be generators of commuting bounded strongly continuous groups, A≡(A1,A2,…,An). We show that, when f has sufficiently many polynomially bounded derivatives, then there
exist k,r>0 such that f(A) has a (1+|A|2)−r-regularized BCk(f(Rn)) functional calculus. This immediately produces regularized semigroups and cosine functions with an explicit representation; in particular, when f(Rn)⫅R, then, for appropriate k,r, t↦(1−it)−ke−itf(A)(1+|A|2)−r is a Fourier-Stieltjes transform, and when f(Rn)⫅[0,∞), then t↦(1+t)−ke−tf(A)(1+|A|2)−r is a Laplace-Stieltjes transform. With A≡i(D1,…,Dn),f(A) is a pseudodifferential operator on Lp(Rn)(1≤p<∞) or BUC(Rn).">
伪差操作员的正则功能计算，半群和余弦函数</t一世tle>
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.expand_btn{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .itQwgq .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .itQwgq ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .itQwgq ol li{margin:10px 0;padding-left:10px;word-break:normal;} .itQwgq ol li a{word-break:break-all;} .itQwgq ol li .reflinks{display:block;} .itQwgq ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .itQwgq ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .itQwgq ol li .reflinks .sep{color:#000000;} .itQwgq .table-wrapper{width:auto;overflow-x:auto;} .itQwgq .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .itQwgq .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.itQwgq .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.itQwgq .table-wrapper{width:auto;}} @media (min-width:1324px){.itQwgq .table-wrapper{width:auto;}} @media (min-width:320px){.itQwgq{margin-bottom:33px;padding:0;}} @media (min-width:992px){.itQwgq{padding:0;margin-bottom:100px;}} @media (min-width:1325px){.itQwgq{margin-bottom:100px;}} .itQwgq .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .itQwgq .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .itQwgq .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;width:100%;} .itQwgq .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .itQwgq .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .itQwgq .floats-partial-middle--thumbs .partial-carousel-dot.active svg{fill:#007B8B;} .itQwgq .partial-carousel-dot{text-align:center;cursor:pointer;border:0;width:100px;padding-bottom:20px;background-color:#fff;display:table-cell;} .itQwgq .partial-carousel-dot:focus-visible{outline-offset:-3px;} .itQwgq .partial-carousel-dot strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.itQwgq .partial-carousel-dot strong{font-size:16px;}} .itQwgq .partial-carousel-dot img{width:90px;height:90px;border:1px solid #979797;margin:10px 0;} .itQwgq .partial-carousel-wrapper .floats-partial-middle{border-top:1px solid #e3e3e3;display:block;margin-bottom:50px;padding-top:1px;} @media (min-width:767.5px){.itQwgq .partial-carousel-wrapper .floats-partial-middle{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;margin-bottom:0;}} .itQwgq .partial-carousel--single-image{overflow:hidden;text-align:center;} .itQwgq .partial-carousel--single-image 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体积<!-- -->
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<p>拉尔夫·德劳本法尔（Ralph Delaubenfels）<!-- -->，，，，<!-- -->
<!-- -->“<span>伪差操作员的正则功能计算，半群和余弦函数</span>”，<!-- --><i>抽象和应用分析</一世>，，，，<!-- -->
<!-- -->卷。<!-- -->2<!-- -->，，，，<!-- -->
<!-- -->文章ID<!-- -->472650<!-- -->，，，，<!-- -->
<!-- -->16<!-- -->
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<h1 class="sc-gPEVay iUuzmH sc-kxynE fsaSer article_title heading-title">伪差操作员的正则功能计算，半群和余弦函数</h1>
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<div class="sc-gpHHfC cdKJIh article_authors">
<hr class="sc-gPzReC jVvWtU hr__author">
<span class="">Ralph Delaubenfels<sup>1</sup>和</span>
<span class="">Yansong Lei<sup>2</sup></span>
<div class="sc-kQsIoO lnoGXA isHide">
<p><sup>1</sup><span>科学研究所邮箱988，美国</span></p>
<p><sup>2</sup><span>美国俄亥俄州大学数学系</span></p>
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<div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok">
<div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished">
<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">已收到</span>
<span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">1996年5月27日</span>
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<article class="sc-hgHYgh itQwgq article_body ">
<div>
<div class="xml-content">
<h4 class="header" id="abstract">抽象的</h4>
<p>让<mml:math alttext="$iA_j(1\leq j\leq n)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
一世</mml:mi>
<mml:msub>
<mml:mi>
一个</mml:mi>
<mml:mi>
j</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
≤</mml:mo>
<mml:mi>
j</mml:mi>
<mml:mo>
≤</mml:mo>
<mml:mi>
n</mml:mi>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>成为通勤有限连续群体的发生者，<mml:math alttext="$A\equiv(A_1,A_2,\ldots,A_n)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
一个</mml:mi>
<mml:mo>
◦</mml:mo>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>
一个</mml:mi>
<mml:mn>
1</mml:mn>
</mml:msub>
<mml:mo>
，，，，</mml:mo>
<mml:msub>
<mml:mi>
一个</mml:mi>
<mml:mn>
2</mml:mn>
</mml:msub>
<mml:mo>
，，，，</mml:mo>
<mml:mo>
…</mml:mo>
<mml:mo>
，，，，</mml:mo>
<mml:msub>
<mml:mi>
一个</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>。我们表明，当<mml:math alttext="$f$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
F</mml:mi>
</mml:math>具有足够多的多项式界限，然后存在<mml:math alttext="$k,r > 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
k</mml:mi>
<mml:mo>
，，，，</mml:mo>
<mml:mi>
r</mml:mi>
<mml:mo>
></mml:mo>
<mml:mn>
0</mml:mn>
</mml:mrow>
</mml:math>这样<mml:math alttext="$f(A)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>有个<mml:math alttext="$(1+|A|^2)^-r$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
|</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
|</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>
2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
r</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>- 调查<mml:math alttext="$BC^{k}(f(\mathbf{R}^n))$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
b</mml:mi>
<mml:msup>
<mml:mi>
C</mml:mi>
<mml:mi>
k</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold">
r</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>功能积分。这立即产生带有明确表示的正规半群和余弦函数。特别是<mml:math alttext="$f(\mathbf{R}^n)\subseteq\mathbf{R}$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold">
r</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mo>
⫅</mml:mo>
<mml:mi mathvariant="bold">
r</mml:mi>
</mml:mrow>
</mml:math>，然后，适当<mml:math alttext="$k,r$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
k</mml:mi>
<mml:mo>
，，，，</mml:mo>
<mml:mi>
r</mml:mi>
</mml:mrow>
</mml:math>，，，，<mml:math alttext="$t\mapsto(1-it)^{-k}e^{-itf(A)}(1+|A|^2)^{-r}$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
t</mml:mi>
<mml:mo>
↦</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
-</mml:mo>
<mml:mi>
一世</mml:mi>
<mml:mi>
t</mml:mi>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
k</mml:mi>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>
e</mml:mi>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
一世</mml:mi>
<mml:mi>
t</mml:mi>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
|</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
|</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>
2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
r</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>是一个傅立叶 - 斯泰尔杰斯的变换，当<mml:math alttext="$f(\mathbf{R}^n)\subseteq[0,\infty)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold">
r</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mo>
⫅</mml:mo>
<mml:mrow>
<mml:mo>
[[</mml:mo>
<mml:mrow>
<mml:mn>
0</mml:mn>
<mml:mo>
，，，，</mml:mo>
<mml:mi>
∞</mml:mi>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:math>， 然后<mml:math alttext="$t\mapsto(1+t)^{-k}e^{-tf(A)}(1+|A|^2)^{-r}$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
t</mml:mi>
<mml:mo>
↦</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
+</mml:mo>
<mml:mi>
t</mml:mi>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
k</mml:mi>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mi>
e</mml:mi>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
t</mml:mi>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
<mml:msup>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
|</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
|</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>
2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>
-</mml:mo>
<mml:mi>
r</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>是Laplace-Stieltjes变换。和<mml:math alttext="$A\equiv i(D_1,\ldots,D_n),f(A)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
一个</mml:mi>
<mml:mo>
◦</mml:mo>
<mml:mi>
一世</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>
d</mml:mi>
<mml:mn>
1</mml:mn>
</mml:msub>
<mml:mo>
，，，，</mml:mo>
<mml:mo>
…</mml:mo>
<mml:mo>
，，，，</mml:mo>
<mml:msub>
<mml:mi>
d</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mo>
，，，，</mml:mo>
<mml:mi>
F</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mi>
一个</mml:mi>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>是伪差的操作员<mml:math alttext="$L^{p}(\mathbf{R}^n) (1\leq p < \infty)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msup>
<mml:mi>
l</mml:mi>
<mml:mi>
p</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold">
r</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:mn>
1</mml:mn>
<mml:mo>
≤</mml:mo>
<mml:mi>
p</mml:mi>
<mml:mo>
<</mml:mo>
<mml:mi>
∞</mml:mi>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>或者<mml:math alttext="$BUC(\mathbf{R}^n)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
b</mml:mi>
<mml:mi>
你</mml:mi>
<mml:mi>
C</mml:mi>
<mml:mrow>
<mml:mo>
（（</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold">
r</mml:mi>
<mml:mi>
n</mml:mi>
</mml:msup>
</mml:mrow>
<mml:mo>
）</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>。</p></div>
<div class="xml-content">
<h4 class="copyright" id="copyright">版权</h4>
<p>版权所有©1997 Hindawi Publishing Corporation。这是根据<a rel="license" href="http://creativecommons.org/licenses/by/3.0/">创意共享归因许可证</a>，只要适当地引用了原始作品，允许在任何媒介中不受限制地使用，分发和繁殖。</p></div>
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<li><a class="sc-htpNat bUhGXt link partnerships" href="//www.newsama.com/publishing-partnerships/" aria-label="Partnerships"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">伙伴关系</a></li>
<li><a class="sc-htpNat bUhGXt link blog" href="//www.newsama.com/blog/" aria-label="Blog"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">博客</a></li>
</ul>
<ul class="_2k5c8zEhMT-84kRD4oDgAz _1SoDWGr_FVsil9klRfjnhb">
<li><a class="sc-htpNat bUhGXt link journals" href="//www.newsama.com/journals/" aria-label="Journals"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iOCIgaGVpZ2h0PSIxNCIgdmlld0JveD0iMCAwIDggMTQiPjxkZWZzPjxjbGlwUGF0aCBpZD0iYSI+PHBhdGggZD0iTTcsMi40MTRsNS4yOTMsNS4yOTNhMSwxLDAsMSwwLDEuNDE0LTEuNDE0bC02LTZhMSwxLDAsMCwwLTEuNDE0LDBsLTYsNkExLDEsMCwwLDAsMS43MDcsNy43MDdaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSg1IDgpIi8+PC9jbGlwUGF0aD48L2RlZnM+PGcgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTggMTkpIHJvdGF0ZSgtOTApIj48cGF0aCBkPSJNNywyLjQxNGw1LjI5Myw1LjI5M2ExLDEsMCwxLDAsMS40MTQtMS40MTRsLTYtNmExLDEsMCwwLDAtMS40MTQsMGwtNiw2QTEsMSwwLDAsMCwxLjcwNyw3LjcwN1oiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDUgOCkiLz48ZyBjbGlwLXBhdGg9InVybCgjYSkiPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0icmdiYSgwLDAsMCwwKSIvPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0iIzZiYTQzOSIvPjwvZz48L2c+PC9zdmc+" height="14">期刊</a></li>
<li><a class="sc-htpNat bUhGXt link article_processing_charges" href="//www.newsama.com/publish-research/authors/article-processing-charges/" aria-label="Article Processing Charges"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iOCIgaGVpZ2h0PSIxNCIgdmlld0JveD0iMCAwIDggMTQiPjxkZWZzPjxjbGlwUGF0aCBpZD0iYSI+PHBhdGggZD0iTTcsMi40MTRsNS4yOTMsNS4yOTNhMSwxLDAsMSwwLDEuNDE0LTEuNDE0bC02LTZhMSwxLDAsMCwwLTEuNDE0LDBsLTYsNkExLDEsMCwwLDAsMS43MDcsNy43MDdaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSg1IDgpIi8+PC9jbGlwUGF0aD48L2RlZnM+PGcgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTggMTkpIHJvdGF0ZSgtOTApIj48cGF0aCBkPSJNNywyLjQxNGw1LjI5Myw1LjI5M2ExLDEsMCwxLDAsMS40MTQtMS40MTRsLTYtNmExLDEsMCwwLDAtMS40MTQsMGwtNiw2QTEsMSwwLDAsMCwxLjcwNyw3LjcwN1oiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDUgOCkiLz48ZyBjbGlwLXBhdGg9InVybCgjYSkiPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0icmdiYSgwLDAsMCwwKSIvPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0iIzZiYTQzOSIvPjwvZz48L2c+PC9zdmc+" height="14">文章处理费用</a></li>
<li><a class="sc-htpNat bUhGXt link print_editions" href="//www.newsama.com/print-editions/" aria-label="Print editions"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">印刷版</a></li>
</ul>
<ul class="_2k5c8zEhMT-84kRD4oDgAz _1SoDWGr_FVsil9klRfjnhb">
<li><a class="sc-htpNat bUhGXt link authors" href="//www.newsama.com/publish-research/authors/" aria-label="Authors"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iOCIgaGVpZ2h0PSIxNCIgdmlld0JveD0iMCAwIDggMTQiPjxkZWZzPjxjbGlwUGF0aCBpZD0iYSI+PHBhdGggZD0iTTcsMi40MTRsNS4yOTMsNS4yOTNhMSwxLDAsMSwwLDEuNDE0LTEuNDE0bC02LTZhMSwxLDAsMCwwLTEuNDE0LDBsLTYsNkExLDEsMCwwLDAsMS43MDcsNy43MDdaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSg1IDgpIi8+PC9jbGlwUGF0aD48L2RlZnM+PGcgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTggMTkpIHJvdGF0ZSgtOTApIj48cGF0aCBkPSJNNywyLjQxNGw1LjI5Myw1LjI5M2ExLDEsMCwxLDAsMS40MTQtMS40MTRsLTYtNmExLDEsMCwwLDAtMS40MTQsMGwtNiw2QTEsMSwwLDAsMCwxLjcwNyw3LjcwN1oiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDUgOCkiLz48ZyBjbGlwLXBhdGg9InVybCgjYSkiPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0icmdiYSgwLDAsMCwwKSIvPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0iIzZiYTQzOSIvPjwvZz48L2c+PC9zdmc+" height="14">作者</a></li>
<li><a class="sc-htpNat bUhGXt link editors" href="//www.newsama.com/publish-research/editors/" aria-label="Editors"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">编辑</a></li>
<li><a class="sc-htpNat bUhGXt link reviewers" href="//www.newsama.com/publish-research/reviewers/" aria-label="Reviewers"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">评论者</a></li>
</ul>
<ul class="_2k5c8zEhMT-84kRD4oDgAz _1SoDWGr_FVsil9klRfjnhb">
<li><a class="sc-htpNat bUhGXt link hindawi_xml_corpus" href="//www.newsama.com/hindawi-xml-corpus/" aria-label="Hindawi XML Corpus"><img alt="" class="sc-EHOje fknadA" title="" role="presentation" src="data:image/svg+xml;base64,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" height="14">雷电竞APP</a></li>
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