Download Applied Mathematics and Parallel Computing: Festschrift for by N. Apostolatos (auth.), Dr. Herbert Fischer, Dr. Bruno PDF
By N. Apostolatos (auth.), Dr. Herbert Fischer, Dr. Bruno Riedmüller, Priv.-Doz. Dr. Stefan Schäffler (eds.)
The authors of this Festschrift ready those papers to honour and convey their friendship to Klaus Ritter at the social gathering of his 60th birthday. Be explanation for Ritter's many buddies and his overseas popularity between math ematicians, discovering members used to be effortless. actually, constraints at the dimension of the publication required us to restrict the variety of papers. Klaus Ritter has performed very important paintings in numerous components, specially in var ious purposes of linear and nonlinear optimization and in addition in reference to facts and parallel computing. For the latter we need to point out Rit ter's improvement of transputer notebook undefined. The large scope of his learn is mirrored through the breadth of the contributions during this Festschrift. After numerous years of clinical study within the united states, Klaus Ritter was once ap pointed as complete professor on the collage of Stuttgart. considering then, his identify has develop into inextricably attached with the frequently scheduled meetings on optimization in Oberwolfach. In 1981 he grew to become complete professor of utilized arithmetic and Mathematical facts on the Technical collage of Mu nich. as well as his college educating tasks, he has made the job of making use of mathematical how to difficulties of to be centrally important.
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As this VlliLL make little sense if also concave rather than only "locally" generalized concave functions enter the discussion, we shaLL only be employing convex domains in this and most parts of the next section. Definitions 1. e. the lexmaxmin order relation) on Xif corresponding to each pair of points x,y E X such that x+y, the relation ~~ i;;. ze[x,J1 such that ~tl) i;;. ~J1 for all LA::(z,J1. ze[x,J1 such that ~tl) i> ~J1 for aLL LA::(z,J1. Theorem 4. '1 on a convex subset X of a real Linear space is semi Locally semistrictly 47 quasiconcave, then it is quasiconcave.
G. ). 2. Optimal Control of a Series of Power Stations Authors: Edenhofer, Rempter, Ritter, M. Ulbrich, S. Ulbrich The aim is to get optimal flow regulation of several river power stations for high water situations in real time. The new mathematical model considers all power stations simultaneously contrary to previous models. In order to simulate big rivers, a one-dimensional model turns out to be sufficiently exact. The simulation was performed on transputer workstations at the department of Prof.
Summarizing, we have the following Corollary. An explicitly midpoint quasiconcave vector-valued function f: X~R" on a convex subset X of a real linear space is explicitly quasiconcave if and only if it is semilocally explicitly quasiconcave. Here, all concavity concepts are taken with respect to i" . Of course, this too can be given a midpoint concave (rather than explicitly midpoint quasiconcave) form: Corollary. A midpoint concave vector-valued function f: X~R" on a convex subset X of a real linear space is explicitly quasiconcave if and only if it is semilocally explicitly quasiconcave.