Showing papers in "Open Mathematics in 2018"
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TL;DR: In this paper, a weak group inverse (WG inverse) was introduced for square matrices of an arbitrary index, and some of its characterizations and properties were derived. And the core-EP order was derived by using the WG inverses.
Abstract: In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. At last, one characterization of the core-EP order is derived by using the WG inverses.
37 citations
TL;DR: In this paper, the existence of positive solutions for systems of singular fractional differential equations with a parameter and integral boundary conditions is investigated by using fixed point theorem in cone, and sufficient conditions which guarantee that positive solutions are obtained are obtained.
Abstract: Abstract In this paper, the existence of positive solutions for systems of semipositone singular fractional differential equations with a parameter and integral boundary conditions is investigated. By using fixed point theorem in cone, sufficient conditions which guarantee the existence of positive solutions are obtained. An example is given to illustrate the results.
31 citations
TL;DR: In this article, the notions of (s, p, α)-quasi-contractions and weak contractions were introduced, and fixed point results concerning such contractions in the setting of b-metric-like spaces were derived.
Abstract: Abstract In this work, we introduce the notions of (s, p, α)-quasi-contractions and (s, p)-weak contractions and deduce some fixed point results concerning such contractions, in the setting of b-metric-like spaces. Our results extend and generalize some recent known results in literature to more general metric spaces. Moreover, some examples and applications support the results.
20 citations
TL;DR: In this article, the boundary Schwarz inequality for analytic functions mapping the unit disk to itself was obtained, and the result contains and improves a number of known estimates, including the one given in this paper.
Abstract: Abstract We obtain an new boundary Schwarz inequality, for analytic functions mapping the unit disk to itself. The result contains and improves a number of known estimates.
18 citations
TL;DR: In this paper, a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises is considered, where the authors consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker.
Abstract: Abstract Considering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.
15 citations
TL;DR: Navic as mentioned in this paper analyzovana oscilatoricnost a neoscilatoric nost pololinearnich diferencialnich rovnic druheho řadu, jejichž koeficienty jsou dane souciny funkci majicimi středni hodnoty a mocninnými funkcemi.
Abstract: Clanek naleži do kvalitativni teorie pololinearnich rovnic, ktere jsou na pomezi linearnich a nelinearnich rovnic a soucasně na pomezi obycejných a parcialnich diferencialnich rovnic. Je analyzovana oscilatoricnost a neoscilatoricnost pololinearnich diferencialnich rovnic druheho řadu, jejichž koeficienty jsou dane souciny funkci majicimi středni hodnoty a mocninnými funkcemi. Je dokazano, že studovane velmi obecne rovnice jsou podminěně oscilatoricke. Navic je nalezena kriticka oscilacni konstanta.
15 citations
TL;DR: In this article, Davvaz et al. studied the relation between ordered semihypergroups and ordered semigroups by weak pseudo-orders, and established the relationships between ordered regular equivalence relations and weak pseudoorders.
Abstract: Abstract In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.
14 citations
TL;DR: In this paper, the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by (CLRST)) of two pairs was studied.
Abstract: Abstract In this paper, we study the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by (CLRST)) of two pairs. Our results improve, extend, complement and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.
14 citations
TL;DR: This paper presents an extending dual Fischer diagonal condition, and making use of this, the regularity of ⊤-convergence spaces is discussed.
Abstract: Abstract (Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we discuss a regularity of ⊤-convergence spaces.
13 citations
TL;DR: In this paper, the singular Cauchy problem was solved for the Euler-Poisson-Darboux equation when the differential Bessel operator acts by each variable, and the solution of the singular cauche problem was obtained for the singular case when the Bessel operators act by different variables.
Abstract: Abstract In this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.
12 citations
TL;DR: In this article, the authors considered a 2nth-order nonlinear difference equation with p-Laplacian and obtained new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions.
Abstract: Abstract We consider a 2nth-order nonlinear difference equation containing both many advances and retardations with p-Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.
TL;DR: In this paper, the entire solution to a certain type of difference-differential equations is studied and an affirmative answer to the conjecture of Zhang et al. is given. But the conjecture is not proved.
Abstract: Abstract In this paper we study the entire solutions to a certain type of difference-differential equations. We also give an affirmative answer to the conjecture of Zhang et al. In addition, our results improve and complement earlier ones due to Yang-Laine, Latreuch, Liu-Lü et al. and references therein.
TL;DR: Experiments show that KGSA provides better results than the other algorithms in finding local and global optima of constrained and unconstrained multimodal functions.
Abstract: Abstract Gravitational Search Algorithm (GSA) is a metaheuristic for solving unimodal problems. In this paper, a K-means based GSA (KGSA) for multimodal optimization is proposed. This algorithm incorporates K-means and a new elitism strategy called “loop in loop” into the GSA. First in KGSA, the members of the initial population are clustered by K-means. Afterwards, new population is created and divided in different niches (or clusters) to expand the search space. The “loop in loop” technique guides the members of each niche to the optimum direction according to their clusters. This means that lighter members move faster towards the optimum direction of each cluster than the heavier members. For evaluations, KGSA is benchmarked on well-known functions and is compared with some of the state-of-the-art algorithms. Experiments show that KGSA provides better results than the other algorithms in finding local and global optima of constrained and unconstrained multimodal functions.
TL;DR: Emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems and computational complexity and intercepted sequence requirements are dramatically reduced.
Abstract: Abstract Decimation-based sequence generators are a class of non-linear cryptographic generators designed to be used in hardware implementations. An inherent characteristic of such generators is that their output sequences are interleaved sequences. This profitable characteristic can be used in the cryptanalysis of those generators. In this work, emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems. Compared with previous cryptanalysis, computational complexity and intercepted sequence requirements are dramatically reduced. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analyzed in terms of simple linear structures.
TL;DR: In this paper, the gamma function is approximated to two asymptotic expansions by using a power series, where the power series is defined by a power-series power function.
Abstract: In this paper, we develop Windschitl's approximation formula for the gamma function to two asymptotic expansions by using a little known power series. In particular, for $n\in \mathbb{N}$ with $n\geq 4$, we have \begin{equation*} \Gamma \left( x+1\right) =\sqrt{2\pi x}\left( \tfrac{x}{e}\right) ^{x}\left( x\sinh \tfrac{1}{x}\right) ^{x/2}\exp \left( \sum_{k=3}^{n-1}\tfrac{\left( 2k\left( 2k-2\right) !-2^{2k-1}\right) B_{2k}}{2k\left( 2k\right) !x^{2k-1}} +R_{n}\left( x\right) \right) \end{equation*} with \begin{equation*} \left| R_{n}\left( x\right) \right| \leq \frac{\left| B_{2n}\right| }{2n\left( 2n-1\right) }\frac{1}{x^{2n-1}} \end{equation*} for all $x>0$, where $B_{2n}$ is the Bernoulli number. Moreover, we present some approximation formulas for gamma function related to Windschitl's approximation one, which have higher accuracy.
TL;DR: In this article, the transitivity conditions of the εm-relation on hyperrings and m-idempotent hyperrings were discussed, and it was shown that on such hyperrings, the relation is a fundamental relation.
Abstract: Abstract On a general hyperring, there is a fundamental relation, denoted γ*, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm on general hyperrings, proving that its transitive closure εm∗$\\begin{array}{} \\displaystyle \\varepsilon^{*}_{m} \\end{array}$ is a strongly regular equivalence relation smaller than the γ*-relation on some classes of hyperrings, such that the associated quotient structure modulo εm∗$\\begin{array}{} \\displaystyle \\varepsilon^{*}_{m} \\end{array}$ is an ordinary ring. Thus, on such hyperrings, εm∗$\\begin{array}{} \\displaystyle \\varepsilon^{*}_{m} \\end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm-relation on hyperrings and m-idempotent hyperrings.
TL;DR: The authors review the main cryptographic schemes applied to date, as well as the most relevant Post Quantum research in the eld to contribute to clarify the strengths and weaknesses of each scheme, as a necessary step towards a broader introduction of REV solutions in binding elections.
Abstract: The implantation of Remote Electronic Voting (REV) systems to Electoral Processes is happening at a slower pace than anticipated. One of the relevant factors explaining that reality is the lack of studies about the Cryptographic Schemes and Primitives applied to the existing REV solutions. In this paper, the authors review the main cryptographic schemes applied to date, as well as the most relevant Post Quantum research in the eld. The aim is twofold: contribute to clarify the strengths and weaknesses of each scheme as well as expose the remaining challenges, as a necessary step towards a broader introduction of REV solutions in binding elections.
TL;DR: In this article, the authors studied spacelike and timelike elastic curves in the Lorentz-Minkowski plane whose curvature is expressed in terms of the pseudodistance to fixed geodesics.
Abstract: Abstract This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 𝕃2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.
TL;DR: In this article, a new kind of nonlocal boundary value problems of multi-term fractional differential equations are introduced and studied, and the existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems.
Abstract: Abstract We introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.
TL;DR: The sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, Mm, n, for all n≥3 and m≥2 are given.
Abstract: Abstract The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing. It is hard to compute exact values of partition dimension for a graphic metric space, (G, dG) and networks. In this article, we give the sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, Mm, n, for all n≥3 and m≥2.
TL;DR: By considering “useful” Csiszár divergence in the integral case, the results for integral majorization inequality are given and the equivalent statements between continuous convex functions and Green functions via majorization inequalities are obtained.
Abstract: Abstract In this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, “useful” Csiszár functional and “useful” Zipf-Mandelbrot law. By considering “useful” Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given.
TL;DR: A Gray map from RkntoFpm2kn is defined and the generator polynomials of constacyclic codes over Rk are given and the MacWilliams identities of linear codes overRk are studied.
Abstract: Abstract In this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈ui2$\\begin{array}{} u^{2}_{i} \\end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k. We define a Gray map from RkntoFpm2kn$\\begin{array}{} R_{k}^n\\,\\,\\text{to}\\,\\,{\\mathbb F}_{p^m}^{2^kn} \\end{array} $ and give the generator polynomials of constacyclic codes over Rk. We also study the MacWilliams identities of linear codes over Rk.
TL;DR: It is proved that a variant of the Courtois-Finiasz-Sendrier signature is strongly existentially unforgeable under chosen message attack in the random oracle model, assuming hardness of the Permuted Goppa Syndrome Decoding Problem.
Abstract: This article proves that a variant of the Courtois-Finiasz-Sendrier signature is strongly existentially unforgeable
under chosen message attack in the random oracle model, assuming hardness of the Permuted Goppa
Syndrome Decoding Problem (also known as the Niederreiter problem).
TL;DR: In this paper, the Hermite polynomials and their squares were derived by making use of the generating function methods and Padé approximation techniques, and some new recurrence formulas were established.
Abstract: Abstract In this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares. These results presented here are the corresponding extensions of some known formulas.
TL;DR: The complex quadric Qm = SOm+2/SOmSO2 is a compact Hermitian symmetric space of rank 2, and it is also a complex hypersurface in complex projective space CPm+1 as mentioned in this paper.
Abstract: The complex quadric Qm = SOm+2/SOmSO2 is a compact Hermitian symmetric space of rank 2. It is also a complex hypersurface in complex projective spaceCPm+1, [1]. Qm is equippedwith two geometric structures: a complex conjugation A and a Kähler structure J. Real hypersurfaces M in Qm are immersed submanifolds of real codimension 1. The Kähler structure J of Qm induces on M an almost contact metric structure (φ, ξ, η, g), where φ is the structure tensor eld, ξ is the structure (or Reeb) vector eld, η is a 1-form and g is the the induced Riemannian metric on M. Real hypersurfacesM in Qm whose Reeb ow is isometric are classi ed in [2]. They obtain tubes around the totally geodesic CPk in Qm when m = 2k. The condition of isometric Reeb ow is equivalent to the commuting condition of the shape operator S with the structure tensor eld φ of M. It is known that a Killing vector eld X on a Riemannian manifold (M̄, ḡ) satis es LX ḡ = 0, where L denotes the Lie derivative. Killing vector elds are a powerful tool in studying the geometry of a Riemannian manifold. A Killing vector eld is a Jacobi vector eld along any geodesic. However the converse is not true: the position vector on the euclidean space Rn is a Jacobi eld along any geodesic of Rn but it is not Killing. Studying when the structure vector eld of a complex projective space is Killing, Deshmukh, [3], introduced the notion of Jacobi type vector elds on a Riemannian manifold. A vector eld Y on M̄ is of Jacobi type if it satis es ∇̄X∇̄XY + R̄(Y , X)X = 0 (1)
TL;DR: It is proved the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almostperiodicity, and some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay are presented.
Abstract: Abstract In this paper, we introduce the concept of Sp-pseudo almost periodicity on time scales and present some basic properties of it, including the translation invariance, uniqueness of decomposition, completeness and composition theorem. Moreover, we prove the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almost periodicity. As an application of the abstract results, we present some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay.
TL;DR: In this article, the notion of upsets in residuated lattices and defining the operator Da(X) was used to construct a new topology denoted by τa and (L, τa) becomes a topological space.
Abstract: Abstract In this paper, by using the notion of upsets in residuated lattices and defining the operator Da(X), for an upset X of a residuated lattice L we construct a new topology denoted by τa and (L, τa) becomes a topological space. We obtain some of the topological aspects of these structures such as connectivity and compactness. We study the properties of upsets in residuated lattices and we establish the relationship between them and filters. O. Zahiri and R. A. Borzooei studied upsets in the case of BL-algebras, their results become particular cases of our theory, many of them work in residuated lattices and for that we offer complete proofs. Moreover, we investigate some properties of the quotient topology on residuated lattices and some classes of semitopological residuated lattices. We give the relationship between two types of quotient topologies τa/F and τa−$\\begin{array}{} \\displaystyle \\mathop {{\\tau _a}}\\limits^ - \\end{array}$. Finally, we study the uniform topology τΛ¯$\\begin{array}{} \\displaystyle {\\tau _{\\bar \\Lambda }} \\end{array}$ and we obtain some conditions under which (L/J,τΛ¯)$\\begin{array}{} \\displaystyle (L/J,{\\tau _{\\bar \\Lambda }}) \\end{array}$ is a Hausdorff space, a discrete space or a regular space ralative to the uniform topology. We discuss briefly the applications of our results on classes of residuated lattices such as divisible residuated lattices, MV-algebras and involutive residuated lattices and we find that any of this subclasses of residuated lattices with respect to these topologies form semitopological algebras.
TL;DR: In this article, a recent generalization of Hofstadter's famous Q-sequence is studied beyond the known methods of generational approaches in order to propose a generalized conjecture regarding the existence of infinitely many different solutions for all corresponding recurrences of this generalization.
Abstract: Abstract Chaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested recurrences. In this study, a recent generalization of Hofstadter’s famous Q-sequence is studied beyond the known methods of generational approaches in order to propose a generalized conjecture regarding the existence of infinitely many different solutions for all corresponding recurrences of this generalization.
TL;DR: In this paper, the Browder spectral properties (VΠ and VΠa) were introduced and studied in connection with Browder type theorems introduced in [1, [2], [3] and [4].
Abstract: Abstract An operator T acting on a Banach space X satisfies the property (UWΠ) if σa(T)∖ σSF+−$\\begin{array}{} \\sigma_{SF_{+}^{-}} \\end{array} $(T) = Π(T), where σa(T) is the approximate point spectrum of T, σSF+−$\\begin{array}{} \\sigma_{SF_{+}^{-}} \\end{array} $(T) is the upper semi-Weyl spectrum of T and Π(T) the set of all poles of T. In this paper we introduce and study two new spectral properties, namely (VΠ) and (VΠa), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property (VΠ) if and only if T satisfies property (UWΠ) and σ(T) = σa(T).
TL;DR: In this paper, it was shown that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular classes.
Abstract: Abstract Strict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.