Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIMEcomputable formula in the existential fragment of Presburger arithmetic. This result marks a significant complexity improvement, as the known algorithms have EXPTIME wo...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

Well-defined carbon polyhedrons with faceted morphologies and hollow internal structures made of self-organized multi-walled carbon nanotubes have been fabricated by gas phase catalytic CVD inside microchannels, of which the confined space is critical for the formation of polyhedral structures with hexagonal, heptagonal and octagonal cross-sections that show superhydrophobic properties, with th...

A compact and sharp-rejection ultra-wideband (UWB) microstrip band-pass filter (BPF) is developed using of left handed metamaterials realized by complementary split ring resonator (CSRR). Moreover, proposed structure consists of two doublets parallel coupling gaps at each side of a microstrip ring. In comparison with some other filters, this structure shows a significantly wider passband due to...

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

Mdm2 can mediate p53 ubiquitylation and degradation either in the form of the Mdm2 homodimer or Mdm2/MdmX heterodimer. The ubiquitin ligase activity of these complexes resides mainly in their respective RING finger domains and also requires adjacent C-terminal tails. So far, structural studies have failed to show significant differences between Mdm2 RING homodimers and Mdm2/MdmX RING heterodime...