Quadtree and pyramid structures have attracted considerable attention in recent years. They are increasingly being applied to the fields of digital image and signal processing. As a result, the efficient embedding of these structures in VLSI arrays has become an important research topic. In this paper, we propose three schemes to embed either quadtrees or pyramids in a rectangular, hexagonal, o...

We study statistical properties of energy spectra of a tight-binding model on the twodimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble, and thus differs from the critical level-spacing distribution observed at the m...

Propagation properties of square, hexagonal and octagonal lattice photonic crystal fibers (PCFs) have been analyzed here for both stressed and unstressed conditions. The analysis has been carried out using finite element method. All types of PCFs are investigated here by varying number of air hole rings with same design and operating parameters. The results show that external stress causes PCFs...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

A wideband dual-polarized aperture antenna array is presented based on elements formed by pairs of octagonal rings. The octagon ring elements are linked by capacitors and kept a defined distance from a ground plane. A broader frequency bandwidth has been achieved by placing a further layer of conductive elements above the array forming a meta-material layer. Expanded polystyrene foam is used to...

We present almost linear area bounds for drawing complete trees on the octagonal grid. For 7-ary trees we establish an upper and lower bound of Θ(n1.129) and for ternary trees the bounds of O(n1.048) and Θ(n), where the latter needs edge bends. We explore the unit edge length and area complexity of drawing unordered trees on k-grids with k ∈ {4, 6, 8} and generalize the N P-hardness results of ...

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. The module $M$ is called {it Rickart} if for any $fin S$, $r_M(f)=Se$ for some $e^2=ein S$. We prove that some results of principally projective rings and Baer modules can be extended to Rickart modules for this general settings.

This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.