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• GLIBC_2.8 not found

  - by Thomas Nilsson

  As a newbie I seem to have messed up my upgrade leaving my system in a very unstable state. I attempted an upgrade from 8.04LTS which ended in an error about libc and kernel upgrades. I tried to upgrade the kernel but am now unsure if that worked, because when I retried my dist-upgrade there was a lot of errors about pre-dependencies and leaving packages un-configured. Now I have a system that answers almost every command with: /lib/libc.so.6: version `GLIBC_2.8' not found (required by /lib/libselinux.so.1) I probably should try a complete re-installation, but I'm investigating if there is any possibility of getting a working glibc so that I at least can have some commands working to ensure that my backups are recent etc. before doing the clean install. not even 'ls' works without saying "glibc_2.8 not found".

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• What constitutes proper use of threads in programming?

  - by Smith

  I am tired of hearing people recommend that you should use only one thread per process, while many programs use up to 100 per process! take for example some common programs vb.net ide uses about 25 thread when not debugging System uses about 100 chrome uses about 19 Avira uses more than about 50 Any time I post a thread related question, I am reminded almost every time that I should not use more that one thread per process, and all the programs I mention above are ruining on my system with a single processor. What constitutes proper use of threads in programming? Please make general comment, but I'd prefer .NET framework thanks EDIT changed processor to process

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• What location to put bootloader, when running multiple drives and partition

  - by Matt G

  I have Win8 on my desktop, where a 120G SSD is used to run windows and some select applications, while I have a 2TB HDD to provide basic file storage and where possible, install applications instead of on the SSD. I want to install Ubuntu on a new partition of the HDD (I allocated 300GB, with 5GB swap file). I've used a USB to install the OS, which seemed to have done the job. However, after prompting for a restart, I can no longer boot to ubuntu. During instillation I was confused about where to install the "boot loader instillation". I ended up selecting "/dev/stb" because I figured I would be able to boot with BIOS by selecting the HDD drive as a priority over the SSD. The bootloader is a large part of where I think I went wrong. My partition system looked something like this: /dev/sta ... //SSD ~120 GB /dev/sta1 NTFS (350 MB) //Win8System /dev/sta2 NTFS (118 GB) //Win8C-Drive /dev/stb ... //HDD ~2TB /dev/stb1 NTFS (1563 GB) //FileStorage /dev/stb5 Free Space (300 GB) //Space I want to use for Linux (NOTE: Created two partitions from the 300GB, ~5GB and 295GB. stb5,stb6.) It'd be great if I could get an explanation of what drive you'd select for the boot loader and why, and what selections won't work with regards to the Boot Loader Instillation. I think I understand what Grub is, but I have no idea on how to use it, or play around with it. I seem to be able to get back into OS from my usb, however I believe it's just showing me a preview/trial of Ubuntu (ie, can't access any of the system NTFS drives). Note, if I try to install from the USB again, it will recognize that a version of Ubuntu 13.10 exists on the system. Apologies in advance, have used windows all my life, don't really know to much about Linux at all. Did have a brief skim over some similar questions, didn't find anything too useful. - Where to install bootloader when installing Ubuntu as secondary OS? - ubuntu 12.10 dual boot with windows 8 on two hdds - Dual-boot Windows 7 and Ubuntu on two SSDs with UEFI

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• Forward .html/.htm to .php with .config

  - by PhilipK

  I'm moving a site from my linux hosted server to a client's windows hosted server. The .htaccess file no longer works and I'm told that windows servers use .config . How can I forward all users accessing .html & .htm files to the equivalent .php file. Server Info... OS/Hosting Type: Windows / Shared Hosting .Net Runtime Version: ASP.Net 2.0/3.0/3.5 PHP Version: PHP 5.2 IIS Version: IIS 7.0 Data Center: US Regional EDIT *Hosting provided by GoDaddy Was told by a friend following should work but it has no effect on the site. <configuration> <system.webServer> <handlers> <add name="PHP-FastCGI" verb="*" path="*.html" modules="FastCgiModule" scriptProcessor="c:\php\php-cgi.exe" resourceType="Either" /> </handlers> </system.webServer> </configuration>

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• Which numeral systems are useful in computer science?

  - by authchir

  I am wondering which numeral system different programmers are using, or would use if their language has support for them. As an example, in C++ we can use: Octal by prefixing with 0 (e.g. 0377) Decimal by default (e.g. 255) Hexadecimal by prefixing with 0x (e.g. 0xff) When working with bitmask, I am using hexadecimal but would sometimes want to be able to express binary numbers directly. I know some programming language support it with 0b syntax (e.g. 0b11111111). Is there any other numeric system useful in some computer science domain (e.g. cryptography, codecs, 3D graphics, etc)?

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• TelnetSocket

  A wrapper for a System.Net.Sockets.TcpClient that performs simple Telnet negotiation and is scriptable.

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• Smooth vector based jump

  - by Esa

  I started working on Wolfire's mathematics tutorials. I got the jumping working well using a step by step system, where you press a button and the cube moves to the next point on the jumping curve. Then I tried making the jumping happen during a set time period e.g the jump starts and lands within 1.5 seconds. I tried the same system I used for the step by step implementation, but it happens instantly. After some googling I found that Time.deltatime should be used, but I could not figure how. Below is my current jumping code, which makes the jump happen instantly. while (transform.position.y > 0) { modifiedJumperVelocity -= jumperDrag; transform.position += new Vector3(modifiedJumperVelocity.x, modifiedJumperVelocity.y, 0); } Where modifiedJumperVelocity is starting vector minus the jumper drag. JumperDrag is the value that is substracted from the modifiedJumperVelocity during each step of the jump. Below is an image of the jumping curve:

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• Customer Support in Silverlight

  Take a screenshot of your running Silverlight app and submit it to your web server. Inclusive a lot of system information

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• Alternative way of developing for ASP.NET to WebForms - Any problems with this?

  - by John

  So I have been developing in ASP.NET WebForms for some time now but often get annoyed with all the overhead (like ViewState and all the JavaScript it generates), and the way WebForms takes over a lot of the HTML generation. Sometimes I just want full control over the markup and produce efficient HTML of my own so I have been experimenting with what I like to call HtmlForms. Essentially this is using ASP.NET WebForms but without the form runat="server" tag. Without this tag, ASP.NET does not seem to add anything to the page at all. From some basic tests it seems that it runs well and you still have the ability to use code-behind pages, and many ASP.NET controls such as repeaters. Of course without the form runat="server" many controls won't work. A post at Enterprise Software Development lists the controls that do require the tag. From that list you will see that all of the form elements like TextBoxes, DropDownLists, RadioButtons, etc cannot be used. Instead you use normal HTML form controls. But how do you access these HTML controls from the code behind? Retrieving values on post back is easy, you just use Request.QueryString or Request.Form. But passing data to the control could be a little messy. Do you use a ASP.NET Literal control in the value field or do you use <%= value % in the markup page? I found it best to add runat="server" to my HTML controls and then you can access the control in your code-behind like this: ((HtmlInputText)txtName).Value = "blah"; Here's a example that shows what you can do with a textbox and drop down list: Default.aspx <%@ Page Language="C#" AutoEventWireup="true" CodeBehind="Default.aspx.cs" Inherits="NoForm.Default" %> <%@ Page Language="C#" AutoEventWireup="true" CodeBehind="Default.aspx.cs" Inherits="NoForm.Default" %> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN""http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head runat="server"> <title></title> </head> <body> <form action="" method="post"> <label for="txtName">Name:</label> <input id="txtName" name="txtName" runat="server" /><br /> <label for="ddlState">State:</label> <select id="ddlState" name="ddlState" runat="server"> <option value=""></option> </select><br /> <input type="submit" value="Submit" /> </form> </body> </html> Default.aspx.cs using System; using System.Web.UI.HtmlControls; using System.Web.UI.WebControls; namespace NoForm { public partial class Default : System.Web.UI.Page { protected void Page_Load(object sender, EventArgs e) { //Default values string name = string.Empty; string state = string.Empty; if (Request.RequestType == "POST") { //If form submitted (post back) name = Request.Form["txtName"]; state = Request.Form["ddlState"]; //Server side form validation would go here //and actions to process form and redirect } ((HtmlInputText)txtName).Value = name; ((HtmlSelect)ddlState).Items.Add(new ListItem("ACT")); ((HtmlSelect)ddlState).Items.Add(new ListItem("NSW")); ((HtmlSelect)ddlState).Items.Add(new ListItem("NT")); ((HtmlSelect)ddlState).Items.Add(new ListItem("QLD")); ((HtmlSelect)ddlState).Items.Add(new ListItem("SA")); ((HtmlSelect)ddlState).Items.Add(new ListItem("TAS")); ((HtmlSelect)ddlState).Items.Add(new ListItem("VIC")); ((HtmlSelect)ddlState).Items.Add(new ListItem("WA")); if (((HtmlSelect)ddlState).Items.FindByValue(state) != null) ((HtmlSelect)ddlState).Value = state; } } } As you can see, you have similar functionality to ASP.NET server controls but more control over the final markup, and less overhead like ViewState and all the JavaScript ASP.NET adds. Interestingly you can also use HttpPostedFile to handle file uploads using your own input type="file" control (and necessary form enctype="multipart/form-data"). So my question is can you see any problems with this method, and any thoughts on it's usefulness? I have further details and tests on my blog.

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• Cannot run one of two OS

  - by Nathan

  first i am happy cuz i updated to ubuntu 12.10! yeah The grub had an error, but using this guide https://help.ubuntu.com/community/Boot-Repair i fixed it. yeah again I show you the page that gives me the program http://paste.ubuntu.com/1370085/ I have the system selection screen in violet, but i cannot run Windows XP. Only Ubuntu. When i press enter to start windows, the screen turns black and it returns automatically to the system selection screen. Is just that little problem, i need to use twos OS for job's reason. Thanks in advance and sorry for my little english!

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• C# WebForms and Ninject

  - by ipohfly

  I'm re-working on the design of an existing application which is build using WebForms. Currently the plan is to work it into a MVP pattern application while using Ninject as the IoC container. The reason for Ninject to be there is that the boss had wanted a certain flexibility within the system so that we can build in different flavor of business logic in the model and let the programmer to choose which to use based on the client request, either via XML configuration or database setting. I know that Ninject have no need for XML configuration, however I'm confused on how it can help to dynamically inject the dependency into the system? Imagine I have a interface IMember and I need to bind this interface to the class decided by a xml or database configuration at the launch of the application, how can I achieve that?

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• Oracle University Nouveaux cours (Week 12)

  - by swalker

  Parmi les nouveautés d’Oracle Université de ce mois-ci, vous trouverez : Database Oracle Enterprise Manager Cloud Control 12c: Install & Upgrade (2 days) Using Oracle Enterprise Manager Cloud Control 12c Introduction to Big Data (1 day seminar) Introduction to Oracle NoSQL Database (1 day seminar) Oracle Database Administration I: Certification Exam Preparation Seminar (Training On Demand) Development Tools Oracle Database SQL: Certification Exam Preparation Seminar (Training On Demand) MySQL MySQL for Beginners (4 days) Fusion Middleware Oracle Service Bus 11g: System Admin, Design & Integrate Accelerated (5 days) Oracle WebLogic Server 11g: Administration Essentials (Training On Demand) Oracle Solaris Developing and Deploying Applications on Oracle Solaris 11 (3 days) Fusion Applications Fusion Applications: Installation and Administration (4 days) E-Business Suite R12.x Oracle E-Business Suite Essentials for Implementers (Training On Demand) R12.x Implement Oracle Workflow (Training On Demand) R12.x Oracle Applications System Administrator Fundamentals (Training On Demand) PeopleSoft PeopleSoft PeopleTools I Rel 8.50 (Training On Demand) Contacter l’équipe locale d’Oracle University pour toute information et dates de cours. Restez connecté à Oracle University : LinkedIn OracleMix Twitter Facebook Google+

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• Design documents as part of Agile

  - by syrion

  At my workplace, we face a challenge in that "agile" too often has meant "vague requirements, bad acceptance criteria, good luck!" We're trying to address that, as a general improvement effort. So, as part of that, I am proposing that we generate design documents that, above and beyond the user story level, accurately reflect the outcome of preliminary investigations of the effect of a given feature within the system and including answers to questions that we have asked the business. Is there an effective standard for this? We currently face a situation where a new feature may impact multiple areas in our "big ball of mud" system, and estimates are starting to climb due to this technical debt. Hopefully more thoughtful design processes can help.

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• How can I create a symlink to the location that Ubuntu 10.10 mounts a CD?

  - by Michael Curran

  In Ubuntu 10.10, when I insert a CD or DVD into my optical drive, the system mounts the CD in a folder called /media/XYZ where XYZ is the disk's label. This has cause problems with Wine, as in order for an application to verify that an application's CD is present, Wine uses a symlinks to point to a mounted CD's folder. In this case, that folder must be /media/XYZ, but when using a different application, the folder would be different. I would like to know if there is a way to create a symlink that will always point to the mounted folder from a given /dev/cdrom* device, or how to force the system to always mount CDs to the same address (i.e. /media/cdrom).

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• Does the latest version of Ubuntu (12.04) support Unity 3D?

  - by Douglas Combs

  I just installed the latest version of Ubuntu (12.04) 64bit. I am using a Radeon HD 7750 vid card. I think I have the Catalyst driver installed correctly. But when I go to system and look at the details, it shows that my graphics is VESA:01. Does this mean I it, I didn't correctly install my driver? System Specs: MB: ASUS P7P55-M CPU: Intel i5 Quad Core MEM: 4GB DD3 VC: HIS Radeon HD 7750 (1GB DDR5) Thanks for help.

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• Boot-up hangs unless I manually select the kernel in the bootloader

  - by The Photon

  In my stock Ubuntu install (forgot which critter its named for, about one year old), I am able to boot up normally only if I manually select the kernel in the bootloader (Grub). If I step away and it boots from the default, the system will hang with the word "Ubuntu" on a graphics screen and a few white/red blinking dots beneath it. umb@digdug:~$ uname -a Linux digdug 2.6.32-42-generic #95-Ubuntu SMP Wed Jul 25 15:57:54 UTC 2012 i686 GNU/Linux Synaptics says I have 'grub-pc' version 1.98-1ubuntu-13 installed. My grub.cfg does have default="0" which I would expect to make the default be the first kernel shown in the selection screen. The system is a laptop with an i7 processor, and I have had trouble with some kernels not being able to boot at all in the past, and power management is not working perfectly, but I have not had problems booting the latest kernel (2.6.32-42) if I select it manually in Grub. Any idea what is going on here and how can I fix it so that I can re-boot unattended?

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• Is it possible to allow the user to access the 'Volumes' without asking the Administrator's password?

  - by Tom

  Am the administrator of my Ubuntu system. Recently I added a new user account. But when ever the user tries to access or open the 'Volumes'(Drives where movies, songs and other files are stored) it asks for the Administrator's password. I created the user account to my other family members and I don't want to tell them my password. So is it possible to allow them to access the Volumes without asking Administrator's password ? UPDATE : Ubuntu was installed alongside Windows in my system. I will provide a screenshot of the Volume details -

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• No graphics after installing AMD Catalyst 12.4 and installing the recommended updates afterwards

  - by Innonic

  Some days ago, I installed Ubuntu 12.04. Since I wanted to use dualview using an external display I installed the propriatary AMD Catalyst 12.4. The graphics are fine, but if I run the updates found by the updates manager, Ubuntu won't be able to start with graphics after reboot. I installed Ubuntu 3 times until I realized what the problem was. So now I got the basic installation with Catalyst running but I can't update the system. Is there any solution to this? Or can I somehow identify which update causes this? My System is a Lenovo y560 Ideapad (Intel Core i7, 8GB RAM, with AMD Radeon HD 6570M/5700 Series. Thank you in advance

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• How can I figure out why Suspend sometimes fails?

  - by Isaac

  Something is causing suspend crash occasionally. When it does crash, the system freezes with a black screen and stays on, not suspending. This makes me have to hold the power button until the system shuts down. One setting difference I have from most people is, I don't use the option that lets you suspend when the laptop lid is closed. So opening and closing the laptop lid has no actions. I like to press suspend manually. Could this preference change be the cause? How can I start looking for what's causing the crash, since the crash doesn't display errors?

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• How to remove Launchpad app/webapp?

  - by Exomancer

  I was browsing Launchpad and it asked to install a helper app. I thought that this was the Firefox extension so I said yes. Now I have this launcher app that will open a Firefox window directly to Launchpad from my unity dash. I want to remove it and I can't. I removed the Firefox extension and it's still there. I removed the Unity webapps Firefox extension and it's still there. I tried to purge "launchpad" and my system says that it doesn't exist. I searched Launchpad for information on this app but found nothing I could understand that seemed to be relevant. But it's still there, staring at me from the Unity dash. Can anyone help me get this thing out of my system? Running Ubuntu 13.10

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• Can you recommend a good tutorial on building custom package versions?

  - by Ivan

  After installing Ubuntu 11.04 I was disappointed by the fact there are still Scala 2.7 (when 2.8 is long ago current actual branch) and Mono 2.6 (when pretty a time has passed after 2.8 release). I am not sure I could build all the packages for Mono myself, but I'd like to try making my own custom version of Scala package (and I want my system to accept it not as a different package but a version of the original, so that if I put it into a configured repository, the system will automatically upgrade to it from currently installed original 2.7). Can you recommend a good tutorial on this subject (Ubuntu deb packages building and hacking for beginners)?

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• SQLIO Writes

  - by Grant Fritchey

  SQLIO is a fantastic utility for testing the abilities of the disks in your system. It has a very unfortunate name though, since it's not really a SQL Server testing utility at all. It really is a disk utility. They ought to call it DiskIO because they'd get more people using I think. Anyway, branding is not the point of this blog post. Writes are the point of this blog post. SQLIO works by slamming your disk. It performs as mean reads as it can or it performs as many writes as it can depending on how you've configured your tests. There are much smarter people than me who will get into all the various types of tests you should run. I'd suggest reading a bit of what Jonathan Kehayias (blog|twitter) has to say or wade into Denny Cherry's (blog|twitter) work. They're going to do a better job than I can describing all the benefits and mechanisms around using this excellent piece of software. My concerns are very focused. I needed to set up a series of tests to see how well our product SQL Storage Compress worked. I wanted to know the effects it would have on a system, the disk for sure, but also memory and CPU. How to stress the system? SQLIO of course. But when I set it up and ran it, following the documentation that comes with it, I was seeing better than 99% compression on the files. Don't get me wrong. Our product is magnificent, wonderful, all things great and beautiful, gets you coffee in the morning and is made mostly from bacon. But 99% compression. No, it's not that good. So what's up? Well, it's the configuration. The default mechanism is to load up a file, something large that will overwhelm your disk cache. You're instructed to load the file with a character 0x0. I never got a computer science degree. I went to film school. Because of this, I didn't memorize ASCII tables so when I saw this, I thought it was zero's or something. Nope. It's NULL. That's right, you're making a very large file, but you're filling it with NULL values. That's actually ok when all you're testing is the disk sub-system. But, when you want to test a compression and decompression, that can be an issue. I got around this fairly quickly. Instead of generating a file filled with NULL values, I just copied a database file for my tests. And to test it with SQL Storage Compress, I used a database file that had already been run through compression (about 40% compression on that file if you're interested). Now the reads were taken care of. I am seeing very realistic performance from decompressing the information for reads through SQLIO. But what about writes? Well, the issue is, what does SQLIO write? I don't have access to the code. But I do have access to the results. I did two different tests, just to be sure of what I was seeing. First test, use the .DAT file as described in the documentation. I opened the .DAT file after I was done with SQLIO, using WordPad. Guess what? It's a giant file full of air. SQLIO writes NULL values. What does that do to compression? I did the test again on a copy of an uncompressed database file. Then I ran the original and the SQLIO modified copy through ZIP to see what happened. I got better than 99% compression out of the SQLIO modified file (original file of 624,896kb went to 275,871kb compressed, after SQLIO it went to 608kb compressed). So, what does SQLIO write? It writes air. If you're trying to test it with compression or maybe some other type of file storage mechanism like dedupe, you need to know this because your tests really won't be valid. Should I find some other mechanism for testing? Yeah, if all I'm interested in is establishing performance to my own satisfaction, yes. But, I want to be able to compare my results with other people's results and we all need to be using the same tool in order for that to happen. SQLIO is the common mechanism that most people I know use to establish disk performance behavior. It'd be better if we could get SQLIO to do writes in some other fashion. Oh, and before I go, I get to brag a bit. Measuring IOPS, SQL Storage Compress outperforms my disk alone by about 30%.

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• Unity works on my PC but not on the Server. What did I miss?

  - by Erik France

  I have a web service using Microsoft Unity to hook the pieces together.  It all works fine on my PC but when I put it on the web server, I receive this error message: System.ServiceModel.FaultException`1[System.ServiceModel.ExceptionDetail]: The value of the property 'type' cannot be parsed. The error is: Method 'GetClaimsForUser' in type 'WebService.Implementation.ClaimsRetriever' from assembly 'WebService.Implementation, Version=1.0.0.0, Culture=neutral, PublicKeyToken=62cac0f1a908971a' does not have an implementation. If I look at the web.config, I see the following: <unity>     <typeAliases>       <typeAlias alias="ITokenGenerator" type="WebService.Interfaces.ITokenGenerator, WebService.Interfaces" />       <typeAlias alias="TokenGenerator" type="WebService.Implementation.TokenGenerator, WebService.Implementation" />       <typeAlias alias="IClaimsRetriever" type="WebService.Interfaces.IClaimsRetriever, WebService.Interfaces" />       <typeAlias alias="ClaimsRetriever" type="WebService.Implementation.ClaimsRetriever, WebService.Implementation" />       <typeAlias alias="TokenGeneratorSettings" type="WebService.Implementation.TokenGeneratorSettings, WebService.Implementation" />       <typeAlias alias="String" type="System.String, mscorlib" />     </typeAliases>     <containers>       <container>         <types>           <type type="ITokenGenerator" mapTo="TokenGenerator">             <typeConfig extensionType="Microsoft.Practices.Unity.Configuration.TypeInjectionElement, Microsoft.Practices.Unity.Configuration">               <constructor>                 <param name="retriever" parameterType="IClaimsRetriever">                   <dependency />                 </param>                 <param name="settings" parameterType="TokenGeneratorSettings">                   <dependency />                 </param>               </constructor>             </typeConfig>           </type>           <type type="IClaimsRetriever" mapTo="ClaimsRetriever">             <typeConfig extensionType="Microsoft.Practices.Unity.Configuration.TypeInjectionElement, Microsoft.Practices.Unity.Configuration">               <constructor>                 <param name="connectionStringName" parameterType="String">                   <value value="devDatabase" type="String" />                 </param>               </constructor>             </typeConfig>           </type>         </types>       </container>     </containers>   </unity> I have another web service, using an almost identical config running on the web server.  But this new web service will not run. Any ideas on what I have not told Unity to do?  Or maybe what I told Unity to do incorrectly?

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• "mountall: Disconnected from Plymouth" error in VirtualBox

  - by jonpavelich

  I installed Ubuntu (from the 11.10 Alternate CD, selecting "command-line only" mode before installing) in Virtualbox (Mac OS X Lion host) like I've done numerous times before. Installation finished without any problems, and I rebooted into my new system. Got the splash screen, it loaded, and right where it should've given me a login prompt, I got (in orange) mountall: Disconnected from Plymouth. I can just hit control + alt (option) + F1 to get the login prompt on tty1, and the system acts normally. This happens on every boot. The disk has two partitions, a 250 MB /boot partition and a 99.75 GB encrypted partition. The encrypted partition has LVM on it. One volume group, 3 volumes (swap, / (root filesystem) , and /home. At first I thought the error was from one of the LVM volumes not mounting, but they are all accessible. It isn't a critical error, but it is annoying. Any ideas?

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• What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

  - by Ein Doofus

  Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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