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Generalized Curves and Extremal Points
SIAM Journal on Control, 1975A nonparametric variational problem is considered in the setting of the theory of generalized curves. Instead of minimizing a functional dependent on a curve joining two given points, a functional defined on a set of Radon measures is considered ; the set of measures is determined by the boundary conditions. It is shown that this functional attains its
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Subordination, Extreme points and support points
Complex Variables, Theory and Application: An International Journal, 1989Let s(F) denote the set of functions subordinate to a function F analytic in the open unit disk Δ. Let be the set of functions f analytic in Δ such that where ∞s(f)denotes the closed convex hull of s(f). Let denote those functions analytic in Δ such that the set of support points of s( f) is .
D. J. Hallenbeck, S. perera
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Extremal Splittings of Point Processes
Mathematics of Operations Research, 1985The sequence with nth term defined by [(n + 1)p] − [np] is an extremal zero-one valued sequence of asymptotic mean p in the following sense (for example): if a fraction p of customers from a point process with iid interarrival times is sent to an exponential server queue according to a prespecified splitting sequence, then the long-term average queue ...
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Mathematics of Operations Research, 1988
The extreme points of sets of probability measures—determined by a finite number of generalized moment conditions—are characterized. Together with an integral representation theorem the characterization is used to optimize affine functionals.
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The extreme points of sets of probability measures—determined by a finite number of generalized moment conditions—are characterized. Together with an integral representation theorem the characterization is used to optimize affine functionals.
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Transactions of the American Mathematical Society, 1981
Hopenwasser, Alan +2 more
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Hopenwasser, Alan +2 more
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Israel Journal of Mathematics, 1966
It is proved that every bounded closed and convex subset ofl 1 is the closed convex hull of its extreme points.
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It is proved that every bounded closed and convex subset ofl 1 is the closed convex hull of its extreme points.
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1997
The (first) conjugate point η(a) was defined in Chapter 0 as the least value c > a such that some nontrivial solution has n zeros in [a, c], including multiplicities. It is known that η(a) is a continuous increasing function.
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The (first) conjugate point η(a) was defined in Chapter 0 as the least value c > a such that some nontrivial solution has n zeros in [a, c], including multiplicities. It is known that η(a) is a continuous increasing function.
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Microbial diversity in extreme environments
Nature Reviews Microbiology, 2021Wensheng, Li-Nan Huang
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Ultra-high temperature ceramics for extreme environments
Nature Reviews Materials, 2023Brian C Wyatt +2 more
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