Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $Ksubseteq X$, respectively. $(X, T)$ is called D-{it lowerable} (resp. {it lowerable}) if for each $0le hle h (T, X
)$ there is a subset (resp. closed subset) $K_h$ with $h^B (T, K_h)= h$ (resp. $h (T, K_h)= h$); is called D-{it hereditarily lowerable} (resp. {it hereditarily lowerable}) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable). In this paper it is proved that each topological dynamical system is not only lowerable but also D-lowerable, and each asymptotically $h$-expansive system is D-hereditarily lowerable. A minimal system which is lowerable and not hereditarily lowerable is demonstrated.
The BaCe0.8Y0.2O3-{delta} proton conductor under hydration and under compressive strain has been analyzed with high pressure Raman spectroscopy and high pressure x-ray diffraction. The pressure dependent variation of the Ag and B2g bending modes from
the O-Ce-O unit is suppressed when the proton conductor is hydrated, affecting directly the proton transfer by locally changing the electron density of the oxygen ions. Compressive strain causes a hardening of the Ce-O stretching bond. The activation barrier for proton conductivity is raised, in line with recent findings using high pressure and high temperature impedance spectroscopy. The increasing Raman frequency of the B1g and B3g modes thus implies that the phonons become hardened and increase the vibration energy in the a-c crystal plane upon compressive strain, whereas phonons are relaxed in the b-axis, and thus reveal softening of the Ag and B2g modes. Lattice toughening in the a-c crystal plane raises therefore a higher activation barrier for proton transfer and thus anisotropic conductivity. The experimental findings of the interaction of protons with the ceramic host lattice under external strain may provide a general guideline for yet to develop epitaxial strained proton conducting thin film systems with high proton mobility and low activation energy.
Let $(X, T)$ be a topological dynamical system (TDS), and $h (T, K)$ the topological entropy of a subset $K$ of $X$. $(X, T)$ is {it lowerable} if for each $0le hle h (T, X)$ there is a non-empty compact subset with entropy $h$; is {it hereditarily l
owerable} if each non-empty compact subset is lowerable; is {it hereditarily uniformly lowerable} if for each non-empty compact subset $K$ and each $0le hle h (T, K)$ there is a non-empty compact subset $K_hsubseteq K$ with $h (T, K_h)= h$ and $K_h$ has at most one limit point. It is shown that each TDS with finite entropy is lowerable, and that a TDS $(X, T)$ is hereditarily uniformly lowerable if and only if it is asymptotically $h$-expansive.
Let $W$ denote a simply-laced Coxeter group with $n$ generators. We construct an $n$-dimensional representation $phi$ of $W$ over the finite field $F_2$ of two elements. The action of $phi(W)$ on $F_2^n$ by left multiplication is corresponding to a c
ombinatorial structure extracted and generalized from Vogan diagrams. In each case W of types A, D and E, we determine the orbits of $F_2^n$ under the action of $phi(W)$, and find that the kernel of $phi$ is the center $Z(W)$ of $W.$
Let $X=(V,E)$ be a finite simple connected graph with $n$ vertices and $m$ edges. A configuration is an assignment of one of two colors, black or white, to each edge of $X.$ A move applied to a configuration is to select a black edge $epsilonin E$ an
d change the colors of all adjacent edges of $epsilon.$ Given an initial configuration and a final configuration, try to find a sequence of moves that transforms the initial configuration into the final configuration. This is the edge-flipping puzzle on $X,$ and it corresponds to a group action. This group is called the edge-flipping group $mathbf{W}_E(X)$ of $X.$ This paper shows that if $X$ has at least three vertices, $mathbf{W}_E(X)$ is isomorphic to a semidirect product of $(mathbb{Z}/2mathbb{Z})^k$ and the symmetric group $S_n$ of degree $n,$ where $k=(n-1)(m-n+1)$ if $n$ is odd, $k=(n-2)(m-n+1)$ if $n$ is even, and $mathbb{Z}$ is the additive group of integers.
Let $S$ be a connected graph which contains an induced path of $n-1$ vertices, where $n$ is the order of $S.$ We consider a puzzle on $S$. A configuration of the puzzle is simply an $n$-dimensional column vector over ${0, 1}$ with coordinates of the
vector indexed by the vertex set $S$. For each configuration $u$ with a coordinate $u_s=1$, there exists a move that sends $u$ to the new configuration which flips the entries of the coordinates adjacent to $s$ in $u.$ We completely determine if one configuration can move to another in a sequence of finite steps.
In this letter, we report the results of detailed studies on Mn- and Cu-substitution to Fe-site of beta-FeSe, namely MnxFe1-xSe0.85 and CuxFe1-xSe0.85. The results show that with only 10 at% Cu-doping the compound becomes a Mott insulator. Detailed t
emperature dependent structural analyses of these Mn- and Cu-substituted compounds show that the structural transition, which is associated with the changes in the building block FeSe4 tetrahedron, is essential to the occurrence of superconductivity in beta-FeSe.
We have carried out a systematic study of the PbO-type compound FeSe_{1-x}Te_x (x = 0~1), where Te substitution effect on superconductivity is investigated. It is found that superconducting transition temperature reaches a maximum of Tc=15.2K at abou
t 50% Te substitution. The pressure-enhanced Tc of FeSe0.5Te0.5 is more than 10 times larger than that of FeSe. Interestingly, FeTe is no longer superconducting. A low temperature structural distortion changes FeTe from triclinic symmetry to orthorhombic symmetry. We believe that this structural change breaks the magnetic symmetry and suppresses superconductivity in FeTe.
