# Showing papers in "Open Mathematics in 2019"

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TL;DR: In this article, a positivity preserving operator splitting nonstandard finite difference (NSFD) scheme for the numerical solution of SEIR reaction diffusion epidemic model is introduced. But the proposed scheme is conditionally stable while the second scheme is unconditionally stable.

Abstract: Abstract In this work, we will introduce two novel positivity preserving operator splitting nonstandard finite difference (NSFD) schemes for the numerical solution of SEIR reaction diffusion epidemic model. In epidemic model of infection diseases, positivity is an important property of the continuous system because negative value of a subpopulation is meaningless. The proposed operator splitting NSFD schemes are dynamically consistent with the solution of the continuous model. First scheme is conditionally stable while second operator splitting scheme is unconditionally stable. The stability of the diffusive SEIR model is also verified numerically with the help of Routh-Hurwitz stability condition. Bifurcation value of transmission coefficient is also carried out with and without diffusion. The proposed operator splitting NSFD schemes are compared with the well-known operator splitting finite difference (FD) schemes.

23 citations

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TL;DR: The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic as discussed by the authors.

Abstract: The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic. It is proved that gp(G) ≥ ω(GSR), where GSR is the strong resolving graph of G, and ω(GSR) is its clique number. That the bound is sharp is demonstrated with numerous constructions including for instance direct products of complete graphs and different families of strong products, of generalized lexicographic products, and of rooted product graphs. For the strong product it is proved that gp(G H) ≥ gp(G)gp(H), and asked whether the equality holds for arbitrary connected graphs G and H. It is proved that the answer is in particular positive for strong products with a complete factor, for strong products of complete bipartite graphs, and for certain strong cylinders.

19 citations

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TL;DR: In this paper, a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge is considered and sufficient conditions are derived for the global stability of the system.

Abstract: Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

14 citations

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TL;DR: In this article, the Hankel determinant of order three is defined and considered for analytic functions associated with sine functions in the region of unit disk on the complex plane, and the aim is to find the determinant.

Abstract: Abstract In this paper we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes our aim is to find the Hankel determinant of order three.

13 citations

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TL;DR: In this article, it was shown that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation.

Abstract: Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

12 citations

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TL;DR: In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed, which inherits the advantage of the classical smoothed Newton method, it only needs to solve one linear system of equations at each iteration, without the need of strict complementarity conditions and the assumption of P0 property.

Abstract: Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

11 citations

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TL;DR: In this article, critical point theory was used to obtain sufficient conditions on the existence of infinitely many positive solutions of the discrete Dirichlet problem involving the mean curvature operator, and they showed that the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to a sequence of pairwise distinct nontrivial positive solutions.

Abstract: Abstract In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the discrete Dirichlet problem involving the mean curvature operator. We show that the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. We also give two examples to illustrate our main results.

10 citations

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TL;DR: The approximate degrees of M-fuzzifying convex structures, M-Fuzzifying closure systems and M- fuzzifying Alexandrov topologies are defined by means of the implication operator → on a completely distributive lattice M to interpret the approximate degrees to which a mapping is an M-turbine convex structure, a closure system and a topology from a logical aspect.

Abstract: Abstract In this paper, by means of the implication operator → on a completely distributive lattice M, we define the approximate degrees of M-fuzzifying convex structures, M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an M-fuzzifying convex structure, an M-fuzzifying closure system and an M-fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of M-fuzzifying convex structures as well as its relations with M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies by inequalities.

10 citations

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TL;DR: In this article, a new generalization of λ-Bernstein operators based on q-integers was introduced, and the moments and central moments of these operators were obtained and a statistical approximation theorem was established.

Abstract: Abstract In this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in some cases the absolute error bounds are smaller than the case of classical q-Bernstein operators to f(x).

9 citations

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TL;DR: In this paper, the axiomatic conditions of hull operators and their relations with convex spaces from a categorical sense were established and it was shown that the category CS of convex space is isomorphic to the category HS of hull spaces, and they are all topological over Set.

Abstract: Abstract In this paper, we establish the axiomatic conditions of hull operators and introduce the category of interval spaces. We also investigate their relations with convex spaces from a categorical sense. It is shown that the category CS of convex spaces is isomorphic to the category HS of hull spaces, and they are all topological over Set. Also, it is proved that there is an adjunction between the category IS of interval spaces and the category CS of convex spaces. In particular, the category CS(2) of arity 2 convex spaces can be embedded in IS as a reflective subcategory.

8 citations

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TL;DR: The approximations proposed in this paper present a high accuracy for the complete domain and are handy and easy computable, avoiding the application of special numerical algorithms.

Abstract: Abstract In this work, we propose to approximate the Gaussian integral, the error function and the cumulative distribution function by using the power series extender method (PSEM). The approximations proposed in this paper present a high accuracy for the complete domain [–∞,∞]. Furthermore, the approximations are handy and easy computable, avoiding the application of special numerical algorithms. In order to show its high accuracy, three case studies are presented with applications to science and engineering.

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TL;DR: In this paper, the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution.

Abstract: Abstract In this paper the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution. Our results rely on an appropriate fixed point theorem in partially ordered normed linear spaces. Illustrative examples are included to demonstrate the validity and applicability of our technique.

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TL;DR: In this paper, a general approach to SURMs under some general assumptions is presented, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best Linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold.

Abstract: Abstract Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this article, we present a general approach to SURMs under some general assumptions, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold. Some fundamental and valuable properties of the BLUPs and BLUEs under the SURM are also presented.

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TL;DR: In this paper, the degree-based topological indices are used to correlate the physical and chemical properties of a molecule with its structure, and these representations are important in structural chemistry.

Abstract: Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

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TL;DR: The notion of MBJ-neutrosophic ideal is introduced in this paper, and its properties are investigated in a BCK/BCI-algebra, and conditions for an MBJ NE ideal to be an NE subalgebra are provided.

Abstract: Abstract The notion of MBJ-neutrosophic ideal is introduced, and its properties are investigated. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal are provided. In a BCK/BCI-algebra, a condition for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal is given. In a BCK-algebra, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal is given. In a BCI-algebra, conditions for an MBJ-neutrosophic ideal to be an MBJ-neutrosophic subalgebra are considered. In an (S)-BCK-algebra, we show that every MBJ-neutrosophic ideal is an MBJ-neutrosophic ∘-subalgebra, and a characterization of an MBJ-neutrosophic ideal is established.

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TL;DR: In this paper, the extinction property of a two species competitive stage-structured phytoplankton system with harvesting was studied. But the authors did not consider the effects of toxic substances.

Abstract: Abstract The extinction property of a two species competitive stage-structured phytoplankton system with harvesting is studied in this paper. Several sets of sufficient conditions which ensure that one of the components will be driven to extinction are established. Our results supplement and complement the results of Li and Chen [Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances, J. Comput. Appl. Math., 2009, 231(1), 143-153] and Liu, Chen, Luo et al. [Extinction and permanence in nonautonomous competitive system with stage structure, J. Math. Anal. Appl., 2002, 274(2), 667-684].

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TL;DR: In this article, the authors established common fixed point results for two families of multivalued mappings fulfilling generalized rational type A-dominated contractive conditions on a closed ball in complete dislocated b-metric spaces.

Abstract: Abstract The purpose of this paper is to find common fixed point results for two families of multivalued mappings fulfilling generalized rational type A–dominated contractive conditions on a closed ball in complete dislocated b-metric spaces. Some new fixed point results with graphic contractions on a closed ball for two families of multi-graph dominated mappings on dislocated b-metric space have been established. An application to the unique common solution of two families of nonlinear integral equations is presented to show the novelty of our results.

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TL;DR: In this paper, a generalized Cesáro sequence space is defined by weighted means and s-numbers of operators from a Banach space X into a Banache space Y are used to construct a pre-quasi Banach operator ideal.

Abstract: Abstract Let E be a generalized Cesáro sequence space defined by weighted means and by using s-numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SE(X,Y):={T∈L(X,Y):((sn(T))n=0∞∈E}, $$\\begin{array}{} \\displaystyle S_{E}(X, Y):=\\Big\\{T\\in L(X, Y):((s_{n}(T))_{n=0}^{\\infty}\\in E\\Big\\}, \\end{array}$$ of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small and the pre-quasi Banach operator ideal constructed by s-numbers is simple Banach space. Finally the pre-quasi operator ideal formed by the sequence of s-numbers and this sequence space is strictly contained in the class of all bounded linear operators, whose sequence of eigenvalues belongs to this sequence space.

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TL;DR: In this article, the generalized Grötzsch ring function and related elementary functions were shown to have monotonicity properties and sharp inequalities for solutions of the Ramanujan generalized modular equation.

Abstract: Abstract In the paper, the authors present some monotonicity properties and some sharp inequalities for the generalized Grötzsch ring function and related elementary functions. Consequently, the authors obtain new bounds for solutions of the Ramanujan generalized modular equation.

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TL;DR: In this article, the authors studied the exponential stability of time-changed stochastic functional differential equations with Markovian switching and obtained the following results: the stability of the time changed Itô formula and the Razumikhin theorem.

Abstract: Abstract This work is mainly concerned with the exponential stability of time-changed stochastic functional differential equations with Markovian switching. By expanding the time-changed Itô formula and the Razumikhin theorem, we obtain the exponential stability results for the time-changed stochastic functional differential equations with Markovian switching. What’s more, we get many useful stability results by applying our new results to several important types of functional differential equations. Finally, an example is given to demonstrate the effectiveness of the main results.

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TL;DR: Based on the three bottom line and stakeholder theory, the relationship and cooperation strategy between the government and the supplier and manufacturer of the green supply chain was considered in this paper, and the results showed that the optimal effort level, green degree of product, reputation and the optimal benefit in collaborative cooperation are obviously higher than the situations of non-cooperation and government promotion.

Abstract: Abstract Based on the “three bottom line” and stakeholder theory, the paper considers the relationship and cooperation strategy between the government and the supplier and manufacturer of the green supply chain. By constructing the dynamic differential game model, the paper discusses the differences in the optimal effort level, green degree of product, reputation and the optimal benefit under the three situations of noncooperation, government promotion and collaborative cooperation. The results show that the optimal effort level, green degree of product, reputation and the optimal benefit in collaborative cooperation are obviously higher than the situations of non-cooperation and government promotion, and the cooperation of the three parties can promote the development of green supply chain. Government promotion is better than noncooperation. The government plays an active role in improving the optimal benefit and reputation of green supply chain. Finally, the reliability of the proposed proposition is verified by an example analysis, which provides an important reference for improving the efficiency of green supply chain.

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TL;DR: In this paper, a new representation of α-openness, αcontinuity, α-irresoluteness, and α-compactness based on L-fuzzy α-Open operators introduced by Nannan and Ruiying was presented.

Abstract: Abstract This paper presents a new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness based on L-fuzzy α-open operators introduced by Nannan and Ruiying [1] and implication operation. The proposed representation extends the properties of α-openness, α-continuity, α-irresoluteness, and α-compactness to the setting of L-fuzzy pretopological spaces based on graded concepts. Moreover, we introduce and establish the relationships among the new concepts.

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TL;DR: In this paper, a Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species is proposed and studied.

Abstract: Abstract A Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species is proposed and studied. For non-delay case, such topics as the persistent of the system, the local stability property of the equilibria, the global stability of the positive equilibrium are investigated. For the system with infinite delay, by using the iterative method, a set of sufficient conditions which ensure the global attractivity of the positive equilibrium is obtained. By introducing the density dependent birth rate, the dynamic behaviors of the system becomes complicated. The system maybe collapse in the sense that both the species will be driven to extinction, or the two species could be coexist in a stable state. Numeric simulations are carried out to show the feasibility of the main results.

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TL;DR: In this paper, the notion of K-ideals associated with Kuratowski partitions is introduced, and connections between K -ideals and precipitous ideals are made, and it is shown that every complete ideal can be represented by some k-ideal.

Abstract: Abstract We introduce the notion of K-ideals associated with Kuratowski partitions. Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal.

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TL;DR: In this paper, the authors make algebraic and singularities studies to the Van Der Pol equation and the 5-parametric family of differential equations, including the Van der Pol equation.

Abstract: Abstract The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential equations yy′=(αxm+k−1+βxm−k−1)y+γx2m−2k−1,y′=dydx $$\\begin{array}{} \\displaystyle yy'=(\\alpha x^{m+k-1}+\\beta x^{m-k-1})y+\\gamma x^{2m-2k-1}, \\quad y'=\\frac{dy}{dx} \\end{array}$$ where a, b, c ∈ ℂ, m, k ∈ ℤ and α=a(2m+k)β=b(2m−k),γ=−(a2mx4k+cx2k+b2m). $$\\begin{array}{} \\displaystyle \\alpha=a(2m+k) \\quad \\beta=b(2m-k), \\quad \\gamma=-(a^2mx^{4k}+cx^{2k}+b^2m). \\end{array}$$ This family is very important because include Van Der Pol equation. Moreover, this family seems to appear as exercise in the celebrated book of Polyanin and Zaitsev. Unfortunately, the exercise presented a typo which does not allow to solve correctly it. We present the corrected exercise, which corresponds to the title of this paper. We solve the exercise and afterwards we make algebraic and of singularities studies to this family of differential equations.

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TL;DR: In this paper, the authors considered an almost periodic commensal symbiosis model with nonlinear harvesting on time scales and established a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system.

Abstract: Abstract In this paper, we consider an almost periodic commensal symbiosis model with nonlinear harvesting on time scales. We establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Our results show that the continuous system and discrete system can be unify well. Examples and their numerical simulations are carried out to illustrate the feasibility of our main results.

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TL;DR: Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this article, where the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed.

Abstract: Abstract Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this paper. According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are defined over a triangular domain. The main properties of the basis functions are studied, which guarantee that the basis functions are suitable for surface modeling. Then, the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed. We prove that the new surface patch has the important properties of surface modeling, such as affine invariance, convex hull property and so on. Finally, based on given control vertices, whose number is finite, a truncated triangular Meyer-König-Zeller surface and a redistributed triangular Meyer-König-Zeller surface are constructed and studied.

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TL;DR: In this paper, the algebraic loop structures on the set of Lie algebra comultiplications were studied and the fundamental concepts of algebraic loops and the set with inversive, power-associative and Moufang properties were investigated.

Abstract: Abstract In this paper, we study the algebraic loop structures on the set of Lie algebra comultiplications. More specifically, we investigate the fundamental concepts of algebraic loop structures and the set of Lie algebra comultiplications which have inversive, power-associative and Moufang properties depending on the Lie algebra comultiplications up to all the possible quadratic and cubic Lie algebra comultiplications. We also apply those notions to the rational cohomology of Hopf spaces.

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TL;DR: The fuzzy variational-like inequality problems is incorporated into the framework of n- dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions.

Abstract: Abstract The existing results on the variational inequality problems for fuzzy mappings and their applications were based on Zadeh’s decomposition theorem and were formally characterized by the precise sets which are the fuzzy mappings’ cut sets directly. That is, the existence of the fuzzy variational inequality problems in essence has not been solved. In this paper, the fuzzy variational-like inequality problems is incorporated into the framework of n-dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions we proposed [Fuzzy Sets and Systems 295 (2016) 19-36]. As a theoretical basis, the existence and the basic properties of the fuzzy variational inequality problems are discussed. Furthermore, the relationship between the variational-like inequality problems and the fuzzy optimization problems is discussed. Finally, we investigate the optimality conditions for the fuzzy multiobjective optimization problems.

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TL;DR: In this paper, a discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated, and sufficient conditions to ensure the permanence of the system are established.

Abstract: Abstract A discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated. We obtain sufficient conditions to ensure the permanence of the system. Also, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. In additional, an example together with its numerical simulation are presented to illustrate the feasibility of the main result.