Showing papers in "Mathematica Slovaca in 2017"
TL;DR: In this paper, it was shown that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
Abstract: Abstract In this paper, we prove that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
34 citations
TL;DR: In this paper, the delta fractional difference was studied by means of a recently obtained inequality, and the following interrelated theorems were obtained, which improved recent results in the literature.
Abstract: Abstract In this paper, by means of a recently obtained inequality, we study the delta fractional difference, and we obtain the following interrelated theorems, which improve recent results in the literature. Theorem A Assume that f : ℕa → ℝ and that Δaνf(t) $\\Delta^\
u_af(t)$ ≥ 0, for each t ∈ ℕa+2−ν, with 1 < ν < 2. If f(a+1)≥νk+2f(a), $f(a+1) \\geq \\frac{\
u}{k+2}f(a),$ for each k ∈ ℕ0, then Δ f(t) ≥ 0 for t ∈ ℕa+1. Theorem B Assume that f : ℕa → ℝ and that Δaνf(t) $\\Delta^\
u_af(t)$ ≥ 0, for each t ∈ ℕa+2−ν, with 1 < ν < 2. If f(a+2)≥νk+1f(a+1)+(k+1−ν)ν(k+2)(k+3)f(a) $$f(a+2)\\geq\\displaystyle\\frac{\
u}{k+1}f(a+1)+\\frac{(k+1-\
u)\
u}{(k+2)(k+3)}f(a) $$ for each k ∈ ℕ1, then Δ f(t) ≥ 0 for t ∈ ℕa+2. Theorem C Assume that f : ℕa → ℝ and that Δaνf(t) $\\Delta^\
u_af(t)$ ≥ 0, for each t ∈ ℕa+2−ν, with 1 < ν < 2. If f(a+3)≥νkf(a+2)+(k−ν)νk(k+1)f(a+1)+(k+1−ν)(k−ν)ν(k+2)(k+1)kf(a) $$f(a+3)\\geq\\displaystyle\\frac{\
u}{k}f(a+2)+\\frac{(k-\
u)\
u}{k(k+1)}f(a+1)+\\frac{(k+1-\
u)(k-\
u)\
u}{(k+2)(k+1)k}f(a) $$ for k ∈ ℕ2, then Δ f(t) ≥ 0, for t ∈ ℕa+3. In addition, we obtain the following result, which extends a recent result due to Atici and Uyanik. Theorem D Assume that f : ℕa → ℝ, ΔNf(t) ≥ 0 for t ∈ ℕa, and (−1)N−iΔif(a) ≤ 0 for i = 0, 1, …, N − 1. Then Δaνf(t) $\\Delta^\
u_af(t)$ ≥ 0 for t ∈ ℕa+N−ν.
28 citations
TL;DR: In this article, a generalization of the exponential sampling series of optical physics is introduced, and pointwise and uniform convergence theorem is established in a quantitative form, also in a generalized form.
Abstract: Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin band-limited functions using both classical and generalized exponential sampling series.
27 citations
21 citations
TL;DR: In this article, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian motion and the brownian bridge are studied, to solve some stochastic differential equations.
Abstract: $L^p$ spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian Motion and the Brownian Bridge are studied, to solve some stochastic differential equations.
20 citations
TL;DR: WituŁa et al. as discussed by the authors introduced the concepts of δ-Lucas numbers, δ -Fibonacci and δLucas polynomials, and discussed the basic properties of such objects, as well as their applications.
Abstract: Abstract In this paper, with reference to the previous work [WITUŁA, R.—SŁOTA, D.: δ-Fibonacci numbers, Appl. Anal. Discrete Math. 3 (2009), 310–329] concerning the, so called, δ-Fibonacci numbers, the concepts of δ-Lucas numbers, δ-Fibonacci and δ-Lucas polynomials are introduced. There are discussed the basic properties of such objects, as well as their applications, especially for description of certain polynomials and identities of algebraic and trigonometric type. Many from among these identities describe the binomial transformations of the respective integer sequences and polynomials. Similarly as for δ-Fibonacci numbers, also for δ-Lucas numbers some attractive identities–bridges are obtained, connecting these numbers in practice with every sequence of integer numbers.
19 citations
TL;DR: The theory of multivariate neural network operators in a Kantorovich type version is introduced and several examples of sigmoidal functions for which the above theory holds have been presented.
Abstract: Abstract The theory of multivariate neural network operators in a Kantorovich type version is here introduced and studied. The main results concerns the approximation of multivariate data, with respect to the uniform and Lp norms, for continuous and Lp functions, respectively. The above family of operators, are based upon kernels generated by sigmoidal functions. Multivariate approximation by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of sigmoidal functions for which the above theory holds have been presented.
16 citations
TL;DR: In this paper, the co-rank of the fundamental group of a smooth closed connected manifold M was studied and the set of all possible combina- tions of b 0(M) and the first Betti number b 1(M).
Abstract: We study b 0(M), the co-rank of the fundamental group of a smooth closed connected manifold M. We calculate this value for the di- rect product of manifolds. We characterize the set of all possible combina- tions of b 0(M) and the first Betti number b1(M) by explicitly constructing manifolds with any possible combination of b 0(M) and b1(M) in any given dimension. Finally, we apply our results to the topology of a Morse form foliations. In particular, we construct a manifolds M and a Morse form ! on it for any possible combination of b 0(M), b1(M), m(!), and c(!), where m(!) is the number of minimal components and c(!) is the maxi- mum number of homologically independent compact leaves of !.
15 citations
TL;DR: In this article, the authors consider the following families of real-valued functions: Darboux, quasi-continuous, Świątkowski functions and strong ǫ-kowalski functions and compare these sets in terms of topology.
Abstract: Abstract We consider the following families of real-valued functions: Darboux, quasi-continuous, Świątkowski functions and strong Świątkowski functions. The aim of this paper is to compare this sets in terms of topology.
14 citations
TL;DR: Fuzzy measures and Choquet asymmetric integral are considered in this article, where some Core-Walras results are given as an application to economics, and they are applied to finance.
Abstract: Fuzzy measures and Choquet asymmetric integral are considered here. As an application to economics some Core-Walras results are given.
13 citations
TL;DR: In this article, the authors derived oscillation criteria for the second order half-linear neutral differential equation [r(t)Φ(z′(t))]′+c(t),x(σ(t)))=0,z(t)=x(t)+b(t,x(τ(t)), $$
Abstract: Abstract In this paper we derive oscillation criteria for the second order half-linear neutral differential equation [r(t)Φ(z′(t))]′+c(t)Φ(x(σ(t)))=0,z(t)=x(t)+b(t)x(τ(t)), $$ \\displaystyle \\Bigl[r(t)\\Phi(z'(t))\\Bigr]'+c(t)\\Phi(x(\\sigma(t)))=0, \\quad z(t)=x(t)+b(t)x(\\tau(t)), $$ where Φ(t) = |t|p−2t, p ≥ 2, is a power type nonlinearity. We improve recent results published in the literature by obtaining better oscillation constants and removing the usual condition σ(τ(t)) = τ(σ(t)). Two methods (comparison method and Riccati equation method) are used.
TL;DR: In this article, the notion of bounded index was extended to holomorphic bivariate functions and necessary and sufficient conditions were presented to ensure that a holomorphic BVF is bounded index.
Abstract: Abstract The following notion of bounded index for complex entire functions was presented by Lepson. function f(z) is of bounded index if there exists an integer N independent of z, such that max{l:0≤l≤N}|f(l)(z)|l!≥|f(n)(z)|n!for alln. $$ \\max\\limits_{\\{l: 0\\leq l\\leq N\\}} \\left \\{ \\frac{|{f^{(l)}(z)}|}{l!}\\right \\} \\geq \\frac{|{f^{(n)}(z)}|}{n!}\\quad\\text{for all}\\,\\, n. $$ The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers M and N such that M and N are the least integers such that max{(k,l):0,0≤k,l≤M,N}|f(k,l)(z,w)|k!l!≥|f(m,n)(z,w)|m!n!for allmandn. $$ \\max\\limits_{\\{(k,l): 0,0\\leq k, l\\leq M, N\\}} \\left \\{ \\frac{|{f^{(k,l)}(z,w)}|}{k!\\,l!}\\right \\} \\geq \\frac{|{f^{(m,n)}(z,w)}|}{m!\\,n!}\\quad\\text{for all}\\,\\, m \\, \\text{and}\\,\\, n. $$ Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.
TL;DR: In this paper, the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type f = 2g(x)+ 2h(y), x⊥y in which ⊥ is the orthogonality in the sense of Rätz in modular spaces is established.
Abstract: Abstract In this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type f(x + y)+ f(x - y) = 2g(x)+ 2h(y), x⊥y in which ⊥ is the orthogonality in the sense of Rätz in modular spaces.
TL;DR: In this article, the boundary value problem for differential equation with φ-Laplacian and state-dependent impulses of the form ( φ(z(t)) )′ = f(t, z (t), z(t)), for a.e.
Abstract: The paper deals with the boundary value problem for differential equation with φ-Laplacian and state-dependent impulses of the form ( φ(z(t)) )′ = f(t, z(t), z(t)), for a.e. t ∈ [0, T ] ⊂ R, 4z(t) = M(z(t), z(t−)), t = γ(z(t)) z(0) = z(T ) = 0, Here, T > 0, φ : R→ R is an increasing homeomorphism, φ(R) = R, φ(0) = 0, f : [0, T ]× R → R satisfies Caratheodory conditions, M : R → R is continuous and γ : R → (0, T ) is continuous, 4z′(t) = z′(t+) − z′(t−). Sufficient conditions for the existence of at least one solution to this problem having no pulsation behaviour are provided. Mathematics Subject Classification 2010: 34B37, 34B15.
TL;DR: In this paper, new oscillation criteria for third order nonlinear dynamic equations with a nonlinear damping term are established, and examples to illustrate the results are included in the paper.
Abstract: Abstract New oscillation criteria for certain third order nonlinear dynamic equations with a nonlinear damping term are established. Examples to illustrate the results are included.
TL;DR: In this paper, it was shown that a pair of proximal Klee-Phelps convex groupoids in a finite-dimensional normed linear space are convex if and only if the groupoids are normed proximal.
Abstract: We prove that a pair of proximal Klee-Phelps convex groupoids $A(\circ)$,$B(\circ)$ in a finite-dimensional normed linear space $E$ are normed proximal, {\em i.e.}, $A(\circ)\ \delta\ B(\circ)$ if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood $N_z(\circ)\subseteq S_z(\circ)$ is convex in $E$ if and only if $N_z(\circ) = S_z(\circ)$.
TL;DR: In this paper, the authors study the Pettis integral of fuzzy mappings in arbitrary Banach spaces and give conditions under which a scalarly integrable fuzzy mapping is Pettis integrability.
Abstract: In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.
TL;DR: In this paper, the concept of λ-super socle of C(X), denoted by Sλ(X) (that is, the set of elements of C (X) such that the cardinality of their cozerosets are less than λ, where λ ≤ |X|) is introduced and studied.
Abstract: The concept of λ-super socle of C(X), denoted by Sλ(X) (that is, the set of elements of C(X) such that the cardinality of their cozerosets are less than λ, where λ is a regular cardinal number with λ ≤ |X|) is introduced and studied. Using this concept we extend some of the basic results concerning SCF (X), the super socle of C(X) to Sλ(X), where λ ≥ א0. In particular, we determine spaces X for which SCF (X) and Sλ(X) coincide. The one-point λ-compactification of a discrete space is algebraically characterized via the concept of λ-super socle. In fact we show that X is the one-point λ-compactification of a discrete space Y if and only if Sλ(X) is a regular ideal and Sλ(X) = Ox, for some x ∈ X.
TL;DR: In this paper, the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation was investigated.
Abstract: Abstract In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation. Our results unify and extend some existing fixed point results in the related literature.
TL;DR: In this article, the authors discuss the dynamical reasons why negative interest rates can happen in second order differential dynamics and how they can influence the variance and expectation of the interest rate process.
Abstract: The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can be suggested, however, they are far beyond a simple practical realization. In this paper we discuss the dynamical reasons why negative interest rates can happen in the second order differential dynamics and how they can influence the variance and expectation of the interest rate process. Such issues are highly practical, involving e.g. banking sector and pension securities.
TL;DR: In this article, MinLOS, R. A., et al. considered a point-like interaction between n fermions and another particle, where the semi-boundedness of the operator is obtained.
Abstract: Abstract In this paper we are concerned with a three-body system with point interaction, which is called the Ter-Martirosian–Skornyakov extension. We locate the bottom of the essential spectrum of that system and establish the finiteness of the discrete spectrum below the bottom. Our work here refines the result of [MINLOS, R. A.: On point-like interaction between n fermions and another particle, Mosc. Math. J. 11 (2011), 113–127], where the semi-boundedness of the operator is obtained.
TL;DR: In this article, a special family of multigeometric series is considered from the point of view of behaviour of their sets of subsums and a sufficient condition for their subsums to be M-Cantorvals is proven.
Abstract: Abstract A special family of multigeometric series is considered from the point of view of behaviour of their sets of subsums. A sufficient condition for their sets of subsums to be M-Cantorvals is proven. The Lebesgue measure of those special M-Cantorvals is computed and it is shown to be equal to the sum of lengths of all component intervals of the M-Cantorvals. A new sufficient condition for the set of subsums of a series to be a Cantor set is formulated and it is used to demonstrate that the discussed multigeometric series always have Cantor sets as their sets of subsums for sufficiently small ratios of the series.
TL;DR: In this article, it was shown that a synaptic algebra is a vector lattice if and only if the elements of the identity element and the carrier of the element are pairwise connected.
Abstract: A synaptic algebra $A$ is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace $V$ of $A$ in regard to the question of when $V$ is a vector lattice. Our main theorem states that if $V$ contains the identity element of $A$ and is closed under the formation of both the absolute value and the carrier of its elements, then $V$ is a vector lattice if and only if the elements of $V$ commute pairwise.
TL;DR: In this paper, a non-bijective Wigner theorem on quantum systems using only basic linear algebra is presented, which is based on showing that any non-zero Jordan ∗-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an anitiunitary map.
Abstract: Abstract We present new proof of non-bijective Wigner theorem on symmetries of quantum systems using only basic linear algebra. It is based on showing that any non-zero Jordan ∗-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an anitiunitary map. As a new application we extend hitherto known results on preservers of quantum relative entropy to infinite quantum systems.
TL;DR: In this article, a comparison of some subfamilies of the family of functions on the real line having the Baire property in porosity terms is given, and it is shown that these sub-families are strongly porous.
Abstract: Abstract The comparison of some subfamilies of the family of functions on the real line having the Baire property in porosity terms is given. We prove that the family of all quasi-continuous functions is strongly porous set in the family of all cliquish functions and that the family of all cliquish functions is strongly porous set in the family of all functions having the Baire property. We prove also that the family of all Świątkowski functions is lower 2/3-porous set in the family of cliquish functions and the family of functions having the internally Świątkowski property is lower 2/3-porous set in the family of cliquish functions.
TL;DR: In this paper, the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces was studied and some uniqueness and Ulam's type stability concepts were presented.
Abstract: Abstract In this paper, we shall present some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results.
TL;DR: In this paper, the authors investigated a class of four-point integral boundary value problems for the nonlinear coupled system involving higher-order Caputo fractional derivatives and Riemann-Stieltjes integral boundary conditions.
Abstract: Abstract In the paper, we investigate a class of four-point integral boundary value problems for the nonlinear coupled system involving higher-order Caputo fractional derivatives and Riemann-Stieltjes integral boundary conditions. By employing Guo-Krasnoselskii fixed point theorem, some sufficient conditions are obtained to guarantee the existence of at least one or two positive solutions for this system. Meanwhile, the eigenvalue intervals of existence for positive solutions are also given. As applications, some examples are provided to illustrate the validity of our main results.
TL;DR: In this article, the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the form P(X) = L 1, L 2, L 3, L 4, L 5, L 6, L 7, L 8, L 9, L 10, L 11, L 12, L 13, L 14, L 15, L 16, L 18, L 19, L 20, L 21, L 22, L 23, L 24, L 25, L 26, L 28
Abstract: Abstract We investigate the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the form P(X) = L1(X)(L2(X)+L1(X)L3(X)) where L1, L2, L3 are linearized polynomials. To our knowledge, the given class has not been studied previously in the literature. We identify several new types of permutation polynomials of this class. While most of the newly identified polynomials are linearly equivalent to permutation monomials, we show that there exist subclasses that are not affine equivalent to monomials, and we describe their forms. One of the newly identified classes contains a subclass of complete mappings. We use these complete mappings to define new sets of mutually orthogonal Latin squares, as well as new vectorial bent functions from the Maiorana-McFarland class. Moreover, the quasigroup polynomials obtained in the process are different and inequivalent to the previously known ones.
TL;DR: It is shown that a probabilistic convergence group induces a natural Probabilistic uniform convergence structure and gives a result on probabilism metrization.
Abstract: Abstract We define probabilistic convergence groups based on Tardiff’s neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as probabilistic limit groups under a t-norm as defined earlier by the authors. We further show that a probabilistic convergence group induces a natural probabilistic uniform convergence structure and give a result on probabilistic metrization.