Fix typo, missing "are"

ads-1.tex

@@ -12489,7 +12489,7 @@ \chapter*{#1}%
 \end{equation*}
 %
 \par
-One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
+One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
 \end{example}
 \begin{example}{Applications of the Gray Code.}{g:example:idm347915442752}%
 One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.%
@@ -18097,4 +18097,4 @@ \chapter*{#1}%
 %% Index locators are cross-references, so same font here
 {\xreffont\printindex}
 %
-\end{document}
+\end{document}

ads-1_print.tex

@@ -12494,7 +12494,7 @@ \chapter*{#1}%
 \end{equation*}
 %
 \par
-One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
+One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
 \end{example}
 \begin{example}{Applications of the Gray Code.}{g:example:idm294775519728}%
 One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.%
@@ -18102,4 +18102,4 @@ \chapter*{#1}%
 %% Index locators are cross-references, so same font here
 {\xreffont\printindex}
 %
-\end{document}
+\end{document}

ads-3-6/knowl/ex-intro-a-to-d-hidden.html

@@ -76,5 +76,5 @@
 \right)
 \end{equation*}
 </div>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></body>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></body>
 </html>

ads-3-6/knowl/ex-intro-a-to-d.html

@@ -80,6 +80,6 @@
 \right)
 \end{equation*}
 </div>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article><span class="incontext"><a href="s-traversals.html#ex-intro-a-to-d">in-context</a></span>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article><span class="incontext"><a href="s-traversals.html#ex-intro-a-to-d">in-context</a></span>
 </body>
 </html>

ads-3-6/knowl/p-3258.html

@@ -13,7 +13,7 @@
 </head>
 <body>
 <h6 class="heading"><span class="type">Paragraph</span></h6>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p>
 <span class="incontext"><a href="s-traversals.html#p-3258">in-context</a></span>
 </body>
 </html>

ads-3-6/s-traversals.html

@@ -418,7 +418,7 @@ <h1 class="heading"><a href="ads.html"><span class="title">Applied Discrete Stru
 \right)
 \end{equation*}
 </div>
-<p id="p-3258">One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></div>
+<p id="p-3258">One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></div>
 <article class="example-like" id="example-160"><a data-knowl="" class="id-ref" data-refid="hk-example-160"><h6 class="heading">
 <span class="type">Example</span> <span class="codenumber">9.4.22</span>. <span class="title">Applications of the Gray Code.</span>
 </h6></a></article><div id="hk-example-160" class="hidden-content tex2jax_ignore"><article class="example-like"><p id="p-3259">One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\text{,}\) is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\text{,}\) where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.</p></article></div>

ads-3-7/knowl/ex-intro-a-to-d-hidden.html

@@ -76,5 +76,5 @@
 \right)
 \end{equation*}
 </div>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></body>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></body>
 </html>

ads-3-7/knowl/ex-intro-a-to-d.html

@@ -80,6 +80,6 @@
 \right)
 \end{equation*}
 </div>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article><span class="incontext"><a href="s-traversals.html#ex-intro-a-to-d">in-context</a></span>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article><span class="incontext"><a href="s-traversals.html#ex-intro-a-to-d">in-context</a></span>
 </body>
 </html>

ads-3-7/knowl/p-3277.html

@@ -13,7 +13,7 @@
 </head>
 <body>
 <h6 class="heading"><span class="type">Paragraph</span></h6>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p>
 <span class="incontext"><a href="s-traversals.html#p-3277">in-context</a></span>
 </body>
 </html>

ads-3-7/s-traversals.html

@@ -414,7 +414,7 @@ <h1 class="heading"><a href="ads.html"><span class="title">Applied Discrete Stru
 \right)
 \end{equation*}
 </div>
-<p id="p-3277">One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></div>
+<p id="p-3277">One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.</p></article></div>
 <article class="example example-like" id="example-160"><a data-knowl="" class="id-ref original" data-refid="hk-example-160"><h6 class="heading">
 <span class="type">Example</span><span class="space"> </span><span class="codenumber">9.4.22</span><span class="period">.</span><span class="space"> </span><span class="title">Applications of the Gray Code.</span>
 </h6></a></article><div class="hidden-content tex2jax_ignore" id="hk-example-160"><article class="example example-like"><p id="p-3278">One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\text{,}\) is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\text{,}\) where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.</p></article></div>

ads.tex

@@ -12499,7 +12499,7 @@ \chapter*{#1}%
 \end{equation*}
 %
 \par
-One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
+One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
 \end{example}
 \begin{example}{Applications of the Gray Code.}{g:example:idm40460211632}%
 One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.%
@@ -31018,4 +31018,4 @@ \chapter*{#1}%
 %% Index locators are cross-references, so same font here
 {\xreffont\printindex}
 %
-\end{document}
+\end{document}

ads_print.tex

@@ -12504,7 +12504,7 @@ \chapter*{#1}%
 \end{equation*}
 %
 \par
-One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
+One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.%
 \end{example}
 \begin{example}{Applications of the Gray Code.}{g:example:idm172460095776}%
 One application of the Gray code was discussed in the Introduction to this book.  Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.%
@@ -31023,4 +31023,4 @@ \chapter*{#1}%
 %% Index locators are cross-references, so same font here
 {\xreffont\printindex}
 %
-\end{document}
+\end{document}

src/S94.xml

@@ -253,7 +253,7 @@ with 0, and then (2) reversing the list of strings in <m>G_n</m> with each strin
 \end{array}
 \right)</me>
 </p>
-<p>One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this <q>decoding</q> is quite easy.</p>
+<p>One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this <q>decoding</q> is quite easy.</p>
 </example>
 
 <example><title>Applications of the Gray Code</title><p> One application of the Gray code was discussed in the Introduction to this book.  Another application is
@@ -357,4 +357,4 @@ as many times as it loses. Every round-robin tournament graph has a Hamiltonian
 
 
 </exercises>
-</section>
+</section>