In the present study, the effects of arrangement and distribution of multifarious types of defects on fundamental frequency of carbon nanotubes are investigated with respect to different chirality and boundary conditions. Interatomic interactions between each pair of carbon atoms are modeled using two types of non–linear spring–like elements. To obtain more information about the influences of d...

The alternating group of degree 6 is located at the junction of three series of simple non-commutative groups : simple sporadic groups, alternating groups and simple groups of Lie type. It plays a very special role in the theory of finite groups. We shall study its new roles both in a finite geometry of certain pentagon in the Leech lattice and also in a complex algebraic geometry of K3 surfaces.

No countable C,-free graph contains every countable C,-free graph as a subgraph, for n 2 4. For n = 4, this was proved earlier by J. Pach.

We propose the decay modes B → a0(→ ηπ)π to determine the CKM phase α. One can analyze these modes through (i) the B → a0π isospin pentagon, (ii) the time dependent Dalitz plot of B0(t) → a±0 π → ηπ+π−, and (iii) the time dependence of B0(t) → a0(→ ηπ0)π0. We show that the a0π modes have certain advantages as compared to the ρπ modes, and strongly recommend the time dependent Dalitz plot analys...

This paper contains some results of pentagons which can be determined by two X-rays. The results reveal this problem is more complicated.

We propose the decay modes B → a0(→ ηπ)π to determine the CKM phase α. One can analyze these modes through (i) the B → a0π isospin pentagon, (ii) the time dependent Dalitz plot of B0(t) → a±0 π → ηπ+π−, and (iii) the time dependence of B0(t) → a0(→ ηπ0)π0. We show that the a0π modes have certain advantages as compared to the ρπ modes, and strongly recommend the time dependent Dalitz plot analys...

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4 − 2 dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O( ) corrections, a result which is the dimensionallyregulated ver...

In this paper we consider deflations (inverse pocket flips) of n-gons for small n. We show that every pentagon can be deflated after finitely many deflations, and that any infinite deflation sequence of a pentagon results from deflating an induced quadrilateral on four of the vertices. We describe a family of hexagons that deflate infinitely for a specific deflation sequence, yet induce no infi...

Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or respectively of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a repr...

An acute triangulation is a triangulation whose triangles have all their angles less than π 2 . In this paper we prove that i) every planar pentagon can be triangulated into at most 54 acute triangles, and ii) every double pentagon can be triangulated into at most 76 acute triangles.