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共查询到17条相似文献，搜索用时 265 毫秒
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In this paper, we give a coding theorem for general source sequence. A source sequence ${\mathcal{T}^{(n)}} = \{ [{X^{(n)}},{p^{(n)}}({X^{(n)}})],[{X^{(n)}} \otimes {Y^{(n)}},{\rho ^{(n)}}({X^{(n)}},{Y^{(n)}})]\}$ is said to be $({R^{(n)}},{d^{(n)}})$-compress, if (i)${R^{(n)}}$, ${d^{(n)}}$ are two sequences of real numbers ${R^{(n)}} \to \infty$； (ii) there exist ${\varepsilon ^{(n)}} > 0({\varepsilon ^{(n)}} \to 0)$ and set ${B^{(n)}} \subset {Y^{(n)}}$ so that $|{B^{(n)}}| \leqslant {2^{{R^{(n)}}(1 + {\varepsilon ^{(n)}})}}$ and ${p^{(n)}}{\text{\{ }}({X^{(n)}}){\rho ^{(n)}}({X^{(n)}},{B^{(n)}}) \leqslant {d^{(n)}}\} \geqslant 1 - {\varepsilon ^{(n)}}$ where ${\rho ^{(n)}}({X^{(n)}},{B^{(n)}}) = \mathop {\min }\limits_{{y^{(n)}} \in {B^{(n}}} {\rho ^{(n)}}({X^{(n)}},{Y^{(n)}})$. A ${\mathcal{T}^{(n)}}$ is said to be $({\mathcal{F}^{(n)}}{D^{(n)}})$-information bounded, if (i)${\mathcal{F}^{(n)}} \to \infty$;(ii) there exist ${\varepsilon ^{(n)}} > 0$ and conditional probability ${Q^{(n)}}({Y^{(n)}}/{X^{(n)}})$ so that probability distribution ${p^{(n)}}({X^{(n)}}{Y^{(n)}}) = {p^{(n)}}({X^{(n)}}){Q^{(n)}}({Y^{(n)}}/{X^{(n)}})$ is satisfied by $\begin{gathered} {p^{(n)}}\{ ({X^{(n)}},{Y^{(n)}}):i({X^{(n)}},{Y^{(n)}}) \leqslant {\mathcal{F}^{(n)}}(1 + {\varepsilon ^{(n)}}), \hfill \ {\rho ^{(n)}}({X^{(n)}},{Y^{(n)}}) \leqslant {\rho ^{(n)}}\} \geqslant 1 - {\varepsilon ^{(n)}} \hfill \\ \end{gathered}$ where $i({X^{(n)}},{Y^{(n)}}) = \log \frac{{{p^{(n)}}({X^{(n)}},{Y^{(n)}})}}{{{p^{(n)}}({X^{(n)}}){p^{(n)}}({Y^{(n)}})}}$ Theorem The necessary and sufficient conditions for a source sequence ${\mathcal{F}^{(n)}}$ to be $({R^{(n)}},{a^{(n)}})$-compress is that ${\mathcal{F}^{(n)}}$ must be $({R^{(n)}},{a^{(n)}})$-information bounded. From the theorem we obtain immediately the coding theorem and its converse for stationary and unstationary sources with memory.  相似文献

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Let G be a k(k ≤3)-edge connected simple graph with minimal degree ≥ 3,girth g,r=g12.For any independent set {a1,a2 , . . . , a 6/(4 k)} of G,if,then G is up-embeddable.  相似文献

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Let $${S_k}$$ be the class of functions $$f(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}}$$ which are regular and univalent in $$\left| z \right| < 1$$ and denote $$S_n^{(k)}(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}}$$. The authors prove that the functions $$S_n^{(2)}(z)$$ are starlike in $$\left| z \right| < \frac{1}{{\sqrt 3 }}$$.  相似文献

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A spanning tree with no more than 3 leaves is called a spanning 3-ended tree.In this paper, we prove that if G is a k-connected(k ≥ 2) almost claw-free graph of order n and σ_(k+3)(G) ≥ n + k + 2, then G contains a spanning 3-ended tree, where σk(G) =min{∑_(v∈S)deg(v) : S is an independent set of G with |S| = k}.  相似文献

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The induced matching cover number of a graph G without isolated vertices, denoted by imc（G）, is the minimum integer k such that G has k induced matchings M1, M2,..., Mk such that, M1∪M2∪…∪Mk covers V（G）. This paper shows if G is a nontrivial tree, then imc（G） E {△0^＊CG）, △0^＊（G） ＋ 1, △0^＊（G） ＋ 2}, where △0^＊（G） = max{d0（u） ＋ d0（v）： u,v ∈ V（G）,uv ∈ E（G）}.  相似文献

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