... bundles. Theorem 1.1 tells us that the theory of matroid bundles
is actually the same as the theory of ordinary vector bundles.
The natural source for matroid bundles lies in the world of CD manifolds.
To ... that the map
THE HOMOTOPY TYPE OF THE MATROID GRASSMANNIAN 945
π|
A
: A →X is a homotopy equivalence; the base case of this induction
is simpl...
... not the behavior of the electromagnetic field per se that is
of interest, but rather its effect on the metric.
THE EINSTEIN-MAXWELL-SCALAR FIELD EQUATIONS 885
In view of the above calculations, the ... formation of
trapped regions. In view of the discussion in the introduction, it is thus only
in a neighborhood of the point p (from which the Cauchy horizon emanat...
... that the Stokes operator in the domain M , subject to
the boundary conditions (37), is equal to the −Δ operator.
As a result of the above and (36) we apply a generalized version of the
Stokes theorem ... account for the buoyancy forces and stratification effects under the
Boussinesq approximation. Moreover, and due to the shallowness of the oceans
and the atmosphere,...
... give further refinements of the asymptotic
behavior of w near Σ
0
, which in turn give us a better understanding of the
behavior of the metric g
w
near infinity.
We begin with the proof of the first ... a global bound:
max
M
n
w
i
≤ C.
The next result summarizes the properties of the limit w = lim
i
w
i
.
Recall from the proof of Theorem 3.5 the definition of...
... 2
−3(d+d
)
µ(S
)|X
1
|,
which is equivalent to the lower bound on the size of S ∧S
that we claimed.
We move on now to one of the more technical aspects of the theory of
Bourgain systems, the notion of regularity.
Definition ... Z) ε. The reader may care to recall the definitions of d(f, Z)
and of f
Z
at this point: they are given at the start of Section 3...
... Ind
F
D
(W
δ
)=M
F
, then M
F
⊕ Ind
F
D
(W
δ
)isan(F,δ)-framed VOA. Before
we prove Theorem 3.21, we note that the conditions of Theorem 3.21 including
the fusion rule (3.21) follow from the conditions of Theorem ... abelian 2-group. Let
V = ⊕
χ∈Irr(Q)
V
χ
be the decomposition of V into the direct sum of eigenspaces of Q, where
Irr(Q) is the set of linear characters...
... no influence on the types of
any of the other particles during [0,s] (and of course no influence on the paths
of these other particles), as long as we stay on I
1
∩I
2
(compare the argument
for ... finite number of B-particles
in the system at time 0. The positions of these initial B-particles are arbitrary,
but they are nonrandom. The B-particles move independently of...
... func-
tion theoretic proof of Theorem 1.19. We include his proof in an appendix at
the end of the paper.
HOLOMORPHIC FUNCTIONS 295
2. The equivalence of the von Neumann inequality
and the extension ... disk of type 2.
This completes the proof of Lemma 5.17.
In light of Lemma 5.17 the proof of Theorem 1.20 will be complete once
we have established our final lemma....
... study the integral invariant theory of the space of pairs of ternary
quadratic forms, and in particular, we show how the content of a quartic ring
Q is related to the number of cubic resolvents of ... bijection: Remarks on Theorem 1. The proof of
Theorem 1 is now complete, at least in cases of nonzero discriminant. Indeed,
the work in Sections 3.2–3.4 makes the b...
... shows six of the twelve ways of connecting five points 1, . . . , 5 by
a 5-cycle, the other six being the complements of these graphs in the complete
graph on five vertices. The negation of the polynomial ... normalized).
Since the values of the structure constants of the ring R(A) are given in
terms of integer polynomials in the entries of A, the discrimin...