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<p class="MsoNormal"><span style="font-size:11.0pt">Hello Mac experts,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I wrote the following code on my Mac but the resulting plot has a weird dashed line. Here are the codes:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">zeta.ppt <- function(v){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> ppt=function(i){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> result <- numeric(length(i))<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> for (j in i){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> if (j < 11) {result[j] <- (11-j)/110}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> else {result[j] <- 3/pi^2/(j-10)^2}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> result<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> p <- ppt(1:10000)<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout <- numeric(length(v))<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> for (k in 1:length(v)) {<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout[k] <- sum(p*(1-p)^v[k])<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">zeta.sept <- function(v){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> sept=function(i){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> result <- numeric(length(i))<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> for (j in i){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> if (j < 11) {result[j] <- (11-j)/110}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> else {result[j] <- 0.5/1.670407*exp(-sqrt(j-10))}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> result<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> p <- sept(1:10000)<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout <- numeric(length(v))<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> for (k in 1:length(v)) {<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout[k] <- sum(p*(1-p)^v[k])<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> }<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> printout<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">tau.ppt <- function(v){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> v*zeta.ppt(v)<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">tau.sept <- function(v){<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> v*zeta.sept(v)<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">}<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">plot(log(tau.ppt(1:20000))~log(1:20000), xlim = c(0,10), ylim=c(0, 5), axes = F, ylab = "", xlab = "", type
= "l")<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">lines(log(tau.sept(1:20000))~log(1:20000), lty = 2, type = "l")<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-size:10.0pt;font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">box()</span><span style="font-size:10.0pt;font-family:"var(--ff-mono)",serif"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Here is the plot I got:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><img width="564" height="414" style="width:5.875in;height:4.3125in" id="Picture_x0020_1" src="cid:image001.png@01D828D3.E0CEA840" alt="Plot 1"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">As we could observe, the end portion of the dashed line is almost a solid line. I posted the question on
<a href="https://stackoverflow.com/questions/71241028/plot-line-types-in-r">https://stackoverflow.com/questions/71241028/plot-line-types-in-r</a> as well and seems they can run my codes with perfect dashed line on Windows OS.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I have tried it on both intel Mac and M1 Mac, both gave me weird dashed lines. I have tried it in both R and RStudio. Here is my sessionsInfo:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<pre style="vertical-align:baseline"><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">></span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> sessionInfo</span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">()</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">R version </span></code><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">4.1</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">.2 </span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">(</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">2021</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">11</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">01</span></span><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">)</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Platform</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> x86_64</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">apple</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">darwin17.0 </span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">(</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">64</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">bit</span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">)</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Running under</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> macOS Monterey </span></code><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">12.2</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">.1<o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p> </o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Matrix products</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> default<o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">LAPACK</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> </span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Library</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Frameworks</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">R.framework</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Versions</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">4.1</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">Resources</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">lib</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">libRlapack.dylib<o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p> </o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">locale</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">[</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">1</span></span><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">]</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> en_US.UTF</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">8</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">en_US.UTF</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">8</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">en_US.UTF</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">8</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">C</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">en_US.UTF</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">8</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">/</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">en_US.UTF</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">-</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">8</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p> </o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">attached base packages</span></code><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">[</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">1</span></span><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">]</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> stats graphics grDevices utils datasets methods base <o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p> </o:p></span></code></pre>
<pre style="vertical-align:baseline"><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">loaded via a namespace </span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">(</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">and not attached</span></code><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">)</span></span><span class="hljs-operator"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">:</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"><o:p></o:p></span></code></pre>
<pre style="vertical-align:baseline"><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">[</span></span><span class="hljs-number"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">1</span></span><span class="hljs-punctuation"><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in">]</span></span><code><span style="font-family:"inherit",serif;border:none windowtext 1.0pt;padding:0in"> compiler_4.1.2 tools_4.1.2 </span></code><span style="font-family:"var(--ff-mono)",serif"><o:p></o:p></span></pre>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Please advise. Thank you!<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Helvetica;color:black">—<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Helvetica;color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Helvetica;color:black">Jialin Zhang (JZ), Assistant Professor of Statistics<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Helvetica;color:black">Department of Mathematics and Statistics<br>
Mississippi State University<br>
tel: (662) 325-7137; <a href="mailto:jzhang@math.msstate.edu" title="mailto:jzhang@math.msstate.edu"><span style="color:#000064">email: jzhang@math.msstate.edu</span></a><o:p></o:p></span></p>
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