Smooth local solutions to weingarten equations and σk\sigma_k-equations

In this paper, we study the existence of smooth local solutions to Weingarten equations and $\sigma_k$-equations. We will prove that, for $2 \leq k \leq n$, the Weingarten equations and the $\sigma_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately

Understanding Governance Structures in Shaping Greenway Implementation in City-Regions: A Case Study in Central Zhejiang Province, China

Greenway implementation in city-regions is a collective action involving a complex range of relations between regional and local agencies, between government departments at the same administrative level, and between adjacent jurisdictions. This paper explores how greenway implementation governance is structured, and why different governance structures result in different greenway implementation processes and outcomes in a city-region. We use a case study approach to a greenway project in central Zhejiang Province (CCCZ), where data are collected through field reconnaissance, in-depth interviews, and document analysis. Preliminary findings reveal that the central Zhejiang Greenway Project has experienced a development from ‘territorially-specialized governance’ to ‘cross-scale governance’. ‘Double-hatted’ agencies comprising government leaders and professional representatives from different agencies can create cross-scale institutional linkages both vertically (across levels of governments) and horizontally (across jurisdictions an

Illusion optics: The optical transformation of an object into another object

We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a virtual boundary into that of the object chosen for the illusion, regardless of the profile of the incident wave. This type of illusion device also enables people to see through walls. Our work extends the concept of cloaking as a special form of illusion to the wider realm of illusion optics.Comment: Including a paper and its auxiliary materia

On the nature of X(3960)

A near-threshold enhancement in the $D_s^+ D_s^-$ system, dubbed as $X(3960)$, is observed by the LHCb collaboration recently. A combined analysis on $\chi_{c0}(3930)~(\to D^+ D^-)$, $X(3960)~(\to D_s^+ D_s^-)$, and $X(3915)~(\to J/\psi\omega)$ is performed using both a $K$-matrix approach of $D_{(s)}\bar{D}_{(s)}$ four-point contact interactions and a model of Flatt\'e-like parameterizations. The use of the pole counting rule and spectral density function sum rule %provides consistent evidence indicate, under current statistics, that this $D_s^+ D_s^-$ near-threshold state has probably the mixed nature of a $c\bar{c}$ confining state and $D_s^+ D_s^-$ continuum.Comment: 8 pages, 4 figures, 5 table