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1
THEORY OF CAUSAL DIFFERENTIAL EQUATIONS
1, since (Bx (3.20) \/V is nondecreasing and —Mx is nonincreasing in x. If (Px) I 0
in Theorem 3.4. 1, we obtain the result for nonincreasing (Qx) and a0, [)0 are
coupled lower and upper solutions of the IVP x' (t) I (Qx) (t) with nonincreasing (
Qx).
S. Leela, V. Lakshmikantham, 2010
2
Combinatorial Matrix Classes
A sequence U =(u1 ,u 2 ,...,u n) of integers is nearly nonincreasing provided ui ≥
uj − 1(1≤ i<j≤ n). Thus the sequence U is nearly nonincreasing if and only if
there is a sequence H =(h1 ,h2 ,...,h n) of 0's and 1's such that U + H is ...
3
Interpolation Theory and Applications: A Conference in Honor ...
Then u is ^-concave if and only if there exists a nonincreasing function D : (0, 1)
— » [0, oo) such that (4.5) u(x) = [ <Z>(t)D(t)dt for all x € [0, 1]. Jo Proof. The three
properties which u is assumed to have here, imply that the composed function u o
...
Michael Cwikel, Laura De Carli, Mario Milman, 2007
4
Computation, Cooperation, and Life: Essays Dedicated to ...
Nonincreasing. Competence. In CDGSs working in =k-comp.-mode of derivation,
a component may start rewriting a sentential form provided it is k-competent on
the string, and it must rewrite as long as it remains k-competent: only when it is no
...
Jozef Kelemen, Alica Kelemenová, 2011
5
Operator Theory and Arithmetic in H [infinity]
function n(a) — k(a) is also nonincreasing in a. The order relation on this lattice is
"pointwise inequality" by Remark 2.4. Assume that there exists an ordinal number
0 such that n(0) ^ {n,n - 1,0}. We then define the functions fci(a) = max{n(a) — 1 ...
6
Partial Differential Equations
Jeffrey Rauch. norm of u(t) is a nonincreasing function of t on [0, oo[. This gives
an independent proof of the H' estimate for s = 0. Thes = 1 estimate can be
derived by the energy method, upon multiplying the equation by Au to find 0 - J A
«(u, ...
7
Stochastic Processes, Physics, and Geometry: New Interplays ...
Since by hypothesis p is a nonneg- ative nonincreasing function on (a, b) and (
3.15) holds, one concludes by Lemma 3.4 that the function ,H-tr(V»V(ff<">(,))) (
3.21) is nonincreasing in some neighborhood of so and hence on the whole
interval ...
Sergio Albeverio, Fritz Gesztesy, 2000
8
Estimating the Price of Privacy in Liver Transplantation
If K and O are TP2, and L{l,k} is monotonically nonincreasing in k ∈ Ψ for all l = L
+ 1, then v(h,l,π) is MLR-nonincreasing in π for any h ∈ Ω and l ∈ Φ. Proof. For
convenience, let, for any given h ∈ Ω and l ∈ Φ, rT(h,l), and gi+1 (π) = r W (h) +λ
...
Burhaneddin Sandikci, 2008
In a similar way, to say that h is convex and h is nonincreasing means that h is
nonincreasing and dom/i extends infinitely in the positive direction. This is
illustrated in figure 3.7. Example 3.12 Some simple examples will illustrate the
conditions ...
Stephen Boyd, Lieven Vandenberghe, 2004
10
Infinite Divisibility of Probability Distributions on the ...
If its left extremity is zero, then the corresponding continuous density f is
nonincreasing iff the nonincreasing canonical density k satisfies k(0+) ≤ 1. Proof.
Let F be a self-decomposable distribution function on R+. We suppose that lF = 0;
this is ...
Fred W. Steutel, Klaas van Harn, 2003
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The 5 scariest things about ETFs for investors
GDP is possibly declining or nonincreasing, because of inequality in europe and lack of equal opportunities. Marx envisages in his theory a ... «MarketWatch, 五月 15»
Sample Topics for Applicants' Research Papers
That is, the sequence of numbers of pebbles removed on each turn is a monotonically nonincreasing sequence. Starting with a pile of 12 ... «New York Times, 九月 13»
