Showing papers in "Mediterranean Journal of Mathematics in 2011"
TL;DR: In this article, the authors investigated the problem of global uniform practical exponential stability of a general nonlinear non-autonomous differential delay equations and showed that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough.
Abstract: In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.
36 citations
TL;DR: In this article, the generalized Hyers-Ulam stability of mixed additive and quadratic functional equations in quasi-β-normed spaces was investigated. But the generalized stability was not investigated in the case of the mixed additive functional equation.
Abstract: In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed additive and quadratic functional equation
$$f(\lambda x + y) + f(\lambda x - y) = f(x + y) + f(x - y) + (\lambda - 1)[(\lambda +2)f(x) + \lambda f(-x)],$$
\({(\lambda \in {\mathbb N}, \lambda
e 1)}\) in quasi-β-normed spaces.
26 citations
TL;DR: In this paper, the spectral property (R) for bounded linear operators defined on a Banach space is introduced, which is related to Weyl type theorems and is also studied in the framework of left polaroid operators.
Abstract: We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.
25 citations
TL;DR: The main aim of as mentioned in this paper is to investigate curvature properties of the Sasakian metrics in the cotangent bundle, and the main result is that they are invariant to the curvature.
Abstract: The main aim of this paper is to investigate curvature properties of the Sasakian metrics in the cotangent bundle.
24 citations
TL;DR: It is proved that a necessary and sufficient condition for a given copula to be the independence or product copula is for the pair of measure-preserving transformations representing the copulato be independent as random variables.
Abstract: We solve a problem recently proposed by Kolesarova et al. Specifically, we prove that a necessary and sufficient condition for a given copula to be the independence or product copula is for the pair of measure-preserving transformations representing the copula to be independent as random variables.
24 citations
TL;DR: In this paper, the authors studied the properties of an operator having the SVEP on the complement of distinguished parts of its spectrum, and showed that the properties (b) and (gb) can be improved.
Abstract: We study the new properties (b) and (gb), which we had introduced in [13], for an operator having the SVEP on the complement of distinguished parts of its spectrum. Classes of operators are considered as illustrating examples.
22 citations
TL;DR: In this article, the authors investigate well-posedness of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Cessenat.
Abstract: This work is a continuation of our previous paper [8]. We investigate well-posedness (in the semigroup theory sense) of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Fine properties of the traces are investigated, extending well-known results by M. Cessenat [15]. For dissipative boundary conditions, we revisit and generalize results from [12, 17] while, for multiplicative boundary conditions we extend techniques from [25]. Finally, we also investigate the case of boundary conditions associated to a boundary operator of norm one, extending the recent results of [6, 27] to more general fields and measures.
20 citations
TL;DR: In this article, a monotonicity property of the superposition operator in higher dimensions was proved and the existence of non-decreasing positive solutions for a system of singular integral equations was established.
Abstract: In this paper, a monotonicity property of the superposition operator in higher dimensions will be proved. Then by using the concept of measure of noncompactness, we will establish the existence of nondecreasing positive solutions for a system of singular integral equations. Furthermore, the results will be used to investigate the solvability of the system of k
th
-order initial value problems.
20 citations
TL;DR: In this paper, comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic metric are proved. But the results are restricted to the case where the original domain is not related to the original one.
Abstract: In this article we prove comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic metric. By a comparative result we mean one which assumes hyperbolicity in one domain and obtains it in a different domain somehow related to the original one. We derive a characterization (simple to check in practical cases) of the Gromov hyperbolicity of a plane domain Ω* obtained by deleting from the original domain Ω any uniformly separated union of compact sets. We present as well a result about stability of hyperbolicity.
20 citations
TL;DR: In this article, the Radon transform on the (flat) torus is studied and an inversion formula for this transform is proved and a characterization of the image of the space of smooth functions is given.
Abstract: We consider the Radon transform on the (flat) torus \({\mathbb{T}^{n} = \mathbb{R}^{n}/\mathbb{Z}^n}\) defined by integrating a function over all closed geodesics. We prove an inversion formula for this transform and we give a characterization of the image of the space of smooth functions on \({\mathbb{T}^{n}}\) .
17 citations
TL;DR: In this article, the characterizations for the general natural anti-Hermitian structures on the cotangent bundles, which are in the eight classes obtained by Ganchev and Borisov, are given.
Abstract: We give the characterizations for the general natural anti-Hermitian structures on the cotangent bundles, which are in the eight classes obtained by Ganchev and Borisov. Considering an anti-Hermitian structure of natural diagonal type on the cotangent bundle, we construct examples for every class of anti-Hermitian structures.
TL;DR: In this article, the question of whether there are groups that are proper in the sense that they are neither p ≥ ω+n -projective nor ω-totally Σ-cyclic is shown to be logically equivalent to a natural question about the structure of valuated vector spaces.
Abstract: Several equivalent descriptions are given of the class of primary abelian groups whose separable subgroups are all direct sums of cyclic groups; such groups are called ω-totally Σ-cyclic. This establishes the converse of a theorem due to Megibben. For n < ω, this is generalized to a consideration of the class of primary abelian groups whose p
ω+n
-bounded subgroups are all p
ω+n
-projective. The question of whether there are such groups that are proper in the sense that they are neither p
ω+n
-projective nor ω-totally Σ-cyclic is shown to be logically equivalent to a natural question about the structure of valuated vector spaces. Finally, it is shown that both of these statements are independent of ZFC.
TL;DR: In this paper, the Lipschitz continuous and compact composition operators C φ (f) = f ◦ φ acting from the hyperbolic α-Bloch class to the Hyperbolic weighted Dirichlet- or Q p -class are characterized by conditions depending on the symbol φ only.
Abstract: Natural metrics in the hyperbolic α-Bloch-, weighted Dirichlet- and Q p -classes are introduced, and these classes are shown to be complete metric spaces with respect to the corresponding metrics. Then Lipschitz continuous and compact composition operators C φ (f) = f ◦ φ acting from the hyperbolic α-Bloch-class to the hyperbolic weighted Dirichlet- or Q p -class are characterized by conditions depending on the symbol φ only.
TL;DR: In this paper, the theory of Differential and Integral Calculus in Riesz Spaces was applied to investigate properties of the g-calculus and solve some types of differential, functional and stochastic equations.
Abstract: We apply the theory of Differential and Integral Calculus in Riesz Spaces introduced in [1] and [4] to investigate some properties of the g-calculus and to solve some types of differential, functional and stochastic equations.
TL;DR: In this article, the notion of a slant light-like submanifold of an indefinite cosymplectic manifold was introduced and necessary and sufficient conditions for the existence of such a sub-manifolds were derived.
Abstract: In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of \({R^{9}_{2}}\) and prove some characterization Theorems.
TL;DR: In this paper, the authors determined the groups of isometries of the Heisenberg group endowed with each of the three left invariant Lorentzian metrics which are possible on it.
Abstract: The paper is mainly devoted to determine the groups of isometries of the Heisenberg group endowed with each of the three left invariant Lorentzian metrics which are possible on it; also, an explicit computation of all the isometries for the (two) non flat Lorentzian metrics is done. Moreover, explicit formulas for the geodesic curves and the Jacobi vector fields for each of these three Lorentzian metrics are computed.
TL;DR: In this paper, it was shown that any generalized Jordan (triple-) derivation on a 2-torsion free semiprime ring is a generalized derivation and that every generalized Jordan higher derivation is a generalization.
Abstract: It is shown that any generalized Jordan (triple-)derivation on a 2–torsion free semiprime ring is a generalized derivation and that any generalized Jordan higher derivation on a 2–torsion free semiprime ring is a generalized higher derivation. Then we give several conditions which enable some generalized Jordan derivations on prime rings to degenerate left or right multipliers. Lastly, we apply these degenerating conditions to discuss the range inclusion problems of generalized derivations on noncommutative Banach algebras.
TL;DR: In this paper, the authors characterized the class of functions f on (0, ∞) for which f(x),...,(xkf(x))(k) are completely monotonic for given k.
Abstract: In this paper we characterize the class \({{\mathcal{C}_k}}\) of functions f on (0,∞) for which f(x), . . . ,(xkf(x))(k) are completely monotonic for given k. In the limit we obtain the well-known characterization of the class of Stieltjes functions as those functions f defined on the positive half line for which (xkf(x))(k) is completely monotonic on (0,∞) for all k ≥ 0.
TL;DR: For the class of boundary functions from C5,λ, 0 < λ < 1, the maximum error of the 9-point finite difference solution of the Laplace equation has been shown to be of order O(n, O(ln, ln + 1) as discussed by the authors.
Abstract: Two new properties of the 9-point finite difference solution of the Laplace equation are obtained, when the boundary functions are given from C5,1. It is shown that the maximum error is of order \({O\,\left(h^6\,(|{\rm ln}\,h| + 1)\right)}\), and this order cannot be obtained for the class of boundary functions from C5,λ, 0 < λ < 1. These properties of the 9-point solution can be used to justify different versions of domain decomposition, composite grids, and combined methods.
TL;DR: In this article, the Minkowski inequality has been used to obtain properties of several mappings which are arisen from the inequality, including superadditivity (subadditivity) and monotonicity.
Abstract: In this paper we obtain properties of several mappings which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refinements of the Minkowski inequality and the Holder inequality.
TL;DR: In this article, a generalized quasi-Sasakian structure is defined on an almost contact metric manifold, and sufficient and sufficient conditions for the complemented framed structure on the distribution of the tangent bundle of a G.Q.S. manifold are studied.
Abstract: On an odd dimensional manifold, we define a structure which generalizes several known structures on almost contact manifolds, namely Sasakian, trans-Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic structures. This structure, hereinafter called a generalized quasi-Sasakian, shortly G.Q.S. structure, is defined on an almost contact metric manifold and satisfies an additional condition. Then we consider a distribution \({\mathcal{D}_{1}}\) wich allows a suitable decomposition of the tangent bundle of a G.Q.S. manifold. Necessary and sufficient conditions for the normality of the complemented framed structure on the distribution \({\mathcal{D}_{1}}\) defined on a G.Q.S manifold are studied. The existence of the foliation on G.Q.S. manifolds and of bundle-like metrics are also proven. It is shown that under certain circumstances a new foliation arises and its properties are investigated. Some examples illustrating these results are given in the final part of this paper.
TL;DR: In this paper, the authors generalize Liouville's theorem on integration in finite terms to allow polylogarithms of any order to occur in the integral in addition to elementary functions.
Abstract: We generalize partially Liouville’s theorem on integration in finite terms to allow polylogarithms of any order to occur in the integral in addition to elementary functions. The result is a partial generalization of a theorem proved by the author for the dilogarithm. It is also a partial proof of a conjecture postulated by the author in 1994 [1]. The basic conclusion is that an associated function to the nth polylogarithm appears linearly with logarithms appearing possibly in a polynomial way with non-constant coefficients.
TL;DR: The Shannon’s sampling theorem is generalized for a class of non band–limited signals which plays a central role in the signal theory, the Gaussian map is the unique function which reachs the minimum of the product of the temporal and frecuential width.
Abstract: For any Gaussian signal and every given sampling frequency we prove an asymptotic property of type Shannon’s sampling theorem, based on normalized cardinal sines, which keeps constant the sampling frequency. We generalize the Shannon’s sampling theorem for a class of non band–limited signals which plays a central role in the signal theory, the Gaussian map is the unique function which reachs the minimum of the product of the temporal and frecuential width. This solve a conjecture stated in [1] and suggested by [3].
TL;DR: In this article, the authors studied the higher-dimensional homology and homotopy prop- erties of the spaces SC(Z, ∗) for any path-connected compact spaces Z and introduced the functor SC(−, −) defined on the category of all spaces with base points and continuous mappings.
Abstract: In our earlier papers we constructed examples of 2-dimen- sional nonaspherical simply-connected cell-like Peano continua, called Snake space. In the sequel we introduced the functor SC(−, −) defined on the category of all spaces with base points and continuous mappings. For the circle S 1 ,t he spaceSC(S 1 , ∗) is a Snake space. In the present paper we study the higher-dimensional homology and homotopy prop- erties of the spaces SC(Z, ∗) for any path-connected compact spaces Z. Mathematics Subject Classification (2010). Primary 54G15, 54G20, 54F15; Secondary 54F35, 55Q52. Keywords. Snake space, Topologist sine curve, asphericity, simple con- nectivity, cell-likeness, semi-local strong contractibility, continuum, free σ-product of groups, van Kampen theorem.
TL;DR: In this paper, a real-algebra isomorphism for uniform algebras was shown to exist in the case that exp A, exp B is the greatest common divisor of m and n, respectively.
Abstract: Let A, B be uniform algebras Suppose that A
0, B
0 are subgroups of A
−1, B
−1 that contain exp A, exp B respectively Let α be a non-zero complex number Suppose that m, n are non-zero integers and d is the greatest common divisor of m and n If T : A
0 → B
0 is a surjection with $${\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}}$$
for all $${f,g \in A_0}$$
, then there exists a real-algebra isomorphism $${\tilde{T} : A \rightarrow B}$$
such that $${\tilde{T}(f)^d = (T(f)/T(1))^d}$$
for every $${f \in A_0}$$
This result leads to the following assertion: Suppose that S
A
, S
B
are subsets of A, B that contain A
−1, B
−1 respectively If m, n > 0 and a surjection T : S
A
→ S
B
satisfies $${\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}}$$
for all $${f, g \in S_A}$$
, then there exists a real-algebra isomorphism $${\tilde{T} : A \rightarrow B}$$
such that $${\tilde{T}(f)^d = (T(f)/T(1))^d}$$
for every $${f \in S_A}$$
Note that in these results and elsewhere in this paper we do not assume that T(exp A) = exp B
TL;DR: In this paper, the existence of at least three solutions of gradient elliptic systems with nonhomogeneous and nonsmooth Neumann boundary conditions with non-homogeneous Neumann conditions is proved.
Abstract: In this paper we prove the existence of at least three solutions of gradient elliptic systems with nonhomogeneous and nonsmooth Neumann boundary conditions. Our investigations complete the results of J. Fernandez Bonder, S. Martinez, J.D. Rossi (NoDEA Nonlinear Differential Equations Appl. 2007). We use a recent generalization of a three critical points theorem of B. Ricceri (Nonlinear Anal. 2008) for locally Lipschitz functionals given by A. Kristaly, W. Marzantowicz, Cs. Varga (J. Global Optim. 2010).
TL;DR: This paper considers integer and rational parametric Bézier curves and study the distance between the curve and its control polygon and uses first and second order moduli of smoothness of vector-valued function to measure the distance.
Abstract: In this paper we consider integer and rational parametric Bezier curves and study the distance between the curve and its control polygon. To measure the distance we use first and second order moduli of smoothness of vector-valued function. We consider also NURBS curves with equidistant knots. Some direct approximation theorems will be presented.
TL;DR: In this article, it was shown that all aperiodic orbits can be removed from the dynamics of the map H of Henon by perturbing H so that the perturbed map H 1 does not have any periodic point of prime period two.
Abstract: The main purpose of this paper is to investigate dynamical systems $${F : \mathbb{R}^2 \rightarrow \mathbb{R}^2}$$
of the form F(x, y) = (f(x, y), x). We assume that $${f : \mathbb{R}^2 \rightarrow \mathbb{R}}$$
is continuous and satisfies a condition that holds when f is non decreasing with respect to the second variable. We show that for every initial condition x0 = (x
0, y
0), such that the orbit
$$ O({\rm{x}}_0) = \{{\rm{x}}_0, {\rm{x}}_1 = F({\rm{x}}_0), {\rm{x}}_2 = F({\rm{x}}_1), . . . \}, $$
is bounded, O(x0) converges provided that the set of fixed point of F is totally disconnected and F does not admit periodic orbits of prime period two. The obtained result is used to show that all aperiodic orbits can be removed from the dynamics of the map H of Henon. The goal can be achieved by perturbing H so that the perturbed map H
1 does not have any periodic point of prime period two.
TL;DR: In this article, a discrete type multi-point BVP of difference equations is considered and sufficient conditions to guarantee the existence of at least three positive solutions are established, and an example is presented to illustrate the main results.
Abstract: This article deals with a discrete type multi-point BVP of difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operators Δx(n) and Δx(n + 1). The difference concerned is a implicit difference equation.
TL;DR: In this article, a new variant of square-like functions generated by some composite wavelet transform is introduced and established Calderon-type reproducing formula and then proved L 2-boundedness of newly defined squarelike functions.
Abstract: The classical square functions play important role in Harmonic Analysis and have a very direct connection with L2-estimates and Littlewood-Paley theory. In this paper we introduce a new variant of square-like functions generated by some composite wavelet transform. We establish Calderon-type reproducing formula and then prove L2-boundedness of newly defined square-like functions.