Showing papers in "Open Mathematics in 2016"
TL;DR: In this article, a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined and the existence and uniqueness of fixed points for this class of mappings are discussed and the results are applied to Ulam stability problems.
Abstract: Abstract In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
51 citations
TL;DR: In this article, a new general definition of local fractional derivative, that depends on an unknown kernel, is presented, and a relation between this new concept and ordinary differentiation is established.
Abstract: In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.
41 citations
TL;DR: In this paper, the authors investigated oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0, t≠tk,xtk+=akx(tk−),tkD αxtk+rxt+qxt=0.
Abstract: Abstract In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. $$\\left\\{ \\begin{array}{l} {t_k}{D^\\alpha }\\left( {p\\left( t \\right)\\left[ {{t_k}{D^\\alpha }x\\left( t \\right) + r\\left( t \\right)x\\left( t \\right)} \\right]} \\right) + q\\left( t \\right)x\\left( t \\right) = 0,\\quad t \\ge {t_0},\\;t \
e {t_k},\\\\ x\\left( {t_k^ + } \\right) = {a_k}x(t_k^ - ),\\quad {t_k}{D^\\alpha }x\\left( {t_k^ + } \\right) = {b_{k\\;{t_{k - 1}}}}{D^\\alpha }x(t_k^ - ),\\quad \\;k = 1,2, \\ldots. \\end{array} \\right.$$ Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.
28 citations
TL;DR: A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented and the proposed bounds improve some existing ones.
Abstract: Abstract In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.
24 citations
TL;DR: In this paper, a refinement of Jensen's integral inequality and its generalization for linear functionals is given, and some applications in Information Theory are also presented in the context of information theory.
Abstract: Abstract In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
23 citations
TL;DR: In this paper, the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions is developed.
Abstract: Abstract We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
23 citations
TL;DR: In this paper, the authors presented some basic properties concerning the derivation algebra of a Lie triple system, the quasiderivation algebra, and the generalized derivation algebras.
Abstract: In this paper, we present some basic properties concerning the derivation algebra ${\rm Der}(T)$, the quasiderivation algebra ${\rm QDer}(T)$ and the generalized derivation algebra ${\rm GDer}(T)$ of a Lie triple system $T$, with the relationship ${\rm Der}(T)\subseteq {\rm QDer}(T)\subseteq {\rm GDer}(T)\subseteq {\rm End}(T)$. Furthermore, we completely determine those Lie triple systems $T$ with condition ${\rm QDer}(T)={\rm End}(T)$. We also show that the quasiderivations of $T$ can be embedded as derivations in a larger Lie triple system.
23 citations
TL;DR: The results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks, though the combinations of all control measures is also effective, however, this strategy is not cost- effective and so too costly.
Abstract: CITATION: Okosun, K. O., Mukamuri, M. & Makinde, D. O. 2016. Global stability analysis and control
of leptospirosis. Open Mathematics, 14(1): 567–585, doi:10.1515/math-2016-0053.
23 citations
TL;DR: In this paper, two types of the Mittag-Leffler-Hyer-Ulam stability of a fractional integral equation were studied and shown to be stable on a compact interval with respect to the Chebyshev and Bielecki norms.
Abstract: Abstract In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.
22 citations
TL;DR: In this paper, a closed-form formula for the enumeration of spanning trees in a simple connected graph G is presented, and upper and lower bounds for the Laplacian Estrada index of G are established based on the vertex degrees of G.
Abstract: Abstract As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of Г(G) based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in Г(G).
22 citations
TL;DR: In this paper, a range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR), which offers a possibility to delete a large part of the outcome space region of the numerators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the SAR.
Abstract: Abstract Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.
TL;DR: In this article, a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method is presented.
Abstract: In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. This class of methods has the efficiency index equal to 8 1 4 ≈ 1.682. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods.
TL;DR: In this article, a new characterization of inextensible flows by using elastica in space is presented, which is completely determined for any space-like curve in de Sitter space.
Abstract: Abstract Elastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space S 1 3 $\\mathbb{S}_{1}^{3}$. Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space S 1 3 $\\mathbb{S}_{1}^{3}$.
TL;DR: Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional as mentioned in this paper.
Abstract: Abstract Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
TL;DR: In this paper, a two-species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied.
Abstract: Abstract A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.
TL;DR: In this paper, the authors introduce a property and use this property to prove some common fixed point theorems in b-metric space, which can be regarded as consequences of their main results.
Abstract: Abstract In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫ a b K 1 (t,r,x(r)) dr, x (t) = ∫ a b K 2 (t,r,x(r)) dr, $$\\matrix {x (t) = \\int \\limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \\int \\limits_a^b {{K_2}}(t, r, x(r))dr,} $$ where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.
TL;DR: In this article, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the nonlinear discrete-time stochastic systems has been analyzed.
Abstract: Abstract In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.
TL;DR: In this article, a multiplicative basis for a locally adequate concordant semigroup algebra is constructed by constructing Rukola-ne idempotents, which allows the decomposition of the locally adequate algebra into a direct product of primitive abundant 0-J*$0{rm{ - }}{\\cal J}*$-simple semigroup algebras.
Abstract: Abstract We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant 0-J*$0{\\rm{ - }}{\\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the ℛ*${\\cal R}*$-classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.
TL;DR: In this paper, the best uniform approximation of degree 2 to a circular arc is given in explicit form, and the approximation is constructed so that the error function is the Chebyshev polynomial of degree 4.
Abstract: Abstract In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.
TL;DR: In this article, the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex is studied and shown to be convergent.
Abstract: The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-
dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.
TL;DR: In this article, the Riemman-Stieltjes-type integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures was developed.
Abstract: Abstract Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology β. We develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F)-continuous operators T : Cb(X, E) → F. As an application, we study (β, || · ||F)-continuous weakly compact and unconditionally converging operators T : Cb(X, E) → F. In particular, we establish the relationship between these operators and the corresponding Borel operator measures given by the Riesz representation theorem. We obtain that if X is a k-spaceand E is reflexive, then (Cb(X, E), β) has the V property of Pełczynski.
TL;DR: In this paper, the authors present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets, where vertices are the stock markets and edges are constructed by the correlation distances.
Abstract: Abstract In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
TL;DR: In this article, the fully degenerate poly-Bernoulli numbers and polynomials were introduced and some properties of these polynomial numbers and numbers were derived from their properties.
Abstract: Abstract In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
TL;DR: In this article, necessary and sufficiently conditions are derived for the decomposition of a second order linear time-varying system into two cascade connected commutative first-order linear time varying subsystems.
Abstract: Abstract Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.
TL;DR: In this paper, some upper bounds and lower bounds for w(T) are presented and a new bound for the zeros of polynomials is driven.
Abstract: Abstract Let Ai ∈ B(H), (i = 1, 2, ..., n), and T=[ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ] $ T = \\left[ {\\matrix{ 0 & \\cdots & 0 & {A_1 } \\cr \\vdots & {\\mathinner{\\mkern2mu\\raise1pt\\hbox{.}\\mkern2mu \\raise4pt\\hbox{.}\\mkern2mu\\raise7pt\\hbox{.}\\mkern1mu}} & {A_2 } & 0 \\cr 0 & {\\mathinner{\\mkern2mu\\raise1pt\\hbox{.}\\mkern2mu \\raise4pt\\hbox{.}\\mkern2mu\\raise7pt\\hbox{.}\\mkern1mu}} & {\\mathinner{\\mkern2mu\\raise1pt\\hbox{.}\\mkern2mu \\raise4pt\\hbox{.}\\mkern2mu\\raise7pt\\hbox{.}\\mkern1mu}} & \\vdots \\cr {A_n } & 0 & \\cdots & 0 \\cr } } \\right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.
TL;DR: A special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S is introduced and the lower and upper approximations based on a fuzzy Ideal in semigroups are defined.
Abstract: Abstract In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.
TL;DR: In this article, the authors studied conformal derivations, central extensions and conformal modules for Lie conformal algebra, and determined its cohomology with trivial coefficients both for the basic and reduced complexes.
Abstract: The purpose of this paper is to study $W(2,2)$ Lie conformal algebra, which has a free $\mathbb{C}[\partial]$-basis $\{L, M\}$ such that $[L_\lambda L]=(\partial+2\lambda)L$, $[L_\lambda M]=(\partial+2\lambda)M$, $[M_\lambda M]=0$. In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.
TL;DR: A new Generalized Oppositional Biogeography Based Optimization (GOBBO) algorithm which is enhanced with Oppositionally Based Learning (OBL) techniques is presented which is compared with other PTS schemes for PAPR reduction found in the literature.
Abstract: Abstract A major drawback of orthogonal frequency division multiplexing (OFDM) signals is the high value of peak to average power ratio (PAPR). Partial transmit sequences (PTS) is a popular PAPR reduction method with good PAPR reduction performance, but its search complexity is high. In this paper, in order to reduce PTS search complexity we propose a new technique based on biogeography-based optimization (BBO). More specifically, we present a new Generalized Oppositional Biogeography Based Optimization (GOBBO) algorithm which is enhanced with Oppositional Based Learning (OBL) techniques. We apply both the original BBO and the new Generalized Oppositional BBO (GOBBO) to the PTS problem. The GOBBO-PTS method is compared with other PTS schemes for PAPR reduction found in the literature. The simulation results show that GOBBO and BBO are in general highly efficient in producing significant PAPR reduction and reducing the PTS search complexity.
TL;DR: In this paper, the authors introduce the notion of annihilators in BL-algebras and investigate some related properties of them, including the necessary and sufficient condition of the homomorphism image of an annihilator.
Abstract: Abstract In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,{0}, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties of them. As an application, we show that if I and J are ideals in a BL-algebra L, then JI⊥$J_I^ \\bot $ is the relative pseudo-complement of J with respect to I in the ideal lattice (I(L), ⊆). Moreover, we get some properties of the homomorphism image of annihilators, and also give the necessary and sufficient condition of the homomorphism image and the homomorphism pre-image of an annihilator to be an annihilator. Finally, we introduce the notion of α-ideal and give a notation E(I ). We show that (E(I(L)), ∧E, ∨E, E(0), E(L) is a pseudo-complemented lattice, a complete Brouwerian lattice and an algebraic lattice, when L is a BL-chain or a finite product of BL-chains.
TL;DR: In this paper, the curvature tensor of a 3D almost Kenmotsu manifold is shown to be harmonic if and only if the manifold is locally isometric to either the hyperbolic space or the Riemannian product ℍ2(−4) × ℝ.
Abstract: Abstract Let M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].