Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

We prove that, the initial value problem associated to u_{t} + i\alphau_{xx} + \beta u_{xxx} + i\gamma |u|^{2}u = 0, x,t \in R, is locally well-posed in Sobolev spaces H^{s} for s>-1/4

A note on local well-posedness of generalized KdV type equations with dissipative perturbations

In this note we report local well-posedness results for the Cauchy problems associated to generalized KdV type equations with dissipative perturbation for given data in the low regularity $L^2$-based Sobolev spaces. The method of proof is based on the {\em contraction mapping principle} employed in some appropriate time weighted spaces.Comment: 14 page

Finite torsors over strongly FF-regular singularities

In this paper, we extend the work by K. Schwede, K. Tucker, and the author on the local \'etale fundamental group of strongly $F$-regular singularities. Let $k$ be an algebraically closed field of positive characteristic. We study the existence of finite torsors over the regular locus of a strongly $F$-regular $k$-germ $(R,\mathfrak{m},k)$ that do not come from restricting a torsor over the whole spectrum. Concretely, we prove that there exists a finite cover $R \subset R^{\star}$ with the following properties: $R^{\star}$ is a strongly $F$-regular $k$-germ, and for all finite group-schemes $G/k$ with solvable connected-component-at-the-identity, every $G$-torsor over the regular locus of $R^{\star}$ extends to a $G$-torsor over the whole spectrum. To achieve this, we obtain a generalized transformation rule for the $F$-signature under finite extensions. This formula also proves that degree-$n$ Veronese-type cyclic covers over $R$ stay strongly $F$-regular with $F$-signature $n \cdot s(R)$. Similarly, this transformation rule is used to show that the torsion of the divisor class group of $R$ is bounded by $1/s(R)$. By taking cones, we show that the torsion of the divisor class group of a globally $F$-regular $k$-variety is bounded in terms of $F$-signatures.Comment: 35 pages, the solvable case was completed, comments are so much welcom

BC Bootstrap Confidence Intervals for Random Effects Panel Data Models

We study the application of bootstrap procedures to the problem of constructing confidence intervals for the coefficients of random effects panel data models, based on GLS point estimation. The central problem is the one of adequately resampling from the estimated residuals of the model, avoiding violations of the structural features of the random shocks.

Statistical Calibration: a simplification of Foster's Prof

Consider the following problem: at each date in the future, a given event may or may not occur, and you will be asked to forecast, at each date, the probability that the event will occur in the next date. Unless you make degenerate forecasts (zero or one), the fact that the event does or does not occur does not prove your forecast wrong. But, in the long run, if your forecasts are accurate, the conditional relative frequencies of occurrence of the event should approach your forecast. [4] has presented an algorithm that, whatever the sequence of realizations of the event, will meet the long-run accuracy criterion, even though it is completely ignorant about the real probabilities of occurrence of the event, or about the reasons why the event occurs or fails to occur. It is an adaptive algorithm, that reacts to the history of forecasts and occurrences, but does not learn from the history anything about the future: indeed, the past need not say anything about the future realizations of the event. The algorithm only looks at its own past inaccuracies and tries to make up for them in the future. The amazing result is that this (making up for past inaccuracies) can be done with arbitrarily high probability! Alternative arguments for this result have been proposed in the literature, remarkably by [3], where a very simple algorithm has been proved to work, using a classical result in game theory: Blackwell´s approachability result, [1]. Very recently, [2] has especialized Blackwell´s theorem in a way that (under a minor modification of the algorithm) simplifies the argument of [3]. Here I present such modification and argument.

Impacts of Climate Change on Human Development

human development, climate change

Incentive-compatible Fiscal Constitutions

It is a fact that in most of the countries (both currently and historically) the wealthier a person is, the higher the amount that he or she has to pay in taxes. This feature of a tax system was actually considered by Adam Smith as the first maxim of a good tax regime. In the Wealth of Nations (book 5, chapter 2, part 2), Smith stated this equality principle as: “The subjects of every state ought to contribute towards the support of the government... in proportion to the revenue which they respectively enjoy under the protection of the state.” On the other hand, the literature on the economy of the state proposes that: • One important reason for the existence of states is that the society needs an agent who can protect it from foreign predation. • A good characterization of the behavior of the state must treat it as a private enterprise, interested in maximizing the rents of the ruling elite. • The focus of the research of constitutional political economists should be the design of Constitutions that provide the state with the incentives to do the job that it is supposed to. In this paper, we attempt to associate all the previous ideas. We analyze the problem in a very simple Principal-Agent framework. Under imperfect information, we assume that the problem of the society is precisely to design a fiscal constitution such that the state has the incentives to protect the wealth of the society. The interesting result is that, under mild assumptions, such incentive compatible constitution implies a strictly increasing dependance of taxes on the wealth of the tax payer. As a by-product, we also find that such constitution cannot be Pareto efficient. The paper is organized as follows. In the next section, some related literature is reviewed. Then, the next two sections set up and solve the problem. As a comparison benchmark, a Pareto efficient constitution is derived. Those are the two most important parts of the paper. The model has assumptions that range from purely technical to strong economic simplifications. For that reason, before stating the concluding remarks we discuss the assumptions and main weaknesses of the paper. An appendix includes a related problem and the proof of one of the results.

What does fairness imply?

Decades back, a most prominent justice philosopher, John Rawls, put forth a clear definition of fairness in problems of social choice. Decision theory, which studies individual, and not social, choice has provided axiomatizations of decision rules in many settings, most prominently in settings where individuals face uncertainty (and not just risk). It turns out that there exists an analytical connection between these two branches of thought. This note exploits the aforementioned connection, by reading the social choice problem in terms of decision theory and (partially) exploiting the existing axiomatization. The purpose of the note is to obtain new and interesting questions more than it is to answer them, so it concludes by proposing a research problem.