Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Rosen-Zener interferometry with Ultracold Atoms

We propose a time-domain "interferometer" based on ultracold Bose atoms loaded on a double well potential. By the adiabatic Rosen-Zener process, the barrier between two wells is ramped down slowly, held for a while, then ramped back. Starting with a coherent state of double well system, the final occupations on one well show interesting interference fringes in the time-domain. The fringe pattern is sensitive to the initial state, the interatomic interaction, and the external forces such as gravity which can change the shape of the double well. In this sense, this interferometric scheme has the potentials for precision measurements with ultracold atoms. The underlying mechanism is revealed and possible applications are discussed.Comment: 4 pages, 5 figure

The Determinants of the TV Demand for Soccer: Empirical Evidence on Italian Serie A for the Period 2008-2015

This article investigates the determinants of the TV audience for Italian soccer in seven Serie A seasons (2008-2009 to 2014-2015). Italian viewers have committed behavior and that outcome uncertainty does not have an impact on the TV audience. When choosing whether to watch a match involving teams other than their favorite team, Italian consumers are attracted by both the aggregate quantity of talent and the matches involving teams at the top of the table. An increase in the TV demand is driven by an enhancement in the performance of the top clubs and in the quality of the entertainment

Landau-Zener Tunnelling in a Nonlinear Three-level System

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.Comment: 8 pages, 8 figure

Rosen-Zener Transition in a Nonlinear Two-Level System

We study Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstern Condensates (BECs) are discussed.Comment: 8 pages, 8 figure

Improved kidney function in patients who switch their protease inhibitor from atazanavir or lopinavir to darunavir

OBJECTIVE: Atazanavir (ATV) and lopinavir (LPV) have been associated with kidney disease progression in HIV positive patients, with no data reported for darunavir (DRV). We examined kidney function in patients who switched their protease inhibitor from ATV or LPV to DRV. DESIGN: Cohort study. METHODS: Data were from the UK CHIC study. We compared pre and post switch estimated glomerular filtration rate (eGFR) slopes (expressed in ml/min per 1.73 m2 per year) in all switchers and those with rapid eGFR decline (>5 ml/min per 1.73 m2 per year) on ATV or LPV. Mixed-effects models were adjusted for age, gender, ethnicity, eGFR at switch and time updated CD4þ cell count, HIV RNA and cumulative tenofovir (tenofovir disoproxil fumarate) exposure. RESULTS: Data from 1430 patients were included. At the time of switching to DRV, median age was 45 years, 79% were men, 76% had an undetectable viral load, and median eGFR was 93 ml/min per 1.73 m2 . Adjusted mean (95% confidence interval) pre and post switch eGFR slopes were 0.84 (1.31, 0.36) and 1.23 (0.80, 1.66) for ATV (P < 0.001), and 0.57 (1.09, 0.05) and 0.62 (0.28, 0.96) for LPV (P < 0.001). Stable or improved renal function was observed in patients with rapid eGFR decline on ATV or LPV who switched to DRV [15.27 (19.35, 11.19) and 3.72 (1.78, 5.66), P < 0.001 for ATV, 11.93 (14.60, 9.26) and 0.87 (0.54, 2.27), P < 0.001 for LPV]. Similar results were obtained if participants who discontinued tenofovir disoproxil fumarate at the time of switch were excluded. CONCLUSIONS: We report improved kidney function in patients who switched from ATV or LPV to DRV, suggesting that DRV may have a more favourable renal safety profile

Note on New KLT relations

In this short note, we present two results about KLT relations discussed in recent several papers. Our first result is the re-derivation of Mason-Skinner MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations directly to MHV amplitude. Our second result is the equivalence proof of the newly discovered S_{n-2} permutation symmetric KLT relations and the well-known S_{n-3} permutation symmetric KLT relations. Although both formulas have been shown to be correct by BCFW recursion relations, our result is the first direct check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction

Improved harmonic approximation and the 2D Ising model at T≠TcT\neq T_{c} and h≠0h\neq0

We propose a new method to determine the unknown parameter associated to a self-consistent harmonic approximation. We check the validity of our technique in the context of the sine-Gordon model. As a non trivial application we consider the scaling regime of the 2D Ising model away from the critical point and in the presence of a magnetic field $h$. We derive an expression that relates the approximate correlation length $\xi$, $T-T_c$ and $h$.Comment: 11 pages, Latex, 3 figures. Accepted for publication in Journal of Physics