Strongly meager sets and their uniformly continuous images

We prove the following theorems:

(1) Suppose that is a continuous function and is a Sierpinski set. Then

(A)

for any strongly measure zero set , the image is an -set,

(B)

is a perfectly meager set in the transitive sense.

(2) Every strongly meager set is completely Ramsey null.

     

On perfectly meager sets in the transitive sense

We prove that assuming one can always find a perfectly meager set, which is not perfectly meager in the transitive sense.

     

Not every finite lattice is embeddable in the recursively enumerable degrees

A certain lattice with eight elements is shown to be not embeddable as a lattice in the recursively enumerable degrees. This refutes the well-known Embedding Conjecture which asserted that every finite lattice could be so embedded.     

Intersection of essential ideals in

The infinite intersection of essential ideals in any ring may not be an essential ideal, this intersection may even be zero. By the topological characterization of the socle by Karamzadeh and Rostami (Proc. Amer. Math.Soc. 93 (1985), 179-184), and the topological characterization of essential ideals in Proposition 2.1, it is easy to see that every intersection of essential ideals of is an essential ideal if and only if the set of isolated points of is dense in . Motivated by this result in , we study the essentiallity of the intersection of essential ideals for topological spaces which may have no isolated points. In particular, some important ideals and , which are the intersection of essential ideals, are studied further and their essentiallity is characterized. Finally a question raised by Karamzadeh and Rostami, namely when the socle of and the ideal of coincide, is answered.

     

Baire and Volterra spaces

In this paper we describe broad classes of spaces for which the Baire space property is equivalent to the assertion that any two dense -sets have dense intersection. We also provide examples of spaces where the equivalence does not hold. Finally, our techniques provide an easy proof of a new internal characterization of perfectly meager subspaces of and characterize metric spaces that are always of first category.

     

Self-similar groups in the sense of an iterated function system and their properties

The notion of self-similarity in the sense of iterated function system (IFS) for compact topological groups is given by ?. Koçak in Definition 3. In this work, first we give the definition of strong self-similar group in the sense of IFS. Then, we investigate the main properties of these groups. We also obtain the relations between profinite groups and strong self-similar groups in the sense of IFS. Finally, we construct some examples of these groups.     

On a characterization of the maximal ideal spaces of commutative -algebras in which every element is the square of another

A topological condition is given for a locally connected compact Hausdorff space on which every complex-valued continuous function is the square of another. The condition need not be necessary nor sufficient unless the space is locally connected.

     

The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps

The convergence of modified Mann iteration is equivalent to the convergence of modified Ishikawa iterations, when T is an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive map.     

The position value is the Myerson value,in a sense

We characterize the position value for TU games with a cooperation structure in terms of the Myerson value of some natural modification of the original game—the link agent form. This construction is extended to TU games with a conference structure.      

Some new two-character sets in PG and a distance-2 ovoid in the generalized hexagon H

In this paper, we construct a new infinite class of two-character sets in and determine their automorphism groups. From this construction arise new infinite classes of two-weight codes and strongly regular graphs, and a new distance-2 ovoid of the split Cayley hexagon of order 4.     

The standard double bubble is the unique stable double bubble in

We prove that the only equilibrium double bubble in which is stable for fixed areas is the standard double bubble. This uniqueness result also holds for small stable double bubbles in surfaces, where it is new even for perimeter-minimizing double bubbles.

     

Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.     

Functions on discrete sets holomorphic in the sense of Ferrand,or monodiffric functions of the second kind

We study the class of functions called monodiffric of the second kind by Isaac.They are discrete analogues of holomorphic functions of one or two complex variables.Discrete analogues of the Cauchy-Riemann operator,of domains of holomorphy in one discrete variable,and of the Hartogs phenomenon in two discrete variables are investigated.Two fundamental solutions to the discrete Cauchy-Riemann equation are studied:one with support in a quadrant,the other with decay at infinity.The first is easy to construct by induction;the second is accessed via its Fourier transform.     

Functions on discrete sets holomorphic in the sense of Isaacs, or monodiffric functions of the first kind

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.     

Coalition formation in the triad when two are weak and one is strong

Eighteen groups of subjects each participated in five different computer-controlled superadditive 3-person characteristic function games with sidepayments, that modeled negotiable conflicts in which two of the players are weak and one is considerably stronger. Both the degree to which the strong player was powerful and the type of communication were experimentally manipulated. The 90 game outcomes rejected any solution concept that predicts a single payoff vector for a given coalition structure, but supported the recently developed single-parameter α-power model that allows range predictions. Both the degree of power and type of communication were found to affect game outcomes and to determine the predictive power of models that make point predictions in 3-person games.     

On the boundaries of self-similar tiles in

The aim of this note is to study the construction of the boundary of a self-similar tile, which is generated by an iterated function system . We will show that the boundary has complicated structure (no simple points) in general; however, it is a regular fractal set.