I'm using vbscript to interact with the WMI classes. I am querying the Win32_GroupUser class which is defined here .  In the definition, it has the following components:  class Win32_GroupUser : CIM_Component {   Win32_Group   REF GroupComponent;   Win32_Account REF PartComponent; };   My vbscript is as follows:  dim objWMIService, o, obj, test, test1, strComputer strComputer = "."  Set objWMIService = GetObject("winmgmts:{impersonationLevel=impersonate}!\\"&amp; strComputer &amp; "\root\cimv2") set obj = objWMIService.ExecQuery("select partcomponent,groupcomponent from win32_groupuser")  for each o in obj     set test = objWMIService.ReferencesTo(o.groupcomponent)     wscript.echo o.groupcomponent     set test1 = test.itemindex(0)     wscript.echo "test is a "&amp;typename(test)&amp;", test1 is a "&amp;typename(test1)     on error resume next     for each j in test1.methods_ 'list all methods         wscript.echo "Method: "&amp;j.name     next     for each j in test1.properties_ 'list all properties         wscript.echo "Property: "&amp;j.name     next     i = test1.properties_("GroupComponent")     wscript.echo "Groupcomponent is a " &amp; typename(i)     wscript.echo "GroupComponent: "&amp;i  next   The output is  \\COMPUTER\root\cimv2:Win32_Group.Domain="TESTDOMAIN",Name="Schema Admins" test is a SWbemObjectSet, test1 is a SWbemObjectEx Property: GroupComponent Property: PartComponent Groupcomponent is a String Groupcomponent: \\COMPUTER\root\cimv2:Win32_NTDomain.Name="Domain: TESTDOMAIN"   However I am having trouble trying to follow the reference to the GroupComponent; it keeps on coming out as a string and not as a win32_group object, hence I cannot access the properties such as SID etc.  How do I access the groupcomponent as a win32_group object and not as the string?
I am trying to get the SIDs of users and groups by querying  get-wmiobject -query 'select groupcomponent,partcomponent from win32_groupuser`   output:  __GENUS          : 2 __CLASS          : Win32_GroupUser __SUPERCLASS     : __DYNASTY        : __RELPATH        : Win32_GroupUser.GroupComponent="\\\\COMPUTER\\root\\cimv2:Win32_Group.Domain=\"TESTDOMAIN\",Name=\                    "Schema Admins\"",PartComponent="\\\\COMPUTER\\root\\cimv2:Win32_UserAccount.Domain=\"TESTDOMAIN\"                    ,Name=\"Administrator\"" __PROPERTY_COUNT : 2 __DERIVATION     : {} __SERVER         : __NAMESPACE      : __PATH           : GroupComponent   : \\COMPUTER\root\cimv2:Win32_Group.Domain="TESTDOMAIN",Name="Schema Admins" PartComponent    : \\COMPUTER\root\cimv2:Win32_UserAccount.Domain="TESTDOMAIN",Name="Administrator"   groupcomponent is a win32_group ().  win32_group is contains an SID ()  However the groupcomponent here is a string and not a win32_group as   get-wmiobject -query 'select groupcomponent.sid from win32_groupuser'   is an invalid query. How can I access groupcomponent's members as a win32_group?
Minimal polynomials and cyclic subspaces I'm trying to make my way through two problems in Curtis's Linear Algebra, chapter 25.  One of the two problems is this one, #5:     Prove that $V$ is cyclic relative to a linear transformation $T \in \mathcal{L}(V)$ if and only if the minimal polynomial of $T$ is equal to the characteristic polynomial.   Part of the issue is that I'm not really sure what it's asking. The statement that $V$ is cyclic seems to suggest that the entire vector space (say it has dimension $n$) is generated by some vector $v \in V$, along with $Tv, T^2v, \ldots T^{n-1}v$; Curtis's definition of a cyclic subspace (as opposed to a space, though I can't see why there should be a difference) seems to reinforce this:     A $T$-invariant subspace $V_1$ of $V$ is called cyclic relative to $T$ if $V_1 \neq 0$ and there exists a vector $v_1 \in V_1$ such that $V_1$ is generated by $\{ v_1, Tv_1, T^2v_1, \ldots T^kv_1 \}$ for some $k$.   However, I've seen several examples that seem to directly contradict this interpretation. For example, we recently had a take-home midterm that required we find elementary divisors, rational canonical form, etc., of a $6\times 6$ matrix; a classmate who received a perfect score on her test found that her matrix's characteristic polynomial was equal to its minimal polynomial &#151; it was $(x+8)^2 (x+14)^2 (x^2+61x+80)$ &#151; and yet the vector space could be written as $\left&lt; v_6 \right&gt; \oplus \left&lt; v_4 \right&gt; \oplus \left&lt; -v_2+v_3+v_6 \right&gt;$ &#151; i.e., as the direct sum of three cyclic subspaces, not as one cyclic subspace.  So that suggests that "$V$ is cyclic" might mean the direct sum of cyclic subspaces. However, while working on the exercise that follows (#6), I came across this:  $$S= \left(\begin{array}{ccc} -1 &amp; 0 &amp; 0 &amp; 0\\ 0 &amp; 1 &amp; 0 &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; 0\\ 0 &amp; 0 &amp; 0 &amp; 2 \end{array}\right)$$  Here, the characteristic polynomial is not equal to the minimal polynomial, which is $m(x) = (x-1)(x+1)(x+2)$. The eigenspace associated with $\lambda = 1$ has dimension $2$. And so it seems as though, if $V$ has basis $\{ v_1, v_2, v_3, v_4 \}$, we can write $V = \left&lt; v_1 \right&gt; \oplus \left&lt; v_2 \right&gt; \oplus \left&lt; v_3 \right&gt; \oplus \left&lt; v_4 \right&gt; $. This would seem to contradict my second interpretation of the original question.  Obviously I'm missing something. Could someone fill me in on what it might be? (I've tried to be thorough, but I'm also trying not to make this ridiculously long; if I've left out necessary information, I'll be happy to append it.) I have a c++ header file containing a class. I want to use this class in several projects, bu I don't want to create a separate library for it, so I'm putting both methods declarations and definitions in the header file:     // example.h #ifndef EXAMPLE_H_ #define EXAMPLE_H_ namespace test_ns{  class TestClass{ public:     void testMethod(); };  void TestClass::testMethod(){     // some code here... }  } // end namespace test_ns #endif   If inside the same project I include this header from more than one cpp file, I get an error saying "multiple definition of test_ns::TestClass::testMethod()", while if I put the method definition inside the class body this does not happen:  // example.h #ifndef EXAMPLE_H_ #define EXAMPLE_H_ namespace test_ns{  class TestClass{ public:     void testMethod(){         // some code here...     } };  } // end namespace test_ns #endif   Since the class is defined inside a namespace, shouldn't the two forms be equivalent? Why is the method considered to be defined twice in the first case? What to look for in the datasheet when choosing a MOSFET? I'm reading Algebraic Number Theory by Jurgen Neukirch. I have some problems with some of the exercises in Section 9 of Chapter 1.  They are:  1) If $L / K$ is a Galois extension of algebraic number fields with non-cyclic Galois group, then there are at most finitely many non-split prime ideals of $K$.  2) Let $L / K$ be a finite (not necessarily Galois) extension of algebraic number fields and $N / K$ the normal closure of $L / K$. Show that a prime ideal $p$ of $K$ is totally split in $L$ if and only if it is totally split in $N$.  I have worked on them for a long time but couldn't get any idea of it.   Can you please help? Thank you! I have enum and use the variables like myEnum.SomeNameA, myEnum.SomeNameB, etc.  When I return one of these variables from a function, can I print their names (such as myEnum.SomeNameA) instead of the value they returned? Is the High Elf's extra cantrip in addition to cantrips from your class? If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$ Let $f:[0,1]\to \mathbb{R}$ is continuous, such that $f(0)=f(1)$. For each $n\in\mathbb{N}$, prove that $\exists x\in [0,1]$ such that $x+\dfrac{1}{n}\in[0,1]$ and $f\left(x+\dfrac{1}{n}\right)=f(x)$.   My approach: The interval $[0,1]$ is connected, then if $f$ is continuous, we have $f([0,1])\subset\mathbb{R}$ is a interval. And I suppose that, I can define a closed path such that $f(0)=f(1)$. Any hint pls, C# - how can I get owner's name for a Mutex I have a shared mutex between 2 applications. I want to create an administration console that shows the current owner's name of the mutex.  How can I get the application name that currently owns the Mutex? Can this identity be derived from the binomial theorem?  $$n(n+1)2^{n-2} = \sum_{i=1}^{n}  i^2 \binom{n}{i}$$    I tried starting from $2^n = \displaystyle\sum_{i=0}^{n} \binom{n}{i}$ and dividing it by $4$ in order to get $2^{n-2}$. Origins of Tension First of all, I have a confusion about the definition and idea of Tension. For example, in my Physics Textbook, the idea of tension is written like this: &quot;Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force.&quot; For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys)  by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are. My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:  Why you can't push a rope, copper wire against a wall?  What happens when I pull on two ends of a wire with 2 different forces?  Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?  Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].  If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)  Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?) Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$ Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$  I thought that $m=ab$ but I was given a counterexample in a comment below.  So all I really know is $m=ax$ and $m=by$ for some $x,y \in \mathbb Z$. Also, $a$ and $b$ are relatively prime since $\gcd(a,b)=1$.   One of the comments suggests to use , i.e., $aq+br=1$ for some $q,r\in\mathbb{Z}$. Any more hints?  New to this divisibility/gcd stuff. Thanks in advance! I dug a large room to specifications, 3 blocks tall and 16 blocks wide as well as long. I dug it at 10 levels above bedrock, in a location {(-240, 0) -> (-224, 16)} specified by  slime finder app. I am definitely more than 24 blocks away and less than 32 away from the spawn room, as specified by the wiki .  Yet, no slimes. I have been sitting in my location patiently listening for the moist slapping sounds of slime. I have gone in to the room every time I heard a phantom slap but still nothing.  Am I just being dumb somehow or do the minecraft lords just hate me?  If it helps/anyone cares here's my seed: 6405460532872068998 How do I remotely control another Ubuntu desktop from Ubuntu? How do I remotely control another desktop (both are Ubuntu 12.04) from my client machine?  Is it possible to use Remmina Remote Desktop Client? Show $f$ is analytic if $f^8$ is analytic This is from Gamelin's book on Complex Analysis.  Problem: Show that if $f(z)$ is continuous on a domain $D$, and if $f(z)^8$ is analytic on $D$, then $f(z)$ is analytic on $D$. (I assume the intention is that $D$ is nice, i.e. open and connected)  I'm not exactly sure how to approach this. I'm guessing it has something to do with zeroes of $f$. For example, around non-zeroes, $f$ is analytic since $z^{1/8}$ is nonzero in a neighborhood. Or something along those lines. The details are eluding me.  Any help would be appreciated! Why are some faces in my mesh darker? While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem? Should you include press interviews and articles about your work in your CV? Is it appropriate to include interviews (published online or in print magazines) in an academic CV?   What about articles/news published about your works? I mean brief (one paragraph) news that professional magazines publish about significant research articles.  If yes, how do you do this to avoid exaggeration? Is it hard to transfer contacts from one iPhone to another iPhone? I just bought a new iPhone 6s, and want to move all the contacts from the old one to the new one. Can iTunes or iCloud help me do this, or are there any other ways? How to remove/apply all modifiers of one object in python Lets assume you have 1 object with 4 modifiers added to it. I am curious how one would approach the task to apply all or to delete all modifiers of a just selected object that has many modifiers already added.  The console reads out the modifier delete as  bpy.ops.object.modifier_remove(modifier="Box Right ")   So "Box Right " I might have to replace with something like active.object.modifier.name and then work each modifier off?  This would be very helpful when you want to generate a static mesh for animation or 3D printing. If someone who is otherwise healthy decided to drink fairly heavily and consistently over a long period of time, what is the healthiest way to do so?  Example: Stay extra hydrated by drinking more water, take a multivitamin, get more sleep, etc.  Obviously the best solution would be to cease drinking, but IF that person is stubborn and won't quit - what's the best way to go about it? What is the simplest way (least error-prone, least lines of code, however you want to interpret it) to open a file in C and read its contents into a string (char*, char[], whatever)?