‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

In this paper we look at the K-theory of a specific C*-algebra closely related to the irrational rotation algebra. Also it is shown that any automorphism of a C*-algebra A induces group automorphisms of K_{1}(A) amd K_{0}(A) in an obvious way. An interesting problem for any C*-algebra A is to find out whether, given an automorphism of K_{0}(A) and an automorphism of K_{1}(A), we can lift them t...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

Background: The ideal teeth arrangement is an important step for success in complete denture fabrication. There are different methods for determining the posterior denture teeth location. The purpose of this study was the comparison of posterior mandibular teeth location in the study group with Pound or Misch theory. Material and methods: An alginate mandibular impression of 80 dentate patients...

1. TANGENT SPHERES. Any four mutually tangent spheres determine six points of tangency. We say that a pair of tangencies {ti , t j } is opposite if the two spheres determining ti are distinct from the two spheres determining t j . Thus the six tangencies are naturally grouped into three opposite pairs, corresponding to the three ways of partitioning the four spheres into two pairs. Altshiller-C...

Vertex-colorings, edge-colorings and total-colorings of the Sierpiński gasket graphs Sn, the Sierpiński graphs S(n, k), graphs S (n, k), and graphs S(n, k) are considered. In particular, χ′′(Sn), χ (S(n, k)), χ(S(n, k)), χ(S(n, k)), χ(S(n, k)), and χ(S(n, k)) are determined.

We describe a new hybrid approach to modeling and animating animals. A pre–defined skin is modeled as a triangle mesh, such as may be purchased from a digital model vendor, or generated with a typical modeling program. This skin is then attached to the underlying bone, muscle, and tissue model. The rest shape of the skin is exactly as given in the surface model of the animal. Internal component...

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...