A fully irreducible outer automorphism φ of the free group Fn of rank n has an expansion factor which often differs from the expansion factor of φ. Nevertheless, we prove that the ratio between the logarithms of the expansion factors of φ and φ is bounded above by a constant depending only on the rank n. We also prove a more general theorem applying to an arbitrary outer automorphism of Fn and ...

In this paper, an example of phase analysis during annealing is presented using in-situ TEM. The demonstrated on amorphous Cu-Mn/C thin films focusing identification in a multicomponent system. transient states following the crystallization Cu-Mn alloy and reaction with C substrate were analyzed by evaluating diffraction patterns recorded at different temperatures. camera constant was calibrate...

As various property studies continue to emerge on high entropy and entropy-stabilized ceramics, we seek a further understanding of the changes across phase boundary between “high-entropy” “entropy-stabilized” phases. The thermal mechanical properties bulk ceramic stabilized oxide composition Mg 0.2 Co Ni Cu Zn O are investigated this critical transition temperature via transient plane-source me...

Hypercubes are known to be able to simulate other structures such as grids and binary trees. It has been shown that an arbitrary binary tree can be embedded into a hypercube with constant expansion and constant dilation. This paper presents a simple linear-time heuristic which embeds an arbitrary binary tree into a hypercube with expansion 1 and average dilation no more than 2. We also give som...

Control of copolymer composition and molecular weight distributions is important, since they partially govern material performance. This work uses a simple but robust approach to approximate predictive control of average composition and molecular weight during free radical copolymerization, based on detailed kinetics obtained by ACOMP (automatic continuous online monitoring of polymerization re...

Although most insulators are expected to undergo insulator to metal transition on lattice compression, tetrahedral semiconductors Si, GaAs and InSb can become metallic on compression as well as by expansion. We focus on the transition by expansion which is rather peculiar; in all cases the direct gap at Γ point closes on expansion and thereafter a zerogap state persists over a wide range of lat...

a r t i c l e i n f o Keywords: molybdenum (Mo) isotopes basaltic weathering riverine inputs estuarine mixing The application of the molybdenum (Mo) isotope system as a proxy for determining changes in the redox state of the oceans is predicated on the assumption that the composition of continental input can be characterised from crustal rock types, and remains constant. However, it has recentl...

We have investigated the local density of optical states (LDOS) in titania and silicon inverse opals – three-dimensional photonic crystals that have been realized experimentally. We used the H-field plane-wave expansion method to calculate the density of states and the projected local optical density of states, which are directly relevant for spontaneous emission dynamics and strong coupling. W...

Abstract: In this research, we attempt to envisage the mirror application using semiconductor photonic crystal with the help of photonic bandgap analysis. The photonic bandgap of photonic crystal structure is simulated using plane wave expansion method, where photonic crystal is realized by 2D triangular photonic crystal structure with gallium arsenide as background material having periodic air...

We prove in this paper an effective recursion formula for all intersection numbers of mixed ψ and κ classes on moduli spaces of curves. Several related general recursive formulas are also proved. Some of these formulas contain certain tautological constants, which are given by the secant Euler numbers and series expansion of Bessel functions of the first kind.