Calculate length of service automatically
How do I get the number of days between two dates in JavaScript?
How to make clickable links and cross-references in pdfs produced by LaTeX? How do I select multiple elements and a class in JQuery Is there a systematic way of finding the conjugacy class and/or centralizer of an element? Is there a systematic way of finding the conjugacy class and centralizer of an element? Could the task be simplified if we are working with "special groups" such as $S_n$ or $A_n$? Are there any intuitive approaches? Thanks. $$\lim_{x\to 0}\frac{10^x - 2^x - 5 ^ x + 1 } {x\tan x} $$ This is an indeterminate limit.  I want help in solving this problem. Thanks in advance MicroSD card is set to Read-only state. How can I write data on it? I have been told [Warning: I leave this because it's what I asked and allows to understand the dialogues in the comments, but Azad, whom I thank, has pointed that the formula does not hold in general in the form it is expressed] that the angular momentum of and rigid body with respect to any point $P$ can always be expressed as $$\mathbf{L}_{P}=\mathbf{r}_{cm}\times M\mathbf{v}_{cm}+\big(\sum_im_iR_i^2\big)\boldsymbol{\omega}$$ where $\mathbf{r}_{cm}$ is the position of the centre of mass with respect to $P$, $M$ the mass of the body, $R_i$ the distance of the $i$-th point, having mass $m_i$, composing the body, and $\sum_im_iR_i^2=I$ its moment of inertia with respect to the instantaneous axis of the rotation around the centre of mass of angular velocity $\boldsymbol{\omega}$.  I know that the velocity $\mathbf{v}_i$ of each point $P_i$, having mass $m_i$, of a rigid body of mass $M$ can be see as the sum of a translation velocity of one of its points $C$ plus a rotation velocity around that point: $\mathbf{v}_i=\mathbf{v}_{C}+\boldsymbol{\omega}\times\overrightarrow{CP_i}$. If we chose $C$ as the centre of mass I see that $$\mathbf{L}_{cm}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{i}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{cm}+\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})$$$$=\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i}) $$because, if I am not wrong, $\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_C=(\sum_i m_i\overrightarrow{CP_i})\times\mathbf{v}_C=\mathbf{0}$ since $\sum_i m_i\overrightarrow{CP_i}$ is the position of the centre of mass with respect to itself, which is $\mathbf{0}$.  How can it be proved that $\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=(\sum_im_iR_i^2)\boldsymbol{\omega}$? I have searched a lot on the Internet and on books, but I find nothing. To give some background of mine, I have studied nothing of analytical mechanics. I find the formula very, very interesting both in itself and because, if the moment of inertia does not depend upon time, $\forall t\quad I(t)= I(t_0)$, the above expression can be differentiated to get the formula of the resultant torque with respect to the centre of mass $\sum\boldsymbol{\tau}_{cm}=\frac{d\mathbf{L}_{cm}}{dt}=I\boldsymbol{\alpha}_{cm}$ where $\boldsymbol{\alpha}$ is the angular acceleration around the centre of mass. I heartily thank you for any answer!    Some unfruitful trials: by using the "BAC CAB identity" as suggested by Azad, whom I heartily thank, $\mathbf{a}\times(\mathbf{b}\times\mathbf{c})=(\mathbf{a}\cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}$, I can see that$$\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=\sum_im_i\|\overrightarrow{CP_i}\|^2\boldsymbol{\omega}-m_i(\overrightarrow{CP_i}\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$which, by decomposing every $\overrightarrow{CP_i}$ into an axial component $\mathbf{A}_i$ and a radial component $\mathbf{R}_i$, whose norms respectively are $A_i$ and $R_i$, with $R_i$ as the distance from $i$ to the axis of rotation, becomes $$\sum_im_iR_i^2\boldsymbol{\omega}+\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$but I cannot prove that $\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}=\mathbf{0}$. NEWID() In Joined Virtual Table Causes Unintended Cross Apply Behavior My actual work query was an inner join, but this simple example with cross join seems to nearly always reproduce the problem.  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT NEWID() TEST_ID ) BB ( B )   With my inner join I had many rows for which I added to each a GUID using the NEWID() function, and for about 9 out of 10 such rows the multiplication with the 2-row virtual table produced the expected results, just 2 copies of the same GUID, while 1 out of 10 would produce different results. This was unexpected to say the least and gave me a really hard time trying to find this bug in my test data generation script.  If you take a look at the following queries using as well non-deterministic getdate and sysdatetime functions, you won't see this, I don't anyway-I always see the same datetime value in both final result rows.  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT GETDATE() TEST_ID ) BB ( B )  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT SYSDATETIME() TEST_ID ) BB ( B )   I'm currently using SQL Server 2008 and my work around for now is to load my rows with GUIDs into a table variable before finishing out my random data generation script. Once I have them as values in a table as opposed to virtual table, the problem goes away.  I have a workaround, but I'm looking for the ways to workaround without actual tables or table variables.  While writing this I tried without success these possibilities: 1) placing the newid() into a nested virtual table:  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT TEST_ID     FROM (         SELECT NEWID() TEST_ID     ) TT ) BB ( B )   2) wrapping the newid() within a cast expression such as:  SELECT CAST(NEWID() AS VARCHAR(100)) TEST_ID   3) reversing the order of appearance of the virtual tables within the join expression  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS JOIN (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A )   4) using uncorrelated cross apply  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS APPLY (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A )   Just before finally posting this question, now I tried this with success it seems, a correlated cross apply:  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS APPLY (     SELECT A     FROM (         SELECT 1 UNION ALL         SELECT 2     ) TT ( A )     WHERE BB.B IS NOT NULL ) AA ( A )   Anyone have any other more elegant, simpler workaround? I really don't want to use cross apply or correlation for a simple row multiplication if I don't have to. How to salt PBKDF2, when generating both an AES key and a HMAC key for Encrypt then MAC? When using Encrypt-then-MAC with AES and HMAC by password, and given 128 bits of payload with the ciphertext to store a random salt, which would be more secure:   Using PBKDF2 with then entire 128 bit random salt and generating 512 bits of derived data to split into a 256 bit AES Key and a 256 bit HMAC key.   or   Using PBKDF2 separately for each key using two 64 bits salts to generate a 256 bit AES Key and a 256 bit HMAC key.    or    Better option? I need to use an alias in the WHERE clause, but It keeps telling me that its an unknown column. Is there any way to get around this issue? I need to select records that have a rating higher than x. Rating is calculated as the following alias:  sum(reviews.rev_rating)/count(reviews.rev_id) as avg_rating A Good Book for Mathematical Probability Theory Why couldn't Bond have backup at the battle of Skyfall? I think I am missing a key plot point here.   Bond had to fake-kidnap M and bring her to Skyfall in order to lure Silva there for one last stand. Why did this have to be a secret from his colleagues at MI6? Why couldn't there have been other agents there to help defend the house and take down Silva?  Also, why did he have to have Q lay a fake trail to get Silva to follow him to Skyfall when he was actually going there, and he wanted Silva to follow him? I am considering buying my first DSLR.  How do I know whether I need a 18-200 lens, 17-85, or 18-55? Or something else? Is my mobile AMD card being used? Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$ What did Ken Thompson mean when he said, "I'd spell creat with an 'e'."? What is Ken referring to? Is there a "creat" command? What lens focal length most closely resembles the perspective of the human eye? I have the following title page in LaTeX: \documentclass{article}  \title{Appendix A: User Manual}  \author{ John Smith\\University XYZ\\Albert Square\\Walford\\NC1 8AE }  \begin{document} \maketitle \end{document}  What is the proper way to add a new page, say, for the contents page and start editing that new page? I am totally stumped for what to do here, any help would be appreciated.   1) What happens if you apply the method of steepest descent to $f(x)=x_1^2+x_2^2+x_3^2$?  2)Lagrange multipliers method- Find the dimensions of the rectangular box open at the top of greatest internal volume, given the surface area of the five faces is $108 \, \mathbb{cm}^2$.  Thanks sed : Ignore line starting whitespace for match I want to replace the default listening port of httpd to 9090. I can edit the line in httpd.conf file using below  sed -i "/^Listen/c\Listen 9090" /etc/httpd/conf/httpd.conf   But the line   Listen 80   may have white space before it.  How do I ignore this white space to match this line? Are all multiplicative functions additive? Suppose $cf(x)=f(cx)$ and $f:\mathbb{R}\to\mathbb{R}$. I believe it follows that $f(x+y)=f(x)+f(y)$.   Proof: There is some $c$ such that $y=cx$. Then  $$f(x+y)=f\left((1+c)x\right)=(1+c)f(x)=f(x)+cf(x)=f(x)+f(cx)=f(x)+f(y)$$  QED.  I wonder if the same thing holds for when $f:\mathbb{R}^n\to\mathbb{R}^n$? I can't use the same trick, because all vectors are not scalar multiples.  I tried thinking of it in terms of basis units, but didn't get anywhere.