Abstract: Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Abstract: Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.
Abstract: As part of national epidemiological survey on bovine
viral diarrhea virus (BVDV), a total of 274 dejecta samples were
collected from 14 cattle farms in 8 areas of Xinjiang Uygur
Autonomous Region in northwestern China. Total RNA was extracted
from each sample, and 5--untranslated region (UTR) of BVDV
genome was amplified by using two-step reverse
transcriptase-polymerase chain reaction (RT-PCR). The PCR products
were subsequently sequenced to study the genetic variations of BVDV
in these areas. Among the 274 samples, 33 samples were found
virus-positive. According to sequence analysis of the PCR products,
the 33 samples could be arranged into 16 groups. All the sequences,
however, were highly conserved with BVDV Osloss strains. The virus
possessed theses sequences belonged to BVDV-1b subtype by
phylogenetic analysis. Based on these data, we established a typing
tree for BVDV in these areas. Our results suggested that BVDV-1b
was a predominant subgenotype in northwestern China and no
correlation between the genetic and geographical distances could be
observed above the farm level.
Abstract: This paper reports on investigations into capacity of a
Multiple Input Multiple Output (MIMO) wireless communication
system employing a uniform linear array (ULA) at the transmitter and
either a uniform linear array (ULA) or a uniform circular array (UCA)
antenna at the receiver. The transmitter is assumed to be surrounded by
scattering objects while the receiver is postulated to be free from
scattering objects. The Laplacian distribution of angle of arrival
(AOA) of a signal reaching the receiver is postulated. Calculations of
the MIMO system capacity are performed for two cases without and
with the channel estimation errors. For estimating the MIMO channel,
the scaled least square (SLS) and minimum mean square error
(MMSE) methods are considered.