GET THE APP

# Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

## Current Issue

### Volume 10, Issue 4 (2021)

Research Pages: 1 - 1

### Prime Multiple Factoriangular Numbers

Swati Bisht

S. Bisht defined a class of sequences called multiple Factoriangular sequences of the form Ft (n,k) = (n!)k +∑nk in a recent paper, and we have a special set of multiple Factoriangular numbers corresponding to each sequence. We expand the concept in this paper to find all the multiple Factoriangular primes

Research Pages: 1 - 2

### A Curious Connection Between Fermat′s Number and Multiple Factoriangular Numbers

Swati Bish

In the seventeenth century Fermat defined a sequence of numbers Fn=22n +1 for n ≥ 0 known as Fermat’s number . If Fn happens to be prime then Fn is called Fermat prime. All the Fermat’s number are of the form n!k+ Σnk for some fixed value of k and n. Further we will prove that after F4 no other Fermat prime exist upto 1050 .

Research Pages: 1 - 2

### Prime Counting Function π (n)

Noor Zaman Sheikh

We have created a formula to calculate the number of primes less than or equal to any given positive integer ‘n'. It is denoted by π (n). This is a fundamental concept in number theory and it is difficult to calculate. A prime number can be divided by 1 and itself . Therefore the set of primes (2,3,5,7,11,13,17.). The Prime Counting Function was conjectured the end of the 18th century by Gauss and by Legendre to be approximately x/Ln(x) But in this paper we are presenting the real formula, by applying the modern approach that is applying the basic concept of set theory.

Mini Review Pages: 1 - 5

### A Convergent C9 Continuous Binary Non-Stationary Subdivision Technique

Kashif Rehan

This paper comprises a smooth limiting curve having C9 continuity using a non-stationary binary six-point approximating subdivision technique. The proposed technique is more efficient and produces more smooth results having a very large domain as compared with its stationary counterpart.

Editorial Pages: 1 - 1

### Editorial Note on 3 Dimensional Study Case

Dover

Today, 3D models are utilized during a good kind of fields. The medical industry uses detailed models of organs; these could even be created with multiple 2-D image slices from an MRI or CT scan. The movie industry uses them as characters and objects for animated and real-life motion pictures. the pc game industry uses them as assets for computer and video games. The science sector uses them as highly detailed models of chemical compounds. The architecture industry uses them to demonstrate proposed buildings and landscapes in lieu of traditional, physical architectural models. The engineering community utilizes them as designs of latest devices, vehicles and structures also as variety of other uses. In recent decades the planet science community has begun to construct 3D geological models as a typical practice. 3D models can also be the thought for physical devices that are built with 3D printers or CNC machines.

### Volume 10, Issue 5 (2021)

2021 Conference Announcement Pages: 1 - 3

### Some Important Properties of Beta Functions

In this paper, we discuss some important properties of Beta functions. These properties make the study of these functions more meaningful. Beta function is also known as the Eulerian integral of the first kind.

Method Pages: 1 - 4

### Multidirectional regression analysis

Koen Van de Moortel

The so-called ‘least squares regression’ for mathematical modelling is a widely used technique. It’s so common that one might think nothing could be improved to the algorithm anymore. But it can. By searching the ‘least squares’ not just in the vertical direction The first test results are very promising, and especially for power functions, often used in biomedical sciences, the conclusions you make from your data can change dramatically. Fermat prime exist up to1050.

Research Pages: 1 - 6

### One Dimensional Heat Equation and its Solution by the Methods of Separation of Variables, Fourier Series and Fourier Transform

Lencha Tamiru Abdisa

The aim of this paper was to study the one-dimensional heat equation and its solution. Firstly, a model of heat equation, which governs the temperature distribution in a body, was derived depending on some physical assumptions. Secondly, the formulae in which we able to obtain its solution were derived by using the Method of separation of variables along with the Fourier series and the method of Fourier transform. Then after, some real-life applications of the equations were discussed through examples. Finally, a numerical simulation of the raised examples was studied by using MATLAB program and the results concluded that the numerical simulations match the analytical solutions as expected.

Editorial Pages: 1 - 1

### Editorial note on number theory

Brief Report Pages: 1 - 1

### "On h-open sets and h-continuous functions

Huseyin Cakalli

The author introduced a new topology depending on the original topology on a non-empty set in the paper entitled”On h-open sets and h-continuous functions” by Fadhil Abbas, published in Journal of Applied and Computational Mathematics [1]. However, there are two false theorems and two false examples, namely Theorem 3.5, Theorem 3.8, Example 2.4, and Example 2.5 are unfortunately wrong. 1) Theorem 3.5 is wrong as a counter-example is given in the following

### Volume 10, Issue 7 (2021)

Editorial Pages: 1 - 1

### Editorial Note on Integrated Analysis

Commentary Pages: 1 - 1

### An Enhanced Method for Tail Index Estimation

Commentary Pages: 1 - 1

### Pooling Problem: Modeling, Global Optimization and Computational Studies Survey

Editorial Pages: 1 - 2

### Verifiable Secret sharing Scheme based on certain Projective Transformation

Research Article Pages: 1 - 8

### Heterogeneous-Homogeneous Reaction Mechanism on the Hydro Magneticnano Fluid Flow a Stretching Cylinder with Prescribed Heat Flux using Hermite Wavelet Method

The current work provides the Hermite wavelet method (HWM) for an incompressible Nanofluid hydromagnetic flow through a stretching cylinder associated with heterogeneous-homogeneous chemical reactions. Single-walled carbon nanotubes (SWCNTs) with multi-walled carbon nanotubes (MWCNTs) as nanoparticles in the form of arranged heat flux are accounted for currently. Regulating equations, which are highly nonlinear coupled, are changed right into non-dimensional ordinary differential equations (ODEs) using appropriate similarity transformations. The desire for exceptional flow constraints on the flow feature is finalized truthfully through tables and graphs. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, concentrations, and nanoparticles. Comparison of the numerical outcomes is made with previously available consequences under particular cases, and the results are found to be in good agreement. The Hermite wavelet technique is hugely proficient and sensible for finding outcomes to this type of coupled nonlinear ODEs. The works are in outstanding accord for coupled nonlinear ordinary differential equations (ODEs) in engineering applications.

### Volume 10, Issue 9 (2021)

Research Article Pages: 1 - 2

### A Curious Connection Between Fermat’s Number and Multiple Factoriangular Numbers

In the seventeenth century Fermat defined a sequence of numbers Fn=22n +1 for n ≥ 0 known as Fermat’s number . If Fn happens to be prime then Fn is called Fermat prime. All the Fermat’s number are of the form n!k+ Σnk for some fixed value of k and n. Further we will prove that after F4 no other Fermat prime exist upto 1050 .

Research Article Pages: 1 - 6

### A Spatial-Nonparametric Approach for Prediction of Claim Frequency in Motor Car Insurance

Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as generalized linear models (GLMs), Poisson regression models, and Bayesian Models have been made available to predict the claim frequency for forthcoming years. However, due to the heterogeneous nature of policies, these methods do not produce precise and reliable prediction of future claim frequencies; these traditional statistical methods rely heavily on limiting assumptions including linearity, normality, predictor variable independence, and an established functional structure connecting the criterion and predictive variables. This study investigated how to construct a spatial nonparametric regression model estimator tor for prediction of claim frequency of insurance claims data. The study adopted a nonparametric function based on smoothing Spline in constructing the model. The asymptotic properties of the estimators; normality and consistency were derived and the inferences on the smooth function were derived. The simulation study showed that the estimator that incorporated spatial effects in predicting claims frequency is more efficient than the traditional Simultaneous Autoregressive model and Nonparametric model with Simultaneous Autoregressive error. The model estimator was applied to claims data from Cooperative Insurance Company insurance in Kenya with n = 6500 observations and the findings showed that the proposed model estimator is more efficient compared to the Local Linear fitted method, which does not account for spatial correlation. Therefore, the proposed method (Nonparametric spatial estimator) based on the findings has significant statistical improvement of the existing methods that are used for the prediction of claims. The study had a number of limitations, where the data used in the study is Lattice data (without a coordinate system); therefore, there was difficulty in classifying the claims to a specific area in the region (County).

Review Article Pages: 1 - 5

### Pulka is 5(Five) Killometers away from Sambisa Forrest, Boko Haram Stronghold Borno State, Hospital Under Mèdecins Sans Frontières Msf-Spain Nurse Shifting using (Lpp) Simplex Method

This paper is to study the contributions, analyze the professional handling of patients needs by the globally recognized a European, non-governmental organization Médecins Sans Frontiéres MSF-Spain, on Nurse Scheduling, through the most less cost effective and workload sharing techniques, in area called Pulka Community that is approximately 5killometers away from Camp Zero called Sambisa forrest, a former Boko Haram stronghold that was formally declared as the insurgents hideout location or headquaters referred as the Caliphate on the 7th August, 2014 by their Leadership. The most difficult and highly volatile, risk area in Borno State Northeast- Nigeria that was classified as a red zone by the security intelligence reports. The task of Nurse Scheduling to meet up with the community counselling, traumatized patients by the armed gunmen, hetherto the hectic and herculean task, when considered the services rendered during the crisis period at the peak of the insurgency, Military hostility and subsequent Government declaration and pronouncement of curfew on all sorts of movements sometimes between the 1000hours to 0700hours without any provision for alternative arrangement for the special health-care workers. We proposed a model to improve both the process and the quality of scheduling techniques. The objective is to maximize the fairness of the schedule among personnel. A numerical illustration and example of workload scheduling for a maximum of 8 hours is obtained and solved by correct simplex method, through elementary row operation, the hospital needs a minimum of professional nurses to meet up with the patients needs to be more effective and efficient.

Perspective Pages: 1 - 2

### Persistent Consequences of a Typical Early Number Opinion

Editorial Pages: 1 - 1

### Volume 10, Issue 8 (2021)

Editorial Pages: 1 - 1

### Number theory

Perspective Pages: 1 - 1

### Analysis on a Nonlinear Diffusion Equations using Numerical Scheme

Perspective Pages: 1 - 1

### Problems of Saturated Flows Modeling on Networks

Research Article Pages: 1 - 3

### A Pair of Formulae to the Goldbach’s Strong Conjecture

The Goldbach’s Strong Conjecture is one of the oldest unsolved problem in number theory in Mathematics. We have created a pair of formulae to the Goldbach's strong conjecture because the statement is based with the basic concept of Mathematics. The main focus before creation was, If we can create a formula or a pair of formulae to the said conjecture, that will bring an interesting events among the students (readers) who love Mathematics, the creations will give them a huge pleasure, when they can solved, the primes whose sum are equal to the positive integer say 46,by applying our created formulae.

Editorial Pages: 1 - 1

### Volume 10, Issue 6 (2021)

Mini Review Pages: 1 - 2

### A Survey on Triangular Number and Factorial Number

Castillo Jack

Objectives:The paper aims to present a survey of both time-honored and contemporary studies on triangular number, factorial, relationship between the 2, and a few other numbers related to them.

Methods: The research is expository in nature. It focuses on expositions regarding the triangular number, its multiplicative analog – the factorial and other numbers associated with them.

Findings: Much had been studied about triangular numbers, factorials and other numbers involving sums of triangular numbers or sums of factorials. However, it seems that no-one had explored the properties of the sums of corresponding factorials and triangular numbers. Hence, explorations on these integers, called factoriangular numbers, were conducted. Series of experimental mathematics resulted to the characterization of factoriangular numbers on its parity, compositeness, number and sum of positive divisors and other minor characteristics. The sequence of factoriangular numbers may be a recurring sequence and it's a rational closed-form of exponential generating function. These numbers were also characterized on when a factoriangular number are often expressed as a sum of two triangular numbers and/or as a sum of two squares.

Application/ Improvement: The introduction of factoriangular number and expositions on this sort of number may be a novel contribution to the idea of numbers. Surveys, expositions and explorations on existing studies may still be a serious undertaking in number theory.

Commentary Pages: 1 - 1

### Commutator Magnus Development Integrators

Mahendran Rajat

Hybrid quantum-classical systems combine both classical and quantum degrees of freedom. Typically, in chemistry, molecular physics, or saterials science, the classical degrees of freedom describe atomic nuclei (or cations with frozen core electrons), whereas the quantum particles are the electrons. Although many possible hybrid dynamical models exist, the essential one is that the so-called Ehrenfest dynamics that results from the simple partial classical limit applied to the complete quantum Schrödinger equation. Few numerical methods are developed specifically for the mixing of this sort of systems. Here we present a preliminary study of the performance of a family of recently developed propagators: the (quasi) commutator-free Magnus expansions. These methods, however, were initially designed for nonautonomous linear equations. We employ them for the nonlinear Ehrenfest system, by approximating the state value at whenever step within the propagation, using an extrapolation from previous time steps.

Research Article Pages: 1 - 2

### A Formula for Prime Counting Function

Noor Zaman Sheikh

We have created a formula to calculate the number of primes less than or equal to any given positive integer ‘n'. It is denoted by π (n). This is a fundamental concept in number theory and it is difficult to calculate. A prime number can be divided by 1 and itself . Therefore the set of primes (2,3,5,7,11,13,17.). The Prime Counting Function was conjectured the end of the 18th century by Gauss and by Legendre to be approximately x/Ln(x) But in this paper we are presenting the real formula, by applying the modern approach that is applying the basic concept of set theory.

Editorial Note Pages: 1 - 1

### Editorial Note on Sensitivity analysis

Theron Waelchi

Sensitivity analysis is that the study of how the uncertainty within the output of a mathematical model or system (numerical or otherwise) are often divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which features a greater specialise in uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.

Editorial Pages: 1 - 1

### A study on Methods to Handle Outliers in Multivariate

Wei Guangwei

Detecting outliers is an integral part of data analysis that sheds light on points that do not conform to the rest of the data. Whereas in univariate data, outliers appear at the extremes of the ordered sample, in the multivariate case they may be defined in many ways and are not generally based on an assumed statistical model. We present here methods for detecting multivariate outliers based on various definitions and illustrate their features by applying them to two sets of data. No single approach can be recommended over others, since each one aims at detecting outliers of a particular kind.

### Volume 10, Issue 11 (2021)

Editorial Pages: 1 - 2

### Analytic Number Theory

Editorial Pages: 1 - 2

### Non -linear Volterra Fractional Integro- differential Equations: Existence Theory and Semi- Analytical Investigation

Letter Pages: 1 - 3

### All methodologies are covered by molecular modeling

Opinion Pages: 1 - 3

### Sensitivity Analysis Principles and Procedures

Perspective Pages: 1 - 2

### Volume 10, Issue 12 (2021)

Research Article Pages: 1 - 10

### Temperature Variation in Transient State of a Thermal Insulator and the Time Fractional Diffusion Equation

This work consists in studying the adequacy of the experimental results and the theoretical results obtained from the time fractional diffusion equation on the variation of the temperature, in transient regime, during the heating of a thermal insulator. called "thermisorel".

Editorial Pages: 1 - 2

### Point wise contact between surfaces is solved using a numerical approach

Research Article Pages: 1 - 10

### Estimation of Some Thermal Diffusion Parameters by Coupling the Fractional Derivative Theory and the Genetic Algorithm

This work consists in calculating values of thermal conductivity and the suitable thickness, of a thermal insulator called "thermisorel", by the coupling of the time fractional diffusion equation and the genetic algorithm, taking into account the data and the objectives of the experiment in the article [1].

Research Article Pages: 1 - 10

### Deduction of the Time Fractional Thermal Diffusion Equation from the Classical Thermal Diffusion Equation

This work presents a transformation of the classical thermal diffusion equation into a fractional thermal diffusion equation with respect to time, considering consistency with the dimensionality of time

Research Article Pages: 1 - 5

### Peeping into the Collatz Conjecture

In the history of mathematics, there are number of conjectures, unsolved till date, Collatz Conjecture is one of them. Lother Collatz introduced a conjecture in which a series of numbers get generated called hailstone numbers, a long chain of numbers, all ended to 1. This conjecture may be considered true if the sequence would not either enter a repeating cycle or increase without bound. In this paper a tangible solution is given that anticipate that no such repeated sequence is possible that increases without bound. Hence support the truthfulness of Conjecture. May be it helps the mathematicians to achieve a pragmatic mode.

### Volume 11, Issue 1 (2022)

Editorial Pages: 1 - 1

### Editorial Note on BRICS Based Panel VAR Model

Editorial Pages: 1 - 1

### Mathematical Model of Fuzzy Linear Programming

Perspective Pages: 1 - 1

### Intricacy Based Data Analysis and Processing

Perspective Pages: 1 - 1

### Model Setting with Variable Selection and Data Description

Commentary Pages: 1 - 1

### Volume 11, Issue 2 (2022)

Commentary Pages: 1 - 2

### Impacts of Linguistic Complexity and Math Difficulty on Word Problem Solving by English Learners

Opinion Pages: 1 - 2

### Computational Complexity of Smooth Differential Equations

Editorial Pages: 1 - 1

### Angle Observability for Semilinear Hyperbolic Systems

Editorial Pages: 1 - 1

### Semi-logical Solution to Jeffery-Hamel Condition

Perspective Pages: 1 - 1

### Volume 11, Issue 4 (2022)

Perspective Pages: 1 - 2

### Computational Thinking in the Primary Mathematics

Opinion Pages: 1 - 2

### Computational Thinking for Ontario K-12 Classrooms

Commentary Pages: 1 - 2

### Computational Estimation and Mathematics Education

Editorial Pages: 1 - 2

### Viable Learning Strategies for Real-Time Image-Guided Adaptive Control

Editorial Pages: 1 - 2

### Volume 11, Issue 7 (2022)

Mini-Review Pages: 1 - 3

### Realization of Convergence Splines/ NURBS of Higher Order Stability in Isgeometric Analysis

Conventional B-splines lack the capacity of local refinement that is required in order to realize ideal convergence order in genuine applications. The challenges with the isogeometric approach include the need to develop an alternative mathematical approach of higher-order equations proven to converge to the shape interface. The main purpose of this study is to determine the realization approach for isogeometric structure in convergence splines/NURBS of distinctive nature of higher-order stability. The basis for this realization approach (i.e. convergence splines/NURBS of higherorder) for B-Spline is degree (order) of realization as used in B-Spline theory. In this approach, the converging (C) order of the basis functions is elevated. An ideal (new) isogeometric structure (i.e. curve or mesh) in convergence splines/NURBS of higher-order stability for improved local refinement has been realized. It is clear that when the order C is enhanced (i.e. realized), converging number n must also be enhanced (i.e. realized) by the equivalent amount of degree. In the process of order enhancement (i.e. the order realization), the stability of every knot value is elevated. Order realization initiates by replicating present knots by the equivalent number as the increase in converging order. In this, every knot vector value is elevated by one point. In line with this, the amount of control points and the basic functions are boosted or amplified from 8 to 13. The refined control points computed was improved where the convergence of higher-order was realized.

Mini Review Pages: 1 - 3

### Application Overview of Quantum Computing for Gas Turbine Design and Optimization

Calculated plans require enhancement strategies to distinguish the best fit in the framework. The article researches the use of quantum calculation in gas turbine plan and recreation issues with momentum advancements, approaches and possible abilities. Quantum streamlining calculations and quantum annealers help in foreseeing by and large effectiveness and enhancing different working boundaries of the gas turbine. An examination of both old style and quantum PCs has been talked about momentarily. The old style model difficulties are moderated with the utilization of quantum calculation. A clever half and half model for recreating gas turbines has been proposed, which comprises of a mix of the two physical science and AI to wipe out not many of the basic issues confronted. This survey explains use of quantum figuring based AI for plan and enhancement of a gas turbine. The general conditions of the gas ways of gas turbines could be examined utilizing the quantum processing model from here on out.

Commentary Pages: 1 - 3

### Capability of Passive DVB-T Radar Component against Illegal UAV Flights

For the present numerous years, unlawful UAV (Unmanned Aerial Vehicle) flights have been seen in various nations and under different conditions. The plan of such unlawful flights might cover modern surveillance up to psychological oppressor assaults. Countering such a topsy-turvy danger is currently of expanding and testing interest for some nations. The really mandatory capabilities for such an enemy of UAV framework will be momentarily examined from recognition, confinement, ID/arrangement, extraction (a UAV must be segregated from different discoveries) to the alarm capability. After this presentation about the unique situation, a depiction of a latent DVB-T (Digital Video Broadcasting Terrestrial) radar part will be given, and its true capacity, concerning the recently portrayed capabilities, will be shown utilizing exploratory outcomes. Such a detached methodology will be in no time contrasted and dynamic radar parts. A few estimation crusades have been led with a seriously colossal assortment of nano-little UAVs (multirotors, for example, ANAFI, Mavik, Phantom 4, F450 up to M600 as well as fixed wings like officer, Disco, X8 and X11) developing under different designs (bistatic bases, different weather patterns) and a choice of the most significant outcomes will be introduced.

Mini Review Pages: 1 - 3

### Robot Fish Caudal Propulsive Mechanisms: A Mini-Review

Scientists have fostered various fake fish to impersonate the abilities to swim of natural species and comprehend their biomechanical underwater abilities. The inspiration emerges from the interest to acquire further appreciation of the effective idea of organic motion, which is the consequence of millions of long stretches of development and transformation. Blade based natural species created remarkable abilities to swim and prominent execution in profoundly unique and complex underwater conditions. Accordingly, in light of examination by established researchers, this little survey focuses on talking about the mechanical gadgets created to execute the caudal propulsive portions of automated fish. Caudal components are of impressive interest since they might be intended to control inertial and gravitational powers, as well as applying extraordinary unique reach in automated fish. This original copy gives a compact survey zeroed in on the designing executions of caudal components of anguilliform, subcarangiform, subcarangiform, thunniform and ostraciiform swimming modes.

Review Article Pages: 1 - 3

### Authentication Methods: A Comprehensive Survey

This paper presents a far reaching examination of current confirmation plans. We start with the significance of verification strategies and the different validation processes. Then, at that point, we present the verification measures utilized and we play out an examination of validation strategies concerning comprehensiveness, uniqueness, collectability, execution, worthiness, and caricaturing. At long last, we present multifaceted verification difficulties and security issues and present future bearings.

### Volume 11, Issue 6 (2022)

Research Article Pages: 1 - 4

### An Interior-Point Method for Nonlinear Constrained Optimization Problem with Trust-Region Mechanism

We introduced an algorithm to solve a Non Linear Constrained Optimization (NLCO) problem in this paper. This algorithm follows Das’s idea of Newton’s interiorpoint method that uses a diagonal matrix of Coleman and Li for NLCO problems. A Trust-Region (T-R) mechanism is used to globalize the algorithm. This algorithm follows Byrd and Omojokun’s idea of step decomposition. It is a successful idea to overcome the difficulty of having an infeasible quadratic T-R sub problem and converts the quadratic T-R sub problem into two unconstrained T-R sub problems.

A global convergence theory of the algorithm is studied under five standard assumptions. This algorithm is different and maybe simpler than similar ideas such that the global convergence theory is not depending on the linear independence assumption on the gradients of the constraints.

Some numerical tests are stated to indicate that the algorithm performs effectively and efficiently in pursuance.

Research Article Pages: 1 - 6

### MMORPG Data Recovery from Player to Player Interactions: Dead Acquisition Including Game Modification Files

Imagine a world that allows for open, unmonitored communication, and the ability to trade currency between individuals anonymously. An environment such as this would present itself as a prime location for malicious intent. Money laundering, exploitation, theft, harassment, and stalking could potentially go unnoticed. When discussing World of warcraft or fortnite, malicious intent would generally not come to mind. However, this is precisely the type of environment that massively multiplayer online role-playing games provide.

Case Report Pages: 1 - 4

### Modelling the Effect of Depletion Rate of Forestry Resources due to Industrialization on the Effect of Population and Population Augmented Industrialization on Forestry Resources

In this work, we used the 0de45 to simulate the behavior of the dynamical system of the nonlinear system of ordinary differential equation at equilibrium. It is shown that if the forest resources is maintained at the given equilibrium, the activities of man will not affect the stability of the forest resource biomass but a little below the equilibrium the system will be unstable.

Mini Review Pages: 1 - 2

### Evolution of Electric and Magnetic Parts of Weyl Tensor in a Space-time

The present paper is intended to study of the evolution of Electric and Magnetic parts of Weyl tensor in a space-time; in particular to measure the components of parts of Weyl tensor of an observer with a time-like 4-unit vector we have attempted to describe the tensors, which are the parts of Weyl tensor concerning for to the observeru. Further, we have established that if eigenvalues of any matrix are zero, real and imaginary then it is a part of Weyl tensor. Afterward, the cases from Petrov types have been obtained therein.

Research Article Pages: 1 - 6

### One Method for the Numerical Resolution of One Type of Fractional Differential Equation of Euler-Lagrange

We propose in this article one method of numerical resolution using the programming under Matlab of one of the fractional differential equations of Euler-Lagrange containing a composition of the left and right fractional derivatives of order α, 0< α<1, of Riemann-Liouville and Caputo respectively.

### Volume 2, Issue 5 (2013)

Editorial Pages: 1 - 2

### Thermostatted Mode ls: Ope n Problems

Carlo Bianca

### Volume 11, Issue 8 (2022)

Research Article Pages: 1 - 5

### Modeling Rainfall Data in Kenya Using Bayesian Vector Autoregressive

Time series modeling and forecasting has ultimate importance in various practical domains in the world. Many significant models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting the normality of the day to day economic and non-economic activities. It causes far-reaching weather changes, which are characterized by precipitation or temperature fluctuations. Rainfall prediction is one of the most important and challenging tasks in the recent today’s world. In Kenya unstable weather patterns which are associated with global warming have been experienced to a greater extent. The objective of this study was to modeled rainfall patterns in Kenya by use of Bayesian Vector Autoregressive (BVAR). To achieve this objective, the data was first statistically diagnosed using Augmented Dicker Fuller and Granger Causality test. The BVAR model was developed using multiple regression analysis in a system of equations. The model sensitivity was performed using confusion matrix and the F-test was used to compare the variances of the actual and forecasted rainfall values. After the first differencing the data was found to be stationary where Augmented Dicker Fuller (ADF) test was statistically significant with P-values <0.05. The Granger Causality test found that; temperature, atmospheric pressure, wind speed and relative humidity influenced the rainfall time series models in all the regions. The model sensitivity was performed using confusion matrix. The BVAR model developed was statistically significant (R2=0.9896). The sensitivity of the model was 82.22%, making it appropriate for forecasting. In conclusion the Bayesian Vector Autoregressive model developed is suitable and sensitive for forecasting rainfall patterns.

Research Article Pages: 1 - 4

### The Influence of Mobile Phone on Colleges of Education Students? Interest on Basic General Mathematics

The study examined the influence of mobile phone on students’ interest in basic general mathematics colleges of education in Enugu state. Three research questions were posed to guide the study. The study adopted survey research design. All the NCE 1 students of government owned colleges of education in Enugu state form the population of the study. Sixty students (60) were sampled from the population using multistage sampling technique. The study sample was exposed to learning basic general mathematics (GSS 122) through mobile phone for period of three weeks. The instrument for collecting data was Basic General Mathematics Interest Questionnaire (BGMIQ) with reliability coefficient of 0.89 obtained from Cronbach alpha. Descriptive Statistic of mean and standard deviation was used to answer the research questions. It was found among others that the learning of basic general through the mobile phone develops the interest of the students in three main constructs (namely: tested, leisure and career). It was recommended among others that lecturers should be encouraged to integrate mobile phone for teaching basic general mathematics so as stimulate the interest of the students thereby improve their achievement in the course.

Research Article Pages: 1 - 4

### Approximate Solution to First-order Integro-differential Equations Using Polynomial Collocation Approach

In this study, power series and shifted Chebyshev polynomials are used as basis function for solving first order volterra integro-differential equations using standard collocation method. An assumed approximate solution in terms of the constructed polynomial was substituted into the class of integro-differential equation considered. The resulted equation was collocated at appropriate points within the interval of consideration [0,1] to obtain a system of algebraic linear equations. Solving the system of equations, by inverse multiplication, the unknown coefficients involved in the equations are obtained. The required approximate results are obtained when the values of the constant coefficients are substituted back into the assumed approximate solution. Numerical example are presented to confirm the accuracy and efficiency of the method.

Method Pages: 1 - 4

### Recurrence Relation When Solving 2nd Order Homogeneous Linear ODEs by Frobenius Method

The Frobenius method, also known as the Extended Power Series method comes into play when solving second-order homogeneous linear ODEs having variable coefficients, about a singular point. The solution is expressed in terms of infinite power series. This straightforward article is merely aimed to lucidly arrive at the recurrence relation/formula by taking proper heed of summation limits and simply manipulating them, which is probably absent in almost all research articles and books. The methodology discussed is followed by a few conspicuous and relevant observations.

Short Commentary Pages: 1 - 3

### Displaying Nonlocal Conduct in Pandemics by Means of a Response Dispersion Framework Consolidating Populace Development along an Organization

The episode of Coronavirus, starting in 2019 and going on through the hour of composing, has prompted reestablished interest in the numerical displaying of irresistible sickness. Late works have zeroed in on fractional differential condition (PDE) models, especially response dispersion models, ready to depict the movement of a pestilence in both reality. These examinations have shown commonly encouraging outcomes in portraying and anticipating Coronavirus movement. Be that as it may, individuals frequently travel significant distances in brief timeframes, prompting nonlocal transmission of the sickness. Such virus elements are not very much addressed by dissemination alone. Conversely, customary differential condition (Tribute) models may effortlessly represent this way of behaving by thinking about divergent locales as hubs in an organization, with the edges characterizing nonlocal transmission. In this work, we endeavor to join these demonstrating standards by means of the presentation of an organization structure inside a response dispersion PDE framework. This is accomplished through the meaning of a populace move administrator, which couples disjoint and possibly far off geographic locales, working with nonlocal populace development between them. We give scientific outcomes showing that this administrator doesn't upset the actual consistency or numerical well-posedness of the framework, and check these outcomes through mathematical tests. We then utilize this strategy to recreate the Coronavirus plague in the Brazilian district of Rio de Janeiro, exhibiting its capacity to catch significant nonlocal ways of behaving, while at the same time keeping up with the benefits of a response dissemination model for portraying neighborhood elements.

### Volume 10, Issue 2 (2021)

Editor Note Pages: 1 - 2

### Complexity in Mathematics

Artur Sowa

Editor Note Pages: 1 - 3

### US Capital Gains Tax Rate Using Markov Chains

Brian Trowbridge

Using Markov-chains (formally a Markov process or Markov system) we will show how to estimate the probabilities of a capital gains tax rate changing from its current rate to another rate within a certain number of years. It is important to recognize that capital gains rates in the United States have their origins in every elected administration of the government that had the power to influence tax policy. The outcome of government elections is dependent on chance factors such as periods of war and peace, economic recession and expansion, current fiscal and monetary policy, changes in population demographics, just to name a few. The delicate balance between the government and the dynamic society that shapes tax policy is difficult to predict using deterministic modeling. Therefore, we look to stochastic modeling using the Markov-Chain processes to see if it could be of use in creating a useful model for capital gains tax rates in the United States

Editor Note Pages: 1 - 3

### Coefficient Inequalities for Uniformly P-Valent Starlike and Convex Functions

Vandna Agnihotria 1, Ran Singh 2

In this paper we obtain some coefficient inequalities for subclasses of uniformly p−valent starlike and convex functions in the open unit disk denoted by SDp (β, α) and KDp (β, α). Growth bounds and distortion bounds are discussed for functions in these classes. For different values of the parameters p, α and β our results of this paper generalize those obtained by several authors in the literature.

Editor Note Pages: 1 - 3

### Behavior of a State-dependent Functional Differential Equation

Yin-Wei Lin, Tzon-Tzer Lu

This paper deals with the state-dependent functional differential equations x(x(t)). We give the strict proof of qualitative properties that Eder’s case and the solution of the state-dependent differential equation is not unique. In some conditions, we also extend Eder’s case.

### Volume 11, Issue 9 (2022)

Opinion Pages: 1 - 3

### Agreement Docking and MM-PBSA Calculations?

The Covid illness 2019 (Coronavirus) is a pandemic that has seriously presented significant wellbeing challenges and guaranteed great many lives. However immunizations have been delivered to stem the spread of this illness, the passing rate stays high since drugs utilized for treatment have helpful difficulties. Serious intense respiratory disorder Covid 2 (SARS-CoV-2), the infection that causes the sickness, has a huge number of likely restorative targets. Among them is the furin protease, which has a cleavage site on the infection's spike protein. The cleavage site works with the section of the infection into human cells through cell combination. This basic contribution of furin in the sickness pathogenicity has made it a reasonable helpful procedure against the infection. This study utilizes the agreement docking approach utilizing Cross breed and AutoDock Vina to basically screen a pre-separated library of 3942 normal item mixtures of African beginning against the human furin protease (PDB: 4RYD). Twenty of these mixtures were chosen as hits in the wake of meeting atomic docking cut-off of-7 kcal.mol-1, present arrangement review, and having ideal furin-ligand connections.

Review Article Pages: 1 - 2

### Computational Therapeutics Against Coronavirus

Drug revelation tests in cell culture and creature models focusing on the hindrance of furin protease as restorative mediation for explicit illnesses have been promising. In 2015, some novel furin inhibitors were tried by means of cell culture tests against flu infection, Bacillus anthracis, and diphtheria poisons. That's what their discoveries showed, within the sight of these inhibitors, the spread of the avian flu infections, H5N1 and H7N1, was firmly repressed. Bacillus anthracis and diphtheria poisons which are not infections however rely upon furin for their engendering gave indications of defensive impact within the sight of the inhibitors.

Mini Review Pages: 1 - 2

### Transport of Jeffrey Liquid with Silver Nanoparticle in the Capricious Annulus

This study researches the effects of warm leap and slanted attractive field on the peristaltic transport of Jeffrey liquid containing silver nanoparticles in the erratic abrogates under the long frequency and low Reynolds number presumption. In clinical examinations, the effect of warm leaps and skewed attractive fields on general wellbeing is of interest. Peristaltic movement's capacity to send heat and make an attractive field has a few purposes in biomedical and bioengineering. The non-Newtonian Jeffrey liquid with silver nanoparticles is viewed as in the space between two barrel shaped tubes that are unusually adjusted. The homotopic bother strategy is semi-logical for demonstrating and nonlinear halfway differential conditions (HPM). Scientific answers for speed, pressure angle, and tension ascent were found. To show what actual boundaries mean for temperature, speed, fixation, frictional power, and tension ascent of inward and external cylinders were plotted. A correlation of the current technique with the specific answer for temperature and nanoparticle focus profile is shown graphically. The current examination of logical arrangement ways to deal with the specific arrangement. The main thing in the ongoing examination is that the Hartmann number and thermophoresis number make the speed profile decline. Jeffrey liquid boundary and attractive field point make the speed rise. The nanofluid's temperature climbs because of the warm leap. What's more, the Jeffrey nanofluid has a higher energy and temperature than the Jeffrey liquid. This examination can more readily assess the needle's infusion speed and liquid stream highlights during disease treatment, conduit blockage expulsion, and diminished draining all through the medical procedure.

Short Commentary Pages: 1 - 3

### Information Revelation based Computational Advances for Clinical Large Information

As of late, the persistent advancement of large information, cloud administrations, Internet+, man-made consciousness, and different advancements has sped up the improvement of information correspondence administrations in the customary drug industry. It assumes a main part in the improvement of my country's drug industry, extending the change of the wellbeing framework, working on the effectiveness and nature of clinical benefits, and growing new advances. In this unique situation, we make the accompanying examination and reach the accompanying determinations: the size of my country's clinical huge information market is continually expanding, and the worldwide clinical large information market is likewise expanding. Contrasted and the worldwide clinical huge information market, China's clinical enormous information has developed at a quicker rate.

Case Report Pages: 1 - 3

### Clinical Framework Utilization of Man-Made Reasoning Artificial Intelligence based Large Information Examination

The short term enrollment framework is straightforwardly connected with the ongoing patient meeting process and is additionally the reason for its development. The principal thing to tackle is the enlistment, which can be handled through the enrollment application and the clinical entryway. The short term enrollment framework utilizes JSP innovation to understand the intercommunication of related data by finishing patient data section, doctor determination, or arrangement the board. During the time spent setting up the framework, lay the foundation for it.

### Volume 10, Issue 3 (2021)

Mini Review Pages: 1 - 2

### Perfect Folding of Graphs

In this paper we introduced the definition of perfect folding of graphs and we proved that cycle graphs of even number of edges can be perfectly folded while that of odd number of edges can be perfectly folded to C3. Also we proved that wheel graphs of odd number of vertices can be perfectly folded to C. Finally we proved that if G is a graph of n vertices such that 2>clique number=chromatic number=k>n, then the graph can be perfectly folded to a clique of order k.

Research Pages: 1 - 6

### Numerical Investigation of Mixed Convection Flows with Variable Viscosity and Prandtl Number and Validation Using ANSYS FLUENT

Purpose: The purpose of present study is to analyze the mixed convection impact for an exponentially decreasing free stream in laminar water boundary layer flow with variable viscosity and Prandtl number. The analysis includes the effect of suction/blowing and heat generation/ absorption. Design/methodology/approach: The non-linear partial differential equation governing the flow and thermal fields are presented in nondimensional form by using appropriate transformations. The Quasilinearization technique in combination with implicit finite difference scheme has been adopted to solve the non- linear coupled partial differential equations. Findings: It was found that the influence of The numerical results are displayed graphically to illustrate the influence of various nondimensional physical parameters on velocity and temperature buoyancy assisting force on both velocity as well as temperature profile is significant. Skin friction coefficient increases with Richardson number and deceleration parameter. The heat transfer coefficient decrease with the increase of heat generation/absorption parameter and increases with an increase in wall suction/injection parameter. Originality/value: The present investigation deals with the solution of steady laminar water boundary layer flows with an exponentially decreasing free stream velocity and temperature-dependent viscosity and Prandtl number applicable to water using practical data.

Research Article Pages: 1 - 3

### A Pair of Formulae to the Goldbach′s Strong Conjecture

The Goldbach’s Strong Conjecture is one of the oldest unsolved problem in number theory in Mathematics. We have created a pair of formulae to the Goldbach's strong conjecture because the statement is based with the basic concept of Mathematics. The main focus before creation was, If we can create a formula or a pair of formulae to the said conjecture, that will bring an interesting events among the students (readers) who love Mathematics, the creations will give them a huge pleasure, when they can solved, the primes whose sum are equal to the positive integer say 46,by applying our created formulae.

Research Article Pages: 1 - 8

### Heterogeneous-Homogeneous Reaction Mechanism on the Hydro Magneticnano Fluid Flow Over a Stretching Cylinder with Prescribed Heat Flux using Hermite Wavelet Method

The current work provides the Hermite wavelet method (HWM) for an incompressible Nanofluid hydromagnetic flow through a stretching cylinder associated with heterogeneous-homogeneous chemical reactions. Single-walled carbon nanotubes (SWCNTs) with multi-walled carbon nanotubes (MWCNTs) as nanoparticles in the form of arranged heat flux are accounted for currently. Regulating equations, which are highly nonlinear coupled, are changed right into non-dimensional ordinary differential equations (ODEs) using appropriate similarity transformations. The desire for exceptional flow constraints on the flow feature is finalized truthfully through tables and graphs. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, concentrations, and nanoparticles. Comparison of the numerical outcomes is made with previously available consequences under particular cases, and the results are found to be in good agreement. The Hermite wavelet technique is hugely proficient and sensible for finding outcomes to this type of coupled nonlinear ODEs. The works are in outstanding accord for coupled nonlinear ordinary differential equations (ODEs) in engineering applications.

Research Article Pages: 1 - 2

### Coding and Decoding of Multiple Factoriangular Numbers and its Application in Cryptographic System

The current work provides the Hermite wavelet method (HWM) for an incompressible Nanofluid hydromagnetic flow through a stretching cylinder associated with heterogeneous-homogeneous chemical reactions. Single-walled carbon nanotubes (SWCNTs) with multi-walled carbon nanotubes (MWCNTs) as nanoparticles in the form of arranged heat flux are accounted for currently. Regulating equations, which are highly nonlinear coupled, are changed right into non-dimensional ordinary differential equations (ODEs) using appropriate similarity transformations. The desire for exceptional flow constraints on the flow feature is finalized truthfully through tables and graphs. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, concentrations, and nanoparticles. Comparison of the numerical outcomes is made with previously available consequences under particular cases, and the results are found to be in good agreement. The Hermite wavelet technique is hugely proficient and sensible for finding outcomes to this type of coupled nonlinear ODEs. The works are in outstanding accord for coupled nonlinear ordinary differential equations (ODEs) in engineering applications.

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

#### Journal Highlights

###### Citations: 1282

Journal of Applied & Computational Mathematics received 1282 citations as per Google Scholar report

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

#### Open Access Journals

arrow_upward arrow_upward