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1
Oscillation Theory for Second Order Linear, Half-Linear, ...
Introduction In this chapter we shall present oscillation and nonoscillation criteria
for all solutions of second order nonlinear differential equations of sublinear type
with alternating coefficients. In Section 5.1, our sublinear oscillation results ...
R.P. Agarwal, Said R. Grace, Donal O'Regan, 2002
2
Fundamentals of Convex Analysis
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal. Gauges are examples of
sublinear functions which are closed. This is not the case of all sublinear
functions: see the function f of ( 1 .2. 1 ); another example in K2 is (0 if r? > 0, ...
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal, 2001
3
Property Testing: Current Research and Surveys
Our goal is to give a flavor of the area of sublinear-time algorithms. We focus on
in our opinion the most representative results in the area and we aim to illustrate
main techniques used to design sublinear-time algorithms. Still, many of the ...
4
Combinatorial Optimization and Applications: Second ...
In order to separate the power of sublinear time computations with different query
complexity bounds, we select the problem to compute the diameter for a se-
quence of points in a metric space. We realized this problem and its connection
to ...
Boting Yang, Ding-Zhu Du, Cao An Wang, 2008
5
Holomorphy and Convexity in Lie Theory
that the sublinear functions are exactly those almost sublinear functions p with p(
V) Q RCC- If P is almost sublinear, then the set Dp := {x € V:p(x) < 00} is a convex
cone, and on Dp fl — Dp the values of p are finite because p(— x) < oo yields ...
6
Functional Analysis I: Linear Functional Analysis
The least upper bound of any family of sublinear functionals which is pointwise
bounded above is sublinear. Example. Let {/Jie/ be a family of real linear
functionals which is pointwise bounded above. Then the functional q(x) = sup.
7
Quasiconvex Optimization and Location Theory
Sublinear. functions. and. directional. derivatives. We already mentioned some
special convex functions: affine and linear functions. Now we define sublinear
functions, Definition 2.3.2 (Definition V.1. 1.1 of Ref. [52]). A function a : Rs — > R
is ...
J.A. dos Santos Gromicho, Joaquim António dos Santos Gromicho, 1998
8
Convex Analysis and Minimization Algorithms I: Part 1: ...
£(x) = (s, x) for all x eRn . (0.3) The definition (0.3) of a linear function is more
geometric than (0.1), and just as accurate. A large part of the present chapter will
be devoted to generalizing the above representation theorem to sublinear
functions.
Jean-Baptiste Hiriart-Urruty, Claude Lemarechal, 1996
9
Comparison of Statistical Experiments
Functions having these properties are called sublinear. Thus a real valued
function ^ on V is sublinear if and only if: (i) }j/(v + w) ^ ij/(v) + ij/(w); v,weV and (ii)
ij/(tv) = tij/{v); veV;t^0. If ij/ is sublinear then: (iii) |^(u) — ij/(w)\ ^ \jt{v — w) v ij/{w —
v); ...
10
From Hahn-Banach to Monotonicity
Functional analysis Lemma 1.2: Sublinear form of the Hahn— Banach theorem.
Let E be a nonzero vector space and P: E — > R be sublinear. Then there exists
a linear functional L on E such that L < P on E. Remark 1.4: Extended sublinear ...
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Stadt-Allometrie mit Computerhilfe
Im Gegensatz dazu wächst die Straßenfläche mit der Stadtgröße sublinear. Andere Faktoren wachsen dagegen weitgehend strikt linear, etwa die Zahl der ... «Technology Review, 七月 15»
Data Mining Reveals How Human Health Varies with City Size
It turns out that the rate of infectious diseases, like chlamydia or meningitis, grows superlinearly with city size while the rate of heart attacks grows sublinearly. «The Predictive Analytics Times, 六月 15»
Dragging Nanoparticles Reveals Extra-Low Friction
Because of this and other factors, the force-area relationship for gold depended on direction, but it was always sublinear. The researchers also showed that their ... «Physics, 十二月 13»
Amdahl's Law vs. Gustafson-Barsis' Law
However, for the most part, sublinear speedup is the norm. Later, we discuss an important limit on speedup: Amdahl's Law. It considers speedup as P varies and ... «Dr. Dobb's, 十月 13»
A New Model for Urban Scaling
If you quantify these assumptions in a certain way, it turns that you can not only explain the sublinear and superlinear behaviors of various urban properties, but ... «Wired, 六月 13»
Metabolic Scaling of Social Insects
Specifically, metabolic rates scale sublinearly with the mass of different animals, which means that as species get bigger, they use less energy per pound:. «Wired News, 八月 12»
Lehrer elided quotes in The New Yorker and reused material in NYT …
Other scientists soon found more than 70 such related laws, defined by what are known as “sublinear” equations. It doesn't matter what the animal looks like or ... «Poynter.org, 六月 12»
The mathematics of Lego
However, the number of piece types grows sublinearly: while a larger set uses more piece types, as sets becomes larger, they use progressively fewer additional ... «Wired.co.uk, 一月 12»
Superlinear cities
It's sublinear; the ratio is 3/4 instead of 4/4. Humans enjoy an economy of scale over mice, as elephants do over us. With each increase in animal size there is a ... «Wired, 七月 11»
Revolutionizing the Rankings: A Look at the Global Poker Index
She went on to point out that the GPI scores difficulty by using a sublinear multiplier applied to buy-in, which is a logarithmic function, anchored at $1,500 buy-in ... «PokerNews.com, 七月 11»
