En空间中张角定理及其应用

本文利用单形的体积公式,得到了n维欧氏空间Eⁿ中的张角定理,由此又证得了单形中的一组恒等式,利用这组恒等式给出了Safta猜想在Eⁿ空间中的加强形式．     

Products of two 1ϕ1 series and implications

An expansion formula into bivariate formal power series is established that implies, as consequences, three remarkable identities of partial theta functions due to Warnaar (2003), Schilling–Warnaar (2002) and Andrews–Warnaar (2007).     

Serrin-Type Overdetermined Problem in $\mathbb H^n$

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $\sigma_k(D^2u-uI)=C_n^k$ in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a $P$ function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.     

与Faa di Bruno公式相关的一些奇异恒等式

文[1]用Faa di Bruno公式找到了一些关于分拆集上求和奇异的恒等式,本文利用类似的方法找到了另外的一些奇异恒等式,并且利用Lagrange公演公式得到一个论。