Serialization using serialVersionUid
What is a serialVersionUID and why should I use it?
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$ If $I$ and $J$ are ideals in a ring $R$ with 1 which are  co-maximal, i.e $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n$ in $\mathbb{N}$  Work done:     Should I proceed using    By taking $$K=I^m+J^m \neq R$$  Let $$S=\{I,J \in R \mid I^m+J^n \neq R \}$$ be the required partially order set ordered by inclusion then  $$I+J \subseteq I^n+J \subseteq I^n+J^m \subseteq \ldots $$  Then, I think this chain doesn't have an upper bound...as $I^m+J^n \neq R$ for all $ m,n \in \mathbb N$. Am I right??  Thanks for any help!! What is the spell save DC and spellcasting modifier for a Rogue with Magic Initiate? As a rogue I'm planning to take Magic Initiate with warlock class. The Magic Initiate feat says:     [...] Your spellcasting ability for these spells depends on the class you   chose: Charisma for warlock [...]    cantrip 1: Booming blade or Green flame blade cantrip 2: Minor illusion 1st-level spell: Hex    My stats bonuses are: STR : -3 | DEX +6 | INT 0 | WIS +1 | CHA +4 | prof : 4  Questions:   Green flame blade :      [...] The second creature takes fire damage equal to your spellcasting   modifier. [...]   What is my spellcasting modifier? 0 from INT as rogue or +4 from CHA as warlock?   Minor illusion :      [...] If a creature uses its action to examine the sound or image, the   creature can determine that it is an illusion with a successful   Intelligence (Investigation) check against your spell save DC. [...]   What is my spell save DC? 12 (8 + 0 from INT + 4 from prof) or 16 (8 + 4 from CHA + 4 from prof)? Label callouts in QGIS Has anyone been using callout labelling with QGIS, either trunk or stable?   Used for clustered points. That means the point stays where it is, the label maybe moved if required and a leader (plain or pointed) shows the linkage between the label and the point.   How could I do it (you know what I mean, no coding....)? Is there a word or phrase for something that one might wish exists, but most certainly doesn't? Geometric proof that a Pythagorean triple has a number divisible by $3$? Can I infer from “If $a,b \in \mathbb{N}$ such that $(a,3)=(b,3)=1$ then $a^2+b^2\neq c^2$ for any $c\in\mathbb{N}$” that any pythagorean triple has a number which is divisible by $3$? If so, how can this relationship be proved geometrically? I have an object already created in blender, a tree, or a human, or a pipe.. and I need this to be drilled with multiple holes.   The holes are painted in an image, that is, it is an image that has a repeating an images pattern (they can be circles, squares, or any form).  Here are some examples for drilling-pattern: Possible Duplicate:          Here is a test case:   void foo(int i, int j) {    printf("%d %d", i, j); } ... test = 0; foo(test++, test);   I would expect to get a "0 1" output, but I get "0 0"  What gives?? How to specify that search should be between two dates in technical specification I'm writing an integration manual that specifies how to use our WCF service for mobile messages and responses. The part in question needs to specify that the search results will be filtered between the start and end dates.  My aim is to make it clear that the time portion of the two dates will be discarded and the result will include everything from the start date to the end date. (In practice the code truncates the dates, adds one day to the end date, and returns the data that conforms to a query something like:  SELECT * FROM Table WHERE DateCreated >= @StartDate AND DateCreated &lt; @EndDate)  But my paragraph looks verbose and clumsy. It doesn't feel right. I feel kind of like John Cleese telling the kids when to put their clothes onto a lower peg. How can I make this less verbose?  Or maybe I'm over-thinking this?     When searching for responses, the search is performed between the supplied dates, after truncating the time portion thereof. The results will include responses with a date-time greater than equal to the start date, and less than one day after the end date. So passing the same value for start and end date will retrieve all responses received on that date, for messages previously sent by that user. integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. Should I use 'was' or 'were' in this example?     I was always delighted when my brother or one of my sisters was/were asked to do them. How can you tell if if a meal is thawed? I am planning to place a meal (salmon + rice) in a refrigerator after having frozen it. How can I tell when it's thawed? I would like to set my monitor's scale under 100%, but Win10 only lets me set it to 100% or higher. Why won't Windows let me do that? Is there any workaround to do that? I am aware of the fact that scaling below 100% will result in merged pixels. Travelling to Italy without my spouse who is a UK citizen I am India citizen married to a UK national who has been issued a Schengen Visa from the Italian consulate as a spouse of a UK national. My husband was supposed to travel with me but now can’t. We have decided that I should still pursue the trip without him as I will be joining our friends there. Please can someone let me know if I will still be allowed to travel to the Schengen region with a valid Schengen Visa issued as a spouse of a EEA national but without my husband joining me there in person ? How do people who do not speak Indian English "prepone" things? I recall Asimov had a character who was The autoc of , clearly based on the word “autokrat” but I don’t recall the exact spelling.  This stumped Google, which would rather correct the spelling to some other word than find a unique word.  In the story, he had gone undercover and the reader did not know either that some other character was in fact the Autoc, until it had been revealed to the main character. How to draw a Sankey Diagram using TikZ I have a problem with the endfloat package and unicode characters.  When I compile the following, everything works as expected:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{graphicx}  \begin{document}  \begin{figure} \caption{Ö} \end{figure}  \end{document}   However, when I also load the endfloat package (\usepackage{endfloat}), I get the following error message:  ! Package inputenc Error: Unicode char \u8:ÖÖ not set up for use with LaTeX.   This could be a bug, but my suspicion is that I'm making a mistake somewhere.  I'm hardly the first person to use special characters with the endfloat package.  However, the above example is so simple, I don't see where I could have made a mistake.  Any advice is appreciated.  Edit: The file is of course encoded using utf-8. Setting items to status-completed before they're deployed In several scenarios, including two today ( and ), we have had bugs set to  simply because the fix has been checked in. Just because the code portion has been completed does not mean the work is done, and this can be confusing for users who come across the same problem. Until then it really is  or maybe a tag that doesn't yet exist (status-checked-in?).  Particularly in times like this week, where the stability of the system is a priority, I don't think this status should be set merely because the code has been checked in - it should happen when the code is actually deployed and verified. Currently the devs are being very good about telling us that the code is done but they're not sure when it will be deployed, but I think that is because of the stability issue. How to prove or disprove following statement :     There are infinitely many primes of the form : $\lfloor \sqrt {3} \cdot n \rfloor $    Note: This is a problem I made myself.  There is a theorem that states :  $\lfloor nx \rfloor = \begin{cases}  n\lfloor x \rfloor, &amp; \text{if } 0 \leq \{x\} &lt; \frac{1}{n} \\  n\lfloor x \rfloor +1, &amp; \text{if } \frac{1}{n} \leq \{x\} &lt; \frac{2}{n} \\  n\lfloor x \rfloor +2, &amp; \text{if } \frac{2}{n} \leq \{x\} &lt; \frac{3}{n} \\  \vdots \\  n\lfloor x \rfloor +n-1, &amp; \text{if } \frac{n-1}{n} \leq \{x\} &lt; 1 \\ \end{cases}$  where $\{x\}$ is a non-integer part of $x$ .  Hence :  $\lfloor \sqrt{3}\cdot n \rfloor = \begin{cases}  n, &amp; \text{if } 0 \leq \sqrt{3}-1 &lt; \frac{1}{n} \\  n +1, &amp; \text{if } \frac{1}{n} \leq \sqrt{3}-1 &lt; \frac{2}{n} \\  n +2, &amp; \text{if } \frac{2}{n} \leq \sqrt{3}-1 &lt; \frac{3}{n} \\  \vdots \\  2n-1, &amp; \text{if } \frac{n-1}{n} \leq \sqrt{3}-1 &lt; 1 \\ \end{cases}$  How can I proceed from here ? How to Remove URLs from Google Search Engine