All the more reason to cut corners and jump curves.
First, to stay alive a company has to be willing;and able to jump curves.
Based on those, by using the exponential conformal mapping, Riemann boundary value problems for periodic sectionally holomorphic functions with periodic closed and periodic quasi-closed contours as their jump curves are solved.
That's because "most organizations define themselves in terms of what they do," he said, "instead of thinking 'what benefit do we provide the customer?' True innovation comes when you jump curves, not when you duke it out for 10% or 15% better".
In fact, it is obvious that the above Φ is a periodic sectionally holomorphic function whose jump curve is L such that (3.5), (2.15), and (2.20) hold.
In [7], Lu mainly discussed PR problems with periodic closed contour as the jump curve and PH problems on the real axis for bounded solutions.
({P R}_{m,n}) problem: Find a periodic sectionally holomorphic function (Phi z)) with L as the jump curve such that left { textstylebegin{array}l} Phi^(t)=G t)Phi^(t)+g(t),quad tin L, operatorname{eOrd}[Phi](+infty i leq n, operatorname{eOrd}[Phi] -infty i)leq m, end{array}disPhi] -inftyi leq
({R}_{m+n}) problem: Find a sectionally holomorphic function (Phi_{sharp}(w)), with Γ as the jump curve, such that left { textstylebegin{array}l} Phi^_{sharp} tau)=G_{sharp} tau Phi^_{sharp} tau )+g_{sharp} tau), quadtauinGamma, operatorname{Ord}[Phi_{sharp}](infty)leq m+n.
({R}_{m,n}^) problem: Find a sectionally meromorphic function (Phi_(w)) having possible pole point at (w=0), with Γ as the jump curve, such that left { textstylebegin{array}l} Phi^ tau)=G_ tau Phi^ tau)+g_ tau),quad tauinGamma, operatorname{Ord} [Phi_ ](0)leq n, operatorname{Ord} [Phi_ ](infty)leq m, end{array}displaystyle right.
The PR problem is formulated as follows (see [7]): Find a periodic sectionally holomorphic function (Phi z)) with L as the jump curve such that Phi^(t)=G t)Phi^(t)+g(t),quad tin L, (2.3) where G and g are given on L with the period aπ, that is, G(t+api =G t),qquad g(t+api =g(t), (2.4) satisfying the normal type condition G t)neq0,quad tin L, (2.5) and the Hölder conditions Gin H(L),quad gin H L).
