. first, according to the definition of modulus of \(\mathfrak {q}\mathbb {c}\) -convexity, we have \(|\nabla \phi (\textbf{p})|>m\) , so $$\begin{aligned} |\nabla (\phi -q)(\textbf{p})| >\frac{m}{2} \end{aligned}$$ (a.20) for any \(q\in {\mathscr {q}}_...
The authors show that a maximum modulus theorem for an analytic function of several complex variables may be derived like in the single variable case from an application of the open mapping theorem for analytic functions, mapping a Banach space into a Banach space, without any application of inte...
A complex Banach space X is complex strictly convex if and only if X-valued analytic functions on the open unit disc in the complex plane satisfy a certain mean growth condition. This extends the Thorp-Whitley maximum modulus theorem. A corresponding characterization of strict convexity in real ...
The maximum modulus principle was well-known to mathematicians of the 19th century. In this section we summarize these elementary facts, for more, see [6]. The principle states that if f is holomorphic on a region of C, and the function jf j attains its maximum in , then f is necessari...
The paper establishes well-posedness and regularity results in suitable function spaces for these integral equations. For an associated optimal control problem, a novel approach is developed using a Liapunov-type theorem and the spike variation technique. This leads to a Pontryagin-type maximum ...
The selection of PDMS was driven by its low modulus of elasticity and its compatibility with the reactive ion etching (RIE) pat- terning process using a metal mask. The thickness of the PA-ABL (= ca. 2.6 µm) was chosen by considering that PA-ABL should be thin enough so as not ...
Our first example is the modulus of the characteristic polynomial of a random GUE matrix over the interval [-1,1] of the spectral parameter. As is well-known, in the limit of large sizes of the matrix the logarithm of that modulus is very intimately related to 1 / f noises [1, 2, ...
We also show how to compute the rate functions using the tilted transition matrix technique and the Gärtner–Ellis theorem. It is to be noted that there is a large body of theoretical work linking the maximum entropy principle and large deviations [27,29]. However, these techniques have ...
1) maximum modulus principle 最大模原理 1. This paper uses several methods of complex functions theorey to prove fundamental theorem of algebra by argument principle,maximum modulus principleand minimum modulus principle. 从复变函数理论出发,利用辐角原理、最大模原理、最小模原理给出代数学基本定理的几...