Projectability and weak homogeneity of pseudo effect algebras

In this paper we deal with a pseudo effect algebra possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, can be represented as an interval of a unital partially ordered group G. We prove that is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of and of G is shown to be valid. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence—Physics of Information (grant I/2/2005).     

Direct product decompositions of bounded commutative residuated ℓ-monoids

The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let be a BCR ℓ-monoid; we denote by ℓ( ) the underlying lattice of . In the present paper we show that each direct product decomposition of ℓ( ) determines a direct product decomposition of . This yields that any two direct product decompositions of have isomorphic refinements. We consider also the relations between direct product decompositions of and states on . This work was supported by Slovak Research and Development Agency under the contract No APVV-0071-06. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).     

Compact images of spaces with a weaker metric topology

If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology. In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that (1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence of point-finite cs-covers such that for each y ∈ Y. (2) Y is a sequentially-quotient compact image of a space with a weaker metric topology if and only if Y has a sequence of point-finite cs*-covers such that for each y ∈ Y. Supported by the NNSF(10471084) of China.     

On the maximal operator of Walsh-Kaczmarz-Fejér means

In this paper we prove that the maximal operator      

On <Emphasis Type="Italic">S</Emphasis>-quasinormal and <Emphasis Type="Italic">c</Emphasis>-normal subgroups of a finite group

Let be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every maximal subgroup of all Sylow subgroups of H is either c-normal or S-quasinormally embedded in G. (2) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every maximal subgroup of all Sylow subgroups of F*(H), the generalized Fitting subgroup of H, is either c-normal or S-quasinormally embedded in G. (3) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every cyclic subgroup of F*(H) of prime order or order 4 is either c-normal or S-quasinormally embedded in G. Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No. 0249001). Corresponding author. Supported in part by the Natural Science Foundation of China (10571181), NSF of Guangdong Province (06023728) and ARF(GDEI).     

Geodesic mapping onto Kählerian spaces of the first kind

In the present paper a generalized Kählerian space Open image in new window of the first kind is considered as a generalized Riemannian space \(\mathbb{G}\mathbb{R}_N \) with almost complex structure F _i ^h that is covariantly constant with respect to the first kind of covariant derivative.Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f: Open image in new window with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space Open image in new window .     

Ends of graphed equivalence relations,II

Given a graphing of a countable Borel equivalence relation on a Polish space, we show that if there is a Borel way of selecting a non-empty closed set of countably many ends from each -component, then there is a Borel way of selecting an end or line from each -component. Our method yields also Glimm-Effros style dichotomies which characterize the circumstances under which: (1) there is a Borel way of selecting a point or end from each -component; and (2) there is a Borel way of selecting a point, end or line from each -component. The first author was supported in part by NSF Grant DMS-0140503. The second author was supported in part by NSF VIGRE Grant DMS-0502315.     

Measure-category properties of Borel plane sets and Borel functions of two variables

Let      

∞-jets of diffeomorphisms preserving orbits of vector fields

Let F be a C ^∞ vector field defined near the origin O ∈ ℝ ⁿ , F(O) = 0, and (F _t ) be its local flow. Denote by the set of germs of orbit preserving diffeomorphisms h: ℝ ⁿ → ℝ ⁿ at O, and let , (r ≥ 0), be the identity component of with respect to the weak Whitney W ^r topology. Then contains a subset consisting of maps of the form F _α(x)(x), where α: ℝ ⁿ → ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then = . In this paper we present a class of examples of vector fields with degenerate singularities at O for which formally coincides with , i.e. on the level of ∞-jets at O. We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials in two variables.      

Algebras of polynomials on locally convex spaces of ultradifferentiable functions and generalized derivation

We consider the space      

Harmonic moments of branching processes in random environments

We consider harmonic moments of branching processes in general random environments. For a sequence of square integrable random variables, we give some conditions such that there is a positive constant c that every variable in this sequence belong to Ac or A1c uniformly.     

Construct weak Hopf algebras by using Borcherds matrix

We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra by adding a new generator J satisfying jm = j for some integer m. We denote this algebra by wUqT（A）. This algebra is a weak Hopf algebra if and only if m = 2,3. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usual quantum envelope algebra Uq （A） of a generalized Kac-Moody algebra A.     

Generalized Besov type spaces on the dual of the Laguerre hypergroup

In this paper we introduce the homogeneous Besov type spaces ∧p,q^γ（K） on the dual of Laguerre hypergroup K and we establish some new harmonic analysis results. We give some character- izations of these spaces using equivalent seminorms. Also we study the non-homogeneous Besov type spaces ∧p,q^γ（K）. We give some properties of these spaces and embeddings results with respect to their parameters p, q and γ.     

A formula for the Bloch norm of a C 1-function on the unit ball of ℂ n

For a C ¹-function f on the unit ball ⊂ ℂ ⁿ we define the Bloch norm by , where is the invariant derivative of f, and then show that . Supported by MNZŽS Serbia, Project No. 144010.     

Diameter preserving surjection on alternate matrices

Let F be a field with ｜F｜ ≥ 3, Km be the set of all m × m （m ≥ 4） alternate matrices over F. The arithmetic distance of A, B ∈ Km is d（A, B） ：= rank（A - B）. If d（A, B） = 2, then A and B are said to be adjacent. The diameter of Km is max{d（A, B） ： A, B ∈ km}. Assume that φ ： Km→Km is a map. We prove the following are equivalent： （a） φ is a diameter preserving surjection in both directions, （b） φ is both an adjacency preserving surjection and a diameter preserving map, （c） φ is a bijective map which preserves the arithmetic distance.     

Selfinjective Koszul algebras of finite complexity

In this paper, we study selfinjective Koszul algebras of finite complexity. We prove that the complexity is a nonnegative integer when it is finite; and that the category Yt of modules with complexity less or equal to t, is resolving and coresolving. We show that for each 0 ≤ 1 ≤ m there exist a family of modules of complexity 1 parameterized by G（l, m）, the Grassmannian of l-dimensional subspaces of an m-dimensional vector space V, for the exterior algebra of V. Using complexity, we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0, via skew group algebra of a finite subgroup of SL（2, C） over the exterior algebra of a 2-dimensional vector space.     

Optimization in the class <Emphasis Type="Italic">W</Emphasis><Stack><Subscript>2</Subscript><Superscript>2</Superscript></Stack> of the boundary control by displacements at one endpoint of a string with the other endpoint being fixed

We consider the problem on the optimal boundary control of string vibrations by a displacement at one endpoint of the string with the other endpoint being fixed. The problem is studied in the space      

Sequential convergences on <Emphasis Type="Italic">MV</Emphasis>-algebras without Urysohn’s axiom

In a previous author’s paper, sequential convergences on an MV-algebra have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv . In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding system of convergences is denoted by conv . Both Conv and conv are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv and Conv . We prove that each interval of conv is a distributive lattice. The system conv has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider also the relations between conv and conv G, where (G, u) is a unital lattice-ordered group with = Γ (G, u). This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of Information, Grant 1/2/2005.     

On potentially nilpotent double star sign patterns

A matrix whose entries come from the set {+, −, 0} is called a sign pattern matrix, or sign pattern. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by (m, 2), is introduced. We determine all potentially nilpotent sign patterns in (3, 2) and (5, 2), and prove that one sign pattern in (3, 2) is potentially stable. Supported by youth scientific funds of the Education Department of Jiangxi Province (No. GJJ09460), Natural Science Foundation of Jiangxi Normal University (No.2058), National Natural Science Foundation of China (No.10601001).     

Iterative separation in distributive congruence lattices

In [PLOŠČICA, M.: Separation in distributive congruence lattices, Algebra Universalis 49 (2003), 1–12] we defined separable sets in algebraic lattices and showed a close connection between the types of non-separable sets in congruence lattices of algebras in a finitely generated congruence distributive variety and the structure of subdirectly irreducible algebras in . Now we generalize these results using the concept of separable mappings (defined on some trees) and apply them to some lattice varieties. Supported by VEGA Grants 2/4134/24, 2/7141/27, and INTAS Grant 03-51-4110.