CONJECTURES

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相关机构：电子科技大学更多>>
相关期刊：《Science China(Physics,Mechanics & Astronomy)》《Journal of Mathematical Research with Applications》《Science China Mathematics》《Communications in Theoretical Physics》更多>>
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Minuscule representations and Panyushev conjectures Dedicated to the Memory of Professor Bertram Kostant
《Science China Mathematics》2018年第10期1759-1774,共16页Chaoping Dong Guobiao Weng 
supported by National Natural Science Foundation of China(Grant No.11571097)
Recently, Panyushev(2015) raised five conjectures concerning the structure of certain root posets arising from Z-gradings of simple Lie algebras. This paper aims to provide proofs for four of them. Our study also link...
关键词：minuscule poser M-polynomial X-polynomial Z-gradings of Lie algebra 
Fekete and Szeg problem in one and higher dimensions被引量：4
《Science China Mathematics》2018年第10期1775-1788,共14页Qinghua Xu Taishun Liu Xiaosong Liu 
supported by National Natural Science Foundation of China(Grant Nos.11561030,11261022 and 11471111);the Jiangxi Provincial Natural Science Foundation of China(Grant Nos.20152ACB20002 and 20161BAB201019);Natural Science Foundation of Department of Education of Jiangxi Province of China(Grant No.GJJ150301)
In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach...
关键词：Fekete and Szego problem Bieberbach conjectures in several complex variables subclasses ofstarlike mappings sharp coefficient bound 
Some conjectures on modular representations of affine sl_2 and Virasoro algebra被引量：2
《Science China Mathematics》2018年第2期385-390,共6页Weiqiang Wang 
supported by the National Science Foundation of USA(Grant No. DMS1405131)
We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset c...
关键词：Virasoro algebra affine algebras module representation 
Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences被引量：2
《Science China Mathematics》2014年第11期2429-2435,共7页WANG Yi ZHU BaoXuan 
supported by National Natural Science Foundation of China(Grant Nos.11071030,11201191 and 11371078);Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110041110039);National Science Foundation of Jiangsu Higher Education Institutions(GrantNo.12KJB110005);the Priority Academic Program Development of Jiangsu Higher Education Institutions(Grant No.11XLR30)
In 2012,Zhi-Wei Sun posed many conjectures about the monotonicity of sequences of form {n√zn},where {zn} is a familiar number-theoretic or combinatorial sequence. We show that if the sequence {zn+1/zn}is increasing(r...
关键词：SEQUENCES MONOTONICITY LOG-CONVEXITY LOG-CONCAVITY 
Proof of three conjectures on congruences被引量：2
《Science China Mathematics》2014年第10期2091-2102,共12页PAN Hao SUN Zhi-Wei 
supported by National Natural Science Foundation of China(Grant Nos.10901078 and 11171140)
This paper proves three conjectures on congruences involving central binomial coefficients or Lucas sequences.Let p be an odd prime and let a be a positive integer.It is shown that if p=1（mod 4）or a〉1then [3/4pa]∑...
关键词：congruences modulo prime powers Fibonacci numbers Lucas sequences 
Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of SCIENCE CHINA on the occasion of its 60th birthday
《Science China Mathematics》2010年第1期105-114,共10页FU BaoHua Institute of Mathematics, Academy of Mathematic and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 
We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.
关键词：Chow groups ABELIAN varieties Bloch-Beilinson CONJECTURES Beauville CONJECTURE Murre CONJECTURE 
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