Showing papers in "Czechoslovak Mathematical Journal in 2009"
TL;DR: In this paper, the foliation of a Morse form ω on a closed manifold M is considered, and conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω.
Abstract: The foliation of a Morse form ω on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of M and ω. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω. The set of the ranks of all forms defining a given foliation without minimal com- ponents is described. It is shown that if ω has more centers than conic singularities then b1(M) = 0 and thus the foliation has no minimal components and homologically non-trivial compact leaves, its folitation graph being a tree.
23 citations
TL;DR: In this article, the authors used the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system − Δu + u · ∇u + ∇p = f, div u = k, u|aΩ = g with u ∈ Lq, q ⩾ n, and very general data classes for f, k, g such that u may have no differentiability property.
Abstract: For a bounded domain Ω ⊂ ℝn, n ⩾ 3, we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system − Δu + u · ∇u + ∇p = f, div u = k, u|aΩ = g with u ∈ Lq, q ⩾ n, and very general data classes for f, k, g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžicka, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669–717, where the existence of a weak solution which is locally regular is proved.
18 citations
TL;DR: In this paper, a convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined, and the properties of the obtained convergence space are investigated and essential links with the pointwise convergence and order convergence are revealed.
Abstract: A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed.
15 citations
TL;DR: In this paper, the Borel transform is used to obtain a duality result via Borel transformation and to prove existence and approximation results for convolution equations, which generalize previous results of this type due to B. Malgrange.
Abstract: In this paper spaces of entire functions of Θ-holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we “construct an algorithm” to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des equations aux derivees partielles et des equations des convolutions. Annales de l’Institute Fourier (Grenoble) VI, 1955/56, 271–355; C. Gupta: Convolution Operators and Holomorphic Mappings on a Banach Space, Seminaire d’Analyse Moderne, 2, Universite de Sherbrooke, Sherbrooke, 1969; M. Matos: Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, 2007; and X. Mujica: Aplicacoes τ (p; q)-somantes e σ(p)-nucleares, Thesis, Universidade Estadual de Campinas, 2006.
15 citations
TL;DR: In this article, a simple formula for the conditional w�-integral of functions on C[0, T] with the conditioning function X petertodd n+1 was derived, and the conditional analytic Feynman w� ϕ-integrals of the functions in a Banach algebra which is an analogue of the Cameron and Storvick algebra.
Abstract: Let C[0, T] denote the space of real-valued continuous functions on the interval [0, T] with an analogue w
ϕ of Wiener measure and for a partition 0 = t
0 < t
1 < < t
n
< t
n+1 = T of [0, T], let X
n
: C[0, T] → ℝ
n+1 and X
n+1: C[0, T] → ℝ
n+2 be given by X
n
(x) = (x(t
0), x(t
1), , x(t
n
)) and X
n+1(x) = (x(t
0), x(t
1), , x(t
n+1)), respectively In this paper, using a simple formula for the conditional w
ϕ-integral of functions on C[0, T] with the conditioning function X
n+1, we derive a simple formula for the conditional w
ϕ-integral of the functions with the conditioning function X
n
As applications of the formula with the function X
n
, we evaluate the conditional w
ϕ-integral of the functions of the form F
m
(x) = ∫
0
(x(t))
m
for x ∈ C[0, T] and for any positive integer m Moreover, with the conditioning X
n
, we evaluate the conditional w
ϕ-integral of the functions in a Banach algebra which is an analogue of the Cameron and Storvick’s Banach algebra Finally, we derive the conditional analytic Feynman w
ϕ-integrals of the functions in
15 citations
TL;DR: In this paper, the authors extend the idea of statistical convergence of a double sequence to μ-statistical convergence and convergence in μ-density using a two valued measure, and they also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences.
Abstract: In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO2) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO2).
14 citations
TL;DR: In this article, the authors consider a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure, and they show that the visosity grows exponentially with increasing pressure.
Abstract: Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.
13 citations
TL;DR: In this paper, the authors give complete description of the comultiplication modules over a Dedekind domain, and if R is the pullback of two local domains, then they classify all indecomposable COMPLICATION R-modules and establish a connection between the COMPLICA modules and the pure-injective modules over such domains.
Abstract: First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if R is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication R-modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
12 citations
TL;DR: In this article, the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class Ck, 1, k ∈ ℕ was proved.
Abstract: Given a domain Ω of class Ck,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense that (∂/∂xn)α(x′, 0) = − N(x′) and that still is of class Ck,1. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class Ck,1. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.
12 citations
TL;DR: In this paper, a structure theorem for idempotent residuated chains is established, and necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotsent chain are given.
Abstract: In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green’s relation \( \mathcal{D} \) on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains, we obtain some characterizations of subdirectly irreducible, simple and strictly simple idempotent residuated chains.
11 citations
TL;DR: In this paper, it was shown that if a ⩾ 1 is an odd integer and M a is a perfect matching in K a,a, then the graph K a,a -M a -a is arbitrarily decomposable into closed trails.
Abstract: Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t 1,..., t p ) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T 1,..., t p ) of pairwise edge-disjoint closed trails in G such that T i is of length T i for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M a,a is a perfect matching in K a,a , then the graph K a,a -M a,a is arbitrarily decomposable into closed trails.
TL;DR: In this paper, the authors consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field and prove the existence of weak solutions under the assumption that the imposed velocity at the boundary of the fluid remains sufficiently small.
Abstract: We consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field. Since the flow is originating from buoyancy, heat transfer has to be included in the model. The stationary system of magnetohydrodynamics is considered, and an approximation of Boussinesq type is used to describe the buoyancy. The heat sources given by the dissipation of current and the viscous friction are not neglected in the fluid. The vessel containing the fluid is embedded in a larger domain, relevant for the global temperature- and magnetic field- distributions. Material inhomogeneities in this larger region lead to transmission relations for the electromagnetic fields and the heat flux on inner boundaries. In the presence of transparent materials, the radiative heat transfer is important and leads to a nonlocal and nonlinear jump relation for the heat flux. We prove the existence of weak solutions, under the assumption that the imposed velocity at the boundary of the fluid remains sufficiently small.
TL;DR: A graph G with p vertices and q edges, vertex set V(G) and edge set E(G), is said to be super vertex-graceful as mentioned in this paper.
Abstract: A graph G with p vertices and q edges, vertex set V(G) and edge set E(G), is said to be super vertex-graceful (in short SVG), if there exists a function pair (f, f+) where f is a bijection from V(G) onto P, f+ is a bijection from E(G) onto Q, f+((u, v)) = f(u) + f(v) for any (u, v) ∈ E(G),
$$ Q = \left\{ \begin{gathered} \{ \pm 1, \ldots , \pm \tfrac{1} {2}q\} , if q is even, \hfill \\ \{ 0, \pm 1, \ldots , \pm \tfrac{1} {2}(q - 1)\} , if q is odd, \hfill \\ \end{gathered} \right. $$
and
$$ P = \left\{ \begin{gathered} \{ \pm 1, \ldots , \pm \tfrac{1} {2}p\} , if p is even, \hfill \\ \{ 0, \pm 1, \ldots , \pm \tfrac{1} {2}(p - 1)\} , if p is odd. \hfill \\ \end{gathered} \right. $$
TL;DR: In this paper, the maximum number of dominating sets in a k-domatic partition of a simple graph with vertex set V (G) is defined as the number of vertices in which every vertex of V(G)-D is adjacent to at least k vertices.
Abstract: Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-dominating set of the graph G is a subset D of V (G) such that every vertex of V (G)-D is adjacent to at least k vertices in D. A k-domatic partition of G is a partition of V (G) into k-dominating sets. The maximum number of dominating sets in a k-domatic partition of G is called the k-domatic number dk(G).
TL;DR: In this paper, it was shown that the semirings of 1-preserving and 0, 1 -preserving endomorphisms of a semilattice are always subdirectly irreducible and under which conditions they are simple.
Abstract: We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.
TL;DR: In this article, it was shown that weakly Lindelof determined Banach spaces are characterized by the existence of a "full" projectional generator, and some other results pertaining to this class of spaces are given.
Abstract: We prove that weakly Lindelof determined Banach spaces are characterized by the existence of a “full” projectional generator. Some other results pertaining to this class of Banach spaces are given.
TL;DR: In this article, the problem of finding the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on block weighted sequence spaces was studied. But the problem was not addressed in this paper.
Abstract: In this paper we consider some matrix operators on block weighted sequence spaces l
p
(w, F). The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on l
p
(w, F). This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour.
TL;DR: In this article, asymptotic properties of the third order trinomial delay differential equation were studied by transforming this equation to the binomial canonical equation, and the results obtained essentially improved known results in the literature.
Abstract: In this paper we study asymptotic properties of the third order trinomial delay differential equation (*) y‴(t) − p(t)y′(t) + g(t)y(τ(t)) = 0 by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.
TL;DR: In this paper, the authors discuss some properties of minus total domination on a graph G and obtain a few lower bounds for γt−(G), denoted as the minimum weight of an MTDF of G.
Abstract: A three-valued function f: V → {−1, 0, 1} defined on the vertices of a graph G= (V, E) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every υ ∈ V, f(N(υ)) ⩾ 1, where N(υ) consists of every vertex adjacent to υ. The weight of an MTDF is f(V) = Σf(υ), over all vertices υ ∈ V. The minus total domination number of a graph G, denoted γt−(G), equals the minimum weight of an MTDF of G. In this paper, we discuss some properties of minus total domination on a graph G and obtain a few lower bounds for γt−(G).
TL;DR: In this paper, a new characterization for the space RBMO(μ) of Tolsa in terms of the John-Stromberg sharp maximal function is established, which is the same as the characterization in this paper.
Abstract: Let μ be a nonnegative Radon measure on ℝd which only satisfies μ (B(x, r)) ⩽ C0rn for all x ∈ ℝd, r > 0, with some fixed constants C0 > 0 and n ∈ (0, d]. In this paper, a new characterization for the space RBMO(μ) of Tolsa in terms of the John-Stromberg sharp maximal function is established.
TL;DR: In this article, it was shown that π is a G-quasifibration if and only if all points in M are regular, under additional assumptions such as the assumption that all points are regular.
Abstract: The orbit projection π: M → M/G of a proper G-manifold M is a fibration if and only if all points in M are regular. Under additional assumptions we show that π is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: π is a G-quasifibration if and only if all points are regular.
TL;DR: In this article, the authors studied the existence of the optimal control for a tracking problem and a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift, and established that the backward differential Riccati equation has a unique, uniformly positive, bounded on ℝ + and stabilizing solution.
Abstract: In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see [2], for finite dimensional stochastic equations or [21], for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [10], [18]). Under stabilizability and uniform observability conditions and assuming that the control weight-costs are uniformly positive, we establish that BDRE has a unique, uniformly positive, bounded on ℝ + and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known [18] that uniform observability does not imply detectability and consequently our results are different from those obtained under detectability conditions (see [10]).
TL;DR: In this article, the monotone meta-Lindelof property is investigated and the relationship between meta-lindelof spaces and other spaces is investigated, including linearly ordered extensions.
Abstract: In this paper, we study the monotone meta-Lindelof property. Relationships between monotone meta-Lindelof spaces and other spaces are investigated. Behaviors of monotone meta-Lindelof GO-spaces in their linearly ordered extensions are revealed.
TL;DR: In this article, a pseudo-effect algebra with interpolation properties is studied and it is shown that a pseudo effect algebra can be represented as an interval of a unital partially ordered group G and G is projectable (strongly projectable) if and only if G is also projectable.
Abstract: In this paper we deal with a pseudo effect algebra
Open image in new window
possessing a certain interpolation property. According to a result of Dvurecenskij and Vettterlein,
Open image in new window
can be represented as an interval of a unital partially ordered group G. We prove that
Open image in new window
is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of
Open image in new window
and of G is shown to be valid.
TL;DR: In this paper, the authors give a useful classification for determining whether a graph is potentially H-graphical (H, n) if every realization of a graph contains a subgraph.
Abstract: The set of all non-increasing nonnegative integer sequences π = (d(v
1), d(v
2), …, d(v
n
)) is denoted by NS
n
. A sequence π ∈ NS
n
is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NS
n
is denoted by GS
n
. A graphical sequence π is potentially H-graphical if there is a realization of π containing H as a subgraph, while π is forcibly H-graphical if every realization of π contains H as a subgraph. Let K
k
denote a complete graph on k vertices. Let K
m
−H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of K
m
). This paper summarizes briefly some recent results on potentially K
m
−G-graphic sequences and give a useful classification for determining σ (H, n).
TL;DR: In this paper, a characterization of continuous images of Radon-Nikodým compacta lying in a product of real lines is presented, and a method for constructing natural examples of such continuous images is presented.
Abstract: We provide a characterization of continuous images of Radon-Nikodým compacta lying in a product of real lines and model on it a method for constructing natural examples of such continuous images.
TL;DR: In this paper, it was shown that if (R,m) is a finitely generated R-module with Supp(L) ⊆ V(a), then ExtiConfiguration (L, H (M, N)) is Matlis reflexive for all i and j in the following cases:
Abstract: Let (R,m) be a complete local ring, a an ideal of R and N and L two Matlis reflexive R-modules with Supp(L) ⊆ V(a). We prove that if M is a finitely generated R-module, then Exti
(L, H
(M,N)) is Matlis reflexive for all i and j in the following cases:
In these cases we also prove that the Bass numbers of H
(M, N) are finite.
TL;DR: In this article, the authors introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.
Abstract: By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.
TL;DR: In this article, the structural properties of Banach spaces admitting arbitrary bump functions depending locally on finitely many coordinates are investigated for higher order smoothness and renorming on the Banach space.
Abstract: The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates
TL;DR: In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated, and the necessary conditions are shown to be sufficient and necessary.
Abstract: In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.