Bijection between homomorphisms $\mathbb Z[i]\to R$ and set $x\in R$ with $x^2+1=0$
Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
Bit error rate calculation for LIN protocol I am having this microcontroller -   I am using an 8MHz external clock. I want to calculate the Bit error rate of my LIN Communication. My LIN Communication Baud rate is 19.2kbps. My questions :  Can I use the LPUART Module in the Mirocontroller for the LIN Communication?  How to find the Bit error rate for the LIN Protocol communication for my baud rate of 19.2kbps and external clock of 8MHz.   I found this below from the reference manual. But not sure, how to calculate the Bit error rate from this.   How to calculate the SBR Register value, OSR and the LPUART ASYNCH Module clock?  Please help freezing header in a table in html I installed Windows 7 in a 3-year-old machine. It installed successfully, took all drivers and running great, but every 5-6 minutes it freezes for a few seconds... 30 seconds to 1 minute, and then it comes back alive.  I checked Event Viewer, but nothing matched the frozen timeline.  I would appreciate any help on how to detect what is causing it, service or hardware.  After it comes alive, everything runs normal. I did run Task Manager and checked CPU usage, at the time it freezes just before and after that no task took more CPU or memory. It was like an idle machine.  There aren't any external USB drives or devices. It is an on-board Intel desktop board with SATA HDD, and the SATA HDD is running in absolute good mode. How to redirect complete outgoing phone's traffic to a proxy server? Eclipse menus are cut off or don't show I'm using Ubuntu 13.10 (with JDK 1.7.0_45).  I've downloaded and uncompressed Eclipse Kepler for Java EE Developers.  The software menus are messed up. I didn't notice similar problems in other software.  When I click any menu in Eclipse, the drop-down seems to be "cut". Sometimes the drop-down shows, but the options are invisible.  I tried Eclipse Indigo, but the same problem occurs. iPhone 4 water damage - how to recover data? I am testing the new  &lt;lightning:datatable&gt;, it is really good, and is a good replacement for most of my use cases which today I use a custom list component that I have developed.  I am getting data from my server through apex method, to populate it into the &lt;lightning:datatable&gt; component. I can bind the returned list directly to the data attribute and if the column names are same as the field names, all data is bound correctly.  The problem occurs when I get data from a parent record. For example - I want the Account name of my contact.  This example can show the problem:  Component Markup    &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}"/&gt;  &lt;aura:attribute name="mydata" type="Object"/&gt; &lt;aura:attribute name="mycolumns" type="List"/&gt; &lt;aura:attribute name="sortedBy" type="String"/&gt; &lt;aura:attribute name="sortedDirection" type="String"/&gt;  &lt;lightning:datatable data="{! v.mydata }"                      columns="{! v.mycolumns }"                      keyField="Id"                      onrowselection="{! c.getSelectedName }"                      onsort="{!c.updateColumnSorting}"                      sortedBy="{!v.sortedBy}"                      sortedDirection="{!v.sortedDirection}"                      hideCheckboxColumn="{!false}" /&gt;        Component Controller  ({     doInit: function (component, event, helper) {         component.set('v.mycolumns', [                     {label: 'Id', fieldName: 'Id', type: 'id', sortable:"true"},                     {label: 'First Name', fieldName: 'FirstName', type: 'text', sortable:"true"},                     {label: 'Last Name', fieldName: 'LastName', type: 'text', sortable:"true"},                     {label: 'First Name Hebrew', fieldName: 'First_name_Hebrew__c', type: 'text', sortable:"true"},                     {label: 'Last Name Hebrew', fieldName: 'Last_name_Hebrew__c', type: 'text', sortable:"true"},                     {label: 'Account', fieldName: 'Account.Name', type: 'text', sortable:"true"},                     {label: 'Email', fieldName: 'Email', type: 'email', sortable:"true"},                     {label: 'Phone', fieldName: 'Phone', type: 'phone', sortable:"true"}                 ]);          var action = component.get("c.getRecordsFromDb");         action.setParams({             sObjectName: "Contact",             commaDelimitedFieldNames: "Id,FirstName,LastName,First_name_Hebrew__c,Last_name_Hebrew__c,Account.Name,Email,Phone",             filter: ""         });         action.setCallback(this, function(response){             var state = response.getState();             if (component.isValid() &amp;&amp; state === "SUCCESS") {                 var data = response.getReturnValue();                  component.set("v.mydata", data);             }         });         $A.enqueueAction(action);     } })   APEX Aura Enabled Method  @AuraEnabled public static List&lt;sObject&gt; getRecordsFromDb(String sObjectName,         String commaDelimitedFieldNames,         String filter) {      system.debug('\n\n\n\ngetRecordsFromDb sObjectName: ' + sObjectName + ', commaDelimitedFieldNames: ' + commaDelimitedFieldNames + ', filter: ' + filter + '\n\n\n\n');      // create a dynamic soql to get the value of the field     String sql = 'SELECT ' + commaDelimitedFieldNames + ' FROM ' + sObjectName;      if (!String.isBlank(filter))         sql += ' WHERE ' + filter;      system.debug('\n\n\n\ngetRecordsFromDb sql: ' + sql + '\n\n\n\n');     List&lt;sObject&gt; records = Database.query(sql);     system.debug('\n\n\n\ngetRecordsFromDb: ' + records + '\n\n\n\n');      return records; }   The problem is with the Account.Name field - the &lt;lightning:datatable&gt; component does not display the column data.   I know that the data is returned ok, and I know that in the object that is returned, the Account is contained like an object (probably this is the problem):    Is there a good way to show parent record data with this component? Did the Big Bang happen at a point? Turning vector grid into individual shapefiles using QGIS? I am using QGIS and I created a vector grid on a crop field in order to cut it into plots. I want to save each grid cell into individual polygon shapefiles automatically.  Here is an example of a vector grid I would like to split into 117 shapefiles:    Eventually, I did it manually with the selection tool and "Save as" but it is really time-consuming when there are more than 100 plots to save.    Is there any way to do it faster and more automatically?  Each plot as an attribute named "Plot" that can discriminate against them (basically being id + 1). It's the attribute used here to label them. In a bash shell script, writing a for loop that iterates over string values $\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$ Trying to compute   I was facing: \begin{align}J=\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx\end{align}  I want to prove that $\displaystyle J=0$, or equivalently, that,  \begin{align}\int_0^1 \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx=-\dfrac{1}{2}\text{G}\end{align}  $\text{G}$ being the Catalan constant.  Read carefully please.   I know, using so-called Feynman's trick, how to prove this. I would like to obtain a proof, using only integration by parts and change of variable in simple integrals (that is, no multiple integrals) I don't know, if, under these restrictions, such computation is possible.  NB: You're probably wondering what is the link between : $\int_{0}^{\frac{\pi}4} \ln(\sin{x}+\cos{x}+\sqrt{\sin{2x}})dx$ and $J$.  The link is, for $x\in\left[0;\frac{\pi}{2}\right]$, $(\sin{x}+\cos{x}+\sqrt{\sin{2x}})(\sin{x}+\cos{x}-\sqrt{\sin{2x}})=1$ and $\sin(2x)=2\sin x\cos x$ Append to the end of a file in C Avoid trailing zeroes in printf() This is a question that keeps bothering me: much of mathematics was created by extending rules to new domains e.g. negative numbers were created by consistently extending arithmetic beyond positive integers. However, with number bases it seems impossible to do this. Number bases are integers, but could they be rational numbers? I've had previous discussions about this, see . One problem can be seen with this example: in base 2.5, 0.22 is greater than one. That's not what we want! What, if anything, can be done about this?  EDIT: To put it another way - if every positional number is less than any digit to its left, why doesn't this apply to fractional base positional numbers? Suspected adware infection of Mac Is this correct?     The person with whom I'm doing the project should be here soon.   If it is, is with always a dative preposition (like mit in German)? When is logistic regression solved in closed form? DRAM Frequency showing 800 instead of 1600 I am running a Core i7 CPU originally at 3Ghz overclocked to 4Ghz using a multiplier of x20 and a Bus Speed of 200 Mhz  My memory is 1600 Mhz OCZ.  I installed CPU-Z to see what is going on - but it shows me (under the "Memory" Tab):  DRAM Frequency 800 Mhz  Channel Triple - NB Frequency 3800.2 Mhz  So what is the actual frequency its running on then? I am slightly confused. How can I create a new extensible symbol? Given an arbitrary thin vertical symbol, can I create a new math delimiter from it (and if so, how)?   Edit: Ideally, I would like to be able to create an extensible symbol, either built out an existing normal symbol, or even made from scratch.  Edit 2: I am pretty sure that what I am after is an explanation of how to create a .tfm file for an extensible symbol (which Werner's answer describes the general structure of, but not how to make one).    For example, let's say I wanted to use the \dagger () or \wr () symbol as a delimiter, and write expressions like    \[\left\ldagger \sum_{n=1}^\infty a_n \right\rdagger\]   where the symbol scaled appropriately. Would there be any distinction between declaring a symmetric delimiter (like \vert), as opposed to one that has inherently different "left" and "right" versions like [ and ]?  Now, even being unaware of the inner workings of TeX, I imagine that there has to be lots of information in the fonts for how a delimiter is to be scaled in different situations, and if I try to make my own delimiter, this information won't be present. Would I need to get deep into FontForge or equivalent to achieve my custom delimiters, or is there an easier way? R/mgcv: Why do te() and ti() tensor products produce different surfaces?