单位圆内无穷级亚纯函数的T-半径和Borel半径

设E1=argz=θj|0≤θ1<θ2<…<θq1<2π,E2=argz=φj0≤φ1<φ2<…<φq2<2π,且E1∩E2=Φ,q1和q2是任意正整数.证明了(1)存在Δ内下级为任一正数的无穷级亚纯函数f(z),恰以E1∪E2为其T-半径且恰以E2为其Borel半径;(2)存在Δ内下级为无穷的亚纯函数g(z),恰以E1∪E2为其Borel半径且恰以E2为其T-半径.

单位圆内有穷正级亚纯函数的T-半径和Borel半径

作者证明了对任意正数λ,正整数q_1和q_2,记E_1={argz=θ_j|0≤θ_1<θ_2<…<θ_(q_1)<2π},E_2={argz=φ_j|0≤φ_1<φ_2<…<φ_(q_2)<2π},使得E_1∩E_2=。则(ⅰ)存在单位圆内的λ级亚纯函数f(z),恰以E_1∪E_2为其T-半径且恰以E_2为其Borel半径,(ⅱ)存在单位圆内级和下级均为λ的亚纯函数g(z),恰以E_1∪E_2为其Borel半径且恰以E_2为其T-半径。

Influences of fillet radius and draft angle on local loading process of titanium alloy T-shaped components

In order to study influences of geometric parameters on the T-shaped components local loading process, a new mathematical model considering the fillet radius and draft angle was established by using the slab method. The results obtained by the mathematical model agree with the data form experiment and numerical simulation, and the results are closer to the experimental and simulation results. The influence of draft angle may be neglected under the forming conditions used. The influence of fillet radius is notable, especially in the case that the ratio of fillet radius to rib width is less than 0.75.