Supported by NSF C(11875196,11375121,11205125,11005016);Xihua University Talent Project(Z201021)。
A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremal...
Supported by NSFC(Grant Nos.11531011,11671320,11601431,11871034 and U1803263);the China Postdoctoral Science Foundation(Grant No.2016M600813);the Natural Science Foundation of Shaanxi Province(Grant No.2017JQ1019)
Let Η be a hypergraph with n vertices. Suppose that di,¢/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t...
partially supported by the Russian Geographical Society(grant No.13-05-41378)
An increase in the extremality of natural processes is a consequence of warming, aridization, and desertification. The authors consider the processes of warming, aridization, and desertification to be the parts of a s...
The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Sch...
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10501046).
Given a compact Riemann surface S with finitely many punctures, in this paper we obtain a new extremality property of a Jenkins-Strebel differentialψon S. As a consequence, we obtain the solutions of several kinds of...
Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a doubl...
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its...
the National Natural Science Foundation of China (Grant No. 10071008).
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combinatio...
the National Natural Science Foundation of China!(No.19531060), the DoctoralProgram Fundation of the Ministry of Education o
It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ,r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and there ...
Consider the Teichmuller mapping f associated with in the unit disc D and the class of all quasiconformal mappings in D with the boundary values of f. For a special holomorphic function, the present paper gives the ne...