共查询到20条相似文献,搜索用时 78 毫秒
1.
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
2.
An edge coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for
a vertex-distinguishing proper edge coloring of a simple graph G is denoted by c¢vd(G){\chi'_{vd}(G)}. It is proved that c¢vd(G) £ D(G)+5{\chi'_{vd}(G)\leq\Delta(G)+5} if G is a connected graph of order n ≥ 3 and
s2(G) 3 \frac2n3{\sigma_{2}(G)\geq\frac{2n}{3}}, where σ
2(G) denotes the minimum degree sum of two nonadjacent vertices in G. 相似文献
3.
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
4.
M. Hasson 《Archiv der Mathematik》2001,76(4):283-291
Let W ì \Bbb Rn\Omega \subset {\Bbb R}^n be a smooth domain and let u ? C0(W).u \in C^0(\Omega ). A classical result of potential theory states that¶¶-òSr([`(x)]) u(x)ds(x)=u([`(x)])-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x)=u(\bar x)¶¶for every [`(x)] ? W\bar x\in \Omega and r > 0r>0 if and only if¶¶Du=0 in W.\Delta u=0 \hbox { in } \Omega.¶¶Here -òSr([`(x)]) u(x)ds(x)-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x) denotes the average of u on the sphere Sr([`(x)])S_r(\bar x) of center [`(x)]\bar x and radius r. Our main result, which is a "localized" version of the above result, states:¶¶Theorem. Let u ? W2,1(W)u\in W^{2,1}(\Omega ) and let x ? Wx\in \Omega be a Lebesgue point of Du\Delta u such that¶¶-òSr([`(x)]) u d s- a = o(r2)-\kern-5mm\int\limits _{S_{r}(\bar x)} u d \sigma - \alpha =o(r^2)¶¶for some a ? \Bbb R\alpha \in \Bbb R and all sufficiently small r > 0.r>0. Then¶¶Du(x)=0.\Delta u(x)=0. 相似文献
5.
Atsushi Shiho 《Selecta Mathematica, New Series》2011,17(4):833-854
Let
X \hookrightarrow[`(X)]{X \hookrightarrow \overline{X}} be an open immersion of smooth varieties over a field of characteristic p > 0 such that the complement is a simple normal crossing divisor and [`(Z)] í Z í [`(X)]{\overline{Z}\subseteq Z \subseteq \overline{X}} closed subschemes of codimension at least 2. In this paper, we prove that the canonical restriction functor between the categories
of overconvergent F-isocrystals F-Isocf(X,[`(X)]) ? F-Isocf(X\Z,[`(X)]\[`(Z)]){F-{\rm Isoc}^\dagger(X,\overline{X}) \longrightarrow F-{\rm Isoc}^\dagger(X{\setminus}Z, \overline{X}{\setminus}\overline{Z})} is an equivalence of categories. We also give an application of our result to the equivalence of certain categories. 相似文献
6.
For a simple connected undirected graph G, c(G), cf(G), Yf(G), f(G), ?G(G){\chi(G), \chi_f(G), \Psi_f(G), \phi(G), \partial \Gamma (G)} and Ψ(G) denote respectively the chromatic number, fall chromatic number (assuming that it exists for G), fall achromatic number, b-chromatic number, partial Grundy number and achromatic number of G. It is shown in Dunbar et al. (J Combin Math & Combin Comput 33:257–273, 2000) that for any graph G for which fall coloring exists, c(G) £ cf(G) £ Yf (G) £ f(G) £ ?G(G) £ Y(G){\chi (G)\leq \chi_f(G) \leq \Psi_f (G) \leq \phi(G) \leq \partial \Gamma (G)\leq \Psi (G)} . In this paper, we exhibit an infinite family of graphs G with a strictly increasing color chain: c(G) < cf(G) < Yf (G) < f(G) < ?G(G) < Y(G){\chi (G) < \chi_f(G) < \Psi_f (G) < \phi(G) < \partial \Gamma (G) < \Psi (G)} . The existence of such a chain was raised by Dunbar et al. 相似文献
7.
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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