共查询到10条相似文献,搜索用时 125 毫秒
1.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2010,62(2):241-258
It is shown that if a point x
0 ∊ ℝ
n
, n ≥ 3, is an essential isolated singularity of an open discrete Q-mapping f : D →
[`(\mathbb Rn)] \overline {\mathbb {R}^n} , B
f
is the set of branch points of f in D; and a point z
0 ∊
[`(\mathbb Rn)] \overline {\mathbb {R}^n} is an asymptotic limit of f at the point x
0; then, for any neighborhood U containing the point x
0; the point z
0 ∊ [`(f( Bf ?U ))] \overline {f\left( {B_f \cap U} \right)} provided that the function Q has either a finite mean oscillation at the point x
0 or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set
[`(\mathbb Rn)] \overline {\mathbb {R}^n} \ f(D) is an asymptotic limit of f at the point x
0. For n ≥ 3, the following relation is true:
[`(\mathbbRn )] \f( D ) ì [`(f Bf )] \overline {\mathbb{R}^n } \backslash f\left( D \right) \subset \overline {f\,B_f } . In addition, if ¥ ? f( D ) \infty \notin f\left( D \right) , then the set f
B
f
is infinite and x0 ? [`(Bf )] x_0 \in \overline {B_f } . 相似文献
2.
H. Karami S. M. Sheikholeslami Abdollah Khodkar Douglas B. West 《Graphs and Combinatorics》2012,28(1):123-131
A set S of vertices in a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number
γ
c
(G) is the minimum size of such a set. Let d*(G)=min{d(G),d([`(G)])}{\delta^*(G)={\rm min}\{\delta(G),\delta({\overline{G}})\}} , where [`(G)]{{\overline{G}}} is the complement of G and δ(G) is the minimum vertex degree. We prove that when G and [`(G)]{{\overline{G}}} are both connected, gc(G)+gc([`(G)]) £ d*(G)+4-(gc(G)-3)(gc([`(G)])-3){{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+4-({\gamma_c}(G)-3)({\gamma_c}({\overline{G}})-3)} . As a corollary,
gc(G)+gc([`(G)]) £ \frac3n4{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \frac{3n}{4}} when δ*(G) ≥ 3 and n ≥ 14, where G has n vertices. We also prove that gc(G)+gc([`(G)]) £ d*(G)+2{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+2} when gc(G),gc([`(G)]) 3 4{{\gamma_c}(G),{\gamma_c}({\overline{G}})\ge 4} . This bound is sharp when δ*(G) = 6, and equality can only hold when δ*(G) = 6. Finally, we prove that gc(G)gc([`(G)]) £ 2n-4{{\gamma_c}(G){\gamma_c}({\overline{G}})\le 2n-4} when n ≥ 7, with equality only for paths and cycles. 相似文献
3.
D. Joyner 《Archiv der Mathematik》1999,73(5):332-340
Following D. Manderscheid, we describe the supercuspidal representations of the n-fold metaplectic cover [`(SL2(F))]\overline {SL_2(F)}, where F is a p-adic field with (p, 2n) = 1. We prove a "Frobenius formula" for the character of a supercuspidal representation of [`(SL2(F))]\overline {SL_2(F)}. Using this formula, we obtain a character relation between corresponding supercuspidal representations of [`(SL2(F))]\overline {SL_2(F)} and of SL2(F)> in the case n = 2. 相似文献
4.
Let n ≥ 2 be a fixed integer, let q and c be two integers with q > n and (n, q) = (c, q) = 1. For every positive integer a which is coprime with q we denote by [`(a)]c{\overline{a}_{c}} the unique integer satisfying 1 £ [`(a)]c £ q{1\leq\overline{a}_{c} \leq{q}} and a[`(a)]c o c(mod q){a\overline{a}_{c} \equiv{c}({\rm mod}\, q)}. Put
L(q)={a ? Z+: (a,q)=1, n \not| a+[`(a)]c }.L(q)=\{a\in{Z^{+}}: (a,q)=1, n {\not\hskip0.1mm|} a+\overline{a}_{c} \}. 相似文献
5.
António Caetano Amiran Gogatishvili Bohumír Opic 《Czechoslovak Mathematical Journal》2011,61(4):923-940
We characterize compact embeddings of Besov spaces B
p,r
0,b
(ℝ
n
) involving the zero classical smoothness and a slowly varying smoothness b into Lorentz-Karamata spaces Lp,q;[`(b)] {L_{p,q;\overline b }}(Ω), where is a bounded domain in ℝ
n
and [`(b)]\overline b is another slowly varying function. 相似文献
6.
Victor Alexandru Angel Popescu Elena Liliana Popescu Sobia Sultana 《Monatshefte für Mathematik》2009,38(3):223-233
Let (K, v) be a perfect rank one valued field and let ([`(Kv)],[`(v)]){(\overline{K_{v}},\overline{v})} be the canonical valued field obtained from (K, v) by the unique extension of the valuation [(v)\tilde]{\widetilde{v}} of K
v
, the completion of K relative to v, to a fixed algebraic closure [`(Kv)]{\overline{K_{v}}} of K
v
. Let [`(K)]{\overline{K}} be the algebraic closure of K in [`(Kv)]{\overline {K_{v}}}. An algebraic extension L of K, L ì [`(K)]{L\subset\overline{K}}, is said to be a v-adic maximal extension, if [`(v)] | L{\overline{v}\mid_{L}} is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in
connection with the v-adic spectral norm on [`(K)]{\overline{K}} and with the absolute Galois groups Gal([`(K)]/K){(\overline{K}/K)} and Gal([`(Kv)] /Kv){(\overline{K_{v}} /K_{v})}. Some other auxiliary results are given, which may be useful for other purposes. 相似文献
7.
Let L\cal{L} be a positive definite bilinear functional, then the Uvarov transformation of L\cal{L} is given by U(p,q) = L(p,q) + m p(a)[`(q)](a-1) +[`(m)] p([`(a)]-1)\,\mathcal{U}(p,q) = \mathcal{L}(p,q) + m\,p(\alpha)\overline{q}(\alpha^{-1}) + \overline{m}\,p(\overline{\alpha}^{-1})
[`(q)]([`(a)])\overline{q}(\overline{\alpha}) where $|\alpha| > 1, m \in \mathbb{C}$|\alpha| > 1, m \in \mathbb{C}. In this paper we analyze conditions on m for U\cal{U} to be positive definite in the linear space of polynomials of degree less than or equal to n. In particular, we show that m has to lie inside a circle in the complex plane defined by α, n and the moments associated with L\cal{L}. We also give an upper bound for the radius of this circle that depends only on α and n. This and other conditions on m are visualized for some examples. 相似文献
8.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
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