Merge pull request #23 from idematos/fix-header

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idematos · Jan 8, 2025 · b3b1586 · b3b1586
2 parents 8e32785 + 79f00de
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diff --git a/research/computing/algorithm/index.html b/research/computing/algorithm/index.html
@@ -49,7 +49,7 @@
         <content>
             <section>
                 <h1>An algorithm is a sequence of instructions to perform an action.</h1>
-                <p>Its primary characteristics are correctness, efficiency, and scalability, but the focus here is on its energy consumption.</p>
+                <p>Its primary characteristics are correctness, efficiency, and scalability, but here I will focus on its energy consumption.</p>
             </section>
 
             <section>
@@ -62,21 +62,21 @@ <h2>Evaluation metrics</h2>
                         <p><b>Space Complexity</b>: The memory usage.</p>
                     </li>
                     <li>
-                        <p><b>Energy Complexity</b>: The energy required to execute it on specific hardware.</p>
+                        <p><b>Energy Complexity</b>: The energy required to execute it.</p>
                     </li>
                 </ul>
 
                 <p>
-                    The energy consumption of an algorithm depends on the number of operations performed, the type of operations, and the hardware's efficiency. 
-                    Algorithms with lower time complexity generally consume less energy because they perform fewer operations. 
+                    The energy complexity of an algorithm depends on the number of operations performed, the type of operations, and the hardware's efficiency. 
+                    Algorithms with lower time complexity generally consume less energy because they perform fewer operations.
                     For example, a merge sort (<i>O(n log n)</i>) is more energy-efficient than a bubble sort (<i>O(n²)</i>) for large datasets.
                 </p>
             </section>
 
             <section>
                 <h2>Optimisation</h2>
                 <p>
-                    Here are some strategies that can help to reduce the energy consumption associated with algorithms and data structures.
+                    These are some strategies that can help to reduce the energy consumption associated with algorithms and data structures.
                 </p>
                 <h3>Algorithmic Improvements</h3>
                 <h4>Complexity</h4>
@@ -121,13 +121,13 @@ <h3>Scheduling and Execution</h3>
                 <h4>Dynamic Voltage and Frequency Scaling</h4>
                 <p>
                     Voltage and frequency can be adjusted dynamically based on the workload. 
-                    For instance, algorithms with non-critical tasks can execute at lower clock speeds.
+                    Algorithms with non-critical tasks can execute at lower clock speeds.
                 </p>
 
                 <h4>Asynchronous Execution</h4>
                 <p>
                     Independent tasks can be executed asynchronously. Event-driven
-                     programming models facilitate this in I/O-bound applications.
+                    programming models facilitate this in I/O-bound applications.
                 </p>
 
                 <h4>Batch Processing</h4>
@@ -142,7 +142,7 @@ <h4>Efficient Data Structures</h4>
                 <ul>
                     <li>
                         <p>
-                            Some data structures minimise computational overhead. For instance, replacing 
+                            Some data structures minimise computational overhead. For example, replacing 
                             linked lists with dynamic arrays for random access operations reduces cache misses.
                         </p>
                     </li>

diff --git a/research/mathematics/number/index.html b/research/mathematics/number/index.html
@@ -9,6 +9,17 @@
   <body>
     <header>
       <nav>
+        <ul class="hide-on-mobile">
+            <li>
+                <a href="/">about</a>
+            </li>
+            <li>
+                <strong><a href="/research">research</a></strong>
+            </li>
+            <li>
+                <a href="/photography">photography</a>
+            </li>
+        </ul>
         <ul>
             <li>
                 <a href="/research/computing">computing</a>

diff --git a/research/mathematics/number/induction/index.html b/research/mathematics/number/induction/index.html
@@ -9,6 +9,17 @@
   <body>
     <header>
       <nav>
+        <ul class="hide-on-mobile">
+            <li>
+                <a href="/">about</a>
+            </li>
+            <li>
+                <strong><a href="/research">research</a></strong>
+            </li>
+            <li>
+                <a href="/photography">photography</a>
+            </li>
+        </ul>
         <ul>
             <li>
                 <a href="/research/computing">computing</a>

diff --git a/research/mathematics/number/prime/index.html b/research/mathematics/number/prime/index.html
@@ -9,6 +9,17 @@
   <body>
     <header>
       <nav>
+        <ul class="hide-on-mobile">
+            <li>
+                <a href="/">about</a>
+            </li>
+            <li>
+                <strong><a href="/research">research</a></strong>
+            </li>
+            <li>
+                <a href="/photography">photography</a>
+            </li>
+        </ul>
         <ul>
             <li>
                 <a href="/research/computing">computing</a>