Weak existence and uniqueness for forward–backward SDEs

We aim to establish the existence and uniqueness of weak solutions to a suitable class of non-degenerate deterministic FBSDEs with a one-dimensional backward component. The classical Lipschitz framework is partially weakened: the diffusion matrix and the final condition are assumed to be space Hölder continuous whereas the drift and the backward driver may be discontinuous in x$x$. The growth of the backward driver is allowed to be at most quadratic with respect to the gradient term.     

Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle

Summary Given two pointsx, yS ¹ randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle, we consider for each >0 the point process obtained by recording the timesn>0 such that |f ⁿ (x)–f ⁿ (y)|. With the further assumption that the density of is bounded away from zero, we show that when tends to zero the above point process scaled by –1 converges in law to a marked Poisson point process with constant parameter measure. This parameter measure is given explicity by an average on the rate of expansion off.Partially supported by FAPESP grant number 90/3918-5     

XYZ particles at Belle

In this paper, I review recent progress in the study of the XYZ particles at Belle. I only focus on studies with charmonium and one or more light mesons in the final states. This covers the X（3872）, X（3915）, Y（4140）, X（4350）, and the charged Z states.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

Growth and spectroscopic characterization of Er: Sr3Y(BO3)3 crystal

This paper reports the growth and spectroscopic characterization of Er³⁺:Sr₃Y(BO₃)₃ crystal. Er³⁺:Sr₃Y(BO₃)₃ crystal with dimensions up to ∅20×35 mm³ has been grown by Czochralski method. The polarized spectroscopic properties of Er³⁺:Sr₃Y(BO₃)₃ crystal were investigated. Based on the Judd-Ofelt theory, the effective intensity parameters Ω_t were obtained: Ω₂=1.71×10⁻²⁰ cm², Ω₄=1.39×10⁻²⁰ cm², Ω₆=0.74×10⁻²⁰ cm² for π-polarization, and Ω₂=1.77×10⁻²⁰ cm², Ω₄=1.44×10⁻²⁰ cm², Ω₆=0.65×10⁻²⁰ cm² for σ-polarization. The emission cross-section σ_em was calculated to be 4.75×10⁻²¹ cm² for π-polarization at 1536 nm and 6.30×10⁻²¹ cm² for σ-polarization at 1537 nm. The investigated results showed that Er³⁺:Sr₃Y(BO₃)₃ crystal may be regarded as a potential laser host material for 1.55 μm IR solid-state lasers.     

Numerical study of nonlinear Schrödinger and coupled Schrödinger equations by differential transformation method

This paper presents the coupled version of a previous work on nonlinear Schrödinger equation [23]. It focuses on the construction of approximate solutions of nonlinear Schrödinger equations. In this paper, we applied the differential transformation method (DTM) to solving coupled Schrödinger equations. The obtained results show that the technique suggested here is accurate and easy to apply.     

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.