(Convex and Plurisubharmonic) Recall. Thenconsists of locally convex functions onX[13, Example 14.2]. Similarly ifis open thenconsists of the plurisubharmonic functions onX[13, p. 63]. 1.3A.3 Basic Properties ofF-Subharmonic Functions The following lists some of the basic limit properties satis...
2. (d(A i,A j) is the distance between A i and A j) In the following we will show that μ n has itsleast valueonly when the length of each edge equals to min 1≤i≠j≤nd(A i,A j) and its infimum is 15+33, which can be got only when the convex 6-gon degenerate to ...
Let \(({\varvec{Z}})_{+}\) be the operator projecting the matrix \({\varvec{Z}}\) onto the convex cone \(\{{\varvec{\Theta }}\succeq \nu {\varvec{I}}\}\), where \(\nu \) is an arbitrarily small positive number. Assuming that the matrix \({\varvec{Z}}\) has ...
We show that the steady-state solution minimizes a convex functional that, in the special case of linear resistors, turns out to be the total dissipated power. Conversely, if the resistor characteristic is a threshold-like function, the steady-state solution becomes the minimum path, where each...
The shape and geometric parameters of the front nose, which contacts soil first, must have a great influence on the penetrating feature of the mole. Consider the axisymmetric mole as a rigid body, remaining undeformed during dynamic penetration. A convex arc shape of the front nose and notations...
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(s) into a list of points. The convex hull of these points is then computed using myConvex Hullfunction, and finally the minimum enclosing circle is ascertained by myMinimum Enclosing Circlefunction. More information about these functions and the various algorithms used can be found on their ...
The set of initial conditions is assumed to be a convex polytope. The problem is reduced to devising a control function whose components are bounded functions over a given interval which maps the vertices of the polytope into a closed ball with the center at the origin, and has the least ...
The −logdet function is strictly convex on the space of symmetric matrices, and it takes the value ∞ for any non-positive-definite matrix, which suits our purpose because H must be positive definite to satisfy the MVEE problem. With this new objective function, the primal form of the ...
4.3 outputs a set of vertices of convex facets. In this section, we describe a method to transfer this representation to a discrete image. Let I denote a 3d label image and J a 3d binary image, both of size \(d_{1}\times d_{2}\times d_{3}\). The discretization procedure is ...