Differentiability Properties of Log-Analytic Functions

Restricted Log-Exp-Analytic Functions and some Differentiability Results

In this article we define restricted log-exp-analytic functions as compositions of log-analytic functions and exponentials whose logarithm are locally bounded. We prove that the derivative of a restricted log-exp-analytic function is again restricted log-exp-analytic and that such a function exhibits strong quasianalytic properties. We establish the parametric version of Tamm's theorem for this class of functions.

随机性与可微性

Randomness and Differentiability

我们通过有效函数的可微性来描述一些主要的算法随机性概念。(1)作为主要结果，我们证明了[0，1]中的实数z是可计算随机的当且仅当每个非减可计算函数[0，1]->R在z处可微. (2)证明了[0，1]中的实数z是弱2-随机的当且仅当每个几乎处处可微的可计算函数[0，1]->R在z处可微. (3)重铸经典语言的结果可以追溯到1975年的建构主义者Demuth，我们表明，真正的z是ML随机的当且仅当每个可计算的有界变差函数是可微的z，同样的绝对连续的功能。我们还使用我们的分析方法来表明，可计算的随机性的真正的基础不变，并得出其他的保存结果的随机性概念。

实解析受限对数-指数解析函数的全局复化

Global Complexification of Real Analytic Restricted Log-Exp-Analytic Functions

本文证明实解析受限对数-指数解析函数存在保持同一函数类的全纯延拓，并进一步给出该结论的参数化版本。

对数解析函数的增长

Growth of Log-Analytic Functions

本文研究对数解析函数的增长性，证明一元函数是多项式有界的，指出高维全局情形可能呈指数增长，并证明其在包含无穷远射线芽的可定义集上多项式有界。

Analytic Tableaux for Justification Logics

In this paper we present analytic tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a syntactic proof of cut elimination. We also show the subformula property for our tableaux, and prove the decidability of justification logics for finite constant specifications.

Analytic continuations of log-exp-analytic germs

We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface of the logarithm. As one application, we give an upper bound on the logarithmic-exponential complexity of the compositional inverse of an infinitely increasing such germ, in terms of its own logarithmic-exponential complexity and its level. As a second application, we strengthen Wilkie's theorem on definable complex analytic continuations of germs belonging to the residue field of the valuation ring of all polynomially…