Effects of cyanuric acid (CA) on the isothermal and nonisothermal crystallization, morphology, polymorphic crystalline structure, and phase transition on PBA have been investigated systematically by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray diffraction (WAXD), and Fourier transform infrared (FTIR) spectroscopy. The nonisothermal crystallization temperature increased upon addition of CA. The crystallization kinetics of isothermal crystallization was quantitatively analyzed. CA is an effective nucleating agent for the enhanced nucleation density and decreased spherulite size of PBA. Addition of CA was favorable for the formation of PBA α modification and accelerated the phase transition from the β modification to the α modification. The mechanisms of nucleation, preferential formation of PBA α modification, and accelerated phase transition have also been proposed.
A $k$-hypertournament $H$ on $n$ vertices is a pair $(V(H),A(H))$, where $V(H)$ is a set of vertices and $A(H)$ is a set of $k$-tuples of vertices, called arcs, such that for any $k$-subset $S$ of $V(H)$, $A(H)$ contains exactly one of the $k!$ $k$-tuples whose entries belong to $S$. Clearly, a 2-hypertournament is a tournament. An antidirected path in $H$ is a sequence $x_1 a_1 x_2 a_2 x_3 \ldots x_{t-1} a_{t-1} x_t$ of distinct vertices $x_1, x_2, \ldots, x_t$ and distinct arcs $a_1, a_{2},\ldots, a_{t-1}$ such that for any $i\in \{2,3,\ldots, t-1\}$, either $x_{i-1}$ precedes $x_{i}$ in $a_{i-1}$ and $x_{i+1}$ precedes $x_{i}$ in $a_{i}$, or $x_{i}$ precedes $x_{i-1}$ in $a_{i-1}$ and $x_{i}$ precedes $x_{i+1}$ in $a_{i}$. An antidirected path that includes all vertices of $H$ is known as an antidirected hamiltonian path. In this paper, we prove that except for four hypertournaments, $T_3^{c}, T_5^{c}, T_7^{c}$ and $H_{4}$, every $k$-hypertournament with $n$ vetices, where $2\leq k\leq n-1$, has an antidirected hamiltonian path, which extends Gr\"{u}nbaum's theorem on tournaments (except for three tournaments, $T_3^{c}, T_5^{c}$ and $T_7^{c}$, every tournament has an antidirected hamiltonian path).
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