XmlSerializer Mixed Content Deserialization
Correct XML serialization and deserialization of "mixed" types in .NET
What are the existing datasets of world maritime routes? In transformers, the ratio of the voltages equals the ratio of the turns - so double the output coil's turns and the output voltage doubles. Then, in order to conserve energy, current halves.  This makes perfect sense in terms of $\mathrm{P=VI}$, but what happened to $\mathrm{V=IR}$? Doubling voltage and halving the current seems to completely contradict this basic law. That is, of course, unless the resistance in the output circuit changes, with R proportional to $\mathrm{V^2}$ - but I don't see how this is possible.  So how can a transformer obey both laws? Can resistance change or am I missing something else? How to make a figure span on two columns in a scientific paper? When functions commute under composition Today I was thinking about composition of functions.  It has nice properties, its always associative, there is an identity, and if we restrict to bijective functions then we have an inverse.  But then I thought about commutativity.  My first intuition was that bijective self maps of a space should commute but then I saw some counter-examples. The symmetric group is only abelian if $n \le 2$ so clearly there need to be more restrictions on functions than bijectivity for them to commute.  The only examples I could think of were boring things like multiplying by a constant or maximal tori of groups like $O(n)$ (maybe less boring).  My question: In a euclidean space, what are (edit) some nice characterizations of sets of functions that commute? What about in a more general space?   Bonus: Is this notion of commutativity important anywhere in analysis? I recall having heard somewhere that the only 1-manifolds (second countable, Hausdorff, connected spaces locally homeomorphic to $\mathbb R$) are $\mathbb R$ and $S^1$. Is this true? If so, is there a reasonably elementary proof? Render result is completely blank A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [ Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! Setting controller variables not reliable from apex:commandButton I'm trying to set a variable inside my controller via an actionFunction, which is called by some Javascript, which is initially called by either by an actionPanel (with styleClass='btn') or a commandButton.  If the caller is the actionPanel then the variable updates reliably. However with the commandButton I can see the updated value flash briefly before reverting to its previous value. Maybe one out of every six clicks of the button actually causes the new value to stick. Sometimes it can take a dozen or more tries, regardless of click frequency.  Can someone please explain what's going on here?  PAGE  &lt;apex:page controller="MyController"&gt;     &lt;apex:form &gt;         &lt;apex:outputPanel id="panel"&gt;             &lt;apex:outputText value="MyString = {!MyString}"/&gt;             &lt;apex:actionFunction name="SetString" rerender="panel"&gt;                 &lt;apex:param name="param1" value="" assignTo="{!MyString}"/&gt;             &lt;/apex:actionFunction&gt;             &lt;script&gt;                 function JSetString() {                     SetString('{!MyString}' + '.');                 }             &lt;/script&gt;             &lt;apex:outputPanel onclick="JSetString()" styleClass="btn"&gt;                 Grow {!MyString} (works)             &lt;/apex:outputPanel&gt;             &lt;apex:commandButton onclick="JSetString()" value="Grow {!MyString} (unreliable)" rerender="panel"/&gt;         &lt;/apex:outputPanel&gt;     &lt;/apex:form&gt; &lt;/apex:page&gt;   CONTROLLER  global class MyController {      public MyController() { MyString = 'hello'; }      public String MyString {get;set;} } I'm currently working on a scene containing 1000+ objects which all need to be set to a different draw type to save on computationally expenses in the viewport. But doing this for every object separately is really tedious. Therefor I'm wondering if there's a way to change the maximum draw type of multiple objects simultaneously. Preferably only the selected objects. I am on Ubuntu 12.04 64-bits  I accidentally deleted a NTFS 255 GB partition using Gparted, and yes it contains LOTS of important data.  Upon realizing the deletion I haven't yet created any file-system on it. So it still shows Unallocated.    I tried Testdisk , but it shows entire partitions created from the beginning.  This sdb is my secondary drive with Xubuntu and Kubuntu on it. And that 255 GB NTFS  partition was cross platform storage drive.  I am currently in sda with Ubuntu and Win7 in dual boot, which enables me to use it as Safe recovery option rather then Live USB drive.   First ,  should i allocate it to ? file-System for better recovery .  Second , i really need to recover data from this drive so please give me possible  suggestions and proven methods of data recovery.  Third ,does Testdisk requires deleted partition to be allocated for its recovery .  I am currently trying the answer seen here  with Testdisk scanning for partition second time, hoping to recover it.   It looks a duplicate but i can't confirm if the OP got it right. Since my first doubt is to allocate it or not.  If any clarification required please do comment ,i will add it.  Edit: TestDisk deeper search results.      The following partitions can't be recovered:          Partition               Start        End    Size in sectors     &gt;  HPFS - NTFS          22241 107 11 55592   3 27  535777280        FAT32 LBA            274460 158 19 460576 228 16 2989957948  NTFS, 274 GB / 255 GiB &amp; for FAT32 LBA 1530 GB / 1425 GiB How to solve the equation $\phi(n) = k$? How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle? How to enable hibernation? What flash slaves can be used with a Canon Speedlite 600EX-RT? My current flash setup is a standard shoe mount but I've been thinking about getting a remote.  I've been drooling over the Speedlite 600EX-RT. It uses radio to control slaves, which is nice (longer distance, doesn't require line of sight, etc.).  One thing I don't understand: do slaves also have to be 600EX-RTs or do other flash units use radio to communicate already? Can any (cheap?) flash slaves can be used with a Canon Speedlite 600EX-RT or do I need to buy the 600EX and a ST-E3-RT transmitter in order (or multiple 600EX-RTs) to have a radio-controlled remote flash setup? Why am I asked for a credit card number to download a free app? I  want to download free app in my iPod touch device and i have the following doubts.  Kindly resolve me doubts.   when i try to download it asks my credit card security number. since i am trying to download free app , why do i need to provide my credit card security code? Will i be debited for downloading the free app from app store?   I cant able to find any information regarding this on apple.  Please provide me some references about this from apple and please resolve my doubts.  Thanks a lot. Removing phone number from iMessage I'd like to remove my phone number from my iMessage account, but still have my phone enabled to receive messages sent to my email address (also used on iPad, Mac). Is there a way of doing this? Filter to change the content of 404 page I have created custom rewrite rules. These rules now go to 404 page as expected. I can use action hook template_redirect to change the template matching query_var.  But I don't want to create separate template files as the page structure depend on the current theme in use. Rather I just want to change the content and title. I have tried change the content using the_content filter, but it seems the filter doesn't even get called for 404 page.  I also tried loading index.php template and then using the_content filter, but it also doesn't work.  Is there any way to achieve this? What are the blue dots next to App names in iOS and macOS? They disappear once you open the apps and then return to the home screen, but I can't tell what they indicate.  Are they apps that haven't been opened since an app update? Or that it thinks have never been opened (not accurate in my case, but that could be a function of a "restore" confusing the phone). How to assign symbols to functions What is the function __construct used for? I have been noticing __construct a lot with classes. I did a little reading and surfing the web, but I couldn't find an explanation I could understand. I am just beginning with OOP.  I was wondering if someone could give me a general idea of what it is, and then a simple example of how it is used with PHP?