Báo cáo toán học: "Asymptotically optimal pairing strategy for Tic-Tac-Toe with numerous directions" doc
Báo cáo toán học: "Asymptotically optimal pairing strategy for Tic-Tac-Toe with numerous directions" doc
... strategy.
the electronic journal of combinatorics 17 (2010), #N33 4
Asymptotically optimal pairing strategy for
Tic-Tac-Toe with numerous directions
Padmini Mukkamala
Rutgers, New Jersey
D¨om¨ot¨or P´a ... eve ry vertex v
in a set V
N
with N 1 has a neighbour f (v) in V
N−1
. Then G contains an infinite path,
v
0
v
1
with v
N
∈ V
N
for all N.
Given a pairing strateg...
Báo cáo toán học: "Asymptotically optimal tree-packings in regular graphs" pps
... Yuster for graphs other than K
r
.
Theorem 1.4. [2] For every γ>0 and for every positive integer h, there exists an
n
0
= n
0
(γ,h) such that for every graph H with h vertices and for every ... necessary estimates for the numbers c(v)andc(u, v).
Lemma 2.3. Let T be a tree with t vertices. Suppose that G is a d-regular graph on n
vertices. Then
(c1) c(v)=(1+o(1))c
T
d
t−1
(d...
Báo cáo toán học: "Asymptotically Optimal Box Packing Theorems" potx
... Rectangle with Polyominoes, Discrete Models for Complex
Systems, DMCS’03 (Michel Morvan and
´
Eric R´emila, eds.), 2003, pp. 81–88.
[3] Richard A. Brualdi and Thomas H. Foregger, Packing Boxes with ... Problem, Oxford Lecture Series
in Mathematics and its Applications, 30, Oxford University Press, Oxford, 2005.
MR 2007i:11052
[20] Michael Reid, Tiling Rectangles and Half Strips with C...
Báo cáo toán học: " Extremum of Mahler volume for generalized cylinder in R3" doc
... [2–5]).
The Mahler conjecture for the class of origin-symmetric bodies is that:
V (K)V (K
∗
) ≥
4
n
n!
(1.1)
with equality holding for parallelepipeds and their polars. For n = 2, the inequality ... u
⊥
= (C|u
⊥
)
∗
for any u ∈ S
1
. Because that (C|u
⊥
)
∗
is a diamond with vertices (−1, 0, 0) and (1, 0, 0),
C
∗
∩ u
⊥
is a diamond with vertices (−1, 0, 0) and (1, 0, 0) for an...
Báo cáo toán học: "Global Existence of Solution for Semilinear Dissipative Wave Equation" doc
... continuous with respect to
(u, u
t
) ∈ R×R for 1 <m<2. For this reason, we modify the arguments by using
the fact that m|u|
m−1
u
t
=
∂
∂t
(|u|
m−1
u), where |u|
m−1
u is Lipschitz continuous
for ... +
1
2
u
t
2
2
.
(3.7)
Therefore, if we choose sufficiently small ε, (3.7) leads to
E
(t) CE(t). (3.8)
Now we apply the Gronwall Lemma 3.1 with C = α and f = 0, we arrive at
E...
Báo cáo toán học: "The Cyclic Sieving Phenomenon for Faces of Cyclic Polytope" docx
... 1
k
, for 1 k d.
For even d, Theorem 1.3 gives the CSP for faces of CP(d + 1, d), under the cyclic group
C = Z
d+1
action. In f act, it is straightforward to prove that this also holds for ... odd, d ≡ 3 (mo d 4)
0 otherwise.
which does not agree with h
(n,d,d−1)
.
For the C
′′
-case, one may come up with an artificial polynomial X(q) with the prop-
erties X(1) = g(n, d,...
Báo cáo toán học: " Near optimal bound of orthogonal matching pursuit using restricted isometric constant" docx
... the maximum for K ≥ 2). In fact, since
f
′
(K) =
(K −2)
√
K −(K − 1)
√
K −1
2
K(K − 1)(K −1)
, (38)
with
K(K − 1)(K −1) > 0 (39)
10
Lemma 2.7. For two disjoint sets I
1
, I
2
with |I
1
| ... fact, it is now well known that m ×n random matrices with i.i.d. entries from the Gaussian
distribution N(0, 1/m) obe y the RIP with δ
K
≤ ǫ with overwhelming probability if the dimen...
Báo cáo toán học: " Outage-optimal opportunistic scheduling with analog network coding in multiuser two-way relay networks" docx
... proposed
different beamforming schemes with amplify-and -for-
ward (AF) and quantize-and-forward (QF) strategies at
the relay. However, to the best of our knowledge, a per-
formance analysis exploiting ... user pair is scheduled for
transmission and has access to relay channel resources
for a given time-slot. We focus on the two-step ANC
protocol whereby the information exchange for...
Báo cáo toán học: "New Optimal Constant Weight Codes" pot
... lower bound for a code matches the upper bound, the code is said to be
optimal. There are a number of different methods for determining upper bounds for
constant weight codes, but for the codes ... these
results by filling in 9 missing constant weight codes, all of which are optimal by the
second Johnson bound. This completes the tables for A(n, 16, 9) and A(n, 18, 10)
up to n = 63...
Báo cáo toán học: "An optimal strongly identifying code in the infinite triangular grid" docx
... and L. B. Levitin, On a new class of codes for
identifying vertices in graphs, IEEE Trans. Inform. Th. 44 (1998) 599–611.
[9] T. Laihonen, Optimal codes for strong identification, Europ. J. Combin. ... an undirected graph, and C ⊆ V . For every v ∈ V ,
we denote by I(v) the set of all elements of C that are within distance one from
v. If the sets I(v) \ {v} for v ∈ V are all nonempty...