First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

We show that a single Bell's inequality with two dichotomic observables for each observer, which originates from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin's theorem is proved in its most general form from which it follows that for pure states Bell's nonlocality and quantum entanglement are equivalent.

Higher levels of body fat are associated with increased risk for development of numerous adverse health conditions. Phytochemicals are potential agents to inhibit differentiation of preadipocytes, stimulate lipolysis, and induce apoptosis of existing adipocytes, thereby reducing adipose tissue mass. Resveratrol decreased adipogenesis and viability in maturing preadipocytes; these effects were mediated not only through down-regulating adipocyte specific transcription factors and enzymes but also by genes that modulate mitochondrial function. Additionally, resveratrol increased lipolysis and reduced lipogenesis in mature adipocytes. In addition, combining resveratrol with other natural products produced synergistic activities from actions on multiple molecular targets in the adipocyte life cycle. Treatment of mice with resveratrol alone was shown to improve resistance to weight gain caused by a high-fat diet. Moreover, dietary supplementation of aged ovariectomized rats with a combination of resveratrol and vitamin D, quercetin, and genistein not only decreased weight gain but also inhibited bone loss. Combining several phytochemicals, including resveratrol, or using them as templates for synthesizing new drugs, provides a large potential for using phytochemicals to target adipocyte adipogenesis, apoptosis, and lipolysis.