Proving $x^3$ is not convex.
$f(x)=x^3$ is convex nor concave without to derivate
At what port did Lorance Effler born about 1787 in Germany come to the US? Javascript function to convert color names to hex codes "Facebook" could not be downloaded due to an error. (495)   How do I solve this error? In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? Can I include the completion of Udacity and Coursera classes I have attended in an academic CV? Can I include in my academic CV that I have attended and completed the  and  classes I have been taking? I understand that these are not anything major, but the courses definitely gives a good overview and starting formal study on the subject becomes less cryptic. If I can include them without any negative impacts, then under what section should I include them? Are mirror lenses good for wildlife photography in daylight? I've recently seen these Rokinon/Opteka mirror lens with whooping focal length (like 500mm, 600mm, 800mm, 1000mm) at a cheap price. And I have seen some of their same pictures in Flickr and vendor sites. But the only thing is that they usually starts from smaller aperture (f/5.6 and upwards)   Now what I was wondering, as they are cheap with quite good IQ - are they good for any bird photography or wild life photography in proper daylight? How to control Windows 7 snap feature with two monitors? There is an  feature in Windows 7. However, it seems to not work when dragging a window to the edge that is adjoined to the second monitor. How to make it work properly? Maybe some regedit modification or something? How do I get Perl to read the contents of a given directory into an array?   can do it, but is there some method using 'scandir' or a similar term? "compare with" or "compare to" Please check both sentences and let me know, which one is correct and why?   She compares me with her boyfriend.  She compares me to her boyfriend. Converting bike from rim brakes to disc brakes I just bought a used  and it comes with regular rim brakes. I'm perfectly happy with them so far, but have been wondering if disc brakes would come handy when it rains.  What is involved in converting a bike from rim brakes to disc brakes (mechanical or hydraulic)?   Is this something that is feasible, or am I better off buying another bike that already has disc brakes? How does one prove that if $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $ \displaystyle n \mid \frac{a^{n}-b^{n}}{a-b}$ where $a,b, n \in \mathbb{N}$.  What i thought of is to consider $$(a-b)^{n} \equiv a^{n} + (-1)^{n}b^{n} \ (\text{mod} \ n)$$ and if we suppose that $n$ is odd then we have, $$(a-b)^{n} \equiv a^{n} -b^{n} \ (\text{mod} \ n)$$ and since $n \mid (a^{n} - b^{n})$ we have $$(a-b)^{n} \equiv 0 \ (\text{mod} \ n) $$  I think i am far away from the conclusion of the problem, but this is what i could work on regarding the problem. Simple bijection $\mathbb N_0 \times \mathbb N_0 \to \mathbb N_0$ I'm looking for a 'simple' bijection $$ \pi \colon \mathbb N_0 \times \mathbb N_0 \to \mathbb N_0, $$  where 'simple' in this context means that it should be as easy as possible to define and it should be self-evident that said function is in fact a bijection. It's a quest for convenience - not minimal complexity in any rigorous sense.  Here are a couple of examples I came up with - none of which satisfy both requirements:   Let $\pi(m,n) = c(2^m3^{n+1})$, where $c \colon \{2^m3^{n+1} \mid m,n \in \mathbb N_0 \}\to \mathbb N_0$ is the order isomorphism (or in fact Mostowski collapse) of its domain under the natural ordering, Let $\pi(m,n) = \langle n,m \rangle$ - Gödel's pairing function, Let $\pi(m,n) = m \oplus n$ - the number resulting from '' $m,n$ (where we imagine both $m$ and $n$ as in infinite decks of cards whose $i$th element is labeled with its respective $i$th digit). ... How do wizards cast spells which appear on their spell list when it has a divine focus component? What does a wizard do to cast a spell which contains a DF component? Take  for example,  Components V, S, DF    A divine focus component is an item of spiritual significance. The divine focus for a cleric or a paladin is a holy symbol appropriate to the character's faith. The divine focus for a druid or a ranger is a sprig of holly, or some other sacred plant. If the Components line includes F/DF or M/DF, the arcane version of the spell has a focus component or a material component (the abbreviation before the slash) and the divine version has a divine focus component (the abbreviation after the slash).  So do wizards have holy/unholy symbols in their spell components pouch or what? The pronunciation of words which begins 'con' and 'com' Add markdown support for hidden-until-you-click text (aka spoilers) I am doing an analysis with 2 groups of patients (control and disease) whose blood pressures have been measured continuously for 24 hours. My first goal is to test the effect of GROUP on BP. In the beginning, I built the mixed effect model with TIME as random effect variable and group as fixed effect model. The model I used is listed below:  mod &lt;- lme(BP ~ factor(GROUP), random=~1+ TIME| ID, data=gdata)   However, the experimenter wants to know the effects of GROUP on the slope of blood pressure changing per hour. In another words, we need to have blood pressure slope, which is the change of blood pressure by time, as response variable in the model. And I generated another model as bellow:  mod &lt;- lme(BP ~ factor(GROUP)*TIME, random=~1+ TIME| ID , data=gdata)   However, in the new model, the time works both as random effect variable and fixed effect variable. I am not sure if this is allowed in the mixed effect model. Whether and how to thank a girlfriend or boyfriend in the acknowledgements of thesis? How is it received by the academia if someone thanks to his/her girlfriend/boyfriend in the acknowledgements of the thesis?  I have seen writers including his/her fiancee in the acknowledgements, however I don't know if including an informal relationship in the thesis will be received well.  If it is acceptable, how should I refer to my girlfriend? Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$ Question: Let $F_n$ the sequence of Fibonacci numbers, given by $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$. Show for $n, m \in \mathbb{N}$: $$F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$$   My (very limited) attempt so far: after creating a small list of the values $F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_{10}=55$ i can see that yes it does seem to work for instance $F_{6+3}=F_5 F_3 +F_6 F_4 = 10 +24 = 34 = F_9$. However, I really don't know where to begin as showing that this must hold in general terms. Should I be looking to use limits? Or perhaps induction? What is the best way to solve this? How to tell which row number is clicked in a table? How can I change the color of a part of a TextView?