Is it possible to create matter?
What keeps mass from turning into energy?
I would like to open 4 Notepad++ windows at once, in the same pannel. Currently, I am only able to split it into two, and would like to know if there is a plugin that enables 4 views at at same time, or 3.   thanks Lets say we have a dependent variable $Y$ with few categories and set of independent variables.    What are the advantages of multinomial logistic regression over set of binary logistic regressions (i.e. )? By set of binary logistic regression I mean that for each category $y_{i} \in Y$ we build separate binary logistic regression model with target=1 when $Y=y_{i}$ and 0 otherwise. Which is correct, "you and I" or "you and me"? Ubuntu 18.04 bond with netplan duplicate MAC address after cloning Does a Readied spell immediately use a spell slot? This is a special case of , which, I think, might have drawn little attention because it was too general. In this question, I would like to consider a specific case.  Take a classical system given by the action $$ S[x] = \int dt \left[ \frac{\alpha}{2} \ddot{x}^2 + \frac{\beta}{2} \dot{x}^2 + \frac{\gamma}{2} x^2 \right]. $$  This action is Lagrangian, but it is not what we are usually dealing with in physics, because the Lagrangian contains second time derivatives.  The equations of motion are:  $$ \alpha \ddddot{x} - \beta \ddot{x} + \gamma x = 0. $$  This can be solved as usual by employing Fourier transform:  $$ x(t) = a_1 e^{i \omega_1 t} + a_1^{*} e^{-i \omega_1 t} + a_2 e^{i \omega_2 t} + a_2^{*} e^{-i \omega_2 t}, $$  where $\omega_1^2$ and $\omega_2^2$ are the two roots of $\alpha \omega^4 + \beta \omega^2 + \gamma$, given by  $$ \omega_{1,2}^2 = \frac{- \beta \pm \sqrt{\beta^2 - 4 \alpha \gamma}}{2 \alpha} .$$  Now by definition the phase space is the space of solutions of equations of motion. In this case it is parametrized by two complex co-ordinates $a_{1,2}$, meaning that it is 4-dimensional.  I would like to know if there's a natural way to associate the symplectic structure (Poisson bracket) on this phase space. I.e.,  $$ \{a_1, a_1^{*}\} = ? $$ $$ \{a_1, a_2^{*}\} = ? $$ $$ \{a_2, a_1^{*}\} = ? $$ $$ \{a_2, a_2^{*}\} = ? $$ $$ \{a_1, a_2\} = ? $$ $$ \{a_1^{*}, a_2^{*}\} = ? $$ Many To Many Relationships I am working on a conceptual model for a database. I have the following entities:  Student (id, name, date of birth, department)  Subject (id, name)   This is a many-to-many relationship, one student may be enrolled in many courses, each course has many students. From what I understand, as I should break this many-to-many relationship by introducing a new into a entity, say 'registered' which allows a one-to-one relationship or one-to-many relationship?  Is this correct design decision? Headers of \chapters* take the headers of their previous \chapter When using book.cls and using \chapter* after a \chapter, the header used in \chapter* is wrong. An example is pasted below.   Is there any known workaround for that? I have tried quite some tricks without success.   \documentclass[]{book}  \begin{document}  \chapter{First Chapter} aslkjdf  \chapter*{Unnumbered Chapter} The GNU General Public License is a free, copyleft license for software and other kinds of works.  The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too.  When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things.  To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others.  For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.  Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it.  For the developers' and authors' protection, the GPL clearly explains that there is no warranty for this free software. For both users' and authors' sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions.  Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users' freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users.  Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free.  The precise terms and conditions for copying, distribution and modification follow.  \end{document} $\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists? Why I can't escape spaces on a bash script? I'm trying to escape the space char for a path in Bash, but neither using a  or  works.  .sh script:  ROOT="/home/hogar/Documents/files/" FILE=${ROOT}"bdd.encrypted" DESTINATION="/home/hogar/Ubuntu\ One/folder"  mv ${FILE} ${DESTINATION}   After execute the script (./file) this is the result:  mv: target 'One/folder' is not a directory   Why does the mv command split the string, and how do I stop this from happening? Zero-dimensional ideals and finite-dimensional algebras I encountered in the literature the term zero-dimensional ideal, however I can not find a relevant definition anywhere in Atiyah-MacDonald or Matsumura. In fact, I encounted the statement:      $I$ is a zero-dimensional ideal of $k[x_1,\dots,x_n]$ $\Leftrightarrow$ $k[x_1,\dots,x_n]/I$ is a finite-dimensional $k$-vector space, where we assume that $k$ is algebraically closed.   Question 1: What is the definition of the dimension of an ideal?  Question 2: How do we prove the above statement?  Question 3: Is $k$ being algebraically closed a necessary condition for the statement to be true? How do I add a custom script on a specific page? I wanted to add custom JavaScript code on certain nodes. I have written this code in the html.tpl.php template, but this doesn't work. (donate is the path alias for a node.) &lt;?php if(arg(0) == 'DONATE'): ?&gt;   &lt;script&gt;     (function() {       // ...     );   &lt;/script&gt; &lt;?php endif; ?&gt; Probably dumb question, but I would like to ask it anyway.  I was to solve this equation:  $z^4 = -16$  At first glance, the way to solve it would be (as any other equation):  $z^2 = \sqrt{-1} * 4 \lor z^2 = -\sqrt{-1} * 4$  $z^2 = 4i \lor z^2 = -4i$  $z = 2\sqrt{i} \lor z = -2\sqrt{i} \lor z = 2i\sqrt{i} \lor z = -2i\sqrt{i}$  However, in suggested answers, there are $z_1, z_2, z_3$ and $z_4$ found using trigonometric formulas. Is there something particulary wrong in my solution and the only proper one uses trigonometric form of complex number? how to get rid of arm64 in apt W: Invalid 'Date' entry in Release file /var/lib/apt/lists/_var_cuda-repo-8-0-local_Release N: Skipping acquire of configured file 'non-free/binary-arm64/Packages' as repository 'http://repository.spotify.com stable InRelease' doesn't support architecture 'arm64' E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-updates/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-backports/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-security/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Some index files failed to download. They have been ignored, or old ones used instead.   After I installed Jetpack for Jetson tx1, my ubuntu constantly tries to fetch arm updates. Is there a way to disable this?  EDIT:   $dpkg --print-architecture amd64  $dpkg --print-foreign-architectures i386 arm64   I see that arm64 is included in foreign architectures. How do I remove it? Why is it important to apply transformation to an objects data? note: This is a question about relativistic effects. I've included some detail about the spacecraft and its orbit for background, but the question is about relativistic effects and their observability.     When the Parker Solar Probe passes within 8.5 solar radii of the Sun, it will be moving really fast.  A perihelion and aphelion of about 6.6 and 109 million kilometers suggests a semi-major axis of 57.8 million kilometers. The standard gravitational parameter for the Sun is:  $$GM_{Sun} \ = 1.327\times 10^{20} m^3/s^2$$  So using the :  $$v^2 \ = \ GM_{Sun}\left(\frac{2}{r}-\frac{1}{a}\right)$$  the orbital velocity at perihelion will be about 195,000 m/s, or about 25 times faster than a satellite in LEO. This is close to one part per thousand of the speed of light! I think this will be a new record for a spacecraft velocity relative to the solar system.  Depth of a gravitational potential well for an object of mass $m$ is approximately given by:  $$u_G \ = \ -GM_{Sun}\frac{1}{r}$$  At 6.6 million kilometers the spacecraft will be 23 times deeper in the Sun's gravitational well than it would be at 1 AU.  Will there be any particularly unique relativistic effects detectable for the Parker Solar Probe during it's close flyby of the Sun?  Just for example, during one close flyby, how much time will its on-board clock gain or lose compared to some convenient standard solar system timescale? I know there are several different choices, "GPS time" might be one but I don't want to arbitrarily choose an inconvenient one.     above: Parker Solar Probe cropped, from .    above: screen shot from NASA's      note: the link seems to be dead now, but there is plenty of related information available at     above: Illustration of the Parker Solar Probe's orbit, from . Can Tamron 16-300mm Macro Lens fit to Canon EOS 600D? I use Canon EOS 600D and I want a lens with a larger range. I found out Tamron 16-300 f/3.5-6.3 Di II VC PZD Macro Lens, I added it into my wishlist. I did some research on it and I'm scared that it couldn't fit to my Canon EOS 600D.  I'm still a beginner... I'm confused with EF, EF-S and APS-C/DX. Can someone please explain it to me? I was really happy when I heard that HoTD would be continued. And even happier when the first new chapter actually came. but now after several months of waiting there still has been no other chapter. So my question is, has HoTD gone on hiatus again ? traveller's cheques; customer's requirements: use of the singular Saxon genitive (and the plural attributive) for association May I ask if the following sentence is grammatical?      Our remit is to conduct research on customer's requirements.   In my understanding, as 'customer' is a countable noun, so the plural form 'customers''' should be used instead for this general reference (without specification of certain customers).   However, I know that we can say 'traveller's cheques' - e.g.,      Traveller's cheques are available at the bank.    In this sense, actually can we say 'customer's requirements' in the first case? I'm not sure which of the following sentences is correct. Is the comma mandatory, optional or unnecessary? I've googled a bit about this topic, but I got confused.     Our mapping contains 2000 words, which map to more than one lemma.   or     Our mapping contains 2000 words which map to more than one lemma.   Context: In total, there are more than 2000 words.  I've read  . If I understand the answers correctly, my "which map to more than one lemma" is a defining clause and no comma is required. But is it wrong to add one?