photoshop CS3 working on windows 10
Will my software work on the next version of Windows
Congruent Modulo $n$: definition In an Introduction to Abstract Algebra by Thomas Whitelaw, he gives examples of the congruence mod operation, such as $13 \equiv5 \pmod4$,  and $9 \equiv -1 \pmod 5$. But when I first learned about the modulo operation my junior year, I would have told you that $13 \equiv 1 \pmod 4$, and that $9 \equiv 4 \pmod 5$.     Is this just a difference in the definition of modulo? Or is this pretty typical (to not take it to the largest factor, or one over)? What happened to Startups SE? I really enjoyed that site. I've only posted on it once, but I enjoyed seeing other people's posts and appreciated reading about entrepreneurial dilemmas. How can animals in the wizarding world go close to extinction? Restoring a backup to an older version of SQL Server When trying to restore a backup to a SQL Server Express 2008 database I got the following error:  Restore failed for Server '...\SQLEXPRESS'.  (Microsoft.SqlServer.SmoExtended) System.Data.SqlClient.SqlError: The database was backed up on a server running version 10.50.1600.  That version is incompatible with this server, which is running version 10.00.2531.  Either restore the database on a server that supports the backup, or use a backup  that is compatible with this server. (Microsoft.SqlServer.Smo)   Is there a way to get a backup which is compatible with the older (in my case 10.00.2531) version from the newer (in my case 10.50.1600) version of SQL Server Express? Gravitational shielding and equivalence principle Convert line voltage heating system to use low voltage thermostats I currently have two line voltage ceiling radiant heating systems in my condo each with their own DPST thermostat. I'd like to use low voltage thermostats such as the nest. I found , but it only has 3 wires. Will this work with a system designed to use DPST thermostats? If not, is there something else out there that will allow me to use low voltage thermostats with line voltage heaters? Can you make a bonus-action attack from Two-Weapon Fighting before you take your action? What is the distribution of primes modulo $n$? Variation of the Kempner series – convergence of series $\sum\frac{1}{n}$ where $9$ is not a digit of $1/n$. It is easy to argue that the  converges:  $$  \sum\limits_{\substack{n \text{ s.t. 9 is}\\\text{ not a digit} \\\text{ of } n}}  \frac{1}{n} &lt; \infty$$  Let $E \subset \Bbb N_{&gt;0}$  the subset of the positive integers  such that $9$ is not a digit of the decimal expansion of $1/n$ (the decimal expansion is not allowed to have a trailing infinite sequence of "$9$"s. For instance $0.24999...$ is not allowed).  Here are the  that don't belong to $E$ : $11,13,17,19,21,23,29,31,34,38,41,…$ (not known by the OEIS, by the way).  My question is:     Does the series    $$ \sum\limits_{n \in E} \frac{1}{n} \tag 1$$ converge?   My attempt is :   Let $1/n = 0,a_1 a_2 \dots a_k \overline{b_1 b_2 \dots b_m}$ with $n \in E$. Since $1/n$ has no digit "9", we have at most $9^{k+m}$ possibilities for the $a_i$'s and $b_j$'s. Moreover, $1/n ≥ 0,00...0\overline{00...01}≥1/10^{k+m}$. But then I can only bound my series $(1)$ from below, by some real number. So, this is not a clue for the divergence of the series. Apparently, the numbers of the form $n=10k+1$ don't belong to $E$. Maybe we can find sufficiently many numbers that have $9$ in the decimal representation of their reciprocals, so that $(1)$ could converge...   Any comment will be appreciated ! How and when did American spelling supersede British spelling in the US? A couple of weeks ago I was travelling in a car (120 km/h approximately) and I saw a  flying in front of me (inside the car, near my nose, windows closed). I wonder how was that possible.   Does it mean is really flying at 120 km/h or the fly is being affected by some kind of gravity/force? How to delete a file with a path too long to be deleted Dear all I think I have a problem with the collation of makeidx.  following some suggestions found here I have got in the text something like this  \index[p]{Plutarco!demalignitate@\textit{De Malignitate Herodoti}!00855 @855A|qt}  \index[p]{Plutarco!demalignitate@\textit{De Malignitate Herodoti}!00868 @868f-869b|nn{\thefootnote}}   the first is an \index entry in the text, the second in a footnote. My problem is that even if I put the sort also on the second level of indexing it keeps keeping them separated.  I use this package information  \usepackage[splitindex]{imakeidx} \makeindex[name=n, title=Nomi di persone e luoghi]  \makeindex[name=p, title=Passi citati nel testo] \makeindex[name=t, title=Altri testi citati] \makeindex[name=pap, title=Papiri e manoscritti citati nel testo]  \newcommand{\nn}[2]{#2 \textit{n}#1} \newcommand{\qt}[1]{\textbf{#1}}   in the .idx file I get this  \indexentry{Plutarco!demalignitate@\textit{De Malignitate Herodoti}!00855 @855A|hyperindexformat{\qt}}{8}  \indexentry{Plutarco!demalignitate@\textit  {De Malignitate Herodoti}!00868 @868 b-c|hyperindexformat{\nn{33}}}{10}   can somebody advise me on what I am doing wrong here, please? I have tried to use \string after the first sort with no effect.    sure, sorry: this is the file I'm using  \documentclass[12pt,a4paper]{book} \usepackage[utf8x]{inputenx}  \usepackage{palatino}        \usepackage[LGR,T1]{fontenc} \usepackage[english,german,polutonikogreek,italian]{babel}  \usepackage[splitindex]{imakeidx} \makeindex[name=p, title=Passi citati nel testo,columns=1] \newcommand{\nn}[2]{#2 \textit{n}#1} \newcommand{\qt}[1]{\textbf{#1}} \usepackage[hidelinks]{hyperref} \begin{document}  (855A\index[p]{Plutarco!demalignitate@\textit{De Malignitate Herodoti}!00855 @855A|qt})% \footnote{DHM 868 B-C\index[p]{Plutarco!demalignitate@\textit{De Malignitate Herodoti}!00868 @868 b-c|nn{\thefootnote}}} \printindex[p] \end{document} In the book , at page 27 we find the exercise asserting that       Exercise I.XXXVI.   The underlying space of a zero-dimensional scheme is discrete; if the scheme is Noetherian, it is finite.     Thoughts I thought that a zero-dimensional scheme is one such that, in every local ring $\mathscr O_{X,p}$, the only prime ideal is its unique maximal ideal $\mathfrak m_{X,p}.$ Hence, supposing that $X=\operatorname{Spec} R$ is affine, we deduce that every prime ideal is maximal, so each ponit in $X$ is closed. But how does this imply the discreteness? It only implies the Hausdorff-ness of $X$, right? Furthermore, I cannot perceive what the "Noetherianity" has to do with the finiteness claimed here. In the affine case, it seems to be claiming that there are only a finite number of prime ideals in a Noetherian ring, if its scheme is zero-dimensional? For example, $\mathbb Z$ is a Dedekind domain, hence its scheme is zero-dimensional, but it has infinitely many primes: does this contradict the statement?    Thanks in advance for any reference or hint, and point out any inappropriate point if any is presented. Edit I see why my example cannot work now: it is one-dimensinoal: don't forget the pirme $(0)$. But I am still wondering why the statement is true... The  is a proposed propulsion mechanism for spacecraft in which some form of microwave device provides the propulsion. The consensus from the physics community, including many voices on this site, is that the proposed device would violate conservation of momentum.   Several experiments have been conducted, by three main groups: (i) , from Satellite Propulsion Research Ltd, (ii) a research group at the Northwestern Polytechnical University in Xi'an, China, and (iii) Eagleworks Laboratories at NASA's Lyndon B. Johnson Space Center in Houston, Texas. However, few of these experiments have been performed in vacuum (and none of the vacuum tests has been published in a peer-reviewed journal), which means the effect of air currents around the device cannot be ruled out.  This device has been the subject of many questions on this site, including          and their many closed duplicates.  Many of these questions ask what the proposed explanations are, but then veer off into territory of the form "assuming it is true, how does it work?", so they have been (rightfully) closed as counterfactual physics. I feel this sort of bundling does a lot of harm to the discussion, and there is some scope to ask what exactly is being proposed as an explanation. So:     What do the proponents of EmDrive claim is the theoretical justification of the device's function?   Please limit answers exclusively to references, and indicate whether they are peer-reviewed or not. Please limit answers to serious attempts at explanations, as opposed to vague claims about the 'quantum vacuum' - or indicate if an experimental paper does not have any such theoretical explanation or reference.  To be clear, this is not the place to discuss whether the explanations are correct or not. If you have specific questions about any of these sources, ask it separately. (However, if your question starts with "assuming that this works", be prepared for it to be closed.) If you feel there are not enough resources on this thread, you can  but please do not post another question asking people to look for more references. Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$ Title of a book telling about people teleported to a hostile planet while in deep meditation I read it sometime in the 90's but it seemed at least 15 years old at that time. The title might be containing something with 'wolves' or 'wilderness'.  Alert - Spoilers below      The book tells of some (I think) earth cult that dictates the practice of meditation. This cult is somewhat of a scam as When reaching the top level of meditation the meditator is either teleported or his consciousness abducted (I can't remember..) to be used as a calculation machine by the abductors.   Any references would be greatly appreciated. Hitting arrow keys adds characters in vi editor When I tried to use arrow keys in insert mode in vi editor the following characters are being inserted in the editor:   for ↓ I get B, for ↑ I get A, for ← I get D, for → I get C.   Please help me in resolve this problem. Humanity meeting another similar intelligent life form deep into space (or not)? I'm looking for a plot line (it should be a short story) that depicts Earth population (or their close descendants) establishing contact with another intelligent life form deep into space.   After careful studying of DNA samples and language / communication symbols they then realize that the civilization in question is also from Earth but that they departed very long ago and travelled throughout the galaxy in the completely opposite direction so that they are now meeting practically at the point of the circle opposite to Earth. There might have been some anatomical differences as well.  As far as I can remember, the story concludes shortly after that.  This should be a work of a well-known SF author, so I'm hoping for a quick response (if time didn't corrupt my memory too much).  I don't think it was part of an anthology, but it's entirely possible it was in a magazine.  As for the timeline, I've read it about 2-3 years ago, but since I have a passion for older SF works it might not be of much use.  Edit: Not sure if this could help but for what it's worth, it might be contained in . How can I network two Ubuntu computers, so that they can "see" each other at an IP address?