Mathematics Commons^™

Mathematical Model Of Cholera Spread Based On Sir: Optimal Control, Noer Hidayati, Eminugroho Ratna Sari, Nur Hadi Waryanto

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

The bacterium Vibrio cholerae is the cause of cholera. Cholera is spread through the feces of an infected individual in a population. From a mathematical point of view, this problem can be brought into a mathematical model in the form of Susceptible-Infected-Recovered (SIR), which considers the birth rate. Because outbreaks that occur easily spread if not treated immediately, it is necessary to control the susceptible individual population by vaccination. The vaccine used is Oral Vibrio cholera. For this reason, the purposes of this study were to establish a model for the spread of cholera without vaccination, analyze the stability of …

Penggunaan Goal Programming Dalam Perencanaan Menu Untuk Lansia Penderita Hipertensi, Diana Islamiyati, Dwi Lestari, Nur Insani

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Penelitian ini bertujuan untuk membangun suatu model goal programming untuk mengoptimalkan perencanaan menu harian lansia penderita hipertensi. Fungsi tujuan model ini yaitu untuk memaksimumkan kandungan gizi makanan lansia sesuai Angka Kecukupan Gizi (AKG), meminimumkan biaya pangan, memaksimumkan kuantitas pangan, dan meminimumkan konsumsi pangan yang mengandung natrium. Berdasarkan eksperimen komputasi yang dilakukan dengan menerapkan model weighted goal programming ini, dihasilkan solusi optimal kebutuhan gizi lansia penderita hipertensi yang sesuai dengan AKG. Adapun perencanaan optimal menu makanan untuk lima hari yaitu terdiri dari 12 jenis pangan dengan pengeluaran biaya sebesar Rp 11.236,- untuk hari pertama, 13 jenis pangan dengan pengeluaran biaya …

Drought-Prone Areas Mapping Using Fuzzy C-Means Method In Gunungkidul District, Kismiantini Kismiantini, Fajra Husniyah, Osval Antonio Montesinos-López

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Gunungkidul district is one of the districts in the Special Region of Yogyakarta that is frequently affected by drought disasters. The purpose of this study is to map drought-prone areas in Gunungkidul district using the fuzzy c-means method, making it easier for the government to allocate water-dropping assistance to drought-affected areas. The research variables include rainfall, soil type, infiltration, slope, and land use. The type of variables is an ordinal scale, so they must be transformed using the successive interval method before being analyzed using the fuzzy c-means method. The cluster validity indexes of the Xie and Beni index, partition …

Decomposable Model Spaces And A Topological Approach To Curvature, Kevin M. Tully

Rose-Hulman Undergraduate Mathematics Journal

This research investigates a model space invariant known as k-plane constant vector curvature, traditionally studied when k=2, and introduces a new invariant, (m,k)-plane constant vector curvature. We prove that the sets of k-plane and (m,k)-plane constant vector curvature values are connected, compact subsets of the real numbers and establish several relationships between the curvature values of a decomposable model space and its component spaces. We also prove that every decomposable model space with a positive-definite inner product has k-plane constant vector curvature for some integer k>1. In …

Winning Strategy For Multiplayer And Multialliance Geometric Game, Jingkai Ye

Rose-Hulman Undergraduate Mathematics Journal

The Geometric Sequence with common ratio 2 is one of the most well-known geometric sequences. Every term is a nonnegative power of 2. Using this popular sequence, we can create a Geometric Game which contains combining moves (combining two copies of the same terms into the one copy of next term) and splitting moves (splitting three copies of the same term into two copies of previous terms and one copy of the next term). For this Geometric Game, we are able to prove that the game is finite and the final game state is unique. Furthermore, we are able to …

Hurwitz Actions On Reflection Factorizations In Complex Reflection Group G₆, Gaurav Gawankar, Dounia Lazreq, Mehr Rai, Seth Sabar

Rose-Hulman Undergraduate Mathematics Journal

We show that in the complex reflection group G₆, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.

Lie-Derivations Of Three-Dimensional Non-Lie Leibniz Algebras, Emily H. Belanger

Rose-Hulman Undergraduate Mathematics Journal

The concept of Lie-derivation was recently introduced as a generalization of the notion of derivations for non-Lie Leibniz algebras. In this project, we determine the Lie algebras of Lie-derivations of all three-dimensional non-Lie Leibniz algebras. As a result of our calculations, we make conjectures on the basis of the Lie algebra of derivations of Lie-solvable non-Lie Leibniz algebras.

The Optimal Double Bubble For Density 𝑟ᵖ, Jack Hirsch, Kevin Li, Jackson Petty, Christopher Xue

Rose-Hulman Undergraduate Mathematics Journal

In 2008 Reichardt proved that the optimal Euclidean double bubble---the least-perimeter way to enclose and separate two given volumes---is three spherical caps meeting along a sphere at 120 degrees. We consider Rⁿ with density r^p, joining the surge of research on manifolds with density after their appearance in Perelman's 2006 proof of the Poincaré Conjecture. Boyer et al. proved that the best single bubble is a sphere through the origin. We conjecture that the best double bubble is the Euclidean solution with the singular sphere passing through the origin, for which we have verified equilibrium (first variation …

A Proof Of A Generalization Of Niven's Theorem Using Algebraic Number Theory, Caroline Nunn

Rose-Hulman Undergraduate Mathematics Journal

Niven’s theorem states that the sine, cosine, and tangent functions are rational for only a few rational multiples of π. Specifically, for angles θ that are rational multiples of π, the only rational values of sin(θ) and cos(θ) are 0, ±½, and ±1. For tangent, the only rational values are 0 and ±1. We present a proof of this fact, along with a generalization, using the structure of ideals in imaginary quadratic rings. We first show that the theorem holds for the tangent function using elementary properties of Gaussian integers, before extending the approach to other imaginary quadratic rings. We …

Sufficient Condition For The Possibility Of Completing The Pursuit, Nodirbek Umrzaqov

Scientific Bulletin. Physical and Mathematical Research

In this paper, the problem of chase is represented by a system of linear differential equations of motion dynamics. In this case, there is an integral limit to the control parameter of the evader, and a geometric limit to the control parameter of the pursuer. The pursuer is allowed to use the control that the fugitive has used so far to build his control. There are enough conditions for the game to end even if it starts from any starting point. An algorithm for constructing the control function of the pursuer is defined. It should also be noted that the …

M-Subharmonic Functions On The Projective Space PN, Gokhan Gogus, Azimbay Sadullaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a class of quasi m-subharmonic functions in the projective space ℙⁿ. Similarly to the m-subharmonic functions, we will show a number of potential properties of quasi m-subharmonic functions. We introduce the concepts of Green’s function V_qm^*(z,K,ℙⁿ), ��_m-measure ω_qm^*(z,E,D) and study m-regularities of compact sets K ⊂ ℙⁿ. In contrast to the complex space ℂⁿ, we will prove that in the projective space ℙⁿ the locally …

Interpretation Of De Sitter Space Of Second Kind, Abdulaziz Artikbaev, Botirjon Mamadaliyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In a five-dimensional pseudo-Euclidean space of index two, the geometry on its sphere is studied. The equivalence of the geometry on a sphere of imaginary radius on de Sitter space is shown. The interpretation of the geometry on a sphere of imaginary radius, inside the sphere of imaginary radius of the Minkowski four-dimensional space, is implemented. We study a curve in a five-dimensional pseudo-Euclidean space of index two and determine the membership condition of the curve to a sphere of imaginary radius.

Dirichlet Problem In The Class Of A(Z)-Harmonic Functions, Shohruh Khursanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This paper work is devoted to the study of the Dirichlet problem in the class of A(z)-harmonic functions.

An Intrinsic Proof Of An Extension Of Itô’S Isometry For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

(R1514) Nano Continuous Mappings Via Nano M Open Sets, A. Vadivel, A. Padma, M. Saraswathi, G. Saravanakumar

Applications and Applied Mathematics: An International Journal (AAM)

Nano M open sets are a union of nano θ semi open sets and nano δ pre open sets. The properties of nano M open sets with their interior and closure operators are discussed in a previous paper. In this paper, we discuss about nano M-continuous and nano M-irresolute functions are introduced in a nano topological spaces along with their continuous and irresolute mappings. Also, nano M-open and nano M-closed functions are introduced and compare with their near open and closed mappings in a nano topological spaces. Further, nano M homeomorphism is also discussed in nano …

(R1519) On Some Geometric Properties Of Non-Null Curves Via Its Position Vectors In \Mathbb{R}_1^3, Emad Solouma, Ibrahim Al-Dayel

Applications and Applied Mathematics: An International Journal (AAM)

In this work, the geometric properties of non-null curves lying completely on spacelike surface via its position vectors in the dimensional Minkowski 3-space \mathbb{R}_1^3 are studied. Also, we give a few portrayals for the spacelike curves which lie on certain subspaces of \mathbb{R}_1^3. Finally, we present an application to demonstrate our insights.

(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, Lemnaouar Zedam, Soheyb Milles, Abdelhamid Bennoui

Applications and Applied Mathematics: An International Journal (AAM)

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, …

(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali

Applications and Applied Mathematics: An International Journal (AAM)

This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type ₄F₃(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.

(R1499) Family Of Surfaces With A Common Bertrand D-Curve As Isogeodesic, Isoasymptotic And Line Of Curvature, Süleyman Şenyurt, Kebire Hilal Ayvacı, Davut Canlı

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish the necessary and sufficient conditions to parameterize a surface family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic or curvature line in \mathbb{E}^3. Then, we calculate the fundamental forms of these surfaces and determine the developability and minimality conditions with the Gaussian and mean curvatures. We also extend this idea on ruled surfaces and provide the required conditions for those to be developable. Finally, we present some examples and graph the corresponding surfaces.

(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

Consolidation Of Mobile Sands With Ameliorants And Phytomelioration, Sharibay Toremuratov, Bakhtiyar Ismailov

Karakalpak Scientific Journal

The results of even a few experiments show the possibility of obtaining a tangible effect when jointly carrying out chemical reclamation and phytomelioration. Reliable habitation of plants is a guarantee of further long-term stopping of the movement of sand and improvement of the ecological situation.

Thus, the sand-fixing crust obtained by this method simultaneously performs several functions: it stops the movement of sand, reduces dust removal, creates favorable conditions for the growth and development of vegetation, contributes to the emergence of soil structures, the accumulation of humus, etc.

A Complete Characterisation Of Vertex-Multiplications Of Trees With Diameter 5, Willie Han Wah Wong, Eng Guan Tay

Theory and Applications of Graphs

For a connected graph G, let D(G) be the family of strong orientations of G; and for any D ∈ D(G), we denote by d(D) the diameter of D. The orientation number of G is defined as d(G)=min{d(D) | D ∈ D(G)}. In 2000, Koh and Tay introduced a new family of graphs, G vertex-multiplications, and extended the results on the orientation number of complete n-partite graphs. Suppose G has the vertex set V(G)={v₁,v₂,… v_n}. For any sequence of n positive integers (s …

Covariant Ergodic Quantum Markov Semigroups Via Systems Of Imprimitivity, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

De Finetti’S Theorem In Categorical Probability, Tobias Fritz, Tomáš Gonda, Paolo Perrone

Journal of Stochastic Analysis

No abstract provided.

On 𝜃- -Closed Sets And 𝜃- -Continuous Functlons, Amin Hamoud Saif, Nahid Mohammed Al-Showhati

Hadhramout University Journal of Natural & Applied Sciences

In topological spaces, the class of 𝜃-closed sets and 𝜃-continuous function have been introduced by Velicko and Fomin respectively. The purpose of this paper is to introduce and study these notions in grill topological spaces by giving the new classes of 𝜃- -closed sets and 𝜃- -continuous functions in grill topological space.

Splitting-Up Technique And Cubic Spline Approximations For Solving Modified Coupled Burgers' Equations, Anwar Abdulla Bassaif

Hadhramout University Journal of Natural & Applied Sciences

In this paper, a finite difference scheme based on the splitting-up technique and cubic spline approximations is developed for solving modified coupled Burgers' equations. The accuracy and stability of the scheme have been analyzed. It is found that the scheme is of first-order accuracy in time and second-order accuracy in space direction and is unconditionally stable. The numerical results are obtained with severe/moderate gradients in the initial and boundary conditions and the steady state solutions are plotted for different values of given parameters. It is concluded that the resulting scheme produces satisfactory results, even in the case of very severe …

Participatory Action Research: Undergraduate Researchers Engaging Secondary Students In Social Justice Mathematics, Isabelle Miller, Alexis Grimes, Camryn Adkison

The Journal of Purdue Undergraduate Research

No abstract provided.

A Clark-Ocone Type Formula Via Itô Calculus And Its Application To Finance, Takuji Arai, Ryoichi Suzuki

Journal of Stochastic Analysis

No abstract provided.

Calculating Infinitesimal Generators, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.