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We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a “two point” local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a certain nonresonance property at zero frequency. The second result, which also requires the almost symmetry condition, is to establish an exponential trichotomy in the energy space via finite dimensional time dependent stable and unstable sub-spaces, with an infinite dimensional complement on which solutions disperse via the usual local energy decay estimate.

We prove integrated local energy decay for solutions to the inhomogeneous Maxwell system on a general class of spherical black hole backgrounds.

We prove that the critical Maxwell-Klein-Gordon equation on ℝ4+1 is globally wellposed for smooth initial data which are small in the energy norm. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.

Background: This multicenter study aimed to examine the reasons for prosthesis rejection and assess the quality of life (QOL) among patients with upper limb deficiency., Methods: Three rehabilitation centers in Japan and 1 academic medical center in the United States participated. Patients between the age of 12 and 75 years with unilateral or bilateral upper limb absence from the level of wrist to shoulder disarticulation were included. Two questionnaires were used, an original questionnaire on prosthesis use and the EQ-5D, which were completed by both the participant and a live-in proxy., Results: Of the 367 patients with upper limb loss invited, 174 patients participated in this study. Eighty percent of the study population were male patients. The most common amputation level was transradial. Trauma was the most common cause of limb loss. The prosthesis rejection rate was 9% (n = 16). The most common reason for abandonment was a lack of prosthesis functionality. Ten of 16 prosthesis nonusers (63%) and 59 prosthesis users (38%) were unemployed or students. The mean EQ-5D utility score was significantly higher in prosthesis users than in nonusers (0.762 versus 0.628, P < 0.01). Live-in proxies significantly overestimated QOL in male patients (0.77 versus 0.807, P =0.01)., Conclusions: The current prosthesis rejection rate is low. QOL was significantly higher in prosthesis users than in nonusers. More prosthesis users were employed compared with nonusers. Care should be taken not to overestimate the QOL of male patients with upper limb loss as their proxies often did.