What does negative $\mu$ physically means? I have recently heard the following statement:  A negative chemical potential means absence of particles.  However, I cannot make this consistent with e.g. a system of free bosons for which $\mu$ must be negative to ensure stability of the partition function.
Meaning of the chemical potential for a boson gas My lecturer told me that $\mu$, the , is zero or negative, and in the following example, mathematically it acts as a normalization constant. But is there any physical insight about why boson gas can be zero or negative? I think it is due to the fact the photon gas can pop up from nowhere (i.e. vacuum fluctuation). $$ f_{BE}(\varepsilon)=\dfrac{1}{e^{(\varepsilon-\mu)/(k_B T)}-1}$$
Which Windows 7 log file contains device connection/disconnection information? Windows 7 frequently plays the usb/new device connection/disconnection sound. It happens both when the computer is idle and under load. All usb device connections have been checked (though I can't rule out a bad cable yet). I thought a good way to track down the issue would be to wait for the sound and then check the log file for the latest connected/disconnected device. I just need to know which log file has this information.  Edit: I'm going to leave the answer accepted, however the issue persists. I get that sound seemingly randomly throughout the day. Anyone else have any ideas? In my question  I asked about the definition and usage of the word "model", for which I was told the following definition:     A formula of propositional logic is true under an interpretation iff   the interpretation assigns the truth value T to that formula. If a   formula is true under an interpretation, then that interpretation is   called a model of that formula.   An interpetation satisfies a formula φ iff it is a model of the formula. Same for a set $\Gamma$ of formulas, if an interpretation satisfies all the formulas in $\Gamma$ then it is a model of $\Gamma$. Then if we say $\Gamma \vDash \varphi$ then $\varphi$ is a semantic consequence of $\Gamma$ / is satisfied in all "models" of $\Gamma$ (true whenever everything in $\Gamma$ is true).  This also matches the definitions for model as seen on the Wiki for  and .  All good so far. But when I get really confused when I see posts like  where they use "models" as a word meaning "satisfies all the axioms in a theory."  From Asaf's answer:     Models are structures, and structures are models. But when we say   "model" we mean that there is a particular theory which holds in the   structure, and when we say "structure" we are mainly interested in an   arbitrary interpretation of the language.   From Metin's answer:     A structure is a set with some interpretable symbols(constants,   relations and functions) within a fixed language. You do not ask for   more from a structure.      However...      A model (of a theory) is a structure which satisfies the axioms of the   theory. It makes more "structural sense"...   And then from one of Asaf's comments:     When I say "a model of 𝖹𝖥𝖢" they also know, immediately, that I am   talking about a model which satisfies all the axioms of 𝖹𝖥𝖢.   So I am unclear on which definition is correct or if this is the same word being used in two different ways or if this is "logical model" versus "semantic model" or something else entirely.  On the one hand we seem to have "model" meaning "any interpretation that satisfies a formula or set of formulas." On the other hand we have "model" meaning "Interpretation that satisfies all the axioms of a theory".  From the Wiki article on  we see also:     For a given theory in model theory, a structure is called a model, if   it satisfies the defining axioms of that theory.   So which is it exactly? Does "model" have a different meaning in propositional logic compared to model theory or first-order logic or set theory etc? How can I use docker without sudo? On Docker's documentation pages, all example commands are shown without sudo, like this one:  docker ps   On Ubuntu, the binary is called docker.io. It also does not work without sudo:  sudo docker.io ps   How can I configure Docker so that I don't need to prefix every Docker command with sudo? I'm working on a python script that passes file locations to an scp subprocess. That's all fine, but I'm in a situation where I may end up concatenating a path with a filename such that there's a double '/ in the path. I know that bash doesn't care if you have multiple file separators, but I'm wondering how exactly that is rectified. Is it bash that strips extra /s or does it really not matter ever?  I ask because it will save me several lines of code to check for extra /s while concatenating. I know it's not a big deal, but I'm curious as well. I have a bash script that has the line cd //usr (instead of cd /usr), which seems to imply there might be a significance to using multiple /s in a path Scala 2.10 + Json serialization and deserialization When transiting between two flights, will my luggage be automatically transferred? Can an html element have multiple ids? Can a class overload methods that also exist in the publicly inherited interface? It seems like this is unambiguous and useful, but compilers (VC, Intel, GCC) all complain, at least by my construction. Below is a toy example. The inherited rebound() function has two clear overloads, yet this will not compile.  If you rename the rebound() method in either class, it works fine, but if they share the same member function name (even though they're overloaded with different argument types!) you get a fatal error of "too few arguments to function call."  The workaround is trivial (I'll just rename the methods) but I'm just trying to understand if this is a C++ restriction (and why it would be).   #include  class Bound { public:   Bound() : x0(0.0), x1(0.0) {};   Bound(double x) : x0(x), x1(x) {};   double width() const {return x1-x0;}   void rebound(const Bound *a, const Bound *b); private:   double x0, x1; };  void Bound::rebound(const Bound *a, const Bound *b) {   if (a && b) {     x0=std::min(a->x0, b->x0);     x1=std::max(a->x1, b->x1);   } }  class Node : public Bound { public:   Node(double x) : Bound(x), left(0), right(0) {};   Node(Node *a, Node *b) : left(a), right(b) {rebound();}   void rebound() { rebound(left, right); } private:   Node *left;   Node *right; };   int main() {   Node A(1.0);   Node B(2.0);   Node C(&A, &B); } What is the cardinality of the set of the empty set? What's the maximum length of the meta keywords tag? Could you please tell me that what is the maximum length for meta keywords? How do you start Windows 10 in safe mode? I've been through the Windows 10 upgrade, and am experiencing a recurring "INTERNAL_POWER_ERROR", which is stopping me from logging in.  I'd like to be able to try to boot to safe mode, but it appears that pressing F8 during boot is no longer enough, so how can I boot in safe mode (or any of the other recovery options) on a Windows 10 PC that doesn't let me log on? Can it be assumed a evaluation order of the function parameters when calling it in C ? According to the following program, it seems that there is not a particular order when I executed it.   #include &lt;stdio.h&gt;  int main() {    int a[] = {1, 2, 3};    int * pa;      pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa), *(pa++),*(++pa));    /* Result: a[0] = 3  a[1] = 2    a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(pa),*(++pa));    /* Result: a[0] = 2  a[1] = 2     a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(++pa), *(pa));    /* a[0] = 2  a[1] = 2 a[2] = 1 */  } Proving the measure of an increasing sequence of measurable sets is the limit of the measures How can I connect two different DC power sources together? How can I connecting two different DC power sources together? for example 15Vdc(5Amp) with 5Vdc(2Amp). I want to make one DC source (20Vdc,7Amp) by more powerful supplies. Command "find -name" must be enclosed in quotes or it doesn't work. Why is that? The Earth is spinning, so why don't we jump and land on a different location? I know there are similar questions on StackExchange but I think it is different and detailed.  The earth is spinning 465 meters/second so why don't we jump and land on a different location?  I googled about this question and I got some answers:   When we jump, we (and the atmosphere itself) also spin along with the earth so we don't land at a different location. (But why we are also spinning along with earth ?) The earth is so big and we are very small relative to earth so the tiny jump won't make any difference.   But according to answer 1, We are also spinning with the earth. But the question is, "why are we also spinning along with earth" ??  Regarding the answer 2, it won't make any difference but logically it doesn't make sense or I just don't understand it.  Here is the followup question,   "When we jump why don't we thrown out of earth due to centrifugal force of the spinning earth ??"  Please provide some detailed answer to these questions. With logic if possible.   This phenomenon is not possible I know, but even if it exists, then traveling will be so easy, we just have to hang on space (with help of helicopter etc.. ) and we can travel the whole world in 24 hours :D Get in vs. get on Possible Duplicate:          I'm an EFL (English as a foreign language) teacher and I haven't been able to come up with a good principle for which preposition to use after get when referring to transportation.  Some examples:   Get in:   a car/taxi/van/truck, etc.  Get on:   a bus/plane/bike/truck, etc.    How can one choose whether to use in or on? Note that in some cases, such as the example with truck, either preposition is possible but the choice affects the meaning.  I've been telling my students that there is no rule, so they just have to memorize which preposition to use, but I'm really hoping I'm wrong.  This question would be better suited for the upcoming  Stack Exchange, but it hasn't entered beta yet. More . Does $\langle\Omega|\mathrm{e}^{\mathrm{i}Px}=\langle\Omega|\mathrm{e}^{\mathrm{i}0x}$? $(\langle\Omega| =$ ground state of the interacting theory) Let $\langle\Omega|$ be the ground state of an interacting theory, just as Peskin &amp; Schroeder(PS) describes on page 82 and page 213. On page 213 PS do the following   $$\tag{1}\langle\Omega|\phi(x)|\lambda_{\vec{p}}\rangle = \langle\Omega|\exp(+\mathrm{i}Px)\phi(0)\exp(-\mathrm{i}Px)|\lambda_{\vec{p}}\rangle \\ =\langle\Omega|\phi(0)|\lambda_{0}\rangle\exp(-\mathrm{i}px)\bigg|_{p^0=E_{\vec{p}}} $$  In the above $|\lambda_0\rangle$ is an eigenstate of the full interacting hamiltonian $H$. The ket $|\lambda_{\vec{p}}\rangle$ is the boost of $|\lambda_0\rangle$ with momentum $\vec{p}.$ Furthermore $E_{\vec{p}} = \sqrt{p^2+m_\lambda^2}$ and $\vec{P}|\lambda_0\rangle = 0.$  I assume PS used $$\tag{2}\langle\Omega|\mathrm{e}^{\mathrm{i}Px}=\langle\Omega|\mathrm{e}^{\mathrm{i}0x}$$ in $(1)$.   Is $(2)$ true?   I thought $\langle0|\mathrm{e}^{\mathrm{i}Px}=\langle0|\mathrm{e}^{\mathrm{i}0x}$ where $\langle0|$ is the ground state of the free theory.   I hope I have provided enough info for the question to make sense. I have a very stupid question. I developed a website that has only one page at the public html directory(index.php).  all content are dynamically loaded as different pages.   How can i SEO my pages for google?  i mean like the what we type in this site are .............i believe stored in database and search engine find these pages like any static pages...  Just a little tip would be appreciable.......! I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row.