A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

An examination of strategic opportunities provided by the conference committee procedure in the U.S. Congress

Deference to committees in Congress has been a much studied phenomena for close to 100 years. This deference can be characterized as the unwillingness of a potentially winning coalition on the House floor to impose its will on a small minority, a standing committee. The congressional scholar is then faced with two problems: observing such deference to committees, and explaining it. Shepsle and Weingast have proposed the existence of an ex-post veto for standing committees as an explanation of committee deference. They claim that as conference reports in the House and Senate are considered under a rule that does not allow amendments, the conferees enjoy agenda-setting power. In this paper I describe a test of such a hypothesis (along with competing hypotheses regarding the effects of the conference procedure). A random-utility model is utilized to estimate legislators' ideal points on appropriations bills from 1973 through 1980. I prove two things: 1) that committee deference can not be said to be a result of the conference procedure; and moreover 2) that committee deference does not appear to exist at all.

O contraditório no procedimento fiscal para o lançamento de ofício: legitimação democrática, transparência e eficiência administrativa

Esse trabalho se propõe a demonstração que o atual procedimento fiscal para o lançamento de ofício carece de um realinhado com os valores constitucionais da democracia e eficiência através da introdução do direito ao contraditório antes da constituição do crédito tributário. Apesar da redemocratização do país e o reconhecimento e valorização do constitucionalismo como sistema jurídico, ainda se adota no Brasil um sistema inquisitório no procedimento de constituição dos créditos tributários pelo lançamento de ofício. O que significa a vedação ao contribuinte da iniciativa de manifestação para demonstrar a inocorrência dos fatos lhe imputados pela fiscalização. A sua participação durante o procedimento se caracteriza pela passividade, quando se limita ao atendimento das intimações para a apresentação das provas e esclarecimentos do interesse da administração tributária; portanto, o contribuinte não participa da formação do ato administrativo de lançamento tributário, apenas cumpre deveres legais. Assim, procuramos demonstrar que apesar da existência de um processo administrativo fiscal após o lançamento e a suspensão da cobrança, o crédito tributário constituído provoca efeitos jurídicos imediatos negativos aos contribuintes, o que justifica o contraditório durante o próprio procedimento de lançamento e não apenas durante o processo que se forma posteriormente. Também enfatiza-se o reconhecimento desse direito ao apontar a contradição entre a necessária colaboração do contribuinte para a revelação dos fatos geradores de efeitos tributários contra si mesmo e a adoção no Brasil de um sistema inquisitório tomado emprestado dos inquéritos policiais.