Transform normal distribution to skewed distribution without changing its support

Question: I've found many questions and answers about transforming skewed distribution to normal. This question might arise because the simplicity of working with normal data. But, is there any function that transform normal to skewed data without changing the interval of the support? how can this be done?
Answer: The support of a normal random variable is $(-\infty,\infty)$. Consider a normal variate, $X$.
You could create a skewed distribution with the same support with a transformation, $Y=T(X)$ such that $T$ is bijective ($\mathbb{R}$ $\to \mathbb R$) and either convex or concave. The result of applying a convex bijective transformation will be right skew and have support $(-\infty,\infty)$ and a concave bijective ($\mathbb{R}$ $\to \mathbb R$) function will be left-skew and have support $(-\infty,\infty)$.
(Concave and convex functions are not the only way to get skew results, however.)
e.g. consider
$T(x)=\begin{cases} x-1\,;& x \leq 1\\ \log(x)\,;& x > 1\end{cases}$
It will take a symmetric sample and squeeze in its values above 1, while leaving the lower values alone, resulting in a left-skew result (changing the parameters of the normal will alter how much impact this transformation has on the skewness).
[If, instead you want the sample range of the values to be the same after transformation, you can take a sample, transform it to the desired shape, and then use a linear transformation to match the minimum and maximum values.]
Comment: +1. A simple family of infinitely differentiable transformations that can achieve any skewness coefficient (beginning with a standard Normal distribution) is $x \to \text{sgn}(\lambda)x + \exp(\lambda x)$, $\lambda\in\mathbb{R}$.
Comment: Sure, but its effect will be small. However, if you know approximately where the mean is going to be (you know $\mu$ should be around $\mu_0$ say) you can replace $T(x)$ with $T_2(x)=T(x-\mu_0)$, say, which would have a much stronger effect.
Comment: Re @whuber's family of transforms: consider starting with $\exp(λx)$ for $λ>0$. This takes $R\to R^+$ and takes us from symmetry to varying amounts of right skewness (specifically, from a normal to a lognormal distribution).  Note that values that start far below 0 end up just above 0. If we add $x$ to our transform, large negative values that were at $x_0$ now stay near $x_0$ (now on $\mathbb{R}$), but large positive values are (relatively) mostly impacted by the $\exp$ term. For left skewness bring in $λ<0$, but use $\text{sgn}(λ)$ so both terms flip the direction of $x$.
Comment: @jlandercy Some links on the general case you ask about -- https://stats.stackexchange.com/a/107690/805  & https://stats.stackexchange.com/a/419585/805
Comment: @Glen_b I'm really bad at math actually. So i'm trying to imagine it. Can the above transformation be applied to normal distribution with negative mean that far from zero?
Comment: @whuber Woww,, I'm impressed. How did you get that? Just wanna know the way you think. thanks!
Comment: There's a lot more could be said about that neat little family and perhaps more things you'd look at while coming to it, but that's the gist of the kind of thought process that one might go through to come up with it.
Comment: Do you have a reference highlighting the link between distribution skewness and transformation convexity?
Comment: Not in general, since you can change the impact on skewness with a shift which doesn't change convexity. Note that the question here assumes we start with a normal distribution  (and the answer focuses on the standard normal, assuming we shift and scale before and after as needed)
Answer: Despite the fancy jargon, the above answer is incorrect over the support mentioned, as neither function is normalizable if the support is x>1, so the functions do not technically define a probability distribution. The functions would be distributions if you define the support to be a closed interval.
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Comment: This does not provide an answer to the question. Once you have sufficient [reputation](https://stats.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://stats.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/353107)


Minimal number of generators in a presentation of a group

Question: I just start learning about presentations of groups. I would like to ask a question. If G is a finitely-presented group with a presentation [S,R] (S denotes the set of generators, R denotes the set of relators) such that the cardinality of S is minimal in the class of all presentations of G. Is it true that the cardinality of S equals the minimal cardinality of generating set of G?
If not true in general, is it true for finite groups?
Comment: Can you define $S$?
Answer: If $S$ is a generating set, then $\langle S,R\rangle$ gives a presentation if we let $R$ be the set of all relations between elements of $S$.
In other words, the collection of sets $S$ that show up in presentations is identical to the collection of sets $S$ that show up as generating sets—so certainly the minimum cardinality is equal.


How do I actually add DRM to a video file for EME to interpret?

Question: So, I've tried googling this a bit but DRM and EME search results haven't pulled up much in the way of actually telling me what to use on the server-side to implement DRM before a video is sent to the browser for the HTML5 player to decode. Is there some sort of ubuntu/Apache plug-in that adds drm to a video file on the fly then streams the DRM'd file to the HTML 5 video tag?
Comment: search google for CENC
Answer: You can use Shaka Packager to package content, so it would be DRMed.
Comment: Thank you for that suggestion. I have some video content I'm starting to release and would prefer for it to be more difficult to be saved to a user's device than just using a normal HTML5 video tag alone - which allows anyone to download the full video file. I'm sure no scheme is 100% but I don't think there are many known work-arounds to this.


Does Stack Exchange do anything to guard against shilling?

Question: I've noticed that certain users get multiple votes for almost every answer they post.  Sometime the answers are clearly not the best.  Sometimes they are wrong.  I assume this is people voting for themselves with extra accounts, having friends give them automatic votes, or groups supporting each other.  This takes a little of the fun out of Stack Exchange.  I don't think this this can be handled by the moderators because the moderators seem to be included in the group of unusually high vote receivers.  It seems there could be rules about the frequency you can vote for the same user.  This would improve the enjoyment participating in Stack Exchange.
Answer:
I assume this is people voting for themselves with extra accounts, having friends give them automatic votes, or groups supporting each other.

Yes, all of these happen. And they are all detected. And reversed. And the people involved get warnings and suspensions, if needed.

It seems there could be rules about the frequency you can vote for the same user

There are. See What is serial voting and how does it affect me?
Comment: @Sha "they are all detected" could just as easily (and possibly was intended to, but maybe I'm wrong) mean "these are all things that are detected", not "all occurrences of these are detected".
Comment: As in real life, the voting fraud we know about is what we can measure, @sha
Comment: We actually have systems in place that *detect* most if not all of that, @Shadow - it just doesn't get *invalidated* automatically in some cases. (for an example of what it might look like if we did, [see a recent test I ran on Ask Ubuntu](http://meta.askubuntu.com/questions/15516/i-lost-3000-rep-as-a-reversal/15521#15521)). Looking to change that in the near future. FWIW, there's almost certainly stuff that we can't see *even when folks flag or email us about it*... Unfortunately, we can't look into the minds of voters, so there's a limit to what we can do; I should probably write about this.
Comment: @Shog9 I have no doubt about all of this. Still, even that last sentence "we can't look into the minds of voters" is enough to contradict "And they are all detected".
Comment: "And they are all detected" - I don't think this is true. Many are detected, true, but I am pretty sure not **all** of them. Smart cheaters take time and sometimes luck to detect.
Comment: @Shog9 so you never get flags from users who detect frauds otherwise not detected by the system or by moderators? Sorry, I don't really believe that. (Of course, it might be true, can't really know)
Comment: Hence my reference to voting fraud IRL (in, say, elections) - we measure the forms of fraud we know about, but there can (and probably do) exist more esoteric or subtle forms. @sha
Comment: I've been visiting electrical engineering StackExchange.  Maybe if the numbers are kept small they are not detected.  Here is an example; http://electronics.stackexchange.com/questions/270533/traffic-light-controller.  There was one answer given which had one upvote as soon as the answer was provided.  The problem is this is clearly not a right answer.  The speed with which the upvote came makes me not believe this is an honest vote.  The problem is that most questions on the EE site get small numbers of votes.  The answer provider has had upvotes for many wrong or rude answers, not fun.
Comment: There's only one answer there and nearly an hour between its creation and the first vote, @owg60. There are also no downvotes, and no other answers in nearly a day. I can't speak to the accuracy of the answer, although if you find it not useful you should at very least downvote it - the biggest failing of the voting system isn't actually fraud, it's that folks don't vote when they should.


Low CPU usage with simulation

Question: I am trying to do a simulation in blender in order to place some objects on a ground. During baking or simulation in real time everything is super slow (less then 1 fps) but CPU usage (6700K i7) is only ca. 30%. GPU 0%. I guess all simulations are calculated by CPU but why Bleder does not use it at 100%?
Comment: Perhaps the simulation is relatively easy to calculate, however it produces lots of data that needs to be written to disk. This could result in an I/O bound task, where the writing speed to disk is the bottleneck. That is complete speculation though. Another reason could be that the implementation uses fewer threads than there are CPU cores
Answer: The simulation is likely only running on one core (with another core being partly used for scene updates).
Many (particularly older) physics simulators are single threaded, or at least some steps are. Multi threading in physics simulators is very hard due to all the possible inter-dependencies between objects, see also: Is Physics calculation multithreading possible?
Blender's rigid body engine is Bullet, which does support some multithreading, but I don't think that part has been integrated with Blender, and from what I hear, still has a fair bit of overhead.

Low CPU usage with simulation


measures defined by shifting is absolutely continuous with respect to Lebesgue measure

Question: Let $\mu$ be a non-zero positive $\sigma$-finite measure on the Borel sigma-algebra $\mathscr{B}(\mathbb{R})$. For $x \in \mathbb{R}$ define a measure $\mu_x$ by
$\mu_x(A) = \mu(A + x)$.
Assume that for any $x,y\in \mathbb{R}$, $\mu_x \ll \mu_y$($\mu_x$ is absolutely continuous with respect to $\mu_y$). Prove that $\mu \ll m$, where $m$ is the Lebesgue measure.
This is a homework problem, I have no idea where to start. Can anyone give a hint or sketch?
Answer: Let $A \subset \Bbb{R}$ be Borel measurable with $m(A) = 0$. We want to show $\mu(A) = 0$.
Since $\mu_x \ll \mu_y$ for all $x,y$, it suffices to show that there is at least one $x \in \Bbb{R}$ with $\mu_x(A) = 0$ (why exactly?)
Now, in measure theory, it is sometimes easier to show that a set is very big instead of just showing that it is nonempty. In our case, if we knew that that set $G := \{x \,:\, \mu(A + x) = 0\}$ of "good points" had full measure (i.e., $G^c$ is a Lebesgue null-set), then we would be done.
To see that this is indeed true, consider
$$
\int \mu (A+x) d m (x)
$$
and try to write this in different ways.
If you don't find it yourself, uncover the spoiler below (but first try it, otherwise you rob yourself of a nice experience).

 $$\int \mu(A+x) dm(x) = \int \int 1_{A+x}(y) d\mu(y) dm(x) = \int \int 1_{A+x}(y)dm(x) d\mu(y) = \int m(y - A) d\mu(y)  = \int m(A) d\mu(y) = 0.$$

 Since the integral vanishes, the set $\{x \,:\, \mu(A+x) > 0\} = G^c$ must be a Lebesgue null set. As seen above, this completes the proof.

Side remark: For the actual computation, we did not use that $\mu_x \ll \mu_y$. This was only used at the very beginning of the proof.
Question: (Where) did we use that $\mu$ is $\sigma$-finite?
Comment: Clear and helpful, thanks very much! For your question, we need $\sigma$-finite to use the Tonelli Theorem to exchange the order of the integral. Just a further question: Why do we define $\mu$ on the Borel $\sigma$-algebra? It looks fine if $\mu$ is defined on the Lebesgue $\sigma$-algebra.
Comment: @Philo: Good question. The main reason probably is that assuming $\mu$ to be defined (and a measure( on the Borel $\sigma$-algebra is a **weaker** assumption (after all, if $\mu$ was defined on the Lebesgue $\sigma$-algebra, we could simply restrict it to the Borel sets). Also, once we have shown that $\mu \ll m$, it follows that $\mu$ (uniquely) extends to the Lebesgue $\sigma$-algebra, by virtue of $\mu(A \cup N) = \mu(A)$ if $N$ is a subset of a Borel measurable Lebesgue null set. Finally, the Lebesgue $\sigma$-algebra is very peculiar and has some properties that are considered **bad** by
Comment: some. For example, if $f : \Bbb{R} \to \Bbb{R}$ is Lebesgue measurable and $h : \Bbb{R} \to \Bbb{R}$ is continuous, it does **not** follow that $f \circ h$ is Lebesgue measurable, but the analogous claim holds if "Lebesgue" is replaced by "Borel" everywhere. Also in the proof above, we used Fubini's theorem. For this, we need to know that $(x,y) \mapsto 1_{A+x}(y) = 1_A (y-x)$ is (Borel or Lebesgue) measurable. If $A$ is Borel measurable, this follows easily, but if $A$ is merely Lebesgue measurable, this is not soooo clear.
Comment: @Philo: For example, Barry Simon literally writes: "In summary, passing from Borel to Lebesgue measurable functions is the work of the devil."
Comment: That's a good reason. Thank again!


Is there a way to exclude specific hosts from a Nagios hostgroup?

Question: I have a Nagios server which includes many hostgroups.
One of these hostgroups include a server which I'd like to exclude from being checked for one specific Nagios Check but I want it to keep being a member of the hostgroup so it may get checked for all the other checks that the hostgroup is checked for.
Is there an option of exclude or something like that which can help me achieve my goal?
Thanks
Answer: Add the specific host with a ! prefix in the service definition.  The service check below will apply to all hosts in agroup apart from ahost.
define service {
    hostgroup_name   agroup
    host_name       !ahost
    service_description Shared NFS mount
    check_command check_nrpe!check_shared_mount
    use generic-service

}
Comment: is it possible to achive this in the host file instead of where the service is defined?
Answer: Haven't yet tried it with hosts, but with hostgroups, prefixing with a ! works. I use this for running a different load check on busy servers:
define host {
    use         physical-host
    host_name   busy-host.example.com
    alias       busy-host.example.com
    address     10.43.16.1
    hostgroups  linux,centos,ldap,http,busy
}

define host {
    use           physical-host
    host_name     normal-host.example.com
    alias         narmal-host.example.com
    address       10.43.1.1
    hostgroups    linux,centos,dns,proxy,ldap,hp,http,puppetmaster
}

define service {
    use                   generic-service
    hostgroup_name        linux,!busy
    service_description   Load
    check_command         check_snmp_load
}

define service {
    use                   generic-service
    hostgroup_name        busy
    service_description   Load
    check_command         check_snmp_load_busy
}

Answer: You can create one or more hostgroup(s) for excluding things - add it/them to hosts where you want to exclude one or more checks - naming it something like ~no-ipv6 or ~no-ssl or whatever makes it pretty obvious what it's meant to do.
Apply the exclude hostgroup to the host(s) you want to exclude in addition to the normal one(s) it's a member of.
In the Service description, where the hostgroup name(s) that have that service applied are defined, use an ! (in this context, meaning "not") to exclude them.
So if you have a hostgroup "webservers", where some hosts can't do ssl, you might create another hostgroup "~no-ssl". In the services.cfg file, on the service definition that checks https, under hostgroup name, you would put webservers,!~no-ssl
The effect of this would be that all hosts in the hostgroup webservers are checked against SSL - but those that are also in hostgroup ~no-ssl won't have SSL checked. Handy!
If there are some checks you want ALL hosts to undergo, aside from a few, you can use *,!~exclusion
This abstraction is tremendously useful; even more so is using templates to assign (or exclude) a whole bunch of services to a type of host (which then means you can use the hostgroups definitions on each host simply for "extra" additional checks you want to run, or specific exclusions - i.e. template is the "norm", hostgroups are the exception(s)).


How do I make the joints and weights skinned with the variables I'm using?

Question: For some time now I have been trying to do skeleton animation using Rust and OpenGL(specifically the gl library), I loaded the animation information correctly(with the gltf library), the bone ids and the influence weights, however I was unable to apply the animation to the 100% correct model.
The screenshot below is the furthest I could get from making the animation look correct, the problem is that if you get close... You can see that between the transition from bone to bone, the joints with a greater deformation prevent the lighting is perfect on the character's skin, creating a slight doll-like sensation in which the joints highlight the skeleton:

This happens because the code I used in the shader is basically this where I only use the first transformation in the model:
// Animation
vec4 tp = vec4(pos,1);
tp = CORRECAO[int(ossosid[0])]*tp;
tp = (ANIMACAO[int(ossosid[0])]*tp);
tp.xyz += ANIMACAO2[int(ossosid[0])];
// Forget that part, that's just because the animation is scaled to appear on the screen...
// It's not part of the animation calculation.
pos = tp.xyz/50;

When I try to follow examples in which I use influence weights... It's not working, more specifically I can give code examples and show how it's not working:

When I try to switch to calculation:
vec4 tp = vec4(pos,1);
tp = CORRECAO[int(ossosid[0])]*tp;
tp = (ANIMACAO[int(ossosid[0])]*tp)*pesos[0] + (ANIMACAO[int(ossosid[1])]*tp)*pesos[1];
tp.xyz += ANIMACAO2[int(ossosid[0])]*pesos[0] + ANIMACAO2[int(ossosid[1])]*pesos[1];
pos = tp.xyz/50;

Totally distorted when:

Using:
vec4 tp = vec4(pos,1);
vec4 tp0 = CORRECAO[int(ossosid[0])]*tp;
tp0 = (ANIMACAO[int(ossosid[0])]*tp0)*pesos[0];
tp0.xyz += ANIMACAO2[int(ossosid[0])];
vec4 tp1 = CORRECAO[int(ossosid[1])]*tp;
tp1 = (ANIMACAO[int(ossosid[1])]*tp1)*pesos[1];
tp1.xyz += ANIMACAO2[int(ossosid[1])];
pos = tp0.xyz+tp1.xyz;
pos = pos.xyz/50;

Another:

vec4 tp = vec4(pos,1);
tp = (CORRECAO[int(ossosid[0])]*tp)*pesos[0];
tp = (ANIMACAO[int(ossosid[0])]*tp);
tp.xyz += ANIMACAO2[int(ossosid[0])]*pesos[0];
tp = (CORRECAO[int(ossosid[1])]*tp)*pesos[1];
tp = (ANIMACAO[int(ossosid[1])]*tp);
tp.xyz += ANIMACAO2[int(ossosid[1])]*pesos[1];
pos = tp.xyz/50;

Just one more:

vec4 tp = vec4(pos,1);
tp = (CORRECAO[int(ossosid[0])]*tp);
tp = (ANIMACAO[int(ossosid[0])]*tp)*pesos[0]+(ANIMACAO[int(ossosid[1])]*tp)*pesos[1];
tp.xyz += ANIMACAO2[int(ossosid[0])];
pos = tp.xyz/50;

In other words... I can't make elbows, knees, shoulders, leg connections and hips as smooth as I can do everything else... Specifically, know that: CORRECAO is the inverse bind matrix, ANIMACAO is the variable that rotates the point and ANIMACAO2 is the position of the point in the animation.
My question is how do I make the joints on the model look smooth? How do I apply this in the vertex shader?
P.S.: The animated model is here: link
Answer: vec4 tp = vec4(0);
vec4 tp1 = (CORRECAO[int(ossosid[0])]*vec4(pos,1));
tp1 = (ANIMACAO[int(ossosid[0])]*tp1);
tp1.xyz += ANIMACAO2[int(ossosid[0])];
tp += tp1*pesos[0];
tp1 = (CORRECAO[int(ossosid[1])]*vec4(pos,1));
tp1 = (ANIMACAO[int(ossosid[1])]*tp1);
tp1.xyz += ANIMACAO2[int(ossosid[1])];
tp += tp1*pesos[1];
tp1 = (CORRECAO[int(ossosid[2])]*vec4(pos,1));
tp1 = (ANIMACAO[int(ossosid[2])]*tp1);
tp1.xyz += ANIMACAO2[int(ossosid[2])];
tp += tp1*pesos[2];
tp1 = (CORRECAO[int(ossosid[3])]*vec4(pos,1));
tp1 = (ANIMACAO[int(ossosid[3])]*tp1);
tp1.xyz += ANIMACAO2[int(ossosid[3])];
tp += tp1*pesos[3];
pos = tp.xyz/100;


Colour difference between Ai file print and PDF file print

Question: I am launching an online stationery business whereby I design stationery for clients who can print the products in their home or at a printers (My remote locate means that I am unable to offer the printing part at an affordable price). I have most of the suites designed already and decided to run a test print from my own printer to see what the "at home" version looks like.
When I print direct from Illustrator the print job is perfect. If I print from the PDF version the colours are all wrong. Black = grey, jade green = faded blue and so on. Why is this? It can't be anything to do with my printer as the printer is capable of printing the correct colours as demonstrated by printing direct from Illustrator.
I have tried print to PDF instead of Save to PDF. I have tried changing from ckmy to rgb (the results were no better), I have saved the pdf with a colour profile and tried saving with PDF/X‑3 and PDF/x1a but no difference.
Something appears to be happening between the conversion from the Ai file to PDF but what? Does anyone know what could be causing this issue?
Comment: Is everything calibrated?
Comment: What color settings are you using?
Answer: You will not be able to control the output profiles if you don't set them across the creative suite -
First check your document colour mode, you will need to set to CMYK. Go to your "Edit' menu and check what colour settings you have - ALSO - Check in EDIT > PREFERENCES > APPEARANCE OF BLACK... make sure you display and export blacks accurately
I have mine set to 'COATED FOGRA39' just as a rule of thumbs, set your creative suite colour prefs through Adobe Bridge so the suite performs colour conversions consistently. (this setting may not be right for your working colour management)
When you are ready to export to pdf > check the OUTPUT intent.
Colour conversion = Convert to destination
Destination = mine is FOGRA39 (use your own setting if different)
Profile Inclusion Policy = Include Destination Profiles
Then check the pdf with your OUTPUT PREVIEW > the colour mix should be the same as you intended in the Illustrator file.
Comment: +1 Great TIP: Set your Creative Suite colour prefs through Adobe Bridge so the suite performs colour conversions consistently.
Answer: When saving to PDF go to "Advance" then change compatibility to Acrobat 4 (PDF 1.3). At the bottom you will find "overprint and transparency flattener option"
Change the preset to "For complex art". That will do the trick.


What is the 1.12 equivalent of /execute if score?

Question: In Minecraft, I want a command to execute when a score is changed.
For example, I have a scoreholder named cameraactive on an objective named Debug. I want a command to run when this score becomes 1.
I know that Minecraft Java 1.13+ has this command:
execute if score Cameraactive Debug matches 1 run say hi

Is there a way to mimic this in 1.12.2? I'm using several mods that don't support 1.13 and above and I don't have the option to upgrade versions.
Answer: The equivalent to 1.13+'s /execute if score is the command /scoreboard players test:
scoreboard players test <scoreholder> <objective> <min> <max>

For example, with scoreholder $debug.camera_active and objective main, the command is:
scoreboard players test $debug.camera_active 1 1

Then you would follow with a chain command block, set to conditional mode, that runs whatever comes next.


Pre-displacement normals

Question: The "Geometry" shader node provides normal information for the geometry being shaded. This can be useful, for example, to mix a snow shader with a rock shader depending on how "flat" the geometry is (angle relative to Z axis). This normal information seems to be calculated after any displacement is applied by the shader (Cycles). In my case, I would like to get the normal information before displacement is applied. Is this possible?
Comment: The way with _Geometry Nodes_ as the given answer by @Nathan suggests is the only way as far as I know, at least you cannot preserve them in the _Shader Editor_ itself. Because the order before rendering is always first comes the original mesh, then the modifiers and afterwards the materials at last, so everything you do there with normals is executed on the altered mesh.
Answer: Assuming we're not using custom normals or sharp edges-- which would be weird with true displacement-- we can capture the vertex normal in geometry nodes and use it in the shader:

The geometry nodes are evaluated before any shader based displacement.  Our output will be in object space, giving us interpolated values, so we need to normalize the vectors and transform into world space in order to use them the same way we'd typically use a normal in the shader.

Pre-displacement normals


Determining for which values of $p$ the improper integral $\int_1^{\infty}\frac{dx}{ x^2\sqrt{x^p -1}}$ converges

Question: Determining for which  values of $p$ the improper integral
$\int_1^{\infty}\frac{dx}{ x^2\sqrt{x^p -1}}$ converges.
i did comparison test and got for every p > -2 why its wrong?
Comment: Ordinarily, the "minus 1" in the expression won't affect convergence.  So we can compare it to $\frac{1}{x^2\sqrt{x^p}}=\frac{1}{x^{2+p/2}}$ which converges precisely when $2+p/2>1$, i.e. $p>-2$.  However, as Sangchul observed, we also require $p>0$, otherwise $x^p-1\leq 0$ which would make $\frac{1}{x^2\sqrt{x^p-1}}$ undefined. So the answer is $p>0$.
Comment: Compare "for which positive values of p" and "got for every p > -2".
Answer: We assume $p>0$.
Since the integrand is continuous over $(1,\infty)$, potential issues are near $1^+$ and near $\infty$.
As $x \to 1^+$, one has
$$
\frac{1}{ x^2\sqrt{x^p -1}}=\frac{1}{ x^2\sqrt{(1+(x-1))^p -1}}\sim\frac{1}{\sqrt{p} \sqrt{x-1}}
$$ giving the convergence of the given integral.
As $x \to \infty$, one has
$$
\frac{1}{ x^2\sqrt{x^p -1}}=\frac{1}{ x^{2+p/2}}\cdot \frac{1}{ \sqrt{1-1/x^p}}\sim \frac{1}{ x^{2+p/2}}
$$ giving the convergence of the given integral for $2+p/2>1$.
Comment: If you consider $p<0$, then how do you define $\sqrt{x^p -1}$ when $x\ge1$?
Comment: yes but the answer is for p > 0
Comment: why assuming p > 0 , and you want to find for which p ?
Answer: Let $y=1/x$, then $z=y^{-p}-1$
\begin{align}
\int\limits_{1}^{\infty} \frac{1}{x^{2} \sqrt{x^{p}-1}} dx &= \int\limits_{0}^{1} \frac{1}{\sqrt{y^{-p}-1}} dy \\
&= \frac{1}{p} \int\limits_{0}^{\infty} \frac{z^{-1/2}}{(z+1)^{1+1/p}} dz \\
&= \frac{1}{p} \mathrm{B}\left(\frac{1}{2},\frac{1}{p} + \frac{1}{2} \right) \\
&= \frac{\sqrt{\pi}\Gamma \left( \frac{1}{p} + \frac{1}{2} \right)}{\Gamma \left( \frac{1}{p} \right)}
\end{align}
The integrand and the limits of integration require that $p \gt 0$. From the
beta function we have $\mathrm{Re} (\frac{1}{p} + \frac{1}{2}) \gt 0$, $p \lt -2$ and $p \gt 0$. Thus we
must have $p \gt 0$.
We have used the following integral definition of the beta function
\begin{equation}
\mathrm{B}(x+1,y+1) = \int\limits_{0}^{\infty} \frac{z^{x}}{(1+z)^{x+y+2}} dz
\end{equation}


In Python, write a program that asks the user to type in four numbers and puts all of them in a list called lst

Question: I've written a program that asks the user to type in four numbers like this:
a = input()
first = int(a)
b = input()
second = int(b)
c = input()
third = int(c)
d = input()
fourth = int(d)

I do not understand how can I put them in a list.
Answer: You should improve your code a little bit:
first = int(input())
second = int(input())
third = int(input())
fourth = int(input())
lst = [first, second, third, fourth]

Answer: Note that you could use list-comprehension:
lst = [int (input ()) for time in range (4)]

This uses a simple for loop to execute int (input ()) 4 times. Now you could just access the inputs by using lst [0], lst [1], 'lst [2], and lst [3].
Answer: First off, you can put your code in a code block by using an empty line and then indenting 4 spaces.
You can put your variables in a list like this:
list_variables = [first, second, third, fourth]

Answer: option one :
lst = [first, second, third, fourth]

option two :
lst = []
lst.append(first)
lst.append(second)
lst.append(third)
lst.append(fourth)

Answer: One more approach is to ask input numbers separated by space and then split them
numbers = input()
numbers_list = numbers.split(' ')
int_numbers_list = map(int, numbers_list)

Possible raise error if count of numbers not equal 4
while True:
    numbers = input()
    numbers_list = numbers.split(' ')
    if len(numbers_list) != 4:
        print('Enter numbers again')
        continue
    int_numbers_list = map(int, numbers_list)
    break

Answer: Here is a 1-liner but does not take care of the 4 input restriction (in case you need):
lst = list(map(int, input().split()))

'''
3 4 5 6
[3, 4, 5, 6]
'''


Deleting the user from Tuser when the user didnt login within 24 hours

Question: When the authentication code in the Tuser is not null   it means the users didnt login the site within 24 hours so i have to delete the rows.
Here is the query which I wrote but it is not deleting correctly
<code> DELETE FROM tusers WHERE auth_code IS NOT NULL
AND auth_code !=''
AND STR_TO_DATE(NOW(),'%Y-%m-%d %T')
> (DATE_SUB(STR_TO_DATE(created_date,'%Y-%m-%d  %T'),INTERVAL -1 DAY))
</code>
Answer: You are in a better position to determine whether it is right or not by testing and letting us know if it works or not.
But I can tell you that it is more complicated than it needs to be. You can compare dates directly like this:
<code>... where date(now()) > date_sub(created_date, interval 1 day)
</code>
Note that if you are going to SUBTRACT a day in order to go back, you should subtract a positive number of days. Subtracting a negative number of days refers to later in time, not earlier.
Comment: I am deleting the row when Date Now checks with the 24 hours ahead of the created date when both match then the row is deleted i want this to happen but not working
Answer: I got the perfect delete which is working perfectly:
<code>  DELETE FROM tusers WHERE auth_code IS NOT NULL AND auth_code !=''
 AND DATE_SUB(NOW() , INTERVAL 24 HOUR) > STR_TO_DATE(created_date,'%Y-%m-%d %T');
</code>
This query deletes the rows by comparing the current date of the system  with the created date of the rows which reaches above 24 hours of the current date.


Do icing limits exist for parked aircraft?

Question: Are there any aircraft that have a limit on the amount of ice or snow that can be on the aircraft when stationary and on the ground?
Answer: I'm not aware of any limits every being published on transport airplanes.  On large aircraft, it's not too big a deal structurally because the bending loads imposed by a snow cover are not significant, since bending load applied by a couple of feet of snow (which weighs about 40lb/sqft) on such a large structure, designed to support 100+ lbs/sqft, is relatively mild.
On little airplanes, this can be a problem however.  Let 2 feet of snow, or 40 lbs/sqft, accumulate on a light aircraft or ultralight with large wings, designed to support maybe 5-15 lbs/sqft of negative load, and you will likely find the wing outboard of the strut is permanently bent down or has collapsed when you want to go flying.  Nature's just done a static load test on your wings and got carried away.
On a metal airplane, you at least take comfort in the fact that if the wing is not permanently bent down after you remove the snow, you're good to go.
On an airplane with wood spars, this is more of a gamble, because wood structures that are overloaded beyond the compression limit of the side in compression (the spar below the strut attachment bolt in the case of snow load) without overloading beyond the tension limit of the side in tension (above the strut attachment bolt, where it just breaks), can suffer from a dormant compression failure in the wood itself.
Compression failures are where the cellular structure of the wood fibres partially collapses.  This can leave the wood apparently undamaged (unless you can inspect the area to detect the tell-tale fine line across the grain), but weaken the wood in tension.  So when you go flying, and the wood below the spar attachment is loaded in tension again and has lost some fraction of its ultimate tensile strength, and you hit a bump that applies some extra G, whoops!
Anyway, if you own a light aircraft with wood spars you need to be aware of this and be extra vigilant about preventing large snow loads on the wings.  I'm not really keen on wood spars on light planes for this reason.  It's a reason you never buy a used Classic with wood spars that's had a wing tip repair (from the tip hitting the ground during a groundloop).  A friend bought an Aeronca Champ once and found his right wing had a wood compression failure above the spar bolt, caused by a wing tip strike, when he took it apart to recover it, after flying it about a year.  He was lucky; any significant negative G in that condition would have been fatal.
You could work out a limit for yourself if you know the wing loading and structural G limit for your own airplane. So if your wing loading at gross is 10 lb/sqft, and it's good for negative 2 Gs in flight, you can estimate that the wing can tolerate 20 lbs/sqft of snow accumulation, or about 1 foot thick and wouldn't want too much more than that to accumulate.
Answer: I've seen a Boeing 727 parked at an air museum that tipped over so that the rear fuselage was on the ground, due to the aircraft being heavily covered with ice.  Presumably it would be desirable to avoid that event in an operational aircraft-- to avoid cosmetic damage to the bottom of the rear fuselage if for no other reason.
Answer: No, However to protect airplane from icing , it is recommended to park in closed hanger and the geographical area where icing occurs frequently they keep airplanes batteries always for charted state so that it is easy to take the plane for flying after normal preflight procedure.
Answer: For transport category airplanes, there are often manufacturer recommendations for storage of aircraft, and engines. The level of storage (length of time and environment) would determine what precautions are recommended.  In the case of transport aircraft I don't know if those requirements are part of the approved maintenance program or not. Standards for maintenance requirements are developed at the industry level by Maintenance Steering Group -3.


Edit a field Not on a Page Layout

Question: I'm trying to load a field via a url on custom button.  I don't want the user to be able to view or change it (read only).  If I remove it from the page layout or make it read-only, The field won't load.  If I put it on the page, the field will load but they can modify it.  Is it possible to load the field without putting it on the page layout?
Answer: Sounds like you are trying to use a URL hack to set a field value.  One option would be to use a picklist and set the default picklist value at the record type level.  In your URL hack you could send the appropriate record type id and auto-populate the drop down.  The field can be Read-Only on the page layout if you use this method.  If you try to directly set a read-only field via a URL hack it will fail.  Setting your values and using a record type can get around that limitation.  The field still needs to be included in the page layout.
For example:
<code>https://[Org Instance]/[sObject Prefix]/e?retURL=%2F[Record Id]&saveURL=%2F[Record Id]&RecordType=[Record Type Id]
</code>
Answer: No. It's possible to load the field when it's not on the page layout. If it's not in page layout and using the field ID won't populate the fields as it's not in HTML and browser won't get Id to assign the value.. if you don't want field on the layout why don't you go with the other option like workflow, trigger or other field update methods..
Comment: I was also trying to create a custom-setting field and populating that via the url.  I couldn't get it to update.  It may be my syntax.  Any help will be appreciated.
Comment: I believe your second sentence should read `It's not possible to ...`

Edit a field Not on a Page Layout


Gravitational force effects on velocities of rotating bodies

Question: If we take a satellite rotating around the earth, then the earth applies centripetal force to the satellite, but what if the satellite suddenly looses kinetic energy, maybe because of collision, the point is that now it goes slower. The gravitational force is the same, but the velocity is less, so does that mean that the satellite aside from rotating, will gain velocity towards earth until the gravitational force is just enough not to accelerate it towards the planet but keep it in uniform circular motion? If so, then the satellite, even when the gravitational force will be just enough, should keep it's velocity, and keep going towards the earth, and the distance should be smaller, and so the gravitational force should increase and the satellite will keep accelerating towards the earth and eventually will crash into the earth (unless it will burn on the way). By this logic the earth should accelerate objects towards itself with acceleration greater than 9.81 because we have to take into account that we all rotate around earth. how can we calculate that acceleration? And shouldn't then even minimal imperfections in the speed of satellites cause them to crash down to earth?
Answer: The satellite will indeed accelerate, but instead of falling to earth, it will form a thinner and longer orbit. And concerning the acceleration on earth, it is indeed changing due to centripetal acceleration, and the change is the smallest on the poles.
Answer: A satellite colliding with a stationary object (in the non-rotating frame of the Earth) would be equivalent to a "retrograde burn".
For a satellite originally moving in a circular orbit, the resulting orbit would be elliptical (thinner), with a smaller semimajor axis. The collision point becomes the apoapsis (highest point) of the new orbit. Even though the velocity of the satellite is reduced by the collision, the time taken to complete an orbit would be reduced.


grafana: how to sum values from query into a singlestat or other plugin?

Question: Is it possible to make a sum of values - depending on multi-selections in query (templating) - and showing those in a singlestat plugin in grafana?
setup:

grafana 3.1.1
datatsource: graphite

Use case:
A query-based dropdownlist allows me to select a logical volume.
The singlestat then shows me the size of this logical volume.
Now I have a multi-select query list so I'd love to achieve that the size value for each of those selected logical volumes is summed and shown in the singlestat.
I've been trying to find some function and I know there are sum functions but in my case, I don't know which are going to be the results of the selections in the templating query and there doesn't seem to exist a way to automatically add an "invisible" query to the metrics section while only showing a sum-of-all-queries-metric.
Are there any options to achieve this?
a sample query:
<code>collectd.$host.$volumegroups.$logicalvolumes
</code>
where all 3 values are from a templating query with results like:
<code>$host => the server in question
$volumegroups => vg00 (LVM Volume Group)
$logicalvolumes => lv_data, lv_root, ... (LVM Logical Volume)
</code>
Now when selecting multiple "$logicalvolumes" from the dropdown ofcourse, the singlestat goes "N/A".
In the list of plugins on grafana website, I don't find any other plugin to match this need.
Comment: groupByNode("sum",1)
Answer: Grafana community provided the answer here: 1
effectively by using the "sumseries" function it works as expected.


create indices by standardising variables

Question: I have 257 variables, which influence behaviour altruism of humans. They can be assigned to the 3 following criteria: internal, external or selection. I check the influence of the individual variable on altruism, further I need to check the influence of all variables, which are part of internal. Can I just standardise these variables and then take the mean of them and consider this as an index?
Comment: Sure: you can apply literally any mathematical formula you like and call it an "index."  The crux of the matter, though, is whether it bears any relationship at all altruism.  To do that, one would think you ought to analyze the possible relationships between the variables and altruism itself.  Since standardization doesn't tell us anything at all about relationships--it's strictly a univariate process--it's difficult to see how it would accomplish anything useful.
Comment: Can you say more about your situation, your data and your goals? I suspect a lot is being assumed here.
Answer: As Gung said, we should know a lot more about your situation to give a really useful specific answer. Anyway, I'll try to give a general one.
The altruistic behaviour you are interested in may be influenced by some of your 257 variables. You need to know which variables do influence altruism, and therefore you should resort to tools like regression or ANOVA that could tell you which variables have a significant influence on altruism. Please notice that such tools check influence of every variable - at least, every variable you tryed to include in your analysis.
However, if you use an index (which in your proposal is just a single linear combination of your variables out of the infinite amount of linear combinations you could use), you will lose a lot of information, and the influence of single variables can be cancelled by the influence of other variables or just get lost in the sum.
Just to put an invented example with two variables: Let's imagine that people with more body weight are more altruistic, and that tall people is less altruistic that short people. If you ran a regression analysis you would find significant positive correlation between body weight and altruism and negative correlation between height and altruism - and that would be what you were searching for. Although, if instead of using body weight and height you use an index made of the (standardized) sum of both, the effects might be cancelled - that is, the most altruistic people (short people with overweight) will get about the same index value as the less altruistic ones (tall slim people), and therefore you wouldn't be likely to find any correlation between your index and altruism.
In summary, if you have a lot of variables, use tools to tell which of them have influence. You may design a useful index if you have good reasons to build it in a particular way, but if you just take an arbitrary index like the standardized sum of all variables, you are just losing information - a lot of information.
Comment: Sorry for the late reply and thank you very much for your good example. I collected data (400 observations) in 40 countries where I gave the person something and checked the reaction. This reaction could be positive (1) or negative (0). I am now interested how this behaviour changes across country based on socioeconomic factors. I analysed the dahlström Dataset [link](http://qog.pol.gu.se/data/datadownloads/qogstandarddata) to check on theoretical connection. Would it I would now like to create a simple model where I assign the variables to either one of the three criterions.
Comment: Now education has a positive influence but gini coefficient has a negative influence. So taking your example with hight and weight, would it be best to analyse the way of correlation first and then adapt them so the effect is always to the same direction, so that e.g. high values are always more altruistic, so a small altruistic person gets a score that is negatively correlated to the actual hight, so that they don't cancel out? Or does this cause other problems @pere


Will glyphosate based herbicide work with a food thickener?

Question: I would like to thicken some Roundup to form a drip-free paint for targeting weeds in groundcover beds. If I use Thick-It starch based food thickener, will I get the result I want? I would be watering down the Roundup 4-5 times normal, because of how thick it would go on. I could also add a wetting agent if it would help maximize contact. Does anyone see any problems with this idea?
Comment: seems like a good idea, if you could end up using less in the long run... you would probably want to experiment, if you go too thick you won't be able to apply it ... there is some potential of the glyphosate forming a conjugate with the starch, or xanthan gum or whatever carbohydrate thickener you use, which would make the glyphosate less available... I don't know that it will happen, and it may be one of those things that happens slowly, or only at high temperatures ...
Comment: This is a ready  make product a bit expensive,  but easy to use https://www.lovethegarden.com/products/weed-control/roundup-gel
Answer: I don't know if it works with food thickener, but it does work with wallpaper paste - mix the wallpaper paste powder with straight Round Up or glyphosate only, no water (unless you're using a glyphosate concentrate which needs to be diluted), to the consistency you want. Adding a wetting agent might help too if you're using plain glyphosate, (in the UK, a squirt of washing up liquid is the commonest one used) but isn't necessary if it's Round up - it already has other ingredients that do this job, which incidentally render it more harmful to the environment. What also helps with tough leaved weeds is to lightly bruise or crush the leaves before applying.
UPDATE IN RESPONSE TO COMMENTS:
J Musser;

the wallpaper paste is likely somewhat less dangerous in the environment than Round Up itself, if you're going to use Round up, but the quantity is small anyway
I'm not sure what you're saying re dilution - if you want a thick mixture to paint onto leaves, why would you want to add water as well, if you don't have to - it just dilutes the glyphosate. As I've said, the usual course is to mix standard glyphosate directly with a bit of wallpaper paste powder till its the right consistency.

UPDATE 2: J. Musser - you've asked about toxicity of wallpaper paste in the outdoor environment. The type I'm talking about (traditional, old fashioned wall paper paste powder that you mix yourself, if you can find it) is fine to use, since the ingredients are only 3-10% solids and these comprise wheat paste, cellulose, potato, tapioca or other starches. It's the Round Up you want to worry about - that binds to soil particles and can still be present in the soil up to 200 days later, though more usually about 3 months.
Comment: @kevinsky,  I have found that Round Up Pro works on Horsetails,  if you give the Horsetails a light brushing first.
Comment: Unfortunately some weeds, even if you crush the leaves first, are resistant to Roundup.  Horsetails or equisetum are one of these.  Now I just pull them.
Comment: @kevinsky sometimes pulling will do lots of damage to the groundcover, also the weeds in question will come back from underground runners.
Comment: @Bamboo What's wrong with watering it down?
Comment: @jmusser - watering down means the glyphosate solution is weakened, though if you're using a glyphosate concentrate which should be diluted before use anyway, that's a different case - normal dilution rates apply, and that is then mixed with dry wallpaper paste powder.
Comment: @kevinsky - it seems that's happening in the UK too - glyphosate resistance in Equisetum I mean, so folks here are having to live with it just by pulling it off, as you say. There's no other treatment available for gardeners that I know of though, is there?
Comment: I think I will take this and run with it over to the question area. Thanks!
Comment: @Bamboo do any chemicals in the wallpaper paste linger in the environment?
Comment: @Bamboo With a thicker liquid that goes on the leaves several times thicker, wouldn't it work to dilute to compensate?
Comment: @Bamboo My train of thought... If the liquid goes on x times thicker than normal, wouldn't there also be x times more glyphosate per sq. inch?
Comment: @jmusser Not really, only in the sense that it sticks to the leaf rather than running off, which is what you want anyway. You'd normally apply it by spray without dilution - all you'll do is add wallpaper paste to make it thick so it sticks better and can be painted on.
Answer: As a followup, I tried my idea, and it worked quite well. The reason for this post is to point out that you can get away with .75% glyphosate on most weeds. I also used some pre-mixed glufosinate on some Canada thistles, and applied similarly, with success. Also, @Bamboo's idea, using wall paper paste, works well too.
Answer: Mix glyphosate with a lawn weed killer containing 24D kills mares tail a treat. The 24D strips the wax from the mares tail so the glyphosate can kill it.


Is it possible to become pregnant indirectly?

Question: Is it possible to become pregnant indirectly? For instance, if there is some wet semen left behind inside tight clothing, jeans for example, and a woman tries them on for a couple of minutes? What is sperm's motility after it's deposited on cloth in room temperature? Can sperm still swim inside from outside if it's near the vaginal opening in the cloth? What are the chances of pregnancy if the woman is/is not wearing any underwear?
Comment: Good question but poorly narrated. Refine your question by reducing questions to just single one. It's sounding pretty curious but snappy question. Once refined, it will be very good question
Answer: yes this is possible, as long as the sperm make it onto the mucus membrane of the vagina. the LIKELYHOOD depends on the fabric and how much semen is in the fabric, if it's still clotted or not, and environmental factors.
Comment: Sorry, I forgot to add that I meant liquefied semen on the cloth so that it appears as a wet spot, the kind of semen smudge you get when it has seeped through thin clothing (underwear) before being deposited on that outer layer (jeans).
Comment: if youre being that specific, it probably happened to you. take a pregnancy test. if positive, there is sadly not much you can do except murder the unborn child. his body your choice


How do I prevent git from requiring sudo on every git command

Question: I created a directory /var/www to store my web apps clone in. When I initially cloned the app from GitHub it required me to use sudo and every time I do a git pull it's requiring sudo. I'm running into some problems because of this. For example, my ssh keys are not matching up. So when I do my git pull, I'm having to use HTTPS instead of ssh and manually enter my username and password every time I want to pull and update my app. How do I configure this so I don't have to use sudo every time I use git?
Answer: A couple of things are going on here:

When you sudo git checkout ..., all those files are owned by the root user and root group. With the standard permissions, that's why subsequent alterations to those files require you be root.
/var/www/ by default is owned by www-data group. Something your user is not by default.

The easiest way to write in /var/www/ is to just add your user to the www-data group. You can of course, change the directory to be owned by your user but this can have some nasty knock-on effects if you're not pre-empting them.
You'll need to re-log in after adding your user to the www-data group.
In your case specifically, you're going to need to fix your current mess of root-owned data. You can either delete it as root (and re-checkout) but if you have unsaved work, it'll just be cleaner to pull everything back to your user. The following example is extremely lazy and assumes what we're talking about is the only thing in /var/www/:
sudo chown -R www-data: /var/www/

Comment: It would be *best* if you stopped running git as root. Aim for that. Any plan that leaves you running it as root has already failed. What you're saying about checking out into a webdirectory is correct - giving people access to your `.git` directory can give them access to things you don't want to let people access, but [you can prevent access to the `.git/` dir](http://serverfault.com/questions/128069/how-do-i-prevent-apache-from-serving-the-git-directory) which mitigates the whole issue.
Comment: Ok, would it be better to just `sudo git checkout` into another directory, and then deploy my app in the /var/www directory? I just read somewhere that it's not generally not a good idea to checkout projects into the var directory to begin with. One person recommended checking out projects into the home directory
Comment: There are also other acceptable directory structures where you have a holding directory for your website where non-hosted stuff goes (including your .git) and inside that there's a public/ directory which you tell Apache to host. The ethos of keeping one website in /var/www/ is very archaic.
Comment: Do you have a recommended directory structure? Basically, I have my checkout, and then I have to bundle that into a .tgz. And then I have to untar that into a node application. It's a meteor application by the way. I'm kind of confused where to keep these three separate folders/files
Comment: @Scott I ran into this same issue.  Subsequent subcommands in the repo (in my case) will call git and try to clone other repos.  The solution, to re-align SSH keys as you stated, was to start the process without using sudo.  A lot of this Q&A and thread discussion is a work-around that will probably have you hitting walls down the road.
Answer: Hm, change folder owner?
I moved my www folder in /home/username, you can change it's location in /etc/apache2/sites-enabled/000-default
Comment: So it has to do with the directory that I'm storing my clone in?
Comment: Yes, exactly. By default `/var/www` can't be written.
Answer: I'm a bit late with this answer, but I found that to avoid entering password each time I had to change the repo from https to ssh.
From Github.com help section:
The git remote set-url command changes an existing remote repository URL.
Open Terminal.
Change the current working directory to your local project.
List your existing remotes in order to get the name of the remote you want to change.
git remote -v
origin  https://github.com/USERNAME/REPOSITORY.git (fetch)
origin  https://github.com/USERNAME/REPOSITORY.git (push)

Change your remote's URL from HTTPS to SSH with the git remote set-url command.
git remote set-url origin firstname.lastname@example.com:USERNAME/REPOSITORY.git

Verify that the remote URL has changed.
git remote -v

# Verify new remote URL
origin  email@example.com:USERNAME/REPOSITORY.git (fetch)
origin  email@example.com:USERNAME/REPOSITORY.git (push)


What is this sea shell?

Question: Found in Belgrade, possibly carried back from the Mediterranean or Aegean coast.
Answer: It is not /Bolma rugosa/, but in fact /Angaria delphinus/, from the Indo-Pacific.
Listing on gastropods.com
Comment: Welcome to Biology.SE! You are more likely to get a positive response to your answer if you explain why your identification is correct. Specifically, please [edit] your answer to add discussion of key features that led you to this conclusion and supporting references or at least validated images. (Answers must also be self-sufficient, not just links.) Without this your answer is indistinguishable from opinion and instead should be a comment on another answer. ——— Please take the [tour] and then consult the help pages for additional advice on [Answer] effectively on this site. Thank you!
Comment: This ID seems accurate. The species varies a lot and it's often like the one from the OP.

What is this sea shell?


In Halo Wars what do the Forerunner life supports do?

Question: I was playing Halo Wars on the skirmish map Blood Gulch or Beasley's Plateau. I found a special feature called "Forerunner life support". I sent a squad of ODST marines in it, but I didn't see anything happen. So what does the Forerunner life support do?
Answer: I believe that's referred to as a Forerunner Lifepod in the Halo wikia. There isn't one on Blood Gulch IIRC, only a bonus reactor and supply depot on each side. They increase your population limit by 10.


Is IE 6 skipped in HTTP-EQUIV compatibility modes?

Question: This article specifies IE 9 (Edge), IE8, IE7 and IE5 as valid HTTP-EQUIV document modes. Why was IE6 skipped? Does it render the same as IE5? My company supports IE6+, so I want to find a reliable way to test IE6 compatibility UI changes without requiring a VM.
Answer: The article specifies the compatibility modes IE (8-9) can run in. IE5(.5) equals to quirks mode. IE8 cannot run in IE6 compatibility mode. IE6 does not absolutely render the same as IE5(.5) (unless it's in quirks mode).
If you want a reliable way to test in IE6, IE7, etc., you should try something like IETester (which I found to be reliable), Spoon, etc. if you don't want to use VMs.
You should also check this SO question. As stated there:

Also, don't trust IE8 compatibility
  mode.
Comment: Spoon no longer supports IE, and I've tried IETester but it often crashes, not to mention according to this SO question (http://stackoverflow.com/questions/2347860/ie-6-or-ie-tester) it doesn't accurately render IE 6 or 7.
Comment: Still much better than compatibility mode. You cannot get better results than with the VPC though :).
Comment: Still, for UI testing, IE Tester seems to be reliable for me.


Proof inequality using the Mean Value Theorem

Question: I'm trying to proof the following inequality:
$x+1<e^{x}<2x+1$ for $0<x\leq log2$
I used the MVT on with $f(t)=e^{t}$ on the interval $(0,x)$ to proof that $x+1<e^{x}$ and I tried to do the same with $(x, log2)$ but I only got to $e^{x}<2x-2log2+2$.  Any help or hint will be appreciated.
Comment: If you have shown that $e^x < 2x+2-2\log(2)$ then use $2- 2\log(2) < 1$ to prove the upper limit.
Answer: Hint:
The left-hand side inequality  is true for all $x$ and results from $\mathrm e^x$ being a convex  function.
As to the right-hand side inequality apply it on $[0,x]$: you obtain a $y\in (0,x)$ such that
$\;\mathrm e^x-1=x\mathrm e^y$. Can you bound $\mathrm e^y$ independently of $x$, knowing $x\in (0,\log 2)$?
Answer: Consider the function $g(t)=e^t-(2t+1)$. We see that $g(0)=0$. Assume that there exists $c\in(0,\log 2)$ such that $g(c)=0$. Now, apply Rolle's theorem (which is only a special case of MVT). You should arrive at a contradiction quickly.
Answer: The Taylor series at the origin of $\frac{e^x-1}{x}$ (which is an entire function) only has positive coefficients, hence it is trivial that $f(x)=\frac{e^x-1}{x}$ is both increasing and convex on $[0,\log 2]$. In particular
$$ \forall x\in(0,\log 2),\quad f(0)< f(x) < f(\log 2) $$
which is equivalent to
$$ \forall x\in(0,\log 2),\quad x+1 < e^x < \frac{x}{\log 2}+1. $$
$\frac{1}{\log 2}<2$ is equivalent to $e<4$.


Sort search results by popularity

Question: Is it possible to sort Google Search results by popularity for a given search term? Also, is it possible to sort results by popularity for a specific website (e. g., Wikipedia)?
Comment: Well, theoretically, they are already sorted by "popularity." Is't that what the search algorithm is all about?
Comment: Specifically, I am referring to view count, but I didn't explain that at first. Is it possible to sort pages by view count?
Answer: Google's search results are sorted by relevancy. The most relevant search results for the user are at the top. Google uses over 200 factors to determine the relevancy. Pure "popularity" might well be one of these factors, but there is no way to directly change the order of these results.
(Aside: But what is "popularity"? Is it the number of times web pages are visited (perhaps determined by analytics)? The number of times webpages are clicked on in the SERPs? The number of inbound links to that website? That last one is certainly one of the most important factors that Google uses - so in a sense "popularity" is already strongly linked to relevance.)

... for a specific website (e. g., Wikipedia)?

To search in a specific website, use the site: operator (no space after "site:"):
site:en.wikipedia.org search phrase goes here

Comment: Is it possible to sort the results by view count (for each page?) That's what I would really like to know.
Comment: "View count" - The number of times a particular web page has been viewed? Google can only know the number of times results have been clicked on in the SERPs, they can not possibly have information about how many times pages have been viewed outside of the Google _bubble_ - if that is what you are after? But as mentioned in my answer, there is no way to change the order of the results in Google Web Search. Google's [Custom Search](https://developers.google.com/custom-search/) does allow you to sort results - but that is a different animal.
Comment: What does "SERPs" refer to?
Comment: [Search engine results pages](http://en.wikipedia.org/wiki/Search_engine_results_page)

Sort search results by popularity


How to stop uncorrect counting of my steps on Huawei Health app?

Question: I have Huawei Mate 9 with Huawei health app preloaded. I travel most of the time by trains. I noticed the Huawei health recogizes any shaking in the train as steps while I am just standing or sitting. That's why I quickly reach 10,000 steps which are not real steps and the burned calories are not real in return.
How do I stop my phone from identifying shaking in public transport as real steps while I am standing still. Do I have something wrong with my device?
Answer: I'm not sure what all sensor data is being used by the app, but most would rely on the input of the accelerometer. And as such it is all based on its algorithm as to what kind of moments it identifies as steps.
While it is hard, the sensor on the device can be giving out wrong values. But I'd still suspect that the companion app is not able to differentiate between steps and the shaking of hands due to you being on the train. It's quite tricky for it too. I'd probably just turn off the app while in the train. We can't expect a very good amount of accuracy from an app which isn't reading anything from the body.
They can probably improve it by using GPS data and other sensor data to understand if the person was actually moving at the natural pace.
Answer: (I know this is an old thread but this is still a big issue with a lot of phones models and ppl might still find this universal solution useful)
Rootmode method
I disabled Samsung Step Counter sensor and Step Counter Detector sensor in android 10 by doing the following:

Uninstall Huawei Health application.
Activate Developer Options: go to Settings > System > About phone>Tap Software info > Build number>Tap Build number 7 times
Enable the Sensor Toggle: to do this go to developer options find and tap "Quick settings developer tiles." enable/toggle "Sensors Off" button, it will turn off your compass, proximity sensor, accelerometer, gyroscope, and any other sensors.
Note: on this step in Lineage OS 17.1 the Sensors off option only added this button/icon in android status bar (near wifi button/bluetooth button/etc) so you still have to tap on it to deactivate sensors.
Once all sensors are off you need to edit your build.prop file (either install a tool like BuildProp Editor- you need root mode, or use file explorer with a built-in text editor).
The 2 lines that I've added in my build.prop file are:
Code:
ro.qc.sdk.sensors.stepdetector=false
ro.qc.sdk.sensors.stepcounter=false
5.Restart phone. Install Huawei Health
Enable back sensors by taping the Sensors Off button in your android status bar. Additionally you can repeat step 3 to remove the sensors button from your status bar.
Open Health and check if the small ! exclamation sign from main window is gone or at least if it doesn't display your steps counter from phone.

PS
I had to do this on one of my phones because Huawei app was restarting the phone randomly. It took me a while to find the culprit and apply this solution.
Since then I tested this method on various other phones I own and it worked on all.
For non rooted phones use adb method ("adb pull /system/build.prop") to edit and upload the build.prop file. For more details on how to use adb pull and push commands google search, there are some nice tutorials out there and I don't want to copy/paste someone else's work.
Trying to to this without respecting the steps will result in failure.


Instant read/write sync with iCal calendars avoiding the use of google calendars

Question: After using iphone/mac for a lot of time, I got a new android phone. I use on my macbook only ical calendars, and wonder what is the best app for syncing ical with my android phone. I have read something that you can sync first ical to google calendars and so on, but I Wonder if we can avoid this workaround.
Answer: If you want to sync with a calendar using the iCal format, there are apps available on the Playstore doing exactly that, like iCalSync or iCalSync2, and there's also The Missing Sync (requiring a paid desktop component) or SyncMate (specifically tailored for Mac, but again requiring a desktop component).
Most likely there are plenty of additional alternatives (take a look e.g. at these search results). Unfortunately, I don't know of any native solution not involving 3rd party tools.


Feature attributes won't update

Question: I am trying to update feature attributes from a .NET application that I'm working on.
I've cleaned the code down to the following example:
string serviceUrl = string.Format("http://***.cloudapp.net/arcgis/rest/services/{0}/{1}/FeatureServer", "***", "Test");
string featureUrl = string.Format("{0}/{1}", serviceUrl, "0");
var table = await ServiceFeatureTable.OpenAsync(new Uri(featureUrl));
if (table.IsInitialized)
{
var found = await table.QueryAsync(1);
    if (found != null)
    {
        found.Attributes["testtext"] = "test";
        await table.UpdateAsync(found);
        if (table.HasEdits)
        {
            var result = await table.ApplyEditsAsync();
        }
    }
}

It finds the feature with OBJECTID = 1, table.HasEdits is true after the update, and the result variable contains a ResultItem in the UpdateResults property, with no errors and Success = true.
So no errors and no indication something went wrong, but the attribute table in ArcGIS doesn't change at all. If I try to change the geometry of the feature, by adding a line like this:
found.Geometry = new Polygon(new List<MapPoint> { new MapPoint(0, 0), new MapPoint(-5, 0), new MapPoint(-5, -5), new MapPoint(0, -5), new MapPoint(0, 0) });

It will update the geometry correctly... but still no update to the other attributes of the feature.
The feature class in question here, has a field called "testtext" which is of type "Text". I've also tried fields with type short, double, date etc, but I'm still not able to update or add any attribute data.
Any clues as to what I'm doing wrong here?
Answer: I found the answer while using Wireshark to look at the web request being sent to ArcGIS server. It never sent any attribute updates, until I put the fields I tried to update into table.OutFields..

Feature attributes won't update


How can I measure a battery's level in percentages using a voltage divider and an ADC?

Question: I want to measure the battery level of 4 AA (R6) batteries using a voltage divider made of 2 resistors which goes into the internal ADC of a PIC16F microcontroller with a 10-bit resolution. Knowing that the discharge curve is not linear, how can I model it so that I obtain a precise percentage of how much "juice" I've got left? Also, is this idea of a circuit good?
Knowing that my current consumption is about 0.5A, how long will the 4 batteries last?
Answer: You will know how much juice is left by always using well specified, known batteries and a coulomb counter to determine how much energy is left. Still you'd need to make a calculations to take temperature and loading effects into account.
If you can cut or measure power consumption from the battery and measure them in a known (battery) temperature, you can make an estimate by using curves available from the manufacturer of the battery.
If you use a voltage divider in a low energy consumption there is a risk of the voltage divider consuming a good portion of the available energy in the voltage division.
Microcontroller allows you to disconnect the voltage divider, so usually that is the easiest way to minimize the current draw for the voltage divider.
Consumption can also be countered by selecting large values for the divider, but then the ADC input impedance or sampling current might affect the measurement. A voltage follower buffer amplifier circuit can overcome that, or you could use a power monitor IC, but that will add complexity and might end up adding power consumption.
If you use microcontroller ADC remember to select the reference voltage to be something that doesn't change when the battery voltage drops.
Comment: Thanks for your input! I need a software implementation of this, not a hardware one (e.g. with a Coulomb counter) - I'd like to keep it as simple as possible. I think the voltage reference is constant because the microcontroller is powered by the buck-boost converter which gives a constant output (am I right?) - If I can't find a precise mathematical function of the ADC value which is dependent of the AA battery I guess i will consider 0% to be  682 =  1V/1.5V * 1023 and 1023 = 1.5V / 1.5V *1023 to be 100%. (the ADC resolution is 10 bit and I know the discharge slope is steep after 1V)
Comment: If you don't get the value from manufacturer then you can check another battery with the same chimistry and capactity to get ball park figures, but only the non-loaded figure will be a good match. Buck boost -converter will operate as you stated, but in practice it will have a minimum voltage, after which the output starts to drop.


How to find $e$ when $p,q,d$ are given?

Question: I have solved till here .....
$$n=p*q$$
$$n=5*11$$
$$\varphi(n)=(p-1)*(q-1)=4*10=40$$
Now, how to find $e$, when $d$ is given as $27$ and message for encryption is $\text{abcdefghij}$.
We have to take $a=1, b=2, c=3$ and so on.
Answer: In this RSA setting, I am assuming encryption key is $e$ and decryption key is $d$. Relationship between encryption and decryption keys is that decryption key should be multiplicative inverse of encryption key in modulo $\phi(n)$ i.e.
$$d=e^{-1} \mod \phi (n)$$
So that,
$$de≡1 \mod \phi(n)$$
So, our goal is to find out $e$ and we can find out this as follows:
$$e=d^{-1}\mod \phi(n)=27^{-1} \mod 40=3$$
You can verify this as follows:
$$27\times 3 \mod 40=81 \mod 40≡1$$
So, $e=3$.
Comment: You can use Extended Euclidean Algorithm to find the multiplicative inverse of 27 in modulo 40. Please google "Extended Euclidean Algorithm" to find out how the algorithm works.
Comment: sir can you please tell me  how to solve:      27^-1 mod 40

How to find $e$ when $p,q,d$ are given?


How to transfer player data for a Minecraft server

Question: I am a server owner of a server for my friends and I. My friends recently started using a new account. Is there a way to transfer the data from his old account to the new?
Comment: yes, simply changing the file with his old uuid to his new one
Answer: You would find their playerdata file, in the server folder/playerdata, and change their latest file to their new UUID. You could also use a plugin or mod that allows you to access their inventory in game, and you could move the invenotory manually this way.
Answer: If your friend's old account is still active then they could put their belongings in a chest and log in to their new account and pick everything up. the only issue with this is the xp levels would still be on their old account.
hope this helped!


What are compressed files within \sitecore\shell\Themes\Standard\?

Question: Does anyone know what are these zip files? Is it safe to delete them?
Answer: Those are thumbnails dispayed in Sitecore backend.
Do not delete them.
First time Sitecore needs any thumbnail, it extractss one of those files and gets the proper thumbnail with requested size.
E.g. when you open Content Editor and select Home item:

you can see that icon it uses is

You can extract Network.zip from that folder you mentioned and in 16x16 folder (size of the file) you will find home.png icon which is displayed in Content Editor:
Comment: Do you know why they put them into zip files instead of standard folders?
Comment: I have no idea. It's like that from ages...


FaceTime calls keep disconnecting the moment I answer

Question: I've recently upgraded my MacBook Pro to macOS High Sierra Version 10.13. So did my friend. We called each other on FaceTime. It took several attempts to establish a FaceTime connection. The first few times the call disconnected immediately when I hit the answer button. It didn't use to be this way before the upgrade. Is there anything I can do to fix this issue?
Answer: Here's a link that might shed some light on that issue. http://support.apple.com/kb/TS5419
D.
Answer: Turn Facetime off and then back on. Make sure it activates and then restart your device.
Also make sure that both of you check your Wi-Fi quality. If you are streaming video or playing video games in the background, your internet speeds will be going to that specific task.
If that doesnt work then sign out of iCloud and then sign back in.


Buying plane tickets "from the other end"

Question: I've been told because of taxes etc in Australia its cheaper to buy round trip flights from outside the country. For example, in the case of going from Perth to Bergen, purchase the ticket in Bergen. How do you do that and is that a fact or fiction?
Answer: It's mostly fiction. It's hard to find a specific example where this would make a significant difference.
For example Bergen <-> Perth in mid February was about $1100 and Perth <-> Bergen was about the same with one decent option being about $40 cheaper.
There is always variability of flight pricing, so it's hard to do an Apples to Apples comparison. Prices depend a lot on season, day of the week, special events at destination or departure, convenience of the connections, supply and demand, competition and many more.
"Buying outside the country" doesn't matter much either. First you need to define what that actually is. Which country is the one you buy in ?

Country of Departure airport: you can't change that unless you change your travel plans
Country of residence: the airlines don't even ask about this
Country of citizenship(s): only important in terms of visa and entry rules
IP address of the computer you book from: can easily be fudged with a VPN
Billing address of your credit card: may affect fees, but that depends often on the card
Currency used for payment: may affect fees and is subject to fluctuation

Typically none of these makes much of a difference.
Comment: How is a Bergen <-> Perth ticket useful if you're in Perth and trying to get to Bergen and back?
Comment: 7. Country where the seller is based. (Doesn't make much of a difference either.)
Comment: @NuclearWang The point was to compare the prices. Most sites will give a price that is local to the point of origin (including currency, specific fares, etc.). If Bergen <-> Perth is not cheaper than Perth <-> Bergen, there's little reason to think Perth <-> Bergen would be cheaper if bought in/from/via/through Bergen rather than Perth.
Comment: I believe there are a few exceptions. There's a thread somewhere about some fares in some South American country (Chile? Peru?) which are a lot cheaper when bought in country rather than from abroad (and the whole point of the thread was whether this was based on residence, place of sale...).


What are the cons of studying in a Ph.D. program that takes much time to confer the degree (about 1 year and a half or 2 years, after dissertation)?

Question: Currently, I am in the second year of a Ph.D. program. However, I am really worried about the amount of time Faculty takes to confer the degree, since It could be detrimental to my academic and professional future.
Comment: Could you clarify why you think "it could be detrimental to my academic and professional future"?
Comment: Tthis is a potentially useful question  but I think the answers might be really  country or institute dependent.
Comment: Admittedly I come from a system (the US) in which the PhD is always conferred at the end of the semester during which it is successfully defended, but....2 years?!?  That seems like an unreasonably long time.
Comment: Many thanks for your interesting answers. I think It could be detrimental in terms of salary (probably universities pay more if I have the degree). At the same time I think it could be a problem if a want to get a tenure track position or to apply to a postdoc position. However, your answers have helped me to understand different solutions and perspectives. (Excuse for my English. I am a native Spanish speaker)
Answer: Many academic positions after graduation are dependent on proof of degree completion, so this could potentially be a problem.  The NSF math postdocs, for example, require a signature from the school that you've completed your degree, and some positions explicitly require a copy of your transcript or diploma that indicate your completion of a Ph.D. program.  The institution where I completed a postdoc was in this latter category, and would only issue an informal offer (and not an official contract) until they received final documentation of my degree, which in my case took several months to arrive after graduation.  One practical problem I faced as a result was difficulty arranging for housing at my postdoc institution; most rental companies want to see their tenant's signed contract as proof of income.  I am also aware of tenure track jobs where the contract specified that the tenure clock only started after conferral of a degree.  I suspect some institutions would be willing to bend the rules a bit in unusual circumstances, but it certainly could be a problem.  (Note that this answer is based on experiences of myself and colleagues in the US.  I have no idea how this practice varies in other countries.)
Comment: my post doc employer (US) did not require such certification. So it really is employer-dependent.
Answer: It's understood that it takes some time from the date the thesis is turned in until the examination, and then again from the examination to the final degree conferral. Consequently, most employers—business, industrial, and academic—who hire Ph.D.'s will be aware of this, and will allow people to start working once they have finished the defense (and sometimes even before then!).
The date of conferral has some impact on when you're eligible to apply for certain programs, but even then, it's usually a window of X years after the conferral date, so you're not going to "lose out" on opportunities just because your faculty takes longer than average. Even in the event where it's after the date of defense, usually schools can issue documentation that the defense took place and was successfully passed.
Comment: In which countries is this true?
Answer: Once you've passed your PhD, ask your supervisor to write and sign a letter (on headed paper) that says you've passed.* (Explain to your supervisor why you need it.) That letter should be convincing enough to anyone that asks, even though it isn't a formal certificate.
*Selection of the right words is crucial. All statements should be honest.
Comment: I had the occasion to inquire into the rules at my own university.  In order to hire a postdoc, they either have to have their degree or a note from the **registrar** saying that all the requirements have been fulfilled and the degree will be conferred on such-and-such a date.  I have been involved in cases where this forced the postdoc to get the degree earlier than was convenient for them.  Again, this is not the case at all North American universities, but it will definitely be a problem in certain cases.
Comment: A letter from your supervisor will not be convincing to (e.g.) many North American universities.  For instance, in order to register as a postdoc in Canada I had to submit a copy of my PhD.  I know the same is true at many (though certainly not all) universities in the US.
Comment: @PeteL.Clark There are many ways to make a letter look convincing. Especially when a supervisor doesn't like bureaucracy. This method mightn't always work, but it should work in many cases. (Thinking of failure cases increases my confidence. E.g., a North America university questions the document's validity, verifies the supervisor's identity, and calls them. The supervisor confirms validity.)
Comment: There are of course cases when this won't work. In case of the requirement for "a note from the registrar saying that all the requirements have been fulfilled and the degree will be conferred on such-and-such a date," that seems possible to resolve: A student can draft a note that the supervisor agrees upon, and the supervisor can urge the registrar to sign. Of course, the registrar may refuse. But, it's worth a try.
Comment: ¡Many thanks for your interesting opinions! You have helped me a lot to analyze possible solutions and cons.


What was the causeway span leading to the Bifrost Bridge made out of?

Question: In the movie 'Thor', the causeway to Bifrost was obviously a power-feed to the bridge. It looks like a deck comprised entirely of some kind of hybrid crystalline and fiber optics power-feed cables routed from the Asgard city grid to the bridge controls. Would this be an accurate assessment and have their been any commentaries about it's composition or construction?
Answer: In the original Norse poems (on which much of the "mythos" in the films Thor and its sequel are based), the bridge is described as being made of the colours of the rainbow;

"Hana muntu sét hafa, kann vera at þat kallir þú regnboga. Hon er með þrim litum ok mjök sterk ok ger með list ok kunnáttu meiri en aðrar
  smíðir"
("Thou must have seen it; it may be that ye call it 'rainbow.' It
  is of three colors, and very strong, and made with cunning and
  with more magic art than other works of craftsmanship.")

I remain unconvinced that this will help with the film adaptation where, as you say the Bridge seems to be composed of glass and electronics.
Comment: Fiberoptic (light) conduits. Those old Norse poems were sure prescient... or were they just talking about what they saw?
Comment: Actually I think the actual 'bridge' would more accurately be the beam/transporter/wormhole/Einstein–Rosen bridge that Heimdall activates. The colored causeway is what feeds 'power?' to the mechanism that activates the bridge (between worlds). Still, your answer is a good step forward.


What to do with money?

Question: Suppose I raise $10 million from venture capitalists for my rocket startup, what are the initial steps I must take (as a person with no experience of making rockets before) to ensure my companies growth in a successful gradual manner?
Comment: $10M will pay ten people pay and benefits for maybe 5-7 years.  That doesn't leave any money over to get any hardware.
Comment: @peaceHoper Well, Elon musk invested about $100 million from 2001-2006 of his private money into SpaceX. Falcon 1 would not achieve orbit until 2008, and that has only about half a ton worth of payload. That should give you an idea.
Comment: Most (90%+) startups fail so there's no way you can ensure its success. The business model of startup IMO is to spend money and build up company's value, then 1) if the company is solid, then become a real enterprise and profit by making stuff (SpaceX, Tesla, GoPro, top 1%), 2) sell the company's value back into money and recover investments and/or take profit (top 5%, check out Google's acquisition, e.g. Nest, Ring, Android, YouTube), 3) die (all others).
Comment: I think it would have a potential but not at big stuff like actual launches - but on modules; a small part that does what others currently do worse. A good magnetic bearing for reaction wheels. An inexpensive but very reliable, fast and small star tracker for use in cubesats. A reliable TEA-TEB ignitor that uses up half the current amount of the fluids to get the work done. Camera firmware for cameras like gopro, that handles the harsh changes in lighting in space better. Then sell that to space industry giants, building up funds for more ambitious projects.
Comment: How much would then be the threshold money to start with?
Comment: @Tristan but it's more than enough [to do something like this](https://space.stackexchange.com/a/43192/12102)!
Comment: I believe, "it is not enough to start anything" is a fair answer here, based on Polygnome's comment. I vote "leave open". I think the option to join an ongoing private rocketry project as an investor, is open.
Answer: Two options:

Become an investor in SpaceX.  \$10M is not enough to start your own rocket company (it takes at least \$1000M), but it would be enough to be taken seriously as an investor in another company that has a record of success, yet still needs cash.
Become a subcontractor.  Build something that a larger company doesn't do themselves, but might be willing to buy from you.  For example, one could start a company that makes space food.
Comment: Space food is an interesting point. Need to produce food lasting long enough for manned Mars missions. As far as I understand, this is currently an issue.
Answer: Citing comments of @Tristan and @Polygnome:

$10M will pay ten people pay and benefits for maybe 5-7 years. That doesn't leave any money over to get any hardware.
Well, Elon musk invested about $100 million from 2001-2006 of his private money into SpaceX. Falcon 1 would not achieve orbit until 2008, and that has only about half a ton worth of payload. That should give you an idea.

I would add to them, that although $10 million is not enough for orbital rocketry, you can still join an already ongoing private rocketry project as a business partner or as an investor.
Comment: @uhoh It depends on your contract with the investors. The example in the other answer, making a company for space food production, I see no reason why it could not work (except that maybe the venture capitalists won't see it profitable and they don't give their money). Getting money from them for investing it into other companies, yes it is far lesser likely but I believe it might be still possible.

What to do with money?