How can I solve this problem? Can you please give me an example or an idea for a potential solution?
I have  a  requirement where a future method need to be called from batch apex ,I came across various articles stating that a future method could not be called from the batch. Is there any alternate solutions for that?
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$ This is question 2.9 #9 from Topics in Algebra by Herstein:     If $o(G)$ is $pq$ where $p$ and $q$ are distinct prime numbers and if $G$ has a normal subgroup of order $p$ and a normal subgroup of order $q$, prove that $G$ is cyclic.   Let $N$ denote the normal subgroup of order $p$ and $M$ denote the normal subgroup of order $q$. Here are a couple things I noted while exploring the problem:   $N$ and $M$ are cyclic, since they have prime order. $G = NM$ [1].   Any hints where to look next?    [1] Since $N,M$ are normal, $NM \le G$. Then $o(NM) \mid o(G)$, so $o(NM)$ is either $1$, $p$, $q$, or $pq$. The first three don't work because they force one of $N$ or $M$ to be $(e)$, so we have $o(NM) = pq$. Therefore, $NM = G$. Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$ Exercise: Let $\tau_1$ and $\tau_2$ be two topological spaces on a  set $X$. Then $\tau_1$ is said to be a finer topology than $\tau_2$ if $\tau_1\supseteq\tau_2$. Prove the identity function $f:(X,\tau_1)\to (X,\tau_2)$ is continuous if and only if $\tau_1$ is a finer topology than $\tau_2$.  Attempted proof: Let $A\in\tau_1$. If $f$ is continuous then $\exists B\in\tau_2$ such $f(A)\subset B\implies A\subset B$ for any $A\in\tau_1$ such that all open sets of $\tau_1$ are open sets of $\tau_2$ hence $\tau_1\supseteq \tau_2$. If $\tau_1$ is a finer topology than $\tau_2$, for any $B\in\tau_2\implies B\in\tau_1$ which implies that $f^{-1}(B)=B$, then $B\in\tau_1$ which proves $f$ to be continuous. Questions: Is my proof right? If not. What is wrong? What are alternatives? Thanks in advance! Interchanging the order of differentiation and summation Could give some examples of nonnegative measurable function $f:\mathbb{R}\to[0,\infty)$, such that its integral over any bounded interval is infinite? Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$ Deteremine the sum of the series $$\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$$  So I first write down the $n^{th}$ term $a_n=\frac{\frac{n(n+1)}{2}}{n!}=\frac{n+1}{2(n-1)!}$.  So from there I can write the series as $$1+\frac{3}{2}+\frac{4}{2\times 2!}+\ldots +\frac{n+1}{2(n-1)!}+\ldots $$  I am quite sure I can do some sort of term by term integration or differentiation of some standard power series and crack this. Any leads? Email to salesforce error While sending an attachment as an email to be attached to the salesforce record.Salesforce is giving the below given error.  Generating server: mx1.madison.gov  6-2j26dncatawfg1112dv2uwxupq9hzfgmjrrlrn2rx48cxm93nt.8-dea8eae.c.le.salesforce.com mx1-asg.mta.salesforce.com # #SMTP#  Is this salesforce problem or it is the Internal company server problem as I could see that error mentions company server name also.But to me doesn't look like company server error. Preserving order with LINQ I use LINQ to Objects instructions on an ordered array.  Which operations shouldn't I do to be sure the order of the array is not changed? Space of probability measures "complete"? (In the other sense) How can I add new autostart programs in Lubuntu? In Lubuntu, there's no 'Add New Program...' button in Desktop Session Settings. Is there an easy way to add new autostart programs in Lubuntu? $\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals I am having trouble comprehending how anyone could come up with this formula:  $$F = \frac{GMm}{d^2}.$$   Could someone walk me through this? Why are Perl 5's function prototypes bad? What is the correct way of installing BOINC software? Idempotent linear operators are projections How to populate options of h:selectOneMenu from database? Finding the volume of the tetrahedron. Find the volume of the tetrahedron with the vertices $P(1,1,1)$, $Q(1, 2, 3)$, $R(3, 1, 2)$, and $S(2, 3, 1)$. I'm trying to show that  $$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$  Where $a_{i}$ are the roots of the function $f(x)$. I've tried to proceed by using a dummy function $g(x)$ and carrying out:  $$\int_{-\infty}^{\infty}dx\,\delta\big(f(x)\big)g(x)$$  Then making the coordinate substitution $u$ = $f(x)$ and integrating over $u$. This seems to be on the right track, but I'm unsure where the absolute value comes in in the denominator, and also why it becomes a sum.  $$\int_{-\infty}^{\infty}\frac{du}{\frac{df}{dx}}\delta(u)g\big(f^{-1}(u)\big) = \frac{g\big(f^{-1}(0)\big)}{\frac{df}{dx}\big(f^{-1}(0)\big)}$$  Can any one shed some light? Wikipedia just states the formula and doesn't actually show where it comes from. Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful. Slow math typing I have been using LaTeX for quite some time, but I find the math writing to be a bit frustrating. It seems to take me a relatively long time to code-write long math expressions, and sometimes it's hard to see where { start and end.  I am interested in writing as fast as possible.  Is code-typing each symbol really the fastest way? Is there any good program (in the spirit of Word's MathType) that enables producing math expressions by button clicking, that you recommend? If I am introducing someone to my daughter's husband's parents can I say "Hi, I'd like to you meet my ___". In-laws would not work here because they are my child's in-laws not my own. Is there a word for this relationship?