguistics and improves the application of spoken language data, allowing for improved communication systems and linguistic insights. In summary, our findings highlight the critical significance of MFCC in gender identification in the Tai language, with ramifications that extend far beyond its local context, promising advances in voice analysis and improving our understanding of language and human communication.

Keywords: Machine Learning methods, Neural Networks, Gender Identification, MFCC, Pitch, Formant Frequency, Chroma.

A NEW FIXED POINT THEOREM FOR GENERALIZED (α, ψ)-CONTRACTION MAPPING OF QUADRATIC TYPE WITH APPLICATIONS.

2024-01-20T09:11:57+00:00

In this paper, we aquaint generalized (α, ψ) - contraction mappings of quadratic type and establish common fixed point results in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results of Karapinar and Lakzian [13], Alharbi et al. [2] and Khuangsatung et al. [16]. We applied our result to facilitate the existence of a solution to an integral equation.

Some Aspects of Radial Graphs Under Boolean Operations

2022-11-16T14:41:21+00:00

Two vertices of a graph $G$ are said to be radial to each other if the distance between them is equal to the radius 
of the graph. The radial graph of a graph $G,$ denoted by $R(G),$ has the vertex set as in $G$ and two vertices are 
adjacent in $R(G)$ if and only if they are radial to each other in $G.$ If $G$ is disconnected, then the two 
vertices are adjacent in $R(G)$ if they belong to different components of $G.$ The main objective of this paper is 
to determine the radial graphs of some families of product graphs.

On a k-Annihilating Ideal Hypergraph of Local Rings

2023-08-21T10:58:43+00:00

The concept of a $k$-annihilating ideal hypergraph of a finite commutative ring is very broad, so one of its structures has been discussed, where $R$ is a local ring. In this paper, we present the structure of a $k$-annihilating ideal hypergraph of a local ring and determine the order and size of a $k$-annihilating ideal hypergraph of $\mathcal{AG}_{k}(R)$. We also find and count the degree of every nontrivial ideal of a local ring containing in vertex set $\mathcal{A}(R,k)$, of a hypergraph $\mathcal{AG}_{k}(R)$. Furthermore, we determine the diameter and the center of $\mathcal{A}(R,k)$ that equals 1 or 2. Finally, we compute the Wiener index of a k-annihilating ideal hypergraph of $R$.