Considering singular Sturm--Liouville differential expressions of the type \[ \tau_{\alpha} = -(d/dx)x^{\alpha}(d/dx) + q(x), \quad x \in (0,b), \; \alpha \mathbb{R}, \] we employ some Sturm comparison-type results in spirit Kurss to derive criteria for $\tau_{\alpha}$ be limit point and circle case at $x=0$. More precisely, if $\alpha \mathbb{R}$ $0 0$ such that $0<x$ sufficiently small, \begi...

In mammals, 7 distinct genes encoding CK1 isoforms (CK1 alpha, CK1 beta, CK1 gamma1, CK1 gamma2, CK1 gamma3, CK1 delta and CK1 epsilon) are expressed which differ mainly in length and primary structure of the C-terminal non-catalytic domain. Furthermore, CK1 alpha splice variants have been detected in many different organisms including vertebrates and mammals. Alternative splicing leads to the ...