Showing papers in "European Journal of Pure and Applied Mathematics in 2021"
TL;DR: In this article, the estimation of the basic reproductive number (R0) using the Next Generation Method (NGM) approach was performed for the COVID-19 pandemic in Ghana.
Abstract: A disease can be defined as an adverse change from a normally functional state of the living body usually characterized with or accompanied with some signs and symptoms which is differing in nature from physical injury. A pandemic is the worldwide spread of a new disease. COVID-19 is one of the global pandemic that emerged in Wuhan, China, in December 2019 and has since then spread over through the world. In Ghana, the first case of COVID-19 was reported in March 14, 2020 and has increased from just one case to over 29000 cases with over 150 deaths as at July 23, 2020. This study focuses on the estimation of the basic reproductive number, R0 using the Next Generation Method (NGM) approach. COVID-19 data in Ghana was collected and parameters were estimated using the Least-Squares Method. The basic reproductive number of Ghana is estimated to be 2.52 whilst the R0 ranges between 1.47 − 2.65 for transmission rates of 0.5 − 0.9.
10 citations
TL;DR: In this article, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order, and some upper bounds for the third and fourth Hankel determinants related to such classes are obtained.
Abstract: The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.
9 citations
TL;DR: The time complexity and comparison of the computer execution time of calculation of the rectangular determinant based on the presented algorithms and comparing them with the algorithmbased on the Laplace method are found.
Abstract: In this paper, we present an approach for the calculation of rectangular determinants, where in addition to the mathematical formula, we also provide a computer algorithm for their calculation. Firstly, we present a method similar to Sarrus method for calculating the rectangular determinant of the order 2 × 3. Secondly, we present an approach for calculating the rectangular determinants of order m ×n by adding a row with all elements equal to one (1) in any row, as well as an application of Chio’s rule for calculating the rectangular determinants. Thirdly, we find the time complexity and comparison of the computer execution time of calculation of the rectangular determinant based on the presented algorithms and comparing them with the algorithm based on the Laplace method.
8 citations
TL;DR: In this article, the concept of global hop domination in graphs resulting from some binary operations has been studied and the minimum cardinality of a global hop dominatingset of a graph is defined as the global hop dominating number of the graph.
Abstract: A set S ⊆ V ( G ) is a hop dominating set of G if for each v ∈ V ( G ) \ S , there exists w ∈ S such that d G ( v, w ) = 2 It is a global hop dominating set of G if it is a hop dominatingset of both G and the complement of G The minimum cardinality of a global hop dominatingset of G , denoted by γ gh ( G ), is called the global hop domination number of G In this paper, we study the concept of global hop domination in graphs resulting from some binary operations
8 citations
TL;DR: In this paper, the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated and the Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation.
Abstract: In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.
6 citations
TL;DR: In this paper, the authors considered one optimal control problem with a multipoint quality functional described by a system of nonlinear hyperbolic equations with Goursat boundary conditions and proved necessary first-order optimality conditions such as the Pontryagin maximum principle and the linearized maximum condition.
Abstract: In this paper, we consider one optimal control problem with a multipoint quality functional described by a system of nonlinear hyperbolic equations with Goursat boundary conditions. Using a modified version of the increment method, various necessary first-order optimality conditions such as the Pontryagin maximum principle and the linearized maximum condition are proved.
6 citations
TL;DR: In this paper, the authors use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences.
Abstract: Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences. Results beyond the extreme value value domain are provided. Explicit asymptotic laws concerning very usual laws and related rates of convergence are listed as well. Some of these laws are expected to be used in fitting distribution.
4 citations
TL;DR: In this article, an operator on a hyper BCI-algebra via application of a left hyper-order was introduced, and the family consisting of the images of subsets under the operator turned out to be a base for some topology.
Abstract: In this paper, we introduce an operator on a hyper BCI-algebra via application of a left hyper-order. The family consisting of the images of subsets under the operator turns out to be a base for some topology on the hyper BCI-algebra. We investigate some important properties of the induced topology on certain hyper BCI-algebras. In particular, we show that the generated topology on a non-trivial hyper subalgebra of an ordered hyper BCI-algebra coincides with the relative topology on this hyper subalgebra.
4 citations
TL;DR: A set S ⊆ V is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that d G (v, w) = 2 as discussed by the authors.
Abstract: A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that d G (v, w) = 2. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by γ h (G)(resp.γ gh (G)) , is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper.
4 citations
TL;DR: In this article, Tensor product of Banach spaces is used to find certain solutions of fractional partial di§erential equations where separation of variables does not work, and the fractional wave type equation using fractional Fourier series.
Abstract: In this paper we Ond certain solutions of some fractional partial di§erential equations. Tensor product of Banach spaces is used to Ond some solutions where separation of variables does not work. We solve the fractional wave type equation using fractional Fourier Series
4 citations
TL;DR: In this article, a solution of finite rank form of fractional Abstract Cauchy Problem is found based on the theory of tensor product of Banach spaces, which is the Conformable derivative.
Abstract: In this paper, we find a solution of finite rank form of fractional Abstract Cauchy Problem. The fractional derivative used is the Conformable derivative. The main idea of the proofs are based on theory of tensor product of Banach spaces.
TL;DR: In this article, it was shown that for every positive integer a and b with 5 ≤ a ≤ b ≤ 2a − 2, there exists a connected graph G for which γit(G) = a and γitt(G), = b.
Abstract: A set S ⊆ V (G) is an independent transversal dominating set of a graph G if S is a dominating set of G and intersects every maximum independent set of G An independent transversal dominating set which is a total dominating set is an independent transversal total dominating set The minimum cardinality γit(G) (resp γitt(G)) of an independent transversal dominating set (resp independent transversal total dominating set) of G is the independent transversal domination number (resp independent transversal total domination number) of G In this paper, we show that for every positive integers a and b with 5 ≤ a ≤ b ≤ 2a − 2, there exists a connected graph G for which γit(G) = a and γitt(G) = b We also study these two concepts in graphs which are the join, corona or composition of graphs
TL;DR: The weighted bivariate Poisson distribution as mentioned in this paper is a synthesis of all the bivariate poisson distributions which, under certain conditions, converge in distribution towards the BPP according to Berkhout and Plug.
Abstract: In the recent statistical literature, the univariate Poisson distribution has been generalized by many authors, among them: the univariate weighted Poisson distribution [13], the generalized univariate Poisson distribution [7], the bivariate Poisson distribution according to Holgate [11], the bivariate Poisson distribution according to Lakshminarayana, Pandit and Srinivasa Rao [15], the bivariate Poisson distribution according to Berkhout and Plug [4], the bivariate weighted Poisson distribution according to Elion et al. [8] and the generalized bivariate Poisson distribution according to Famoye [9]. In this paper, We highlight the weighted bivariate Poisson distribution and show that it is the synthesis of all the bivariate Poisson distributions which, under certain conditions, converge in distribution towards the bivariate Poisson distribution according to Berkhout and Plug [4] which can be considered like the standard distribution in N2 as is the univariate Poisson distribution in N.
Abstract: In this paper, we give a definition of a b(αn,βn) -hypermetric spaces over Banach algebras. The purpose of this paper is to prove the concept of extension of fixed point theorems in b(αn,βn) -hypermetric spaces over Banach algebras.
TL;DR: In this paper, the Fourier series expansion of Tangent polynomials is derived and the integral representation and explicit formula at rational arguments of these polynomial are established.
Abstract: In this paper, Fourier series expansion of Tangent polynomials are derived and the integral representation and explicit formula at rational arguments of these polynomials are established.
TL;DR: In this paper, the notion of Γ-LA-semirings was introduced and the terms left ideals, right ideals, bi-ideal, quasi ideals, almost prime and weakly almost prime ideals were discussed.
Abstract: In this note, first we add some new results in Gamma LA-rings and then we initiate the notion of Γ-LA-semirings. Moreover, we introduce and discuss the terms left ideals, right ideals, bi-ideal, quasi ideals, almost prime and weakly almost prime ideals of a Γ-LA-semiring and their characterizations.
TL;DR: In this paper, a hybrid inversive congruential generator (HICG) based on a second order recurrence using the inversive modulo M, a power of 2, was proposed.
Abstract: Though generating a sequence of pseudorandom numbers by linear methods (Lehmer generator) displays acceptable behavior under some conditions of the parameters, it also has undesirable features, which makes the sequence unusable for various stochastic simulations. An extension which showed promise for such applications is a generator obtained by using a first-order recurrence based upon the inversive modulo a prime or a prime power, called inversive congruential generator (ICG). A lot of work has been dedicated to investigate the periods (under some conditions of the parameters), the lattice test passing, discrepancy and other statistical properties of such a generator. Here, we propose a new method, which we call hybrid inversive congruential generator (HICG), based upon a second order recurrence using the inversive modulo M, a power of 2. We investigate the period of this pseudorandom numbers generator (PRNG) and give necessary and sufficient conditions for our PRNG to have periods M (thereby doubling the period of the classical ICG) and M/2 (matching the one of the ICG). Moreover, we show that the lattice test complexity for a binary sequence associated to (a full period) HICG is precisely M/2.
TL;DR: In this paper, a compilation of definite integrals involving the Lerch, Polylogarithm, Hurwitz functions and fundamental constants is presented, and connections to previous work are compared and discussed.
Abstract: This is a compilation of definite integrals involving the Lerch, Polylogarithm, Hurwitz functions and fundamental constants. Connections to previous work is compared and discussed. This collection of definite integrals is new in current literature.
TL;DR: In this article, the DEA method was applied to the agriculture sector in Burkina Faso, with data taking into account cultivated area, manual (human) labour, the liquidity fund of the working household, the number of crops (products) and the expected farm incomes.
Abstract: In this paper, we used the DEA method, to apply to the agriculture sector in Burkina Faso. We applied the method with forty-one (41) agricultural farmers with data taking into account cultivated area, manual (human) labour, the liquidity fund of the working household, the number of crops (products) and the expected farm incomes. The results highlight the seven (7) technical efficiencies. Taking into account the variable scale yields, fourteen (14) efficient farms are obtained. These results show how non-efficient farms in the DEA sense are indexed to efficient farms that can serve as benchmarks or benchmarks in terms of performance improvement. This study shows that efficiency does not depend on the category of operator but on overall performance (efficiency and productivity).
TL;DR: The notion of k-fair total domination was introduced in this article, where the cardinality of the minimum dominating set γkf td(G) is defined as the minimum number of dominating sets of G such that |NG(u) ∩ S| = k for every u ∈ V (G) ∈ S|.
Abstract: Let G = (V (G), E(G)) be a simple non-empty graph. For an integer k ≥ 1, a k-fair total dominating set (kf td-set) is a total dominating set S ⊆ V (G) such that |NG(u) ∩ S| = k for every u ∈ V (G)\S. The k-fair total domination number of G, denoted by γkf td(G), is the minimum cardinality of a kf td-set. A k-fair total dominating set of cardinality γkf td(G) is called a minimum k-fair total dominating set or a γkf td-set. We investigate the notion of k-fair total domination in this paper. We also characterize the k-fair total dominating sets in the join, corona, lexicographic product and Cartesian product of graphs and determine the exact values or sharp bounds of their corresponding k-fair total domination number.
TL;DR: In this article, the fundamental solution of the operator O(m,m,k) is studied and applied to solve for the problem of finding the solution of f(x), where f is a generalized function and x is an unknown function.
Abstract: In this article, we study the fundamental solution of the operator $\oplus _{m}^{k}$ , iterated $k$ -times and is defined by $$ \oplus _{m}^{k} = \left[\left(\sum_{r=1}^{p} \frac{\partial^2} {\partial x_r^2}+m^{2}\right)^4 - \left( \sum_{j=p+1}^{p+q} \frac{\partial^2}{\partial x_{j}^2} \right)^4 \right ]^k, $$ where $m$ is a nonnegative real number, $p+q=n$ is the dimension of the Euclidean space $\mathbb{R}^n$ , $x=(x_1,x_2,\ldots,x_n)\in\mathbb{R}^n$ , $k$ is a nonnegative integer. At first we study the fundamental solution of the operator $\oplus _{m}^{k}$ and after that, we apply such the fundamental solution to solve for the solution of the equation $\oplus _{m}^{k}u(x)= f(x)$ , where $f(x)$ is generalized function and $u(x)$ is unknown function for $ x\in \mathbb{R}^{n}$ .
TL;DR: In this paper, a monophonic eccentric neighborhood of a graph G is used to construct a topology on a vertex set of the graph G. In this type of construction, those graphs that induced the indiscrete topology, the discrete topology and a particular point topology are characterized.
Abstract: In this paper, we present a way of constructing a topology on a vertex set of a graph using monophonic eccentric neighborhoods of the graph G. In this type of construction, we characterize those graphs that induced the indiscrete topology, the discrete topology, and a particular point topology.
TL;DR: In this article, the second order linear two-point boundary value problems are treated using new method based on hybrid cubic B-spline, where the value of the free parameter plays an important role in giving accurate results.
Abstract: In this research, second order linear two-point boundary value problems are treated using new method based on hybrid cubic B-spline. The values of the free parameter,Gamma , are chosen via optimization. The value of the free parameter plays an important role in giving accurate results. Optimization of this parameter is carried out. This method is tested on four examples and a comparison with cubic B-spline, trigonometric cubic B-spline and extended cubic B-spline methods has been carried out. The examples suggest that this method produces more accurate results than the other three methods. The numerical results are presented to illustrate the efficiency of our method.
TL;DR: In this paper, the authors explored to model, using regression, the daily temperature in the province of Laguna The daily maximum and minimum temperature from 1960 to 2018 were modeled using the classical Ornstein-Uhlenbeck (OU) process with additive seasonality.
Abstract: The behavior of temperature is one of the major factors in the study of climate change which has already invited a lot of researchers and policymakers These studies help in deciding the best adaptation and mitigation strategy However, there are little studies on the progression of climate change in a local setting, such as in a municipal or provincial level This study explored to model, using regression, the daily temperature in the province of Laguna The daily maximum and minimum temperature from 1960 to 2018 were modeled using the classical Ornstein-Uhlenbeck (OU) process with additive seasonality The model showed that the province saw an increase of $116^\circ$C (resp $055^\circ$C) in the mean daily minimum (resp maximum) temperature from 1960 to 2018 It was also found that minimum temperature showed a steadier increase than maximum temperature, which poses threats to agricultural activities Consistent with other international predictions, there was a $002^\circ$C annual increase in 1960 to a $005^\circ$C starting in 2010 The proposed model can be used by authorities in designing and creating adaptive measures that would be more effective to the province of Laguna
TL;DR: In this paper, the exponential Diophantine equation of the form Mxp + (Mq + 1)y = z2 for Mersenne primes Mp and Mq and non-negative integers x, y, and z.
Abstract: In this paper, we study and solve the exponential Diophantine equation of the form Mxp + (Mq + 1)y = z2 for Mersenne primes Mp and Mq and non-negative integers x, y, and z. We use elementary methods, such as the factoring method and the modular arithmetic method, to prove our research results. Several illustrations are presented, as well as cases where solutions to the Diophantine equation do not exist.
TL;DR: In this article, the localization of hopfian and co-hopfian objects in the categories A-Mod of left A-modules, AGr(A-Mod) of graded left A -modules and COMP(AGr(A)-modules were studied.
Abstract: The aim of this paper is to study the localization of hopfian and cohopfian objects in the categories A-Mod of left A-modules, AGr(A-Mod) of graded left A-modules and COMP(AGr(A-Mod)) of complex sequences associated to graded left A-modules. We have among others the main following results : 1. Let M be a noetherian graded left A-module, S a saturated multiplicative part formed by the non-zero homogeneous elements of A verifying the left Ore conditions, N a submodule of M, M_{*} is a noetherian quasi-injective complex sequence associated with M and N_{*} is an essential and completely invariant complex sub\--sequence of M_{*}. Then, S^{-1}(N_{*}) the complex sequence of morphisms of left S^{-1}A\--modules is cohopfian if, and only, if S^{-1}(M_{*}) is cohopfian ; 2. let M be a graded left A\--module and S a saturated multiplicative part formed by the non-zero homogeneous elements of A verifying the left Ore conditions. If M_{*} is a hopfian, noetherian and quasi-injective complex sequence associated with M, then the complex sequence of morphisms of left S^{-1}(A)-modules S^{-1}(M_{*}) has the following property : {any epimorphism of sub-complex S^{-1}(N_{*}) of S^{-1}(M_{*}) is an isomorphism } ; 3. let M be a graded left A-module, N a graded submodule of M, S a saturated multiplicative part formed by the non-zero homogeneous elements of A verifying the left Ore conditions. M_{*} the quasi-projective complex sequence associated with M and $N_{*}$ a superfluous and completely invariant complex sub\--sequence of $M_{*}$. Then the complex morphism sequence of left $S^{-1}(A)$\--modules $S^{-1}(N_{*})$ is hopfian if, and only if, $S^{-1}(M_{*}/N_{*})$ the complex sequence associated with S^{-1}(M/N) is hopfian.
TL;DR: In this paper, the existence of a weak solution of the complete compressible Navier-Stokes system is proved. But this work is based on the symmetric hyperbolic theory.
Abstract: In This paper we prove the existence of a weak solution of the complete compressible Navier-Stokes system. We follow an previous work where we added an artificial viscosity in the continuity equation and then rewrite the system in hyperbolic and symmetric form. Our study is based on the symmetric hyperbolic theory. We use for this aim a successive approximation in time to show the existence of the hyperbolic system solution and by the fixed point theorem the compacity property of some appropriate sobolev spaces and some established a priori estimates we can pass to several limits to prove our result. As state law, we use the Stiffened gas law.
TL;DR: In this paper, the authors presented the characterizations of connected co-independent hop dominating sets in the join, corona and lexicographic product of two graphs and discussed the corresponding connected coindependent hop domination numbers of the aforementioned graphs.
Abstract: Let G be a connected graph. A subset S of V (G) is a connected co-independent hop dominating set in G if the subgraph induced by S is connected and V (G)\S is an independent set where for each v ∈ V (G)\S, there exists a vertex u ∈ S such that dG(u, v) = 2. The smallest cardinality of such an S is called the connected co-independent hop domination number of G. This paper presents the characterizations of the connected co-independent hop dominating sets in the join, corona and lexicographic product of two graphs. It also discusses the corresponding connected co-independent hop domination numbers of the aforementioned graphs.
TL;DR: The nth l-isosceles triangular number as mentioned in this paper is a generalization of triangular numbers defined to be the arithmetic sum of the form T(n, l) = 1 + (1 + l) + ( 1 + 2l) + · · · + (n − 1)l).
Abstract: Triangular numbers have been of interest and continuously studied due to their beautiful representations, nice properties, and various links with other figurate numbers. For positive integers n and l, the nth l-isosceles triangular number is a generalization of triangular numbers defined to be the arithmetic sum of the form T(n, l) = 1 + (1 + l) + (1 + 2l) + · · · + (1 + (n − 1)l). In this paper, we focus on characterizations and identities for isosceles triangular numbers as well as their links with other figurate numbers. Recursive formulas for constructions of isosceles triangular numbers are given together with necessary and sufficient conditions for a positive integer to be a sum of isosceles triangular numbers. Various identities for isosceles triangular numbers are established. Results on triangular numbers can be viewed as a special case.
TL;DR: The numerical results show that the new modification outperforms the recent conjugate gradient methods such as CG-Descent, Dai and Liao, and others in terms of number of functions evaluations, number of gradient evaluations,number of iterations, and CPU time.
Abstract: The conjugate gradient (CG) method is a useful tool for obtaining the optimum point for unconstrained optimization problems since it does not require a second derivative or its approximations. Moreover, the conjugate gradient method can be applied in many fields such as machine learning, deep learning, neural network, and many others. This paper constructs a four-term conjugate gradient method that satisfies the descent property and convergence properties to obtain the stationary point. The new modification was constructed based on Liu and Storey's conjugate gradient method, two-term conjugate gradient method, and three-term conjugate gradient method. To analyze the efficiency and robustness, we used more than 150 optimization functions from the CUTEst library with different dimensions and shapes. The numerical results show that the new modification outperforms the recent conjugate gradient methods such as CG-Descent, Dai and Liao, and others in terms of number of functions evaluations, number of gradient evaluations, number of iterations, and CPU time.