Carleman Estimates for the Schrdinger Equation and Applications to an Inverse Problem and an Observability Inequality

The authors prove Carleman estimates for the Schrdinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining Lp-potentials. An L2-level observability inequality and unique continuation results for the Schrdinger equation are also obtained.     

Efficacy of physical exercise using the balance board game on physical and psychological function in patients with hematological malignancies confined to a bioclean room

Objective: This study aimed to define the efficacy and features of physical therapy (PT) using the Nintendo Wii Fit U (Nintendo Inc., Kyoto, Japan) in patients with hematological malignancies confined to a bioclean room. Method: A total of 33 patients with hematological malignancies confined to a bioclean room were enrolled in this study. This study was designed as a randomized crossover test between two weeklong interventions: PT program (Therapist PT) and Wii Fit U program (Wii PT). We compared the efficacy of Wii PT and Therapist PT with regard to physical and psychological function test scores. Results: Of the 33 patients, 22 were analyzed. The validity of the crossover design was demonstrated, as there were no significant differences in period and carryover effects between the two groups. Therapist PT resulted in significantly better improvements in fatigue scores and total mood disturbance (TMD) scores in the Profile of Mood States short-form Japanese version compared to Wii PT (fatigue score, -5.2±8.3 vs 2.7±8.2; TMD score, -22.5±32.8 vs -2.6±20.5; p<0.05). Physical function improved post-Wii PT and post-Therapist PT interventions (p<0.05), and there was no difference in treatment effect. Conclusion: Improvements in physical function were clearly observed following the use of Wii PT in patients confined to a bioclean room. However, compared to Therapist PT, Wii PT was less effective in improving the psychological function of patients.     

Frequency Doubling of a Laser Diode Using a Domain-Inverted LiTaO3Waveguide with a Monolithic Bragg Reflector

We report wavelength stabilization of a laser diode using a highly efficient distributed Bragg reflector (DBR) grating formed on a LiTaO₃ quasi-phase-matched second harmonic generation (QPM-SHG) device. Fabricating the second-order DBR on the LiTaO₃ waveguide, the reflectivity of 90% and FWHM wavelength bandwidth of 0.2 nm were obtained. By stabilizing the oscillation wavelength of the laser diode, 3.1 mW of blue light was generated in the QPM-SHG device with the monolithic grating.     

Two-Dimensional Parabolic Inverse Source Problem with Final Overdetermination in Reproducing Kernel Space

A new method of the reproducing kernel Hilbert space is applied to a twodimensional parabolic inverse source problem with the final overdetermination. The exact and approximate solutions are both obtained in a reproducing kernel space. The approximate solution and its partial derivatives are proved to converge to the exact solution and its partial derivatives, respectively. A technique is proposed to improve some existing methods. Numerical results show that the method is of high precision, and confirm the robustness of our method for reconstructing source parameter.     

GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES

§1. Introduction √ Let k ∈R, λ> 0 and i = ?1. We consider an acoustic scattering problem by animpenetrable obstacle D ? R2: ?u k2u = 0, in R2 \ D, …