Báo cáo toán học: "Two Characterizations of Hypercubes" potx
Báo cáo toán học: "Two Characterizations of Hypercubes" potx
... journal of combinatorics 18 (2011), #P97 2
Two Characterizations of Hypercubes
Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen
Department of Mathematics, University of Oulu
University of Oulu, ... vertex of G has degree n i.e. G is regular of degree
n.
Claim 3.The graph G is bipartite.
Proof of C l aim 3. If a prime convex P
i
cuts off an edge of a cycle it must cut off...
Báo cáo toán học: "Spectral characterizations of dumbbell graphs" docx
... spectrum of D
a,b,0
(with δ 3).
Lemma 3.4. The spectrum of D
a,b,0
with δ = gcd(a, b) 3 consists of the eigenvalues
of C
δ
(except 2 and −2) with multiplicity 3, the eigenvalues of C
a
and ... eigenvalues of C
a
∪ C
b
and be of multiplicity 1.
This ends the proof.
From the above lemma we know to some extent the spectrum of D
a,b,0
. If H is a
tentative cospectral mate of...
Báo cáo toán học: "LATIN SQUARES OF ORDER" potx
... independent computations of the number of Latin squares of order 10.
We also give counts of Latin rectangles with up to 10 columns, and estimates of the number of
Latin squares of orders up to 15.
Mathematics ... subgraph of degree one. A one-factorization
of G is a partition of E(G) into one-factors. Clearly, the rows of a Latin rectangle R correspond
to the one-factors...
Báo cáo toán học: "Evolutionary Families of Sets" potx
... the
members of i
S
[S] account for at least five of the seven nonempty subsets of S. Without losing
generality we may assume that the complement in P(S) − {∅} of i
S
[S] is a subset of one of
the following:
(a) ... single member of S.Ifa
(unique) member of S is of cardinality 1, then its unique element is considered to be a distin-
guished vertex of G. The connectedness of...
Báo cáo toán học: "On Convergence of Two-Parameter Multivalued Pramarts and Mils" ppt
... L. Sucheston, Convergence of classes of amart indexed by directed
sets, Canad. J. Math. 32 (1980) 86–125.
13. U. Mosco, Convergence of convex sets and of solutions of variational inequalities,
Adv. ... one-parameter discrete case, the notion of 1-mils coincides with
the original notion of mils introduced by Talagrand [16].
The following lemma will be needed in the proof of the...
Báo cáo toán học: " Efficiency of Embedded Explicit Pseudo Two-Step RKN Methods on a Shared Memory Parallel Computer" ppsx
... respectively.
The proof of this theorem follows the same line as in the proof of a very
similar theorem formulated in [9, proof of Theorem 2.1].
2.2. Embedded Formulas
Efficiency of Embedded Explicit ... the f-evaluations
of s components of the big vector F(t
n
e + h
n
c, Y
n
) over a number of available
processors. An additional computational effort consists of a recomputation...
Báo cáo toán học: "New Characterizations and Generalizations of PP Rings" ppt
... ⊆
ker(α) = 0, and so M is projective, as required.
The proof of (5) ⇒ (1) is similar to that of (7) ⇒ (2) in Theorem 3.7.
(7) ⇒ (1). By the proof of Proposition 2.3, every P -injective right R-module
is ... Wakamatsu’s Lemma [6, Proposition 7.2.4].
Thus M is P -injective by the proof of (7) ⇒ (2).
New Characterizations and Generalizations of PP Rings 107
projective, as required....
Báo cáo toán học: "The Structure of Locally Finite Two-Connected Graphs" potx
... subgraphs of G;thus,toprove
that G = G(T
e
), it suffices to show
Lemma 4 Each finite subgraph of G is contained in G
0
(T
n
) for some n.
Proof: It suffices to show that each edge of G belongs to one of ... incontractible, then G
α
is a multilink, and each component of T−α corresponds
to a union of some of the bridges of the endpoints of e. If some such component, say T
,
corr...
Báo cáo toán học: "RHOMBUS TILINGS OF A HEXAGON WITH TWO TRIANGLES MISSING ON THE SYMMETRY AXIS" pdf
... part of the proof. An outline of the proof is given in the next section. The
details are filled in in the subsequent sections.
2. Outline of the proofs of Theorems 1 and 2
Outline of the proof of ... in
Theorem 1, so the proof of Theorem 1 is complete.
The proof of Theorem 2 is given in Section 9. Analogously to the proof of The-
orem 1, it is enough to count the rhombus tili...
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