We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ℝn, n ≥ 3, for the magnetic Schrödinger operator with L ∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives. © 2014 Springer-Verlag Berlin Heidelberg.

We prove uniform Lpestimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding result of [3] in the case of Laplace-Beltrami operators on Riemannian manifolds. In doing so, we follow the methods, developed in [1] very closely. We also show that spectral regions in our Lpresolvent estimates are optimal.

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $R^n$ for the perturbed polyharmonic operator $(-\Delta)^m +q$ with $q\in L^{n/2m}$, $n>2m$, determines the potential $q$ in the set uniquely. In the course of the proof, we construct a special Green function for the polyharmonic operator and establish its mapping properties in suitable weighted $L^2$ and $L^p$ spaces. The $L^p$ estimates for the special Green function are derived from $L^p$ Carleman estimates with linear weights for the polyharmonic operator.

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schr\"odinger operator with a gain of two derivatives.

We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric potential in $L^{n/2}_{\text{loc}}(\mathbb{R}^n)$, is purely absolutely continuous. Previously known results in the case of a general metric are obtained in [12], see also [8], under the assumption that the metric, as well as the potential, are reflection symmetric.

We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along the double characteristics are elliptic.

We show that a first order perturbation A(x) · D + q(x) of the polyharmonic operator (-Δ)m, m ≥ 2, can be determined uniquely from the set of the Cauchy data for the perturbed polyharmonic operator on a bounded domain in ℝn, n ≥ 3. Notice that the corresponding result does not hold in general when m = 1. © 2013 American Mathematical Society.

Objectives

To describe the incidence, anthropometric parameters, and clinical significance of weight loss in older outpatients.

Design

Four-year prospective cohort study.

Setting

University-affiliated Veterans Affairs Medical Center.

Patients

Two hundred forty-seven community-dwelling male veterans 65 years of age or older.

Measurements

Anthropometrics (weight, height, skin-folds, and circumferences), health status measures (Sickness Impact Profile scores, health care utilization, self-reported ratings of health), and bloodwork (cholesterol, albumin, others) were obtained at baseline and followed annually for 2 years. Outcome measures (hospitalization, nursing home placement, and mortality rates) were followed for a minimum of 2 years after any identified weight change.

Main results

The mean annual percentage weight change for the study population was -0.5% (SD: +/- 4.0%; range: -17% to +25%). Four percent annual weight loss was determined to be the optimal cutpoint for defining clinically important involuntary weight loss using ROC curve analysis. The annual incidence of this degree of involuntary weight loss was 13.1%. At baseline, involuntary weight losers were similar to nonweight losers in age (73.9 +/- 7.9 vs 73.3 +/- 6.7 years), body mass index (26.8 +/- 3.9 vs 26.9 +/- 4.1 kg/m2), and all other anthropometric, health status, and laboratory measures. Relative to nonweight losers, involuntary weight losers had significantly (P < or = .05) greater decrements in central skinfold and circumference measures (subscapular skinfolds, -2.9 vs -0.4 mm; suprailiac skinfolds, -4.2 vs -0.2 mm; and waist to hip ratio, -.01 vs + .00). Both groups had significant decreases in their triceps skinfolds (an estimate of peripheral subcutaneous fat), whereas arm muscle area and albumin levels did not decline significantly in either group. Over a 2-year follow-up period, mortality rates were substantially higher (RR = 2.43; 95% CI = 1.34-4.41) among involuntary weight losers (28%) than among nonweight losers (11%). Of interest, a similar increase in 2-year mortality (36%) was also observed among subjects with voluntary weight loss (by dieting). Survival analyses adjusting for differences between weight losers and nonweight losers in baseline age, BMI, tobacco use, and other health status and laboratory measures yielded similar results.

Conclusions

These results indicate that involuntary weight loss occurred frequently (13.1% annual incidence) in this population of older veteran outpatients. When involuntary weight loss occurred, the predominant anthropometric changes were decrements in measures of centrally distributed fat (trunkal skinfolds and circumferences). Finally, involuntary weight loss greater than 4% of body weight appears to be clinically important as an independent predictor of increased mortality.

Five studies demonstrated that people selectively use general moral principles to rationalize preferred moral conclusions. In Studies 1a and 1b, college students and community respondents were presented with variations on a traditional moral scenario that asked whether it was permissible to sacrifice one innocent man in order to save a greater number of people. Political liberals, but not relatively more conservative participants, were more likely to endorse consequentialism when the victim had a stereotypically White American name than when the victim had a stereotypically Black American name. Study 2 found evidence suggesting participants believe that the moral principles they are endorsing are general in nature: when presented sequentially with both versions of the scenario, liberals again showed a bias in their judgments to the initial scenario, but demonstrated consistency thereafter. Study 3 found conservatives were more likely to endorse the unintended killing of innocent civilians when Iraqis civilians were killed than when Americans civilians were killed, while liberals showed no significant effect. In Study 4, participants primed with patriotism were more likely to endorse consequentialism when Iraqi civilians were killed by American forces than were participants primed with multiculturalism. However, this was not the case when American civilians were killed by Iraqi forces. Implications for the role of reason in moral judgment are discussed.