Showing papers in "Open Mathematics in 2011"
TL;DR: Niroom et al. as mentioned in this paper characterized all finite dimensional non-abelian nilpotent Lie algebras with s(L) = 1; 2, where L is the Schur multiplier.
Abstract: Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
$$
where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.
51 citations
TL;DR: In this article, the authors give an analytical approach to the definition of additive and multiplicative free convolutions based on the theory of Nevanlinna and Schur functions and prove a Khintchine type theorem for the factorization of elements of this semigroup.
Abstract: We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the factorization of elements of this semigroup. An element of M contains either indecomposable (“prime”) factors or it belongs to a class, say I
0, of distributions without indecomposable factors. In contrast to the classical convolution semigroup, in the free additive and multiplicative convolution semigroups the class I
0 consists of units (i.e. Dirac measures) only. Furthermore we show that the set of indecomposable elements is dense in M.
47 citations
TL;DR: In this paper, the authors classify smooth complex projective threefold X with −KX big and NEF but not ample, Picard number γ(X) = 2, and their anticanonical map is small.
Abstract: In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify smooth complex projective threefolds Xwith −KX big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X+ are not both birational.
47 citations
TL;DR: In this paper, an introduction to geography of log models with applications to positive cones of Fano type (FT) varieties and to geometry of minimal models and Mori fibrations is given.
Abstract: This is an introduction to geography of log models with applications to positive cones of Fano type (FT) varieties and to geometry of minimal models and Mori fibrations.
39 citations
TL;DR: In this article, it was shown that Hori-Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials, and they were shown to admit a Laplacian interpretation as well.
Abstract: We prove that Hori-Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.
39 citations
TL;DR: Two unary operators G and H on a relatively pseudocomplemented lattice form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “ it has always been the case” which is an extended version for the classical logic.
Abstract: We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame.
38 citations
TL;DR: In this paper, an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the fixed points of a non-pansive mapping, and the solutions of variational inclusion in a real Hilbert space is presented.
Abstract: In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.
36 citations
TL;DR: In this paper, the authors consider the nonlinear Kirchhoff-type equation and prove that the solution blows up in finite time under suitable conditions on the initial datum, with initial conditions and homogeneous boundary conditions.
Abstract: In this paper, we consider the nonlinear Kirchhoff-type equation $$
u_{tt} + M(\left\| {D^m u(t)} \right\|_2^2 )( - \Delta )^m u + \left| {u_t } \right|^{q - 2} u_t = \left| {u_t } \right|^{p - 2} u
$$
with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.
33 citations
TL;DR: In this paper, it was shown that if T: A → B is a surjective real-linear isometry, then there exists a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: Chb → ChA such that T(f) = κ(f ∘φ) on K and \(T\left( f \right) = \kappa \overline {fo\
Abstract: Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and \(T\left( f \right) = \kappa \overline {fo\phi }\) on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.
29 citations
TL;DR: Hartshorne and Hirschowitz as mentioned in this paper extended this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., the union of schemes obtained by degenerating pairs of skew lines).
Abstract: R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙ
n
, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).
29 citations
TL;DR: In this article, it was shown that for any ω1-monolithic compact space X, if Cp(X) is star countable then it is Lindelof.
Abstract: For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω1-monolithic compact space X, if Cp(X)is star countable then it is Lindelof.
TL;DR: In this paper, a weighted and unweighted version of the Karhunen-Loeve expansions of the Wiener process were studied. But the authors focused on the distribution function of the Laplace transform and its asymptotic behavior.
Abstract: We study Karhunen-Loeve expansions of the process(X
()
)t∈[0,T) given by the stochastic differential equation
% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
% Ubqee0evGueE0jxyaibaieYdh9Lrpeeu0dXdh9vqqj-hEeeu0xXdbb
% a9frpm0db9Lqpepeea0xd9q8as0-LqLs-Jirpepeea0-as0Fb9pgea
% 0lrP0xe9Fve9Fve9qapdbaqaaeGaciGaaiaabeqaamaaeaqbaaGcba
% acbaGaa8hzaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOa
% iGjGcIcacWaMasySdeMaiGjGcMcaaaGccWaMaAypa0JamGjGgkHiTm
% acyc4caaqaiGjGcWaMasySdegabGaMakacyc4GubGamGjGgkHiTiac
% yc4G0baaaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOaiG
% jGcIcacWaMasySdeMaiGjGcMcaaaGccGaSa+hzaiac8c4G0bGamWlG
% gUcaRiac8c4FKbGaiGmGdkeadGaYaUbaaSqaiGmGcGaYaoiDaaqajG
% mGaOGaiGmGcYcacGaGaInaaaWG0bGamaiGydaaayicI4SaiaiGydaa
% ai4waiacaci2aaaaicdacGaGaInaaaGGSaGaiaiGydaaamivaiacac
% i2aaaacMcaaaa!8F89!
$$
dX_t^{(\alpha )} = - \frac{\alpha }
{{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)
$$
, with the initial condition X
0
()
= 0, where α > 0, T ∈ (0, ∞), and (B
t
)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loeve expansions of X
(α). As applications, we calculate the Laplace transform and the distribution function of the L
2[0, T]-norm square of X
(α) studying also its asymptotic behavior (large and small deviation).
TL;DR: In this article, the authors consider metric regularity properties of order q for set-valued mappings and establish several characterizations of these concepts in terms of Holder-like properties of the inverses of the mappings considered.
Abstract: We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Holder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.
TL;DR: In this paper, it was shown that the only minimal surface with a canonical principal direction in the Euclidean space is the catenoid, which is the only surface in the whole space with a principal direction.
Abstract: In the present paper we classify all surfaces in \( \mathbb{E} \)3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space \( \mathbb{E} \)3 is the catenoid.
TL;DR: In this article, a covariant version of the Stinespring theorem for Hilbert C*-modules was proved and a bijective correspondence between operator valued completely positive maps, (u′, u)-covariant with respect to the dynamical system (G, η, X) on Hilbert C *-modules and (u −, u −civariant operator valued significantly positive maps on the crossed product G × ηX of X by η was shown.
Abstract: In this paper, we prove a covariant version of the Stinespring theorem for Hilbert C*-modules. Also, we show that there is a bijective correspondence between operator valued completely positive maps, (u′, u)-covariant with respect to the dynamical system (G, η, X) on Hilbert C*-modules and (u′, u)-covariant operator valued completely positive maps on the crossed product G ×ηX of X by η.
TL;DR: In this article, the Morse index for the signed area of a cyclic configuration of a planar polygonal linkage has been studied, and it has been shown that it depends not only on the combinatorics of the configuration, but also on its metric properties.
Abstract: It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.
TL;DR: In this article, Henning et al. showed that every connected cubic graph on n vertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating sets is at most (n+2)/2.
Abstract: In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating set is at most (n+2)/2, and this bound is essentially best possible.
TL;DR: In this article, the subgroup embedding properties of S-semipermutability, semipermutable, and seminormality are studied. But the authors focus on the problem of finding the subgroups of a group whose order is relatively prime to that of a given subgroup.
Abstract: The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal. We also establish that the solvable groups in which S-permutability is a transitive relation are precisely the groups in which the subnormal subgroups are all S-semipermutable. Local characterizations of this result are also established.
TL;DR: In this article, a new definition of a narrow operator is given, where a vector lattice as the domain space of a linear operator is replaced with a lattice-normed space.
Abstract: The aim of this article is to extend results of Maslyuchenko, Mykhaylyuk and Popov about narrow operators on vector lattices. We give a new definition of a narrow operator, where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator is narrow if and only if its exact dominant is so.
TL;DR: In this paper, the authors show that Gruss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE).
Abstract: We show that Gruss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Gruss inequality but also improve upon recently derived Gruss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance.
TL;DR: In this paper, limit and Dieudonne type theorems in the setting of (l)-groups with respect to filter convergence are proved, extending earlier results, and some limit and dieudonne types are proved for (l) groups.
Abstract: Some limit and Dieudonne-type theorems in the setting of (l)-groups with respect to filter convergence are proved, extending earlier results.
TL;DR: In this article, it was proved that the (p, 1)-total labeling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that G ≥ 8p+4 or g ≥ 6p+2 and g ≥ 4.
Abstract: A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.
TL;DR: In this paper, the k-Fibonacci matrix is defined as an extension of the classical Fibonacci matrices and relationed with the K-FIBonacci numbers.
Abstract: We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
TL;DR: In this paper, a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold are obtained.
Abstract: We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components of the curvature tensor. The formulae also deal with a set of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For a special choice of the functions our formulae involve the Newton transformations of the co-nullity tensor.
TL;DR: In this paper, a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold are studied using pseudodifferential uniformization, which reduces the problem to a pseudodependential operator acting in sections of infinite-dimensional bundles.
Abstract: We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.
TL;DR: In this paper, the authors determine those elements of Γ(X) whose centralizers have simple structure and characterize α ∈ (X) such that various Green's relations in C(α) coincide.
Abstract: For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = {β ∈ g/g(X): αβ = βα} be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green's relations in C(α) coincide, characterize α ∈ Γ(X) such that the
% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy
% Ubqee0evGueE0jxyaibaieYdh9Lrpeeu0dXdh9vqqj-hEeeu0xXdbb
% a9frpm0db9Lqpepeea0xd9q8as0-LqLs-Jirpepeea0-as0Fb9pgea
% 0lrP0xe9Fve9Fve9qapdbaqaaeGaciGaaiaabeqaamaaeaqbaaGcba
% Wefv3ySLgznfgDOfdaryqr1ngBPrginfgDObYtUvgaiyaacqWFjeVs
% aaa!46C9!
$$
\mathcal{J}
$$
-classes of C(α) form a chain, and describe Green's relations in C(α) for α with so-called finite ray-cycle decomposition. If α is a permutation, we also find the structure of C(α) in terms of direct and wreath products of familiar semigroups.
TL;DR: In this paper, it was shown that a 2-testable monoid is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five.
Abstract: A monoid S
1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S
1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.
TL;DR: In this paper, a translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations.
Abstract: A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions of nonlinear parabolic partial differential equations.
TL;DR: In this article, the authors extend the construction of moment-angle complexes to simplicial posets by associating a certain Tm-space ZS to an arbitrary simplicial Poset S on m vertices, and give rise to new classes of Gorenstein and Cohen-Macaulay rings.
Abstract: We extend the construction of moment-angle complexes to simplicial posets by associating a certain Tm-space ZS to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space ZS has many important topological properties of the original moment-angle complex ZK associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of ZS is isomorphic to the Tor-algebra of the face ring ℤ[S]. This leads directly to a generalisation of Hochster’s theorem, expressing the algebraic Betti numbers of the ring ℤ[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of ZS from below by proving the toral rank conjecture for the moment-angle complexes ZS.
TL;DR: The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata in this paper, and a modification of the condition of integral closure and partial derivatives were discussed in this paper.
Abstract: The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.