How could I catch an exception from the default initialization of members in a constructor?
Catching exceptions from a constructor's initializer list
The dimension of the Hilbert space is determined by the number of independent basis vectors. There is a infinite discrete energy eigenbasis $\{|n\rangle\}$ in the problem of particle in a box which can be used to expand a general state $|\psi\rangle$ as: $$|\psi\rangle=\sum\limits_{n=0}^{\infty} C_n |n\rangle$$ Here, the basis implies that the Hilbert space has countably infinite number of basis vectors. But one could well expand $|\psi\rangle$ in any other basis as well, say the continuous position basis. Then that superposition, $$|\psi\rangle=\int dx \psi(x)|x\rangle$$ is also possible. But this basis $\{|x\rangle\}$ is continuous and uncountably infinite. Such sets cannot be equal because they have different cardinality. Then my questions is how many independent basis vectors are really there in this Hilbert space? Without using Axiom of Choice, prove that $$\forall\alpha\geq\omega,~~|L_\alpha|=|\alpha|,$$  in which $\alpha$ is an ordinals, $\omega$ is the set of natural numbers, $L_\alpha$ is the $\alpha$-th constructiable set, $|x|$ is the cardinals of $x$.  I am learning a set theory, and I have read a proof by using AC. The AC is used only when $\alpha$ is a limit ordinals during the transfinite inductive method for $\alpha$ . I wonder if there is a proof without AC. 　THANKS! Something weird is going on with my login on at least one site I must be missing something with regards to setting up PostgreSQL. What I'd like to do is create multiple databases and users that are isolated from each other so that a specific user only has access to the databases I specify. However, from what I can determine, any created user has access to all databases without any specific grants being given.  Here is what I do on an Ubuntu Server 12.04:   apt-get install postgresql sudo -u postgres createuser -DRSP mike1 (Specifying the password for the new user) sudo -u postgres createdb data1 psql -h localhost -U mike1 data1 (Specifying the password for the user mike1 to login)   It seems that new user "mike1" has no problem connecting to database "data1" and creating tables etc. And this without running any GRANT command at all (and the owner of "data1" is "postgres" since I didn't specify an owner in step 3). Is this really how it is supposed to work?  What I'd like to do is grant mike1 full access to data1 and then repeat this for more users and databases, making sure that the users only have access to one (or possibly several) databases of my choice. Does Windows still rely on MS-DOS? I am just about to start an OS course and as an Apple user I am not very familiar with the underlying details of Windows OS. I was wondering, is MS DOS still used with Windows running on top or is ONLY Windows used now as the OS? I was a little confused because I read somewhere that MS-DOS is used for booting but Windows has all other OS capabilities built into it and thus is used for all other OS operations... Arduino-controlled slot cars - alternative to MOSFETs for speed control? I'm attempting to control the speed of two slot cars in a set using Arduino.    Each car is controlled by a controller with a variable resistor that looks like this:    They're wired in parallel to the same 17V DC power supply:    Simplified:    For Arduino control, I experimented with manipulating a single car's speed using a MOSFET. It worked really well. Using a PWM output on the Arduino, I was able to pulse the MOSFET on and off to throttle the current and change the car's speed. The behavior of the MOSFET seemed to be exactly the same as the variable resistor controller; the resistance, voltage, and current fluctuated the same way on various parts of the circuit.  Enter car B. I added a MOSFET to the setup and mimicked the MOSFET wiring for car A, grounding them both to the Arduino ground. The result looks like this:    Here's a sketch:    Close up, MOSFET A:    MOSFET B:    At first, all seemed well. I sent signals to MOSFET A and successfully changed Car A's speed. I stopped Car A and pulsed MOSFET B, and I was able to control Car B's speed just fine.  Then, I turned Car B to a constant speed, and sent a signal to MOSFET A while Car B was still running. Car A started, but Car B's speed immediately dropped as a result of running Car A.  I hooked a multimeter up across the rails of Car B and watched its voltage while it ran on its own. Then, sure enough, when Car A started running alongside it, Car B's voltage dropped dramatically.  I figured this was because of my wiring configuration, so I left the multimeter on Car B, and made one change. I replaced MOSFET A with the original slot car controller:    I started running Car B again using its MOSFET. The multimeter showed a steady voltage, so I began to squeeze Car A's controller (the variable resistor), and Car A's speed increased. This time, however, unlike using a MOSFET to control Car A, the variable resistor did not affect Car B's voltage at all. Car B remained at a steady speed the whole time.  Any idea why this happens? The MOSFET seemed to function the same as the variable resistor (empirically) with a single car, but had totally different behavior with two cars in parallel. Is it because the MOSFET is not really changing resistance to current, but just switching it on and off, so it opens up another path for current to flow fully every time it closes? Is there an Arduino-controllable alternative to a MOSFET that would fluctuate actual resistance like the variable resistor? Digital potentiometer? Servo hooked up to a potentiometer? ;) I'm really curious what the difference is and what causes the major differences in behavior. How to draw line through group plots in pgfplots? $ echo $(( 255 )) 255 $ echo $(( 33 )) 33 $ echo $(( ~33 )) -34 $ echo $(( ~255 )) -256 $    and my kernel is:  $ uname -a Linux HOSTNAME 3.2.0-40-generic-pae #64-Ubuntu SMP Mon Mar 25 21:44:41 UTC 2013 i686 i686 i386 GNU/Linux     QUESTION: ~ is for negating the number AFAIK. But why does ~33 produce -34 and why does ~255 produce -256? I see many posts on both this forum and elsewhere the discuss the use of a wide angle on a crop sensor.  For example, they discuss how at 14mm lens is 14mm on a 35mm film or full frame, but with a 1.6x crop sensor it is an effective 28mm.  My question is, is a 14mm on a crop sensor the same image as a 28mm on a full frame.  Or does "effective" include some other conotation.  I read that a 14mm can create distortion on a full frame and some vignette, so people seem to say using it on a crop takes out some of those edge problems. My confusion is how the lens is actually taking in the extra image.  Reading kenrockwells blog I learned that wide angle keeps lines straight, while fish eye actually skews the lines.    So with this as my understanding, I am still a bit confused how a lens that is curved in order to get a greater angle of view, will be the same as a cropped version of a less curved lens.  Or does "effective" only refer to the objects to the sides but not to the distortion of the image.  Or, if it is different, is it so small that for photography it does not matter?  A technically description would be welcome as long as a basic understanding of the situation.  Thanks!  Edit: To be more clear after the comments,  I am specifically talking about the end resulting 2d projection from 3d space.  I have read both those previous answers.  the first one is closer to what I am talking about.  However, it is still confusing for me.  I have experience with 3d modeling and projection matricies, which might be confusing me with this.  But for example, i dont understand the images having a 50 mm lens being drawn Starting from the sensor, so it shows a different fov for crop and full frame . If the lens is the same, it takes the same amount of information from the world, which makes a ray from a certain degree off the last lens projected into a smaller space, there is no projection from the sensor, so drawing the line from the sensor doesnt make sense to me.  The distance of the sensor to the rear of the lens must have some impact on the light projected but is not represented in the images.  Further, again from that first answer it says cropping is the same as zoom, but from what i understand from how perspective works, it is different, since a wide angle will project lines differently than a small fov to the same size, so cropping the center of a wide angle and zooming into something is very different.  This is easily recreated in an opengl application with varying fov projection matrix, i imagine in painting class people learn this as well.  A fisheye would be a good example, since if cropping was the same as zooming, a fish eye lens would keep the center exactly like a normal lens and then a gradient weighted towards the outside would rapidly create a warped perspective, but from what I see, it is even.  To me those images just look like its comparing cropped with full frame in regards to orthogonal projections. opengl storing multiple indices into indices buffer After parsing collada files I found out that we have to load two(or more) indices each pointing to say a vertex or normal etc. like this (&lt;p>3 0 2 0 0 0&lt;/p>)  Is there a way to load (and use)these indices to indices buffer(ELEMENT_ARRAY_BUFFER) like this (vnvnvn...) ; where v is vertex pointer, n is normal pointer from the above. with vertices loaded to VBO1 like (vvvv...) and in VBO2 like (nnnn...). So that we dont have to repeat the normals in VBO2.  VBO like (vnvnvn...) is also ok. (and not something like this ), I'm not trying to use multiple indices buffer. I'm trying to put all the given indices into one index buffer and use them alternately.  (If I wasnt clear i will try for more clarification.) How to use a special character as a normal one in Unix shells? Check out the below program.   try {     for (String data : Files.readAllLines(Paths.get("D:/sample.txt"))){         String[] de = data.split(";");         System.out.println("Length = " + de.length);     } } catch (IOException e) {     e.printStackTrace(); }   Sample.txt:   1;2;3;4 A;B;; a;b;c;   Output:   Length = 4 Length = 2 Length = 3   Why second and third output is giving 2 and 3 instead of 4. In sample.txt file, condition  for 2nd and 3rd line is should give newline(\n or enter) immediately after giving delimiter for the third field. Can anyone help me how to get length as 4 for 2nd and 3rd line without changing the condition of the sample.txt file and how to print the values of de[2] (throws  ArrayIndexOutOfBoundsException)? I've been working on some animations recently, and I've noticed that I'm having poor luck with certain things, namely the fact that I don't really use Blender's graph editor very well.  One of the major issues that I have is pretty widespread among 3D graphics programs; when I create an animated object, it defaults to using a curved graph instead of a linear graph, which means that the most movement is at the middle of the animation, and stuff just practically stops near the beginning or the end. While this helps with organic camera movements or such, it's also not what I usually want. Can I set animation curves to default to linear? In the 3d viewport I am using a border region to only render things inside the selected region. I did this with CtrlB. I cannot get rid of the region. How can I make the border disappear? How to add a gif file to my LaTeX file? Related:          I have an image file -- a gif file, which is the graph of a function. How do I add it to a LaTeX file? Will it come out OK in the subsequent pdf file? I recently purchased a MacBook Pro 13&quot; with the M1 chip and transferred all my data over using a Time Machine backup. Homebrew packages are currently installed in /usr/local/opt/ but it is my understanding that they should be under /opt/homebrew for Apple Silicon Macs. How can I:  Get the list of packages I currently have installed Remove those from /user/local/opt Reinstall them under /opt/homebrew  I kind of assumed Homebrew would be clever enough to do this automatically but apparently it needs some manual maintenance. Here's my Homebrew config if it helps: HOMEBREW_VERSION: 2.7.2 ORIGIN: https://github.com/Homebrew/brew HEAD: dad7dc6a1498b80770d98f2d7cd6fb927c300bbb Last commit: 3 days ago Core tap ORIGIN: https://github.com/Homebrew/homebrew-core Core tap HEAD: 2b1d79d038bffdbfcee93283051d48919a4caf3d Core tap last commit: 16 hours ago Core tap branch: master HOMEBREW_PREFIX: /usr/local HOMEBREW_REPOSITORY: /usr/local/Homebrew HOMEBREW_CELLAR: /usr/local/Cellar HOMEBREW_CASK_OPTS: [] HOMEBREW_MAKE_JOBS: 8 Homebrew Ruby: 2.6.3 =&gt; /System/Library/Frameworks/Ruby.framework/Versions/2.6/usr/bin/ruby CPU: octa-core 64-bit arm_firestorm_icestorm Clang: 12.0 build 1200 Git: 2.30.0 =&gt; /usr/local/bin/git Curl: 7.64.1 =&gt; /usr/bin/curl macOS: 11.1-arm64 CLT: 12.3.0.0.1.1607026830 Xcode: N/A Rosetta 2: false  Thanks in advance! phpinfo() and php -v shows different version of PHP I wanted to know which php version I am using so I wrote the standard script:   phpinfo();   Which gives me  PHP version 5.6.10   The correct PHP version needed for my application. When I tried in terminal:  php -i   or  php -v   It shows me:  PHP version 5.3.2   Which I don’t need. Then I tried with:  which php   It shows me:  /usr/bin/php   Now I am confused which version of PHP I am using. The files are uploaded to the hosting website and I cannot make any changes to the config files like httpd.conf or php.ini. running rmi server, classnotfound How to tell Max CP? What are XML namespaces for? This is something that I always find a bit hard to explain to others:  Why do XML namespaces exist?  When should we use them and when should we not? What are the common pitfalls when working with namespaces in XML?   Also, how do they relate to XML schemas? Should XSD schemas always be associated with a namespace?