I purchased a Corned Beef Brisket from the store and forgot to put it in the refrigerator. It was sealed. The package was cool in the morning. Is it safe to still use?
If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?
How can friction do no work in case of pure rolling? I have read various answers , on PSE and elsewhere , and most of them explain that the point of contact of the rolling object undergoes 0 instantaneous displacement in the direction of friction, I agree , but then there is a feeling that the friction does provide a torque , so how can it do 0 work . ( The pure rolling here is under a constant external force on the object so friction does act ). Get names of all keys in the collection How can one rig a Stirling engine? (Piston) I've only done a very little animation and rigging before, and I keep getting stuck trying to rig the pistons and rotor of the Stirling engine I built.     What should happen is that one piston moves in as the other moves out, and through the attached arms, the rotor should spin. Animating the rotor and the piston heads was easy enough, but getting the arms that go from the piston heads to the end of the shaft arm to move right endlessly confuses me.   Each end of each arm moves differently over the course of a cycle. With animating, I can't figure out how to interpolate so the arms stay where they should.  With armatures, I have tried for a while, but keep getting stuck when it comes to how to have one end of a bone moving in a circle while the other end is moving in a straight line.  Edit: The answer below elegantly resolved my problem, so i've updated this with the finished .blend file in case it's useful someone else.   Here is the .blend file: As you are all most likely aware already all domain registrars ask for your personal information.   Such personal information includes:   Forename and surname Address information Email address Telephone number   Personal information via WHOIS  Depending on the domain type such as  or  this information may become immediately available after the registration of the domain via a simple whois. If you do not want that (and in most cases you certainly don't) they offer a service where you can remove this information from the whois service but of course hiding your personal information adds yearly costs to the domain  purchase.  What happens if I use fake details when registering a domain? What's the difference between these two sentences? And which one's grammatically correct? Formally, is it correct to write:     A number of questions has been asked here.   or:     A number of questions have been asked here.   As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.  Moreover, is it the same for "a myriad of", "a plethora of", and so on? When are "because", "since","for" and "as" interchangeable? I am not a native speaker. On a previous question of mine, I thanked for an answer by saying:     So the phrase is not an idiom, since it is applied in its literal sense.   I consciously chose since over because, because — well, I like that usage of since, even though I know that some (native speakers) don't like it. Nonetheless, that choice got me thinking for a while, and it occurred to me that I even could have used more alternatives, namely as or for, without changing the meaning.   So, on a general note, here are the alternatives:        Statement A (is true), because statement B (is true).   Statement A (is true), since statement B (is true).   Statement A (is true), as statement B (is true).   Statement A (is true), for statement B (is true).      Are these completely interchangeable? Or interchangeable in certain situations? Or can you point out any (not-so-)subtle differences between any of them? Are there even more synonyms? Guaranteed lifetime of temporary in C++? Does C++ provide a guarantee for the lifetime of a temporary variable that is created within a function call but not used as a parameter?  Here's an example class:  class StringBuffer { public:     StringBuffer(std::string &amp; str) : m_str(str)     {         m_buffer.push_back(0);     }     ~StringBuffer()     {         m_str = &amp;m_buffer[0];     }     char * Size(int maxlength)     {         m_buffer.resize(maxlength + 1, 0);         return &amp;m_buffer[0];     } private:     std::string &amp; m_str;     std::vector&lt;char&gt; m_buffer; };   And here's how you would use it:  // this is from a crusty old API that can't be changed void GetString(char * str, int maxlength);  std::string mystring; GetString(StringBuffer(mystring).Size(MAXLEN), MAXLEN);   When will the destructor for the temporary StringBuffer object get called?  Is it:   Before the call to GetString? After GetString returns? Compiler dependent?   I know that C++ guarantees that a local temporary variable will be valid as long as there's a reference to it - does this apply to parent objects when there's a reference to a member variable?  Thanks. Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$ Let $({\Bbb R},{\mathcal A},\mu)$ be the measure space where ${\mu}$ is the Lebesgue measure.  Assume that $\int_{\Bbb R}|f|^pd\mu&lt;\infty$ ($p\geq1$). There is an exercise for proving that       $$\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s).$$   If one formally let $s=t^p$, then $ds=pt^{p-1}dt$ and one would immediately get the equality above. However, how can I justify it rigorously in the sense of Lebesgue integration?    [Edited] What puzzles me is that I have the "change of variable" theorem for Riemann integration, but all the integrations here are in the Lebesgue sense. Unless one has shown that the integrands are also Riemann integrable, how can I directly use "change of variable"? Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula $m + Lr$, where $L$ is the Cholesky lower factor so that $S=LL^T$ and $r = (r_1,...,r_n)^T$.  What about if one wants samples from singular Gaussian i.e. $S$ is still symmetric but not more positive definite (only positive semi-definite). We can assume also that the variances (diagonal elements of $S$) are strictly positive. Then some elements of $x$ must have linear relationship and the distribution actually lies in lower dimensional space with dimension $&lt;n$, right?  It is obvious that if e.g. $n=2, m = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, S = \begin{bmatrix} 1 &amp; 1 \\ 1 &amp; 1\end{bmatrix}$ then one can generate $x_1 \sim N(0,1)$ and set $x_2=x_1$ since they are fully correlated. However, is there any good methods for generating samples for general case $n&gt;2$? I guess one needs first to be able identify the lower dimensional subspace, then move to that space where one will have valid covariance matrix, then sample from it and finally deduce the values for the linearly dependent variables from this lower-dimensional sample. But what is the best way to that in practice? Can someone point me to books or articles that deal with the topic; I could not find one. Mismatch Reputation in the thumbnail and the actual Reputation We let a>0 and b>0 and  we have $\sum_{n=0}^{\infty}b^n-a^n$. We have to find all values a,b>0 where $\sum_{n=0}^{\infty}b^n-a^n$ is convergent. I think I can use that $$\sum_{n=0}^{\infty} b_n &lt; \infty , \sum_{n=0}^{\infty} a_n &lt; \infty \implies \sum_{n=0}^{\infty} (b_n-a_n) &lt; \infty. $$. And I think $\sum_{n=0}^{\infty}b^n$ and $\sum_{n=0}^{\infty}a^n$ is convergent if a&lt;1 and b&lt;1? It will make sense. But how can I show it? No hyper refs from citation to bibliography using BiBTeX, hyperref and harvard Are split infinitives grammatically incorrect, or are they valid constructs? Mark's generosity in this crisis seems to more than make up for his earlier stinginess.   Should those sentences always be avoided, or are there cases where they are valid? Reference label with included file and relaxed clearpage I am running into a rather weird error that apparently originates from the combination of \include, \let\clearpage\relax and a referenced label after a page break.  In this particular example, the label mylabel defined in the listing cannot be referenced anymore when the reference and the label are close enough to a page break.  The MWE consists of two files, the main-file and an included file. I am using the \let\clearpage\relax command to . The error does not occur if the file is \input instead of \included.  \documentclass[11pt,twoside]{book} %  \usepackage[utf8]{inputenc} % Enoding \usepackage[english]{babel} % Language \usepackage{listings} \usepackage{forloop}  \begin{document} \begingroup \let\clearpage\relax  \include{includedfile} % changing include for input would work  \endgroup \end{document}   Included file:   \newcounter{ct} \forloop{ct}{1}{\value{ct} &lt; 40}% {%     .\\ }  Listing \ref{mylabel}.  \begin{lstlisting}[caption=somecaption, label=mylabel] some code; \end{lstlisting}   Running this example will have an output where the label cannot be referenced (even after multiple runs):    Now, one solution is to use \input as mentioned earlier but I am rather interested in why this happens. Does the \clearpage command fulfil an important function for references to work? And can the error be avoided without removing \let\clearpage\relax while using \include?  EDIT: I just found  with the same issue (though it does not have a definite answer). Why does the series $\sum_{n=1}^\infty\frac1n$ not converge? In terms of purely set theory, the axiom of choice says that for any set $A$, its power set (with empty set removed) has a choice function, i.e. there exists a function $f\colon \mathcal{P}^*(A)\rightarrow A$ such that for any subset $S$ of $A$, $f(S)\in S.$ Is this correct?  My question then is about proving this fact, so that we do not need to put it as an axiom. Now as per the research done on this single object- Axiom of Choice, I believe here that there should be some falsity in my argument. I do not find the mistake.  For any $S\in \mathcal{P}^*(A)$, since $S\neq \emptyset$, $\exists s\in S$. Define $f(S)=s$. Then $f$ is a choice function.  This was showing me that the axiom of choice is proved, but then why it had been put as an axiom? For example, in  book, the author asserts that      It is a metatheorem of mathematical logic that it is impossible to specify the function that assigns to each non-empty subset of $\mathbb{R}$, an element of itself.     There are several notes and books on axiom of choice, but here I am trying to understand through doing some argument for some problem, where problem actually arises. I commonly use the word 'guys' to refer to a group of males colloquially. It's colloquial but not rude, off putting, condescending, patronizing (though I wouldn't use it with a group of men at a board meeting (hypothetically of course), unless I knew them). So, some that I would not consider as replacements would be    buddies: too old-fashioned dudes: too informal boys: too patronizing men, gentlemen: too formal or false respect   I realized that I had also been using it for any group of people, males and females, even just females. It worked for me and I didn't think of the gender implications, that women might not care for it. No one ever complained, directly or indirectly (rule of life: sometimes people don't complain about things they should).   But it occurred to me (maybe by reading something that sparked realization) that the intended hearers might not all care for it.  What might be a female gendered or non-gendered version of 'guys'?  Some that I've considered don't feel right about (though these may be reasonable answers) are:   dolls: too old-fashioned babes: too informal  ladies: too formal or I've heard from women, too creepy women: too factual girls: too patronizing (as much as 'boys') everyone, you all: too bland y'all: perfectly non-sexist but too regional (might work, but not everywhere)   Hopefully I haven't eliminated all the possibilities -- any suggestions? I am having a problem running the CDC change capture job against some of my test databases.  The error message I'm getting is the following:     Executed as user: NT AUTHORITY\NETWORK SERVICE. Cannot execute as the database principal because the principal "dbo" does not exist, this type of principal cannot be impersonated, or you do not have permission. [SQLSTATE 42000] (Error 15517).   How can I fix this? How can I use an array of function pointers? How should I use array of function pointers in C?  How can I initialize them?