Device for simultaneous measurement of the Peltier and Seebeck coefficients verification of the Kelvin relation

We have designed and built an experimental device, which we called a "thermoelectric bridge." Its primary purpose is simultaneous measurement of the relative Peltier and Seebeck coefficients. The systematic errors for both coefficients are equal with this device and manipulation is not necessary between the measurement of one coefficient and the other. Thus, this device is especially suitable for verifying their linear relation postulated by Lord Kelvin. Also, simultaneous measurement of thermal conductivity is described in the text. A sample is made up of the couple nickel¿platinum, taking measurements in the range of ¿20¿60°C and establishing the dependence of each coefficient with temperature, with nearly equal random errors ±0.2%, and systematic errors estimated at ¿0.5%. The aforementioned Kelvin relation is verified in this range from these results, proving that the behavioral deviations are ¿0.3% contained in the uncertainty ±0.5% caused by the propagation of errors

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.