<Emphasis Type="Italic">∂</Emphasis>-operations and <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-fields

The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.     

On the ideal (<Emphasis Type="Italic">v</Emphasis><Superscript>0</Superscript>)

The σ-ideal (v ⁰) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v ⁰) to the family of Ramsey null sets. To describe add(v ⁰) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v ⁰) = add(v ⁰) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v ⁰) = ω ₁ implies that (v ⁰) has the ideal type (c, ω ₁, c).      

Consecutive customer losses in regular and oscillating <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">n</Emphasis> systems

We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M ^X /G/1/n systems.     

Fundamental groups of manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-category 2

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁,W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹ → M ⁿ . We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.      

Localization of <Emphasis Type="Italic">LM</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-algebras

The aim of this paper is to define the localization LM _n -algebra of an LM _n —algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM _n -algebra of fractions (defined in [3]) and the LM _n -algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM _n -algebras of localization.     

Analysis of GI<Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)//<Emphasis Type="Italic">N</Emphasis> systems with stochastic customer acceptance policy

We investigate GI ^X /M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.      

An <Emphasis Type="Italic">ω</Emphasis>-category with all Duals is an <Emphasis Type="Italic">ω</Emphasis>-groupoid

We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.      

On <Emphasis Type="Italic">k</Emphasis>-Spaces and <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-Spaces

In this note we study the relation between k _R -spaces and k-spaces and prove that a k _R -space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k _R -space with a point-countable k-network consisting of compact subsets need not be a k-space. This work was supported by the NSF of China (10271056).     

On locally <Emphasis Type="Italic">A</Emphasis>-convex <Emphasis Type="Italic">H</Emphasis>*-algebras

We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.      

The flatness properties of <Emphasis Type="Italic">S</Emphasis>-poset <Emphasis Type="Italic">A</Emphasis>(<Emphasis Type="Italic">I</Emphasis>) and Rees factor <Emphasis Type="Italic">S</Emphasis>-posets

Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of _S S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor S-posets have property (P _w ). Research supported by nwnu-kjcxgc-03-18.     

<Emphasis Type="Italic">ω</Emphasis>-Convergence theory of filters in <Emphasis Type="Italic">Lω</Emphasis> -spaces

In this paper, an ω-convergence theory of filters in an Lω-space is established. By means of the ω-convergence theory, some important characterizations with respective to the ω-closed sets, ω T ₂ separation and (ω ₁, ω ₂)-continuous mappings are obtained. Moreover, the mutual relationships among ω-convergence of molecular nets, ω-convergence of ideals and ω-convergence of filters are given.     

<Emphasis Type="Italic">f</Emphasis>-Colorings of some graphs of <Emphasis Type="Italic">f</Emphasis>-class 1

An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f（G）. Any simple graph G has the f-chromatic index equal to △f（G） or △f（G） ＋ 1, where △f（G） =max v V（G）{[d（v）/f（v）]}. If X′f（G） = △f（G）, then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f（G） colors are given.     

Primary abelian <Emphasis Type="Italic">n</Emphasis>-Σ-groups

We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ^ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ^ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7]. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007.     

New examples of Cantor sets in <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript> that are not <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-minimal

Although every Cantor subset of the circle (S¹) is the minimal set of some homeomorphism of S¹, not every such set is minimal for a C¹ diffeomorphism of S¹. In this work, we construct new examples of Cantor sets in S¹ that are not minimal for any C¹-diffeomorphim of S¹.     

On elongations of totally projective groups and <Emphasis Type="Italic">α</Emphasis>-<Emphasis Type="Italic">Σ</Emphasis>-groups

We prove that a special α-elongation of a totally projective group is an α-Σ-group if and only if it is a totally projective group. This parallels our recent result in [5].     

Monadic <Emphasis Type="Italic">GMV</Emphasis>-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed. The first author was supported by the Council of Czech Government, MSM 6198959214.     

On the stability of <Emphasis Type="Italic">θ</Emphasis>-derivations on <Emphasis Type="Italic">JB</Emphasis>*-triples

We introduce the concept of θ-derivations on JB*-triples and prove the Hyers–Ulam-Rassias stability of θ-derivations on JB*-triples. We deal with the Hyers-Ulam-Rassias stability that was first introduced by Th. M. Rassias in the paper “On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300”. The first author was supported by Korea Research Foundation Grant KRF-2005-070-C00009.     

Cohomologie <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> en degré 1 des espaces homogènes

The L ^p -cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.      

<Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-nearest neighbor estimators of entropy

For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based on the Euclidean distances between the n sample points and their k _n -nearest neighbors, where {k _n : n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.      

Geometric interpolation by planar cubic <Emphasis Type="Italic">G</Emphasis><Superscript>1</Superscript> splines

In this paper, geometric interpolation by G ¹ cubic spline is studied. A wide class of sufficient conditions that admit a G ¹ cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the verification is added. AMS subject classification (2000)  65D05, 65D07, 65D17