Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Applications of Treatment Effects Models and Semiparametric Estimation

This thesis is composed of an introductory chapter and four applications each of them constituting an own chapter. The common element underlying each of the chapters is the econometric methodology. The applications rely mostly on the leading econometric techniques related to estimation of causal effects. The first chapter introduces the econometric techniques that are employed in the remaining chapters. Chapter 2 studies the effects of shocking news on student performance. It exploits the fact that the school shooting in Kauhajoki in 2008 coincided with the matriculation examination period of that fall. It shows that the performance of men declined due to the news of the school shooting. For women the similar pattern remains unobserved. Chapter 3 studies the effects of minimum wage on employment by employing the original Card and Krueger (1994; CK) and Neumark and Wascher (2000; NW) data together with the changes-in-changes (CIC) estimator. As the main result it shows that the employment effect of an increase in the minimum wage is positive for small fast-food restaurants and negative for big fast-food restaurants. Therefore, it shows that the controversial positive employment effect reported by CK is overturned for big fast-food restaurants and that the NW data are shown, in contrast to their original results, to provide support for the positive employment effect. Chapter 4 employs the state-specific U.S. data (collected by Cohen and Einav [2003; CE]) on traffic fatalities to re-evaluate the effects of seat belt laws on the traffic fatalities by using the CIC estimator. It confirms the CE results that on the average an implementation of a mandatory seat belt law results in an increase in the seat belt usage rate and a decrease in the total fatality rate. In contrast to CE, it also finds evidence on compensating-behavior theory, which is observed especially in the states by the border of the U.S. Chapter 5 studies the life cycle consumption in Finland, with the special interest laid on the baby boomers and the older households. It shows that the baby boomers smooth their consumption over the life cycle more than other generations. It also shows that the old households smoothed their life cycle consumption more as a result of the recession in the 1990s, compared to young households.