The Most Beautiful Times

The Most Beautiful Times is a series of narrative depicting a woman\u27s psychological experiences with sexual passion, in which she struggles, suffers, submits, and sacrifices. It is in these moments that profound emotions exist, which transform the meaning of her life. This body of work is both literal and metaphorical, as well as remembered and fantasized. The work is based on real experiences re-imagined in constructed images to examine the character\u27s internal conflicts, her loss of innocence and desire. The work explores how a story can be told through freezing performance as still frames, as well as how and to what extent a personal story can be revealed through still images, while at the same time can convey universal emotions and sensual sentiments shared by human beings

Central Limit Theorems in Deterministic Systems

This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in dynamic system in the cases of martingale and backward martingaleComment: 15 page

Soft vibrational mode associated with incommensurate orbital order in multiferroic CaMn7_7O12_{12}

We report inelastic light scattering measurements of lattice dynamics related to the incommensurate orbital order in $\mathrm{CaMn_7O_{12}}$. Below the ordering temperature $T_\mathrm{o} \approx 250 \,\mathrm{K}$, we observe extra phonon peaks as a result of Brillouin-zone folding, as well as a soft vibrational mode with a power-law $T$-dependent energy, $\Omega = \Omega_{0}(1 - T/T_{\mathrm{o}})^{1/2}$. This temperature dependence demonstrates the second-order nature of the transition at $T_\mathrm{o}$, and it indicates that the soft mode can be regarded as the amplitude excitation of the composite order parameter. Our result strongly suggests that the lattice degrees of freedom are actively involved in the orbital-ordering mechanism.Comment: 7 pages, 8 figure

A Double Saddle-Node Bifurcation Theorem

In this paper, we consider an abstract equation F(lambda, u) = 0 with one parameter lambda, where F epsilon C-P(R x X, Y), p \u3e= 2, is a nonlinear differentiable mapping, and X, Y are Banach spaces. We apply Lyapunov-Schmidt procedure and Morse Lemma to obtain a double saddle-node bifurcation theorem with a two-dimensional kernel. Applications include a perturbed problem and a semilinear elliptic equation