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Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

Current Issue

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

    Rasolomampiandry G, Rakotoson R, Randimbindrainibe F

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    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

    Alfredo Gay Neto

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    When modeling rigid or versatile multibody systems, one is usually curious about establishing contact interaction models. this is often a very important concern for particles modeling . A global-scale search sometimes has the target of distinctive and neglecting unbelievable contact pairs. For that, it always employs fast and inexpensive process algorithms, since varied searches ar sometimes to be performed. one finds a kind of algorithms for world contact detection. it's necessary to repeat the worldwide search inside a given cyclicity on the model answer, since a non-probable contact on a given configuration could become a probable one when the system configuration has modified.

    Research Article Pages: 1 - 10

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

    Rasolomampiandry G, Rakotoson R, Randimbindrainibe F

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    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

    Research Article Pages: 1 - 10

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

    Rasolomampiandry G, Rakotoson R, Randimbindrainibe F

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    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

    Khurshid Ahmad Bhat

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    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 2, Issue 5 (2013)

      Editorial Pages: 1 - 2

      Thermostatted Mode ls: Ope n Problems

      Carlo Bianca

                    

      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 10, Issue 3 (2021)

          Mini Review Pages: 1 - 2

          Perfect Folding of Graphs

          El Kholy*

          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

          Abhishek Kumar Singha

          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 nondimensional 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 nondimensional 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

          Noor Zaman Sheikh

          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

          Raghunatha K R

          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

          Swati Bisht

          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 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 ? (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

              Ibadul Qadeer

              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

              Miller*

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              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

                Damore Cassie*

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                Commentary Pages: 1 - 1

                An Enhanced Method for Tail Index Estimation

                Jim Kate*

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                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

                Raghunatha KR* and Kumbinarasaiah S

                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

                  Swati Bisht* and Dr. Anand Singh Uniyal

                  DOI: 10.37421/2168-9679.2021.10.485

                  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

                  Kipngetich Gideon*

                  DOI: 10.37421/2168-9679.2021.10.484

                  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

                  Buba MT Hambagda*, Ridwan AtanHussaini, Nafisat Usman Dagona and Usman Adam Muhammad

                  DOI: 10.37421/2168-9679.2021.10.486

                  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.

                  Volume 10, Issue 8 (2021)

                    Editorial Pages: 1 - 1

                    Number theory

                    Gideon Langat*

                    DOI: 10.37421/2168-9679.2021.10.e117

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                    Research Article Pages: 1 - 3

                    A Pair of Formulae to the Goldbach’s Strong Conjecture

                    Noor Zaman Sheikh*

                    DOI: 10.37421/2168-9679.2021.10.483

                    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

                    3 Dimensional Study Case

                    Dovor D*

                    DOI: 10.37421/2168-9679.2021.10.e116

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                    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)

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