Understanding the Roles of Genius and Taste in the Production of Beauty:A Kantian Approach to Artistic Intention

The intention of achieving objectives through art seemingly conflicts with Kant's tenet that judgments of taste should be devoid of conceptual determinations.According to Kant,beautiful art must be viewed as the product of genius,a rare gift of nature that operates through the work of aesthetic ideas.This prompts inquiries into the respective roles of genius and taste in the production of beautiful art.It has been proposed that genius is a mere concept,a universal capacity,or a collaborator with taste,but these accounts are found to be deficient.Drawing upon Kant's distinction between free beauty and adherent beauty,this paper demonstrates that genius is neither sufficient nor necessary to produce beautiful art.Furthermore,this paper investigates the significance of taste in artistic production,taking into consideration the autonomy and refinement of taste over time.

Kobayashi＇s and Teichmiiller＇s Metrics on the Teichmiiller Space of Symmetric Circle Homeomorphisms

We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.

A function model for the Teichmüller space of a closed hyperbolic Riemann surface

We introduce a function model for the Teichmüller space of a closed hyperbolic Riemann surface.Then we introduce a new metric on the Teichmüller space by using the maximum norm on the function space.We prove that the identity map from the Teichmüller space equipped with the Teichmüller metric to the Teichmüller space equipped with this new metric is uniformly continuous. Moreover, we prove that the inverse of the identity, i.e., the identity map from the Teichmüller space equipped with this new metric to the Teichmüller space equipped with the Teichmüller metric, is continuous(but not uniformly). Therefore, the topology induced by the new metric is the same as the topology induced by the Teichmüller metric on the Teichmüller space.Finally, we give a remark about the pressure metric on the function model and the Weil-Petersson metric on the Teichmüller space.

Mesh-Free Interpolant Observables for Continuous Data Assimilation

This paper is dedicated to the expansion of the framework of general interpolant observables introduced by Azouani,Olson,and Titi for continuous data assimilation of nonlinear partial differential equations.The main feature of this expanded framework is its mesh-free aspect,which allows the observational data itself to dictate the subdivision of the domain via partition of unity in the spirit of the so-called Partition of Unity Method by Babuska and Melenk.As an application of this framework,we consider a nudging-based scheme for data assimilation applied to the context of the two-dimensional Navier-Stokes equations as a paradigmatic example and establish convergence to the reference solution in all higher-order Sobolev topologies in a periodic,mean-free setting.The convergence analysis also makes use of absorbing ball bounds in higherorder Sobolev norms,for which explicit bounds appear to be available in the literature only up to H^(2);such bounds are additionally proved for all integer levels of Sobolev regularity above H^(2).

Geometric Gibbs theory

We extend the classical Gibbs theory for smooth potentials to the geometric Gibbs theory for certain continuous potentials.We study the existence and uniqueness and the compatibility of geometric Gibbs measures associated with these continuous potentials.We introduce a complex Banach manifold structure on the space of these continuous potentials as well as on the space of all geometric Gibbs measures.We prove that with this complex Banach manifold structure,the space is complete and,moreover,is the completion of the space of all smooth potentials as well as the space of all classical Gibbs measures.There is a maximum metric on the space,which is incomplete.We prove that the topology induced by the newly introduced complex Banach manifold structure and the topology induced by the maximal metric are the same.We prove that a geometric Gibbs measure is an equilibrium state,and the in mum of the metric entropy function on the space is zero.

Slodkowski定理的Chirka证明的一些注解(英文)

通过在一个积分算子上运用Schauder不动点定理,Chirka对Slokowski的全纯运动扩张定理提供了一个优美的简单证明.本文中,作者对构造此证明的启发提供一个参考同时用此方法通过不同方式来构造全纯扩张.一个自然的问题是研究这些用不同方式得到的全纯扩张是否相同.因此对全纯扩张唯一性已有的判断法提供一个简单的综述.最后介绍在全纯扩张唯一性存在时的一个应用.