A degree sum condition for graphs to be covered by two cycles

Let $G$ be a $k$-connected graph of order $n$. In [1], Bondy (1980) considered a degree sum condition for a graph to have a Hamiltonian cycle, say, to be covered by one cycle. He proved that if ${\sigma }_{k+1}\left(G\right)>(k+1)(n?1)/2$, then $G$ has a Hamiltonian cycle. On the other hand, concerning a degree sum condition for a graph to be covered by two cycles, Enomoto et al. (1995) [4] proved that if $k=1$ and ${\sigma }_3\left(G\right)\ge n$, then $G$ can be covered by two cycles. By these results, we conjecture that if ${\sigma }_{2k+1}\left(G\right)>(2k+1)(n?1)/3$, then $G$ can be covered by two cycles. In this paper, we prove the case $k=2$ of this conjecture. In fact, we prove a stronger result; if $G$ is 2-connected with ${\sigma }_5\left(G\right)\ge 5(n?1)/3$, then $G$ can be covered by two cycles, or $G$ belongs to an exceptional class.     

Stochastic thermoelastic problem of a functionally graded plate under random temperature load

This study attempts to derive the statistics of temperature and thermal stress in functionally graded material (FGM) plates exposed to random external temperatures. The thermomechanical properties of the FGM plates are assumed to vary arbitrarily only in the plate thickness direction. The external temperatures are expressed as random functions with respect to time. The transient temperature field in the FGM plate is determined by solving a nonhomogeneous heat conduction problem for a multilayered plate with linear nonhomogeneous thermal conductivity and different homogeneous heat capacity in each layer. The autocorrelations and power spectrum densities (PSDs) of temperature and thermal stress are derived analytically. These statistics for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304) are computed under the condition that the fluctuation in the external temperature can be considered as white noise or a stationary Markov process.     

Changes in the Hydration State of a Block Copolymer of Poly(N‐isopropylacrylamide) and Poly(ethylene oxide) on Thermosensitive Micellization in Water

A diblock copolymer of poly(N‐isopropylacrylamide) and poly(ethylene oxide) (PiPA‐b‐PEO) has been prepared by radical polymerization with a ceric ion initiation system. Its thermosensitive micellization has been investigated by means of IR and fluorescence spectroscopy. The PiPA segments are critically dehydrated above 33.5°C (5 wt.‐%) and associate through hydrophobic interaction to form the hydrophobic core of the micelle. In contrast, the change in the hydration state of the PEO segments upon micellization is small.