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1
Lectures on Entire Functions
Logarithmically subharmonic functions A notion of logarithmically subharmonic
function is rather useful. Definition. A nonnegative function u(z) is called
logarithmically subharmonic if the function v(z) = logu(z) is subharmonic. For
example, if ...
2
Introduction to the Theory of Entire Functions of Several ...
This property, which is a special case of (b), may be given a slightly different
formulation if we introduce the concept of logarithmically subharmonic function.
Definition. A nonnegative function u(x) is said to be logarithmically subharmonic if
the ...
3
Interpolation of Linear Operators
A positive function u(t) given on an interval I of the real axis is said to be
logarithmically convex if the function 1n u(t) is convex on I . It follows from (1.1)
that this definition is equivalent to the requirement that “2((tl 'l' l'2)/2) 4 u(tI)“(tz)- (1-
9) If u(t) ...
S. G. Krein, E. M. Semenov, 2002
4
Introduction to Complex Analysis: Functions of Several Variables
Functions of Several Variables B. V. Shabat. (a) (b) Figure 9 rithmically convex
hull of M (i.e., the intersection of all the logarithmically convex sets that contain M
) is obtained if we consider the inverse image of the convex hull of the set A(Af ) .
5
Holomorphic Functions of Several Variables: An Introduction ...
A Reinhardt domain is called i) proper if G = 0 or 0 e G , ii) complete if P (i (z)) c G
for each z e G n C*", Hi) logarithmically convex if {(loglzj |, . . . , log|zj); z e Gn C*"}
is a convex subset of\R".~ Hence, Reinhardt domains can be characterized in ...
6
CRC Concise Encyclopedia of Mathematics, Second Edition
Logarithmically Concave Function A function f(x) is logarithmically concave on
the interval [a, b] iff>0 and lnf(x) is CONCAVE on [a, b]. The definition can also be
extended to R* -» (0, oo) functions (Dharmadhikari and Joag-Dev 1988, p. 18).
7
Methods of the Theory of Functions of Many Complex Variables
according to the remark following the theorem in section 10.9, be the limit of a
decreasing sequence of continuous logarithmically plurisubharmonic functions it,
for or: 1. 2, . Then, the function 1w(r; u) is also the limit of a decreasing sequence
...
Vasiliy Sergeyevich Vladimirov, Leon Ehrenpreis, 2007
8
Metric, Myth & Quasicrystals
Logarithmically Periodic Solids, Nova Science, 2011, ISBN 978-1-61122-977-6
Quasicrystals' 2D tiles in 3D superclusters, UHRL, 2010, ISBN: 978-0-9789839-2
-5 Quasicrystals – and quasi drivers, UHRL, 2009, ISBN 978-0-9789-8391-8 ...
Antony J. Bourdillon, 2012
9
More Fallacies, Flaws & Flimflam:
[8] from a story about corruption and drugs: “ 'The drug situation is a horror story,
increasing logarithmically.'” [9] from a more recent story: “Street crime, fed by an
explosion of drug abuse, has risen exponentially.” [10] These sorts of examples ...
10
High Performance Optimization
of logarithmically homogeneous barriers, which has been developed by Nesterov
and Nemirovski [100]. Definition 4.33 Let K be a closed, solid and pointed convex
cone. Then F : int /C - > R is a v-logarithmically homogeneous barrier for K, if F ...
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IL-12 conditioning improves retrovirally mediated transduction …
We found that T cells conditioned with IL-12 were able to expand logarithmically (Figure 4b). Furthermore, IL-12 conditioning did not alter the ... «Nature.com, 7月 15»
Digital Seashells and David Raup
Snail shells have a very important feature—they spiral logarithmically. This feature was noted Greek philosophers, Christopher Wren, and ... «Deep-Sea News, 7月 15»
The Cost Of A Free Agent
... a linear scale instead of logarithmically, which would show the variation a little better. I wanted to keep consistency between all of the figures, ... «Dawgs By Nature, 7月 15»
Money and Happiness? It's Complicated
A Gallup poll surveying 1,000 U.S. residents showed that life satisfaction rises proportionally when plotted against income (logarithmically ... «Huffington Post, 7月 15»
Reddit's sound and fury
Additionally, the system favors newer content over old logarithmically, so links that are both new and get lots of votes very quickly are heavily ... «The Verge, 7月 15»
Density-dependent adaptive resistance allows swimming bacteria to …
The intensity of fluorescently labeled cells is scaled logarithmically. Migrating populations can be seen as laterally moving fronts. Magnified ... «Nature.com, 7月 15»
Sounding Off: Does local infrastructure in your community need …
These costs will grow logarithmically. This underfunding is evident if you look around at the patchwork repair of roads, crumbling bridge ... «Dallas Morning News, 6月 15»
How Long Is Too Long to Take the Pill?
"The clot risk is logarithmically higher in pregnancy than from one of these methods," Dr. Rabin says. But what about taking hormonal methods ... «New York Magazine, 6月 15»
Owls could provide the solution for quieter wind turbines
This is not only a considerable amount (because noise is measured logarithmically), but it also managed to achieve this without having a ... «Hydrogen Fuel News, 6月 15»
Owls May Hold the Secret to Quieter Wind Turbines and Jets
... noise generation by 10 decibels (a significant amount since noise is measured logarithmically), without significantly affecting aerodynamics. «Wired, 6月 15»