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734,143 | [
"https://physics.stackexchange.com/questions/734143",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/196/"
] | My understanding of polarization of light is that a photon can be horizontally polarized, or vertically polarized, or some angle in between (eg 45 degrees from horizontal) — leaving aside circularly polarized for now.
This means basically that the electromagnetic wave oscillates in just this direction.
If you put a pol... | Water is incompressible. So you can put a bucket under your stream and let it run for some time. That way you measure the volume of water coming out per time [units m<span class="math-container">$^3/$</span>s]. Divide by the cross-sectional area of the orifice [m<span class="math-container">$^2$</span>] to get the wate... | A simple method to get a more precise location of where the water stream intersects a plane is by letting it fall through the plane and to intercept the two edges of the stream with a sharp edge. Even small disturbances of the stream by the edge should be easily noticeable. I would guestimate that you will get sub-mm p... | https://physics.stackexchange.com |
496,923 | [
"https://physics.stackexchange.com/questions/496923",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85662/"
] | While working out through some problems I encountered this problem :
<blockquote>
A ball moving with a velocity <span class="math-container">$v$</span> hits a massive wall moving towards the ball with a velocity <span class="math-container">$u$</span>. An elastic impact lasts for a time <span class="math-container"... | Speed is the magnitude of velocity and hence must always be a positive quantity.<br>
This means that the distance travelled, <span class="math-container">$\displaystyle \int_{t_{\rm initial}} ^{t_{\rm final}} v\,dt$</span> must always be positive and so the time average <span class="math-container">$\displaystyle \dfra... | If you end up where you started, your average velocity will be zero over that time frame:
<pre><code>v = dx/dt
</code></pre>
For the average speed, you would want the path length over time. If you've left your original position, even to return, your path length is now non-zero, so you've got an average speed of grea... | https://physics.stackexchange.com |
3,062 | [
"https://mechanics.stackexchange.com/questions/3062",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1621/"
] | I sometimes will stay in the car for extended periods with music player, parking lights turned on and engine turned off. I was wondering how long can the car battery survive this load. Should I be worried about this?
| I have a heavy duty truck battery in my car, and I can run a 640 Watt stereo system all day and all night, with the interior lights on without having any problems starting the car.
But once I accidentally left the lights on for two weeks while on holiday, and the battery was flat.
Those two datum points give an idea ... | The question can only be answered if you determine the load that is being put on the batteryand the load capacity of the battery.I have run the radio in my truck for two hours and it started without a problem.I have seen a luxury car with 12 or 14 interior lights run a battery down in 90 minutes from a door left open.M... | https://mechanics.stackexchange.com |
45,093 | [
"https://physics.stackexchange.com/questions/45093",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15631/"
] | The problem I am working on is:
<blockquote>
<em>A uniform, thin, solid door has height 2.10 m, width 0.835 m, and mass 24.0 kg.</em>
<em>(a) Find its moment of inertia for rotation on its hinges.</em>
<em>(b) Is any piece of data unnecessary?</em>
</blockquote>
I am not really certain of what I am doing at all. So, he... | You're right about not needing the height. You then calculate the moment of inertia by in principle summing up the moment of inertia of infinitesimal mass elements. The moment of inertia of an infinitesimal mass element $\mathrm dm$ is $\mathrm dm\cdot r^2$, in which $r$ represents the distance from the mass element to... | Thats initiative, i mean its obvious that forma uniform door the mass of each slice is the same, you dont need to calculate <span class="math-container">$x\times h$</span> but you could say <span class="math-container">$m=\rho V = \rho A L$</span> where <span class="math-container">$\rho$</span> is density, and <span c... | https://physics.stackexchange.com |
14,334 | [
"https://security.stackexchange.com/questions/14334",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/3537/"
] | Let's say I have a web server I setup, and then a database server.
However, they are communicating locally and are behind firewall. In my opinion, no SSL is needed here right?
The only time to use SSL to encrypt the database connection would be between a web server that exists in a server that remotely communicates ... | It looks like the two previous answers to this question more or less strongly recommend to turn on SSL anyway, but I'd like to suggest a different reasoning angle (although I'm not recommending not to turn on SSL).
The two key points in assessing whether you need SSL or not are (a) what SSL protects you against and (b... | When the local network that includes the database server and clients might include other processes then you should encrypt the connection between the two.
This is almost always the case since, even if you assume that the local network is impenetrable (you shouldn't), besides the database client and server there are us... | https://security.stackexchange.com |
251,464 | [
"https://softwareengineering.stackexchange.com/questions/251464",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/94768/"
] | I work for a company that, in my opinion, should be doing all of it's web development work in a fully agile manner. We have vague, competing ideas about the product at any given time. And we have strict deadlines. So, in the web arena it seems to make sense to operate in as agile a manner as possible.
However, I could... | There's a <em>very serious</em> problem with choosing a methodology on a "per-project" basis, which is that most Agile methodologies <strong>reject the notion of projects</strong>.
A project implies fixed scope and fixed time, and for many of the more dysfunctional organizations, also a fixed budget. This is anathema ... | I don't see the benefit of trying to do everything the same unless you're willing to turn-down projects that don't fit your particular model. Otherwise, you get a bad fit and the client isn't going to be happy either way.
If you're so sure you know the specs in one case and are very confident they won't change, you ca... | https://softwareengineering.stackexchange.com |
1,945,739 | [
"https://math.stackexchange.com/questions/1945739",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/188265/"
] | To prove this statement, i used proof by contradiction.
Suppose O$\in$int(bd(E)), the any x in O is not a boundary. Thus, O is not a subset of bdE and cannot be a subset of int(bd(E)).
However, my proof does not use that E is closed. Is my proof wrong? Where is it wrong?
| Let $x \in \partial E$, where $\partial E$ is the boundary of $x$. By definition of being in the boundary, every neighborhood $U$ of $x$ intersects both $E$ and $E^c$. By definition of closure of the set $E$, $\partial E \subset E$.
Now, let $x$ be an interior point of $\partial E$. Then, there exists a neighborhood o... | I find it humorous the way the question says "an" empty set; as if there is more than one empty set. There is only one empty set. It is more correct to say <em>the</em> empty set rather than <em>an</em> empty set. To prove the set S is equal to the empty set, it is sufficient to only prove there does not exist any elem... | https://math.stackexchange.com |
577,078 | [
"https://physics.stackexchange.com/questions/577078",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/256066/"
] | We've a potential given as:
<span class="math-container">$V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$</span>.
We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barr... | Filling in the <span class="math-container">$V$</span>, as given in the problem (the "one step up <span class="math-container">$V$</span>"), in the Schrödinger equation, you'll get the wavefunction <span class="math-container">$ψ_2(x)=e^{αx}$</span> for the positive values of <span class="math-container">$x$<... | This has to do with the definition of the transmission coefficient <span class="math-container">$T$</span> in quantum scattering experiment. What we want to know is how a particle will behave when it's "shot" at the barrier. In a general situation, part of the wave function probability will reflect off the ba... | https://physics.stackexchange.com |
46,424 | [
"https://quant.stackexchange.com/questions/46424",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/27799/"
] | Very basic question I'm confused about :
Is there a formula that relates total return of a bond as a function of yields and its roll down returns?
I mean ignoring reinvestment risk, would the total return of a bond be roll down return + yield?
| Yes I think you can say that the total return for a bond over a period equals to first order the sum of
A) yield
B) change in yield over the period * dv01 of the bond.
The question is, what assumption to make about the change in yield. The term <em>roll down pnl</em> is usually defined to mean that the yield curv... | Total return approximately equal to the sume of three components:
<ul>
<li>issue OAS + rolldown = carry</li>
<li>mark to market OAS</li>
<li>falling angel cost if you are investing IG-only </li>
</ul>
| https://quant.stackexchange.com |
117,670 | [
"https://mathoverflow.net/questions/117670",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25854/"
] | Let $k$ be an arbitrary field, we work with schemes $X$ of finite type over $k$. Does every irreducible projective scheme have a finite surjective morphism to a projective space $\mathbb{P}^n_k$?. What if I just assume that $X$ is equidimensional. Does the same argument work?
We know that a proper $k$-scheme with thi... | Let $X$ be any projective scheme of dimension $n$ over an arbitrary field $k$. Then there exists a finite surjective morphism from $X$ to $\mathbb P^n_k$.
Embed $X$ in some $P=\mathbb P^N_k$. By the homogeneous prime avoidance lemma, there exists a hypersurface $H_0$ of $P$ which doesn't contain any generic point of ... | I assembled the comments above into an answer:
Assume that the field of definition is infinite (or allow finite extensions of the base field in the construction). Let $X$ be a projective scheme over a field $k$ and let $n$ be the dimension of $X$. Let $N$ be smallest such that there exists a finite morphism $X\to \mat... | https://mathoverflow.net |
536,825 | [
"https://physics.stackexchange.com/questions/536825",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/177275/"
] | In quantum mechanics of the harmonic oscillator, when we use the operator method to find out the solutions, we find that the action of <span class="math-container">$\hat{a}$</span> is to lower the energy of a state by <span class="math-container">$\hbar\omega$</span> and the action of <span class="math-container">$\hat... | Expanding on J. Murray's answer (which basically is the answer), we can start from the so-called number operator and have <span class="math-container">$\hat{N} = a^{\dagger}a$</span>. As it was explained Murray's answer, its spectrum is non-negative, because
<span class="math-container">$$ \langle \psi | \hat{N} | \psi... | The eigenstates of the operator <span class="math-container">$N = a^\dagger a$</span> can be labeled by their eigenvalues, i.e. <span class="math-container">$N \phi_n = n \phi_n$</span>, where <span class="math-container">$n$</span> is an integer. Note that
<span class="math-container">$$n = \langle \phi_n,N\phi_n\ran... | https://physics.stackexchange.com |
1,444,692 | [
"https://math.stackexchange.com/questions/1444692",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/269290/"
] | <blockquote>
If $a | b$, prove that $\gcd(a,b)$=$|a|$.
</blockquote>
I tried to work backwards. If $\gcd(a,b)=|a|$, then I need to find integers $x$ and $y$ such that $|a|=xa+yb$. So if I set $x=1$ and $y=0$ (if $|a|=a$) or if I set $x=-1$ and $y=0$ (if $|a|=-a$), is this good enough?
| If $a \mid b$, then $|a| \mid b$. Moreover, we have $|a| \mid a$. Thus $|a|$ divides both $a$ and $b$. If $q > |a|$, then $q \nmid a$ by definition, so $|a|$ is the greatest common divisor of $a$ and $b$.
| That doesn't prove anything, since this relation is true even if $a$ and $b$ are coprime. It is the first step in the <em>Extended Euclid's algorithm</em>.
Just observe that <em>any</em> common divisor of $a$ and $b$ must divide $a$, and by hypothesis $a$ is a common divisor of $a$ and $b$. Hence it ($\lvert a\rvert$... | https://math.stackexchange.com |
381,273 | [
"https://physics.stackexchange.com/questions/381273",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/131639/"
] | <blockquote>
Say we are given a conveyor belt with sand falling onto it at rate <span class="math-container">$\Omega$</span>. I am trying to find the power it takes for the belt to operate if it goes forward with constant velocity <span class="math-container">$v$</span>, but using two different approaches I get two dif... | Your first answer gives you the rate at which the sand gains kinetic energy whereas your second answer gives you the rate at which work has to be done on the conveyor belt to keep it moving at constant speed.
When the sand falls on the belt in order to accelerate the sand to the same velocity as the belt there must be ... | The answer by Farcher is right. I will comment further in hopes of increasing clarity and in order to clear up some mistakes introduced in other answers.
This kind of problem can be tackled by considering conservation of momentum. We also have conservation of energy, but that is more difficult to apply correctly becaus... | https://physics.stackexchange.com |
166,468 | [
"https://dba.stackexchange.com/questions/166468",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/98445/"
] | There is something not very clear in my mind and that I wanted to know when performing queries that retrieve large result sets:
Is a result set entirely loaded into memory and send to the client or only a part of it is loaded, send and then the memory is reused to load the next part until all data has been processed ... | Copying the data directory, as you mentioned, is one way to accomplish what you need. Here are the steps, and if you face any error, please post it.
<ol>
<li>Shut MySQL server down; or in a terminal flush tables with lock <code>FLUSH TABLES WITH READ LOCK</code> [<strong>Important:</strong> Keep the terminal open]</l... | Establish LVM on the filesystem. Then a snapshot takes less than a second, regardless of the dataset size. You get a separate copy of the <em>disk</em>, but with unchanged blocks shared. Changed blocks are "copy-on-write", so you need to blow away the snapshot before it grows too big. (Soulds like that is no proble... | https://dba.stackexchange.com |
51,556 | [
"https://dba.stackexchange.com/questions/51556",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/16418/"
] | I am developing a database which has data sourced from many different applications. In my first pass at design, I placed the staging tables each in a schema named for their source application.
As several of the source applications have similar data and similar table names, I use the schema name to differentiate the ... | From the description you gave I don't think security is the concern here. As you said your application receives data from multiple sources. The security comes/implemented when you have role based security kind of things on retrieval/access methods of that data.
I am guessing the there must be first some kind of consoli... | I am going to mention both logical and physical design here.
I know IBM recommends placing staging tables into their own schema(s) and even into their own table spaces (database implementation specific to DB2 in this case) for reasons of management. Schemas allow you to manage better via separation of concerns and sec... | https://dba.stackexchange.com |
4,135,519 | [
"https://math.stackexchange.com/questions/4135519",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/926163/"
] | I would like to use the field of 2 elements (<span class="math-container">$\mathbb{Z}/2\mathbb{Z}$</span>) to construct a vector space consisting of 8 elements.
I have succeeded in constructing vector spaces of 2 elements and 4 elements but I don't see how it is possible to create an 8 element set of vectors that is cl... | <span class="math-container">$\mathbb Z/2\mathbb Z$</span> is a field known as <span class="math-container">$\mathbb Z_2$</span> (amongst other things) which has two elements <span class="math-container">$0,1$</span> (or odd, even if you want to be quirky).
A vector space over a field can have any dimension you like - ... | <span class="math-container">$\mathbb F_8$</span> is a vector space of dimension <span class="math-container">$3$</span> over its prime subfield <span class="math-container">$\mathbb F_2$</span> (as any finite field <span class="math-container">$\mathbb F_{p^n} $</span> can be thought of as an <span class="math-conta... | https://math.stackexchange.com |
63,848 | [
"https://cs.stackexchange.com/questions/63848",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/58478/"
] | How do I prove that diameter of undirected Ring Topology is n/2?
| To prove that the diameter of the undirected ring topology is $n/2$:
<ol>
<li>Find two vertices $x,y$ at distance $n/2$.</li>
<li>Show that any two vertices $x,y$ are at distance at most $n/2$.</li>
</ol>
By the way, the diameter is more accurately $\lfloor n/2 \rfloor$.
| I tried this:<br>
If n is even then n/2th node is the <strong>farthest node</strong>, else (n-1)/2th or (n+1)/2th node would be the farthest node.<br>
In case of 'n' nodes the number of edges is 'n'<br>
Assuming : If we have a ring of n/2 nodes(in case of <strong>even</strong> number of nodes) or (n-1)/2 (in case if n ... | https://cs.stackexchange.com |
40,300 | [
"https://mathoverflow.net/questions/40300",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1272/"
] | Let $\mathcal{V}$ be an outer measure on $X$,
$(A_\alpha)_{\alpha\in I}$ be a chain of increasing subsets of $X$.
<ol>
<li>Is it true that $\mathcal{V}(\bigcup_{\alpha\in I}A_\alpha)=\sup_{\alpha\in I}\mathcal{V}(A_\alpha)$?</li>
<li>If this is not true in general, are there classes of spaces $X$ and outer measures $... | Just to add to Carl's answer:
If $M=(M,E)$ is a model of set theory ($M$ and $E$ sets), for instance one obtained from
the completeness theorem using the assumption that ZFC is consistent, then $M$ typically
is a nonstandard model, with the internal natural numbers actually being "longer" than
our familiar $\mathbb N... | I will try to answer two questions:
1: "But how does set theory "know" which $n$ is meant?"
Within ZFC, we have a standard construction of the natural numbers. So for each natural number $n$ in the metatheory, and any model $M$ of ZFC, we can identify a set in $M$, say $n^M$, which plays the role of $n$ within $M$. ... | https://mathoverflow.net |
153,588 | [
"https://electronics.stackexchange.com/questions/153588",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/61257/"
] | Im trying to figure out the current limitations of a mosfet(SISA18ADN) I'm planning to use to check how much headroom I have.
The datasheet states Continuous Drain Current that it can handle as 12.1Amps at Ta=70degreeC during 10seconds, and 38.3Amps at Tc=25C with no time specification.
But in the Safe Operating Area... | The safe operating area is voltage versus current, whose product is power dissipation. The reason that the maximum current is low for, around 0.2A, versus 10V for continuous DC operation is that you have to look at the product of these values: 2W. Note that for a lower voltage drop, the device can handle a lot more cur... | The limitation is based on temperature rise in this case. Maximum thermal resistance (steady-state) junction-to-ambient is stated to be 81°C/W so at 25°C ambient, a power dissipation of 1.5W is the highest acceptable at an ambient temperature of 25°C (less when it's warmer) resulting in a junction temperature of 150°C ... | https://electronics.stackexchange.com |
3,082,968 | [
"https://math.stackexchange.com/questions/3082968",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/356308/"
] | Page 11, <em>Nonlinear Dynamics and Chaos</em>, by Strogatz, says the following:
<blockquote>
This is the domain of classical applied mathematics and mathematical physics where the linear partial differential equations live. Here we find Maxwell's equations of electricity and magnetism, the heat equation, Schrödinge... | Not knowing more about <span class="math-container">$x$</span>, about all you can write is
<span class="math-container">$$S\le\max_{t\in[-1,\frac12]}x^2(t)\,\zeta(5)=\left(\max_{t\in[-1,\frac12]}|x(t)|\right)^2\,\zeta(5)$$</span>
| The inequality you claim is not true. Take <span class="math-container">$x(t)=1$</span> for all <span class="math-container">$t$</span> and note that <span class="math-container">$\sum\limits_{k=1}^{\infty} \frac 1 {k^{5}} >1$</span>. What you can say is <span class="math-container">$S\leq c \max \{|x(t)|^{2}: -1\le... | https://math.stackexchange.com |
17,637 | [
"https://mechanics.stackexchange.com/questions/17637",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2618/"
] | I was wondering if it is bad (for the frame or the drive train) to leave my 4WD V6 Tacoma on 4 jack stands for several days while I work on the transmission. I could certainly lower it down after taking the tranny off and raise it again to put it back on but would rather not do it if it is safe to leave it on 4 jack s... | I have seen a lot of qualified mechanics leave the car on jack stands for months without any problems. It is more a question of where the car is being stored while on jack stands. In a garage where it is safe from accidentally being leaned on and possibly tipped over would be best (and out of sight from vandals/hooliga... | We have a few project cars and have left them on jack stands for long stretches of time while we were rebuilding stuff. I'll second Tariq that if the vehicle is held up at proper jack points you should have no problems. It's also a good point to have the vehicle somewhere secure, if only to keep curious people, pets,... | https://mechanics.stackexchange.com |
51,607 | [
"https://chemistry.stackexchange.com/questions/51607",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7213/"
] | $$\ce{3Na2CO3 + 2FeBr3 + 3H2O -> 6NaBr + 2Fe(OH)3 + 3CO2}$$
Why $\ce{Fe(OH)3}$? Where do these $\ce{-OH}$ groups come from?
This is from a series of reactions in a Russian sample exam question.
P.S.
Following Ivan't hints, I've gone through the process of reaction, and I get some water in the right-hand side o... | You have certainly already recognized $\ce{Na2CO3}$ as the base in your equation.
Did you also consider the following:<br>
When $\ce{FeBr3}$ is dissolved in water, the hexaaqua complex $\ce{[Fe(H2O)6]^3+}$ is formed. This complex is fairly acidic:
$$\ce{[Fe(H2O)6]^3+ + H2O<=> [Fe(H2O)5OH]^2+ + H3O+}$$
Ignoring ... | Draw a lewis diagram of the molecules to give you visual clues. From a glance it looks like the halides that are connected to the iron take their electrons leave and then are captured in solution to the sodium molecules. (this wouldnt be such a great bond since its ionic and the sodium and bromine ions would really act... | https://chemistry.stackexchange.com |
438,875 | [
"https://stats.stackexchange.com/questions/438875",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/267402/"
] | I already asked this question is SO; however, I realized that this may be a better place for this type of question.
I am well aware that when using categorical features with tree based models such as random forest and gradient boosting there is no need to drop one level from N-level categorical features. For example, ... | It's true that you're not missing information when you use only <span class="math-container">$k-1$</span> categories. In linear models, we are all familiar with the dummy variable trap and the relationship between a model with <span class="math-container">$k-1$</span> levels and an intercept and a model with <span clas... | Go with your <strong>Option I</strong> - there is no need to do one-hot encoding when there are only two categories. <br> These two columns <code>Gender_M</code> and <code>Gender_F</code> carry the exact same information (since it's binary, at least in your example).<br>
I think some frameworks need binary <em>classes<... | https://stats.stackexchange.com |
5,159 | [
"https://scicomp.stackexchange.com/questions/5159",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/529/"
] | I am a PhD student in Scientific Computing and over the past few months, I spent a good amount of time learning Python and C++ the right way. I feel that I have learnt C++ well and I can use Python to do what I want if I keep a good reference book around.
I also know MATLAB enough to prototype my ideas and get solutio... | I will address only the comparison of C to C++. While it is true that anything written in C can be ported to C++ with a few syntactic touch-ups, the communities have different values.
The C library community, more than almost any other, values <em>binary</em> stability.
Binary stability is critical for low-level librar... | Rather than "learning C", I'd suggest that you're at a point now where you've done enough programming and worked with enough programming languages that you should focus instead on improving your programming technique and broader knowledge of computer science. Then learn C if and when you need it for a particular proje... | https://scicomp.stackexchange.com |
145,920 | [
"https://cs.stackexchange.com/questions/145920",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/145463/"
] | Let's say that we have a language <span class="math-container">$L$</span> that is finite.<br />
How can I prove that the complement of <span class="math-container">$L$</span>, i.e., <span class="math-container">$\bar{L}$</span>, is always an infinite language?
Obs.: infinite language in this case means that is possible... | The set <span class="math-container">$\Sigma^*$</span> is an infinite set (you can build a bijection between the naturals and the words in <span class="math-container">$\Sigma^*$</span> if you wish to prove this, or you can observe that, for every <span class="math-container">$k \in \mathbb{N}$</span>, <span class="mat... | Here is a formal proof for the statement (<strong>warning</strong>, this really <em>is</em> a formal proof, and hence is not very intuitive):
Let <span class="math-container">$\Sigma$</span> be a non-empty alphabet (either finite or infinite), and let <span class="math-container">$L\subset \Sigma^*$</span>, with <span ... | https://cs.stackexchange.com |
2,685,505 | [
"https://math.stackexchange.com/questions/2685505",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/258202/"
] | <blockquote>
Given that $k$ is continuous on $[0,1]$ and
$$\langle k,v \rangle=\int_0^1 k(x)v(x) \,\mathrm{d}x=0, \quad \forall v\in{V}$$
where$$
V=\{v: [0,1]→\mathbb{R},\ v \text{ is continuous},\ v(0) = v(1) = 0,\\ v′\ \text{ is piecewise continuous and bounded}\},
$$
show that $ k(x)\equiv0$ for $x\in [0,1... | That's correct way to start, then we have
$$V(10+\Delta x)=V (10)+V'(10)\cdot\Delta x\implies \Delta V=V'(10)\cdot\Delta x$$
Note also that we need to assume $\Delta x=2\cdot 0.2=0.4$.
Then we have
<ul>
<li>$V'(10)=300$</li>
<li>$\Delta x= 0.4$</li>
<li>$\Delta V=120$</li>
</ul>
Note that we can also calculate by ... | Assuming "0.2 fiberglass" is $0.2$ inch thick, we are interested in $V(10.4)-V(10)$ (since the cost is applied to both sides). Considering the definition of $V'(x)$, we have
$$
V(10.4)-V(10)\approx V'(10)\cdot 0.4
$$
| https://math.stackexchange.com |
35,032 | [
"https://quant.stackexchange.com/questions/35032",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19002/"
] | <strong>Background:</strong>
I am preparing for interviews and I was told to try and answer as many problems in the Mark Joshi book as possible.
<strong>Question:</strong>
<blockquote>
Suppose an asset takes values from a discrete set $v_j$ and the probabilities of $v_j$ is $p_j$.
Write an algorithm that produce... | Yes. Mark Joshi's book is a good preparation.
For this question you are given some function <em>random()</em> yielding a uniform random number and what we want is a function <em>next()</em> which yields realizations of a random $X$ variable with values $v_j$ such that $P(X=v_j)=p_j$.
From standard textbooks we know ... | I am sure you have seen the $n=2$ case:
Write a program that returns "Yes" with probability p and "No" otherwise. You are given a function runif(), which returns a random number between 0 and 1.
Solution:
r = runif(); if $r<p$ then return "YES"; else return "NO".
From this well known example you have to genera... | https://quant.stackexchange.com |
564,656 | [
"https://physics.stackexchange.com/questions/564656",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/160629/"
] | I've wondered about that for a while but all I read is commonly just "Warm/hot air has a higher energy so when it hits the surface of a liquid, it has a higher probability to transfer energy, resulting in water molecules leaving the liquid".
Though it makes sense, I don't think that is actually a reason. It o... | It's about the water, not the air. Water, and other substances, have a "vapor pressure": a pressure at which molecules leaving the surface are in dynamic equilibrium with vapor molecules reattaching to the surface. If you pull a vacuum above liquid water, the vacuum will be repopulated with water molecules u... | It is easier to think of this in terms of molecular motions. If the air is warmer, it will warm the surface temperature of a liquid in which it is in contact. This will increase the thermal energy of molecules in the liquid, increasing the probability that a molecule has enough energy to leave the liquid and join the v... | https://physics.stackexchange.com |
220,913 | [
"https://stats.stackexchange.com/questions/220913",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/121444/"
] | I am new to machine learning and advanced statistics (anything beyond first-year college statistics), and I have been exploring the effectiveness of various classifiers on modeling different hand gestures based on some IMU data I've gathered.
I have been told by multiple colleagues that I should train my model on 'pos... | Adding random noise to a training set doesn't make a model more accurate; it makes it less accurate (albeit by adding variance, not bias, assuming the noise is unbiased, as is usually assumed).
What people mean when they say that you need negative examples in your training data is that when you have a binary classifie... | I think you're conflating known negatives with random noise. The advice to include negatives lets you assess the specificity of the model (assuming you're creating a binary classifier, which I infer you mean by using "positive" and "negative" terms).
Think of it like this. A good model can find true positives when t... | https://stats.stackexchange.com |
1,424,928 | [
"https://math.stackexchange.com/questions/1424928",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/229317/"
] | How to find minimum of the expression
$$\, \big(\!-x+y+1 \big)^2 + \big( x-y-2\big)^2 + \big(x+2y-3 \big)^2 \,$$
without using partial derivatives?
It is easy to find the answer $\; x = 2, \; y = \dfrac{1}{2}\; $
by computing gradient of the expression above, but I do not see the way to do so without using partial der... | By completing the square,
$$ \big(-x+y+1 \big)^2 + \big( x-y-2\big)^2 + \big(x+2y-3 \big)^2 = 3(x-2)^2+6(y-\frac{1}{2})^2 +\frac{1}{2}$$
the minimun is $\frac{1}{2}$
| <strong>hint</strong>:
$a = y-x+1, b = x-y-2, c = x+2y-3$, then find an equation in $a,b,c$ and use CS inequality.
| https://math.stackexchange.com |
16,145 | [
"https://mathoverflow.net/questions/16145",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3380/"
] | Let $K$ be a field and $G:=SL_2(K)$, then $G$ is a $K-$split reductive group (to use some big words). These groups are classified by a based root datum $(X,D,X',D')$. Let $G'$ be group associated to $(X',D',X,D)$, the so called dual group.
Is it correct that $G'=PGL_2(K)$?
I"m wondering how $PSL_2(K)$ fits into this ... | Yes, the dual of $SL_2$ is $PGL_2$.
But you're not going down the right track with $PSL_2$. The problem with $PSL_2$ is that it's not a variety at all! You can quotient out the variety $SL_2$ by the subgroup $\pm1$ but the quotient is the variety $PGL_2$ (recall that quotients in the category of sheaves (for these are... | As Kevin says, the "right" definition of ${\rm{PSL}}_n$ is as representing the quotient sheaf ${\rm{SL}}_n/\mu_n$, just as one defines ${\rm{PSO}}(q) = {\rm{SO}}(q)/Z_{{\rm{SO}}(q)}$ (with $Z_G$ denoting the scheme-theoretic center of a smooth group $G$). So really, there is no difference between ${\rm{PSL}}_n$ and ${... | https://mathoverflow.net |
148,354 | [
"https://physics.stackexchange.com/questions/148354",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11617/"
] | When the electric scalar potential is expanded into spherical coordinates, one gets
\begin{align}
\phi (\vec r) = \frac{1}{4\pi\varepsilon_0} \sum_{l=0}^{\infty} \sum_{m=-l}^l \sqrt{\frac{4\pi}{2l+1}} Y_{lm} (\theta, \varphi) \frac{Q_{lm}}{r^{l+1}}
\end{align}
with the electric multipole tensor
\begin{align}
Q_{lm... | If we let $\mu_0=1$, $\epsilon_0 =1$ (adopting a system of units where $c=1$), then Maxwell's equations become completely symmetric to the exchange of ${\bf E}$ and ${\bf B}$ via a rotation (see below).
$$ \nabla \cdot {\bf E} = 0\ \ \ \ \ \ \nabla \cdot {\bf B} =0$$
$$ \nabla \times {\bf E} = -\frac{\partial {\bf B}}{... | If it is eventually found that magnetic monopoles exist, then M would not be always zero and Maxell's equations would become fully symmetrycal on E and B.
| https://physics.stackexchange.com |
30,828 | [
"https://quant.stackexchange.com/questions/30828",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/22715/"
] | I want to calculate $E_t[(X_T-K)^+]$ where
$$dX_t=\frac{3}{X_t}dt+2X_t dW_t$$
and $X_0=x$. I don't know how extact the strong solution of this SDE. Indeed I used Ito's lemma but it was not usefule.
Thanks for attantion.
| Note that
\begin{align*}
d\left(X_t^2\right) &= 2X_t dX_t + d\langle X, X\rangle_t\\
&=(6+4X_t^2)dt + 4X_t^2dW_t,
\end{align*}
which can be solved using the technique with an <em>integral factor</em>. Specifically, note that
\begin{align*}
d\left(e^{4t-4W_t}X_t^2 \right) &= X_t^2 d\left(e^{4t-4W_t}\right) +... | You shouldn't say: "Ito's lemma wasn't useful". Set
$$Y_t=-2W_t+2t\tag 1$$
Note $W_0=0$ thus $Y_0=0$.We have
$$dY_t=2\,dt-2\,dW_t\tag 2$$
Set $Z_t=e^{Y_t}$. By application of Ito's lemma, we have
$$dZ_t=e^{Y_t}\,dY_t+\frac{1}{2}e^{Y_t}d[Y_t,Y_t]\tag 3$$
therefore
$$dZ_t=4e^{Y_t}dt-2\,e^{Y_t}dW_t=4Z_tdt-2Z_tdW_t\tag 4$... | https://quant.stackexchange.com |
291,616 | [
"https://physics.stackexchange.com/questions/291616",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/73357/"
] | Is it possible to have a travelling wave in a duct? I understand that wave motion in a duct with reflections at the ends of the duct (open or closed boundary) creates a standing wave pattern. What boundary conditions would create a travelling wave in a duct? Or is it even possible?
| This is just a conceptual mistake. The Ohm's law states that the voltage drop developed across a conductor is proportional to the current flowing through the conductor, the proportionality being a property of the conductor itself- it's resistance. This is what we write mathematically as
$$V=IR$$
Now, when you con... | <blockquote>
I guess more generally I'm confused as to why things with zero current
going through them have a voltage drop at all as V=IR.
</blockquote>
Ohm's law applies to <em>ohmic</em> devices; if the voltage across a device is proportional to the current through, the device is ohmic otherwise it isn't.
<em>O... | https://physics.stackexchange.com |
2,258,406 | [
"https://math.stackexchange.com/questions/2258406",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/441782/"
] | Considering ${\sqrt{x}}=y$, what is the resolution process of $x^{\sqrt{x}}=\sqrt{x^x}$, with results S={1,4}?
| Square both sides to get
$$x^{2\sqrt x}=x^x$$
Either $x=1$, or $2\sqrt x=x\implies x=4$.
| Take logs of both sides to get:
$\sqrt x \log x = \frac 12 x\log x$
which has solutions of either $\log x = 0 \implies x = 1$
or:
$\sqrt x = \frac 12 x$
which has solutions of $x = 0,4$. Exclude $x=0$ as it is inadmissible in the original equation, leaving the solutions $x = 1,4$.
| https://math.stackexchange.com |
60,105 | [
"https://physics.stackexchange.com/questions/60105",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/927/"
] | I've learnt that the lattice enthalpy (defined as the energy change from a solid ionic lattice to separate gaseous ions) is always positive, obviously. However, I've seen it explained as the opposite other places, so it's negative.
What is correct?
| When it is explained as opposite, it is usually the heat RELEASED when a crystal is formed, and since the word "released" already makes up for the sign of heat(i.e. if heat is -10 that means the heat released or evolved is +10) , it is taken as positive. Nonetheless, some books also present a negative value to it but i... | Lattice energy is defined as when 1 mole of cation and 1 mole of anion combined to form 1 mole of solid crystal, energy is released. The energy released is known as lattice energy because we know anion and cation has highewr energy than crystal lattice therefore when bond is formed between cation and anion energy is re... | https://physics.stackexchange.com |
27,522 | [
"https://mathoverflow.net/questions/27522",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6679/"
] | Hi,
We have a real symmetric matrix M with diagonal elements 0's, the eigenvalues and eigenvectors of M are computed.
Now we wish to change its diagonal elements arbitrarily to minimize the sum of absolute eigenvalues. Does there exist a way to find such modifications?
If we add a constraint : keep Tr(M)=0, would th... | The sum of the absolute value of the eigenvalues is the same (since the matrix is real and symmetric) as the sum of the singular values. This sum is called the nuclear norm of the matrix. So what you are saying is that you have an affine space of matrices (a "matrix pencil") over which you would like to minimize the ... | If it helps, here is code using Matlab and Yalmip:
<pre><code>n = 5;
%Random symmetric matrix
A = 10*rand(n,n);
A=A'*A;
%Zero on the diagonal
A(sub2ind([n n],1:n,1:n)) = 0;
X = sdpvar(n,n,'symmetric');
%Equal to A off the diagonal
C=[];
for i=1:n
for j=i+1:n
C = [C; set(X(i,j) == A(i,j))];
end
end
... | https://mathoverflow.net |
56,338 | [
"https://mathoverflow.net/questions/56338",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12965/"
] | It's hard to do a Google search on this problem.
If I was using Maple correctly, there are no other positive solutions with n at most 10000.
I know some of these Diophantine questions succumb to known methods, and others are extremely difficult to answer.
| sage: E = EllipticCurve([0,0,1,0,-1])
sage: E
Elliptic Curve defined by y^2 + y = x^3 - 1 over Rational Field
sage: E.integral_points()
[(1 : 0 : 1), (7 : 18 : 1)]
| Let $\omega$ be a third root of unity, then $\mathbb{Z}[\omega]$ is a PID.
We have $m^3 = n^2 + n + 1 = (n-\omega)(n-\omega^2)$.
$\gcd(n-\omega,n-\omega^2) = \gcd(n-\omega,\omega-\omega^2) \mid (1-\omega)$, and $(1-\omega)$ is the ramified prime lying over $3$ in $\mathbb{Z}[\omega]$, so from unique factorization of ... | https://mathoverflow.net |
75,899 | [
"https://dba.stackexchange.com/questions/75899",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1396/"
] | <pre><code>mysql> show variables like 'version';
+---------------+-------------------------+
| Variable_name | Value |
+---------------+-------------------------+
| version | 5.5.38-0ubuntu0.12.04.1 |
+---------------+-------------------------+
1 row in set (0.00 sec)
</code></pre>
The follo... | I discovered that pgAdmin III does this by default. When you create a new foreign key constraint using the GUI, there is a checkbox "Auto FK Index" on the Definition tab. I hadn't noticed this until just now so it explains why the index was being created.
| <blockquote>
What could explain why this gets created?
</blockquote>
<em>You</em> created the index. Or the <em>client software</em> you are working with did it for you. Postgres certainly didn't.
<blockquote>
Do I still need to create another index on my product column to improve performance of queries on it?
</... | https://dba.stackexchange.com |
217,978 | [
"https://electronics.stackexchange.com/questions/217978",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/100784/"
] | I've looked around for a while, and my question appears to be very specific and I was hoping that someone who knew more about audio amplifiers could help.
I'm doing some research assistance where sound sources with impedances from 20-40 Ohms are going to need to be driven at 20W. Based on some Googling I've done, this... | An ordinary audio power amplifier should be able to handle your application. For example, an amplifier rated for 100 watts into 8 ohms has to supply an output voltage of about 28 VRMS. This voltage, with a 40 ohm load, will develop 20 watts. With a 20 ohm load, it could provide 40 watts. There should be no problem u... | Shouldn't be a problem, You can drive a 40 ohm source with an an amp specified for 8 ohms... you just need to make sure you have enough voltage. V^2/R = 20 Watts.
| https://electronics.stackexchange.com |
207,416 | [
"https://softwareengineering.stackexchange.com/questions/207416",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/97843/"
] | I am in the middle of a disagreement (cordial, of course) with my lead about proper branch naming. This applies to bug-fix and small feature branches, not long-running feature branches. For long-running feature branches, we agree that human-readable names are better. Here are the two points of view:
Mine:
Naming b... | In this case it seems like you could both compromise on a naming convention that has both the number and description:
Example:
team-name/(12345)-fix-that-sql-bug
team-name/(53719)-expand-http-parser
There really is no correct answer here, it is subjective depending on your point of view.
But if you both compromis... | It really doesn't matter as long as there is a consistent system that everyone agrees and understands.
I would say though that going by ticket number would keep things easier to remember for which branch to work on. As they directly tie to the issue number rather than a description. Doing only description does seem ... | https://softwareengineering.stackexchange.com |
185,962 | [
"https://physics.stackexchange.com/questions/185962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74430/"
] | I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me.
We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that squaring it and multiplying it with a distance differential would result in a dimensionless quantity. An example of this is:
... | This is a very interesting question. I don't know if there is a general and definitive answer, but I'll try to make some comments. I apologize if this ends up rambling; I'm finding this out as I write this answer.
Operators have dimensions, since their eigenvalues are physical quantities. For bras and kets it gets mor... | This question is fun, and I'm not sure there is really a right answer, so I wanted to offer a slightly different perspective.
What are units all about? Units tell us how quantities transform under a change of scale. The reason we say a distance <span class="math-container">$d$</span> has units of length, is that the nu... | https://physics.stackexchange.com |
29,985 | [
"https://cs.stackexchange.com/questions/29985",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/21758/"
] | In the book introduction to automata theory and languages, $L^*$ is defined as
$$L^* = \bigcup_{i=0}^\infty L^i $$
The book also says that $\emptyset^* = \{ \epsilon \}$. But since $\emptyset$ is the empty set
$$L^* = L^0 \cup L^1 \cup L^2 ... $$
$$= L^0 \cup \emptyset$$ -- since $ \emptyset\emptyset = \empty... | $O$ is not only used in simple statements like $f(n)=O(g(n))$. It is also used to give error terms as in $f(n) = 14\, n\log n + O(n)$. The interpretation is still the same as @usul has described in his answer: There is a function $h \in O(n)$ so that $f(n) = 14\, n\log n + h(n)$.
Here, writing $f(n) \in 14\, n\log n ... | As Yuval comments, "misconception" isn't the right term for the notation. It's well-defined notation, which I agree is somewhat bad and unfortunate, but it's valid. It might make sense once we say that, whenever you see a $O(\cdot)$ in a statement, you are being told that <em>there exists</em> a choice from the set $O(... | https://cs.stackexchange.com |
218,543 | [
"https://security.stackexchange.com/questions/218543",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/204820/"
] | Can there theoretically be any possible malicious code hidden in .ics files, which would steal your calendar data or something similar? For an example case, we'd be importing the .ics file into Google Calendar.
| The real risk here would be the application importing the .ics file, the file in itself is harmless. Only if that application would improperly handle parts of the file content you would be at risk. With Google Calendar, I think those chances are very, very slim.
| Yes.
If the application importing the ICUS file had a vulnerability that a malicious ICS file took advantage of that could open up various possibilities for code execution. That's true for any application that reads data.
| https://security.stackexchange.com |
96,478 | [
"https://physics.stackexchange.com/questions/96478",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35515/"
] | I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to some distant observer sitting fixed relative to the black hole.
I am no expert in GR, but I know these quickly turn into ... | Indeed there is such an expression, which is dependent on the value of the Schwarzschild metric at various values of the coordinate $r$ and does not actually involve complicated integrals at all! We need to be careful in how we talk about distances here, because the radial coordinate does not, strictly speaking, corres... | Since in Schwarzschild coordinates the metric components are independent of Schwarzschild time, $\partial_t$ must also be Killing vector field, and therefore every orbit with four-velocity $u$ has conserved specific energy
$$\epsilon = -\partial_t\cdot u = \left(1-\frac{2M}{r}\right)\frac{\mathrm{d}t}{\mathrm{d}\tau}\t... | https://physics.stackexchange.com |
440,399 | [
"https://physics.stackexchange.com/questions/440399",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1643/"
] | If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.
What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?
| <blockquote>
If a person is sitting on a chair his momentum is zero...
</blockquote>
How close to zero?
The uncertainty principle says that if <span class="math-container">$\Delta x$</span> is the uncertainty in position and <span class="math-container">$\Delta p$</span> is the uncertainty in momentum, then <span c... | If we pretend that person is a quantum mechanical particle of mass <span class="math-container">$m=75$</span> kg and we localize him in a box of length <span class="math-container">$L=1$</span> m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velo... | https://physics.stackexchange.com |
139,468 | [
"https://dba.stackexchange.com/questions/139468",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/95386/"
] | In company we are working in project on very big database. It uses 100GB RAM. What's weird before first running a query PLE is 11k~, after running it drops to about 70, anyway when after 15 mins I check PLE again its about 1k~ and when I run query again it drops to 60. Why is it happening? If in time between running qu... | It is not unusual for a query to drop PLE. Queries can consume arbitrary amounts of memory. This generally happens for two reasons:
<ol>
<li>Work memory for sorting and hashing.</li>
<li>Filling the buffer pool with data that was read.</li>
</ol>
You can prove that (1) is happening by watching outstanding memory gran... | So, there really is insufficient information to answer this question. How large is the Results table? Where is the query plan?
I am assuming it is very large...so when you run this query, PLE plummets because you are bringing in a large amount of data that wasn't previously cached, and PLE is dropping to around 70. ... | https://dba.stackexchange.com |
48,704 | [
"https://electronics.stackexchange.com/questions/48704",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5874/"
] | Why does everyone use PLCs in industrial environments, instead of a microcontroller based solution?
For a longer task, the PLC program is as complicated as a microcontroller program.
A microcontroller based solution may be more customisable, and of lower price.
| I'd think a major factor is people. The engineers that can design a microcontroller to run a factory are busy making batches of small devices. Engineers that work on brand name PLCs use standard software packages, they don't have to deal with lower level programming, most problems they encounter someone else has alread... | The higher cost of PLCs is offset by the testing (often in nasty environments) they are (or should be) submitted to. Could you design a custom microcontroller system? Yes, but then you'd probably need to certify it.
Customizability is not really a major issue when you have a large plant full of equipment; in fact, yo... | https://electronics.stackexchange.com |
53,877 | [
"https://math.stackexchange.com/questions/53877",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/13791/"
] | Are there any galois fields which consist of product of two primes, as in <span class="math-container">$\mathrm{GF}(2\cdot 3) = \mathrm{GF}(6)$</span>?
| No; finite fields must have order a power of prime, and for every prime $p$ and every $n\gt 0$, there is one and only one (up to isomorphism) field of order $p^n$.
To see why the order must be the power of a prime: note that the characteristic of an integral domain must be a prime; since a field is an integral domain,... | No, because for any reasonable interpretation of the example given, 2 and 3 are zero-divisors (as is 4) and have no multiplicative inverse, so the structure is not a field.
However there are Galois extensions of fields which have degree 6 (the general cubic over the rationals is an example) - and the Galois group then... | https://math.stackexchange.com |
287,562 | [
"https://math.stackexchange.com/questions/287562",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/43741/"
] | Consider the statement,
$1.$ "If it is Tuesday, then it is raining".
In propositional logic, 1 would read as, "$p \implies q$." Now, in accordance with the rules and definitions prescribed in logic, we have a plethora of logical equivalences. We can rewrite 1 as $ \neg p \vee q$, and in English,
$2.$ "It is not Tu... | Technically speaking no they do not have to be equivalent. In your particular case it depends on the interpretation given to the "or" conjunctive in the English Language. Many people (and I am not saying it is wrong or right) interpret the statement "$A$ or $B$" as "$A$ is true, or $B$ is true, but not both at the same... | While it’s perhaps not immediately evident, the statement <em>It is not Tuesday or it is raining</em> does at least imply the statement <em>If it is Tuesday, then it is raining</em> even in everyday language: if the first statement is true, and if today really is Tuesday, then it must in fact be raining. The second pro... | https://math.stackexchange.com |
593,125 | [
"https://electronics.stackexchange.com/questions/593125",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/299090/"
] | Any LTspice Mac user knows that hotkeys are necessary to be efficient. I would like to create my own (for example, D for diode, R for resistor, V for voltage source, etc), but all the directions I find on how to set my own hotkeys are only for the Windows version. What is the procedure for customizing LTspice hotkeys o... | I contacted the LTspice team. They said that there was not currently a way to change hotkeys on the Mac version, and that even the way to change them on the Windows version was a "hack". They also said that the product is still under development and that they will try to implement it in future versions, but t... | locate the LTspiceXVII.ini file or equiv in MAC and edit them
Text_Anchor_Marks=A<br />
Place_Ground=G<br />
Place_Resistor=R<br />
Place_Capacitor=C<br />
Place_Inductor=L<br />
Place_Diode=D<br />
Draw_Lines=(none)<br />
Draw_Rectangles=(none)<br />
Draw_Circles=(none)<br />
Draw_Arcs=(none)<br />
Reset_T_0=0 )<br />... | https://electronics.stackexchange.com |
84,460 | [
"https://dba.stackexchange.com/questions/84460",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/48178/"
] | Recently stumbled across the following problem: changing metadata changes query output.
Here is how to get it.
<pre><code>CREATE TABLE [dbo].[prod]
(
[ID] [tinyint] NOT NULL,
[values] [tinyint] NOT NULL
)
GO
</code></pre>
The following query always returns ‘This is the end’ (error always raised). Also the filter sh... | <blockquote>
<em>Is this behaviour correct?</em>
</blockquote>
It is intentional (by design) behaviour; whether it is 'correct' or not is more a matter of opinion.
The general point is: <strong>SQL Server does not guarantee the timing or number of evaluations of expressions</strong>. This behaviour exists to give t... | Interesting.
It seems this is due to the addition of the unique constraint, which adds an index on ID, which in turn causes the optimizer to use an index seek rather than a table scan.
Unfortunately I have no idea why the index seek doesn't seem to throw a divide by zero error, as it shows the division in the seek ... | https://dba.stackexchange.com |
3,969,220 | [
"https://math.stackexchange.com/questions/3969220",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Show that <span class="math-container">$$B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$$</span> is an open set in the Euclidean space <span class="math-container">$(\Bbb{R^2},d_2),$</span> where <span class="math-container">$d_2(x,y)=\sqrt{(x_1-y_1)^2+(x_2-y_2)^2}$</span>.
</blockquote>
Defining <span class="m... | You can show <span class="math-container">$B^C$</span> is closed.
In fact <span class="math-container">$B^C = \{x,y\in \mathbb{R}^2,xy\leqslant 0\}$</span>.
If you take <span class="math-container">$(x_n,y_n)$</span> a sequence of elements of <span class="math-container">$B^C$</span> that converges to <span class="math... | For <span class="math-container">$(x,y) \in A$</span> notice that
<span class="math-container">$$(x,y) \in B\left((x,y),\frac12\min\{|x|,|y|\}\right) \subseteq A$$</span>
and the same thing for <span class="math-container">$E$</span>.
For example, if <span class="math-container">$(x',y') \in B\left((x,y),\frac12\min\{|... | https://math.stackexchange.com |
1,924 | [
"https://mechanics.stackexchange.com/questions/1924",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/788/"
] | Recently I changed the oil in my vehicle's rear differential. The manual recommended the use of a "Hypoid" oil, but the guy at the auto parts store suggested a "Limslip" oil instead. I went along with his recommendation since he probably knows more about vehicle maintenance than I do and because the viscosity rating ... | You should use what your manual specifically says, not the guy at the auto parts store.
Nick C's answer in most situations will probably be correct, that it is just more expensive with more stuff in it that won't apply to your diff and not hurt anything.
However, depending on your specific differential, those additio... | From what I can tell, Limslip oil is designed for vehicles with limited slip differentials, and thus has extra additives over a normal hypoid gear oil. Hypoid oils have additives to help them cope under extreme pressure, but as limited slip diffs still have hypoid gears in, I would assume limslip oil also has the same ... | https://mechanics.stackexchange.com |
175,120 | [
"https://physics.stackexchange.com/questions/175120",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60086/"
] | I'm currently sourcing Li-Po batteries and need to find an average mAh per cm3 to implement it into my product.
From what I read (wikipedia), the energy density of Li-Po ranges from 250 to 730 W.h/L
I also read that : $$Q(mAh) = E(Wh) x 1000 / V(v)$$
What I did (be careful, you might facepalm), in order to get a mAh/... | Take for example, the case when the charge Q at the centre is negative, so the force is attractive.
If it gets displaced even by a small value $\delta r$ towards either, the separation with this particular vertex would be $(\frac{l}{\sqrt 2}-\delta r)$, while it is slightly larger for the others. Due to the inverse ... | Consider the square to be in the x-y plane. Then see what happens when you displace the central charge in the z-direction.
Of course, the answer will depend upon whether Q is positive or negative and possibly also on the direction of displacement.
| https://physics.stackexchange.com |
295,257 | [
"https://electronics.stackexchange.com/questions/295257",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/28887/"
] | I have a gadget which includes a small 80mAh DC vibration motor connected to a CR2032 3V coin battery. The motor needs to keep running as long as the battery has juice, but instead of having it run at full speed and slow down gradually as the battery drains I prefer to have it running at constant speed more or less as ... | An "80mAh motor" sounds rather unusual. Are you sure that's what you meant? A datasheet for the motor would be useful, but I'll assume you want to maintain 3V across it.
For a constant speed you need a constant voltage across the motor. Therefore you want a device that can convert varying lower voltages from the cel... | battery voltage will drop when it is discharging
so you can do a little bit of a trick you should buy at least a 5-volt battery and connect it to a 3.3 regulator so if the battery voltage drops you still get your fixed 3.3 volts and you will run at maximum speed
| https://electronics.stackexchange.com |
288,231 | [
"https://softwareengineering.stackexchange.com/questions/288231",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/142752/"
] | I understand the structure of binary trees and how to traverse them. However, I am struggling to realize their actual uses, purposes in programs and programming. When I think about 'real life' examples of hierarchical data they almost certainly have more than 2 children. For example, in a family tree, a mother may ofte... | No, binary trees are not for storing hierarchical data in the sense you're thinking of. The primary use case for n-ary trees, where <code>n</code> is a fixed number, is <em>fast search capability</em>, not a semantic hierarchy.
Remember the old game where one person thinks of a number between 1 and 100, and the other... | Any tree structure, where a node can have unlimited numbers of children, can be implemented using a binary tree.
For each node in your tree, replace it with a node with a right and left pointer. The left pointer goes to the first of the node's children. The right node goes to the next sibling of the node. All the chil... | https://softwareengineering.stackexchange.com |
452,931 | [
"https://physics.stackexchange.com/questions/452931",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140647/"
] | A space-craft, also of rest-mass <span class="math-container">$M_0$</span> and initially at rest, is propelled by
reflecting a plane-parallel beam of photons, generated at a rate <span class="math-container">$αM_0$</span> from a stationary
source mounted on the launch pad, off a perfectly reflecting mirror mounted on t... | Answer 1 is right; answer 2 has the wrong rate of arrival of photons. Suppose the source emits some photons in a pulse which is <span class="math-container">$N$</span> wavelengths long. The time taken to emit them must be the time taken for light to travel the distance <span class="math-container">$N \lambda$</span>, w... | In the rest frame of the photon source the force is 2E/c.
| https://physics.stackexchange.com |
130,536 | [
"https://electronics.stackexchange.com/questions/130536",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/23924/"
] | Is it possible to manufacture semiconductors in a way that places logic (for example, a CPU core) on the same die with non-volatile flash (or other EEPROM memory) circuits? What about DRAM?
It certainly seems to be possible to have on-CPU-die SRAM (in the form of various caches); is there a technical reason that DRAM ... | There are two fundamental laws of electricity that you must always keep in mind - Kirchoff's Current Law, and Kirchoff's Voltage Law.
I consider Kirchoff's Laws as scientific wording of what should be common-sense observations - unfortunately, common sense isn't as common as we might like, so we have to spell these th... | You can't specify the current AND the voltage. Either you are applying 5V or you are applying 1A. Since you have a batery symbol drawn, I will assume you are applying 5 volts.
This 5v is applied across two 1 ohm resistors in series. Total resistance of two 1 ohm resistors in series is 1 + 1 = 2 ohms. V = I * R t... | https://electronics.stackexchange.com |
17,324 | [
"https://datascience.stackexchange.com/questions/17324",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/27279/"
] | I had an interesting discussion come up based on a project we were working on: why use a CNN visual inspection system over a template matching algorithm?
Background: I had shown a demo of a simple CNN vision system (webcam + laptop) that detected if a particular type of object was "broken"/defective or not - in this c... | The engineer in question that proposed traditional CV methods for your application simply did so out of habit. Using template matching is extremely outdated and has been shown to perform very poorly. However, I do think a CNN is overkill depending on your dataset's size.
How does template matching work?
<strong>Tem... | The answer depends on the task. Template matching can work for some tasks but not for all. CNNs potentially have the ability to generalize to unseen inputs that don't match any of your templates, so can potentially generalize better.
But whether CNNs will beat template matching will depend on the specific task and w... | https://datascience.stackexchange.com |
144,496 | [
"https://dba.stackexchange.com/questions/144496",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/100619/"
] | I have a field defined as <code>Question VARCHAR(1024) CHARACTER SET utf8 NOT NULL</code>. Our application stored double-encoded data into this field. For example, <code>é</code> shows up as <code>é</code> in phpMyAdmin, and <code>C383C2A9</code> when passed to <code>HEX</code>.
I've added a second field (<code>Doubl... | <pre><code>CONVERT(CONVERT(CONVERT(`Question` USING latin1) USING binary) USING utf8)
</code></pre>
| The data appears to be correctly encoded in UTF-8. phpMyAdmin is rendering the UTF-8 string using latin1 configuration.
Fix your phpMyAdmin and/or web server configuration, not your data. You may have set the default configuration of your webserver to ISO-8859-1 instead of UTF-8, or phpMyAdmin may be setting this... | https://dba.stackexchange.com |
111,644 | [
"https://physics.stackexchange.com/questions/111644",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46037/"
] | If you turn on a fan in a warm room, it feels as if cold air is being pushed from the fan out in the direction that it's facing, but what's actually happening on a molecular level?
When an object is heated, its molecules are excited and they can in turn excite other molecules around them thereby passing on heat throug... | As mentioned in the comments, air from a fan feels colder because of two reasons. Firstly, the air is cooler than your body so as it passes, your body heat transfers in part to the air, which is then carried away. Second, as the air passes, it evaporates moisture on your skin, which takes absorbs heat in the process.
... | The temperature of the air didn't change. What you are experiencing is an increase in rate of evaporation from your skin - and this evaporation is what makes you feel cooler.
Why does the rate of evaporation increase? Well - evaporation is a balance between water molecules going from liquid to vapor, and from vapor to... | https://physics.stackexchange.com |
603,386 | [
"https://math.stackexchange.com/questions/603386",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/115210/"
] | Recall that a curve of the form $Ax^2+Cy^2+Dx+Ey+F=0$ is a parabola, ellipse, hyperbola, line, or 2 lines. Show that given any 4 points in the plane, there is such a curve that contains them.
| Well, Take the four points $(x_1,y_1)$, ..., $(x_4, y_4)$.
If you replaces this points in main equation you have $A x_k^2+B y_k^2+D x_k +E y_k +F = 0$, for $k=1,2,3$ and $4$.
In this case you have four linear equations for five variables $(A,B,C,D,E,F)$, you can solve this equations with linear algebra,...
| The way I see it, the poser of the question posits four points and the template of a quadratic expression in x and y which has no xy term and which is to be equated to 0. The absence of the xy term means that the axes of the locus are not to be oblique to the coördinate axes, and further that the locus can indeed be un... | https://math.stackexchange.com |
90,169 | [
"https://dba.stackexchange.com/questions/90169",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24265/"
] | I'm trying to copy data from a SQL Server 2014 Express database to a SQL Server 2008R2 Express database.
Compatibility level for the 2008R2 Express database is set to 100.
As soon as I hit Next in the Select Source Tables and Views window, I get the following error:
<blockquote>
[dbo].[Client] -> [dbo].[Client]: T... | I can't point to anything authoritative, but if you think through the details of such an implementation, the potential down sides are evident.
Having a "shared" <em>subsidiary</em> table is problematic primarily because if two "parent" tables (say, <code>Customer</code> and <code>Employee</code>) both utilize the same... | The motivation for piling every kind of address into a single table is usually a misinterpretation and misapplication of the notion of code reuse.
People can make the mistake of assuming that because you have two entities with some common set of attributes, that those attributes belong in their own table. Sometimes... | https://dba.stackexchange.com |
216,022 | [
"https://electronics.stackexchange.com/questions/216022",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37643/"
] | I am trying to understand the physical phenomenon that leads to increase in gain of an amplifier as the output impedance increases.
When we have resistive loads in a single stage amplifier, they convert the signal current change into voltage variation. Higher the value of load, more will be the conversion and hence
th... | Most of us think of a coupon as a small tear out thing in a magazine or sales mailer that is used to save money when you buy something. In the PC board world these were generally added to the periphery of a PCB layout (or at the periphery of a matrix of boards when a batch are step and repeated on a panel). The design ... | Their placement next to the CPU would likely signify it's a jumper for a selectable option. They would have a standard 0.1" jumper or dip switch. If you had mentioned the board manufacturer or part number, or the intended CPU type, we could confirm.
| https://electronics.stackexchange.com |
8,690 | [
"https://stats.stackexchange.com/questions/8690",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/795/"
] | Suppose I wanted to fit a model of the form
$$y_i = \beta_0 + \sum_{1 \le j \le k} \beta_j X_{i,j} + \gamma_i Z_i + \epsilon_i,$$
to some data, where the regressors $X$ and $Z$, and the regressand $y$ are observed, and where $\gamma_i$ is a Bernoulli random variable that equals one with (unknown) probability $p$ and is... | I will try to answer the questions 2 to 4. Suppose that we observe sample $(y_i,\mathbf{x}_i,z_i,\gamma_i,\varepsilon_i)$. Suppose that our model is
$$y_i=\mathbf{x}_i\beta+\gamma_iz_i+\varepsilon_i$$
and
$$E(\varepsilon_i|\mathbf{x}_i,z_i,\gamma_i)=0.$$
The least squares estimate of the regression will be
\begi... | Maybe I'm missing something here, but couldn't you rearrange the equation and do a logit or probit analysis on gamma?
| https://stats.stackexchange.com |
10,782 | [
"https://math.stackexchange.com/questions/10782",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/3647/"
] | Here is how I have worked it out so far:
$\log _2(x-4)+\log(x+2)=4$
$\log _2((x-4)(x+2)) = 4$
$(x-4)(x+2)=2^4$
$(x-4)(x+2)=16$
How do I proceed from here?
$x^2+2x-8 = 16$
$x^2+2x = 24$
$x(x+2) = 24$ Which I know is not the right answer
$x^2+2x-24 = 0$ Can't factor this
| It is $x^2-2x-8 = 16$ my friend. So you get $x^2 - 2x -24 = 0$, which factors as $(x-6)(x+4) = 0$. Hence, $x=6$ or $x = -4$.
| After $(x-4)(x+2)=16$, you get $x^2-2x-24=0$ (the coefficient of $x$ is $-2$ not $2$). So $x=\frac{2\pm \sqrt{100}}{2}$ by the quadratic formula. So $x=6$ or $x=-4$
| https://math.stackexchange.com |
454,472 | [
"https://physics.stackexchange.com/questions/454472",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/219937/"
] | Let's just say we're looking at the classical continuous canonical ensemble of a harmonic oscillator, where:
<span class="math-container">$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$</span>
and the partition function (omitting the integrals over phase space here) is defined as
<span class="math-container">$... | In the formulation of the question there are a couple of mistakes, or simply there is no definition of <span class="math-container">$R$</span>. Statistical Mechanics says that for a classical system each independent <strong>quadratic</strong> coordinate of the phase space contributes to the energy with a factor <span c... | The equipartion theorem states you get kb*T/2 for each quadratic degree of freedom, not just each dimension. It is very specific and comes from doing the quadratic integrals explicitly, as these are Gaussian their result is well known. So, to answer your question, if w(T) was included then the integral technique woul... | https://physics.stackexchange.com |
524,246 | [
"https://physics.stackexchange.com/questions/524246",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98822/"
] | Imagine a balloon (again) that finds itself on the bottom of a mass deep water. The balloon is filled with air. The deep mass of water finds itself on a heavy (w.r.t. Earth) planet.
Initial, the balloon stays put (on the bottom)
After it's not stayed put anymore (it's let loose), what will happen and why?
It's clear... | Due to the immense pressure, the balloon will shrink in size. Once let loose, the balloon will start accelerating by quite a bit (somewhat both 2 and 3) and will eventually attain terminal velocity at a point. Then onwards, the balloon will rise at the same pace.
| At room temperature and 1 atmosphere pressure air weighs 1.3 g/l. The pressure will increase the density by a factor of 1099, making it denser than water. Obviously the ideal gas law no longer applies and also the air can no longer be gaseous but actually is solid. Solid air is heavier than water at 1 atmosphere but th... | https://physics.stackexchange.com |
240,296 | [
"https://physics.stackexchange.com/questions/240296",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44132/"
] | Suppose you had two balloons, one inside the other (a inside b).
Would filling balloon "a" with the 80% nitrogen/20% oxygen mix you find in the surrounding air at ground level, and then filling balloon "b" with 100% helium provide you with any benefit? In other words would you be able to use less helium to provide a... | No. The buoyant force on the balloon is a function of the difference in density inside and outside the balloon. If the density inside the balloon is higher, it sinks; if it's lower, it rises. Putting a plain-air balloon inside a helium balloon increases the overall density compared to a pure helium balloon of the same ... | It's a matter of volume and weight.
Suppose the (outer) volume of the balloon is 1 cubic meter.
The air inside that volume has a certain weight, roughly 1 kg.
The upward force of the balloon is just the difference between the weight of what's in it, and the weight of the same volume of air.
The reason helium balloons ... | https://physics.stackexchange.com |
11,576 | [
"https://mechanics.stackexchange.com/questions/11576",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/6582/"
] | I have my eyes on my childhood dream, Yamaha TZR 125.
But, as it turns out, this motorcycle doesn't have any type of fuel meter.
<img src="https://i.stack.imgur.com/KR1cr.jpg" alt="http://upload.wikimedia.org/wikipedia/commons/c/c2/Yamaha_TZR_125_1991_cockpit.jpg">
And, I'm pretty sure, it doesn't have any sensor... | I would not do that. To do the real one is a lot of work to do. Open the tank, find the swimmer, do and seal a hole, find modules to regulate the swimmer and then the right fuel meter. It's also pretty danger. Maybe you will find an other tank with a fuel meter in it and right module for it.
| I'm pretty sure what is used is just mileage calculation to figure out how many miles are left in a tank of gas. Other than that, you pop the cap off, look down the hole and see how much fuel is in the tank. Once you have been riding the bike for a while, you'll know just how far a tank of gas will carry you and also b... | https://mechanics.stackexchange.com |
251,872 | [
"https://mathoverflow.net/questions/251872",
"https://mathoverflow.net",
"https://mathoverflow.net/users/99516/"
] | Does the equation
$$(a^{2}-b^{2})^{4}(a^{2} + b^{2}) = 4a^{2}b^{2} $$
Have any nonzero solutions, where $a^2$ and $b^2$ are both rational ?
If yes, i suspect there should be infinitely many of them, can they be parametrized ?
| It seems that my previous answer was completely wrong, and that the fact is <b>true</b> for all nonzero integer (not necessarily prime) $p$.
Let $M=[m_{ij}]_{i\leq n,\;j\leq m}$. If there is no $x$ satisfying the requirements (we regard all entries as integers, not residues!), then one of the sums of the form $\sum_{i... | This is a proof of @LucGuyot 's statement:
For $p=2$, the assumption is linear independence of $m$ columns. Thus, $M$ has column rank $m$. Also, it has row rank $m$. In particular $n\geq m$, otherwise $\mathrm{rank}M=m$ is impossible. For any nonzero $w\in\mathbb{F}_2^m$, there is $x\in\mathbb{F}_2^n$ such that $x M =... | https://mathoverflow.net |
256,341 | [
"https://security.stackexchange.com/questions/256341",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/180331/"
] | I have been conducting some minor research into the various forms of exploitation, such as buffer overflows and similar.
Most tutorials seem to focus on executing shellcode, that is code which executes a shell. I was wondering if the cause of this is because of limited space available, otherwise why not execute an enti... | It is usually a trade-off between user experience and security. How the trade-off is made depends on the actual threats. While mail can be seen as inherently insecure, it does not mean that every mail gets intercepted for sure. If the impact of a potential interception is low then it might be acceptable to prefer easy ... | I will first describe what I have understood from your question:
<ul>
<li>For meetings you are sending username password pairs to the participants - they are used to retrieve documents</li>
<li>the username and the password are sent in different emails</li>
<li>all the participants at a meeting share the same username ... | https://security.stackexchange.com |
24,585 | [
"https://mathoverflow.net/questions/24585",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2264/"
] | There seems to be a few papers around with Erdős written as Erdös. For example:
MR0987571 (90h:11090) Alladi, K.; Erdös, P.; Vaaler, J. D. Multiplicative functions and small divisors. II. J. Number Theory 31 (1989), no. 2, 183--190. (Reviewer: Friedrich Roesler) 11N37
<blockquote>
Would it be incorrect to cite suc... | We cite papers to show our respect to the authors and to help our readers find stuff. For the second purpose, I suspect most people would just type in names without diacritical marks, and most search facilities would find what you're looking for based on the letters alone, so it doesn't really matter. But for the first... | <img src="https://gilkalai.files.wordpress.com/2010/05/erdos-comp.jpg" alt="alt text">
A proposed compromise
| https://mathoverflow.net |
313,807 | [
"https://math.stackexchange.com/questions/313807",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/45682/"
] | The title says it all. I'm currently taking an introductory course in linear algebra and this issue has not been adressed spesifically. What I'm wondering is this: Given a transformation matrix $A$ and vector $\vec{x}$ such that $A\vec{x}$ is some transformation of $\vec{x}$ (rotation, scaling, etc), is it true that if... | It depends on what you mean by $Ax$. Row operations are changes of coordinates, so what is true is that if $A$ and $B$ are related by row operations, then they represent the same operation in different coordinates. However, for some fixed column vector $x$, we will have $Ax\ne Bx$ in general; see the example already gi... | This in no true. For example, take $A$ to be a $2\times 2$ identity matrix $I$. Now let $B=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ (it is $A$ after interchanging the rows). Then clearly $Ax \neq Bx$ (for $x\neq 0$).
| https://math.stackexchange.com |
497,907 | [
"https://electronics.stackexchange.com/questions/497907",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/217749/"
] | If I connect the receiver and TV body to the earth, does it reduce or increase the chance of lightning strikes the dish antenna?
| The purpose of bonding metal objects to earth is primarily to reduce the chance of a lightning strike. This works by allowing charges from the earth to migrate up a metal conductor (grounding cable, antenna mast, or the classic pointed lightning rod), leak off into the atmosphere, and so help to dissipate the charge b... | <blockquote>
<em>If I connect the receiver and TV body to the earth, does it reduce or
increase the chance of lightning strikes the dish antenna ?</em>
</blockquote>
Lightning will not see a length of cable connected to earth as a preferred path until it actually hits the installation. Think about a lightning cond... | https://electronics.stackexchange.com |
59,886 | [
"https://cs.stackexchange.com/questions/59886",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/53899/"
] | I have read that intersection of regular language and context-free language is always context-free. Most of the places an standard example has been used to prove this, e.g.,
\begin{align*}
L_1 &= L(a^*b^*)\\
L_2 &= \{a^nb^n\mid n\geq 0\} \quad\text{(which is context free)}\\
L_1\cap L_2 &= \{a^nb^n\mid n\g... | The claim is that the intersection of a regular language and a context-free language is context-free. You've intersected a regular language (<span class="math-container">$\{ab\}$</span>) and a context-free language (<span class="math-container">$\{a^nb^n\mid n\geq 0\}$</span>) and the result was a context-free language... | Your mistake is in interpreting the meaning of the statement
<blockquote>
The intersection of a regular language and a context-free language is a context-free language.
</blockquote>
This statement means that if $R$ is regular and $L$ is context-free then $R \cap L$ is context-free. It <em>doesn't</em> state that $... | https://cs.stackexchange.com |
1,259,339 | [
"https://math.stackexchange.com/questions/1259339",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/235761/"
] | Consider the set $X={300,301,302,...,29999,30000}$ (the set of all integers from $300$ to $30,000$ inclusive.) You do not need to simplify the numeric answers.
How many elements in $X$ are of the form $3k + 1$ for some integer $k$?
One friend says the answer is $7425$ and another said $9900$, but I'm not sure how eit... | Since
$$\frac{30000}{3} = 10000$$
the largest number of the form $3k + 1$ that is in the set $X$ is $29998 = 3 \cdot 9999 + 1$. Since
$$\frac{300}{3} = 100$$
the largest number of the form $3k + 1$ that is not in the set $X$ is $298 = 3 \cdot 99 + 1$. Thus, there are $9999 - 99 = 9900$ numbers in the set $X$ that a... | So we have the set $\{300, 301, 302, \cdots, 29998, 29999, 30000\}$. NOte that the minimum and maximum values that are multiple of 3 are 300 and 30000 respectively.
The previous multiple of 3 from 30000 is 29997.
Since any integer of the form $3n+1$ is just immediately next integer to $3n$ so we have to find out how... | https://math.stackexchange.com |
584,549 | [
"https://physics.stackexchange.com/questions/584549",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/205969/"
] | Bremermann's limit, as maximum possible computation power or CPU total computing frequency, is known to be on the order <span class="math-container">$10^{50}~\text{Hz}/\text{kg}$</span>.
Why max computation frequency for unit mass can exceed Plank frequency, which is on the order of <span class="math-container">$10^{43... | It's bits per second. It's not a frequency. It could be 1 bit being processed <span class="math-container">$10^{50}$</span> times per second, which would be faster than the Planck frequency, but it could also be <span class="math-container">$10^{50}$</span> bits being processed once per second each, which wouldn't.
You... | Maybe I have not expressed my question in a good way. The core thing which I was interested in was,- Can a Bremermann's limit be calculated using only Plank units or at least approximated by it ?
Thanks to @user253751, I can now understand that. Usually maximum possible bit-rate is achieved by equating quanta energy to... | https://physics.stackexchange.com |
322,220 | [
"https://softwareengineering.stackexchange.com/questions/322220",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/210985/"
] | My current scrum master is a true believer who is not willing to budge on the official forms of scrum. I don't want this to sound ranty, I am really asking about the orthodox solution to this issue because I have been successful resolving issues with him in the past by recasting things in official terms.
The current ... | <blockquote>
So, how officially are issues of dependencies between stories and inherently serial stories handled by the methodology?
</blockquote>
As with anything else in Agile: <code>Individuals and interactions over processes and tools</code>
If your process isn't serving you, then you mold it into something use... | One of the features of kanban, which I believe bleeds over into scrum, is that the process as a whole optimizes for the <em>team</em>, not the individual. In other words, it's no sin if someone on the team is idle for part of the sprint.
If the team as a whole chooses X story points, it really doesn't matter (to the ... | https://softwareengineering.stackexchange.com |
229,405 | [
"https://security.stackexchange.com/questions/229405",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/198191/"
] | I want to know that what the security impact is if someone leaks the password of a PKCS12 certificate. I am referring to the password which is required when we export the certificate.
| The password is needed to decrypt the private key stored in the file. Without the file, the password has no value (unless the password is also used for something else, but that should never be done).
If someone has the encrypted file without the password, they can attack the password offline using software like hashca... | The password unlocks the encrypted private key of the certificate, so an attacker always needs both, the PKCS-file and a password to successfully use the certificate.
Please mind, that most humans tend to use the same password for more than one purpose, so there are chances that a other person can make his way to the... | https://security.stackexchange.com |
17,065 | [
"https://electronics.stackexchange.com/questions/17065",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2737/"
] | I'm trying to generate a combination of 2 waves with different frequencies. For example 1Khz and 5Khz - so I could recognize it on my PC using FFT.
It seems that feat is not possible using arduino.
Any one succeeded? is it possible with any other way? physically possible?
Thanks!
| If 5kHz is the highest frequency you need, then according to <strong>Nyquist</strong> (some say Shannon) you need at least a 10kHz <strong>sample frequency</strong>. That's a sample periode of 100\$\mu\$s, which should be doable for any modern microcontroller. You'll have to make <strong>lookup tables</strong> for your... | If you just want to test fft just use a square wave the frequency an amplitude of the components are well know, and the waves are easy to generate.
| https://electronics.stackexchange.com |
264,772 | [
"https://mathoverflow.net/questions/264772",
"https://mathoverflow.net",
"https://mathoverflow.net/users/84068/"
] | Let $G=(V,E)$ be a connected graph. Here $V$ is the set of all vertices of $G$, and $E$ is the set of all edges of $G$. Suppose that $G$ is locally finite, i.e., $\sharp\{y\sim x:y \in V \}$ is finite for any $x\in V$. We denote by $m(x)=\sharp\{y\sim x:y \in V \}$. We denote by $d(\cdot,\cdot):V\times V\to [0,\infty)$... | Yes. More precisely for every $x \in V$, $m(x) \leq (C-1)^2$.
This follows from the volume doubling inequality for $r=1$, which says that for all $x \in V$, $m(x) + \sum_{y \sim x} m(y) \leq C m(x)$, or equivalently $\frac{1}{m(x)} \sum_{y \sim x} m(y) \leq C-1$. In particular, there is $y \sim x$ such that $m(y) \leq... | EDIT: as noted by Mikael de la Salle, my answer below is incorrect according to the definitions in the question. Notice, however, that this relies specifically on the case $r=1$. If we restrict our attention to $r>1$, or consider closed instead of open balls, then my answer is valid. I am leaving it here for this re... | https://mathoverflow.net |
188,689 | [
"https://dba.stackexchange.com/questions/188689",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136800/"
] | I have a small scenario here and I think using composite primary keys would be a good solution. I'm doing this in SSMS. Here is the code to create the table:
<pre><code>CREATE TABLE [PSDesk].[dbo].[Local](
[UserID] [varchar](10) NOT NULL,
[FullName] [varchar](50) NOT NULL,
[ComputerName] [varchar](15) NOT ... | Is that syntax correct? Yes. You could also create the PK afterward and with a few different syntax options, but this will build.
But there are a lot of answers to this question. And a lot of questions in this question. "Is this a good idea?" Well it depends – and that is sort of opinion and situation based so the qu... | This is not 3rd normal form.
If two or more users share a computer then you would have duplicate entries for the computer. If there is no sharing then you can just use the computername alone.
Should have separate tables for user and computer. Then a 3rd junction table.
| https://dba.stackexchange.com |
9,269 | [
"https://stats.stackexchange.com/questions/9269",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | I can't seem to do a comparison with a sum of numbers and get the right answer (lines alternate between my input and R output):
<blockquote>
(.6 + .3 + .1) == 1
[1] FALSE
(.6 + .3 + .1)
[1] 1
1
[1] 1
</blockquote>
I've tried with and without parenthesis, tried comparing to 1.0, tried using as.numeric, but can't get it ... | You may need to clarify what you mean by
<blockquote>
"accounting for the fact that I have taken repeated measures..."
</blockquote>
You say that
<blockquote>
"I would like to know if the mean chocolate consumption per day is higher among happy
people than those who are not happy..."
</blockquote>
This sugg... | You may think about happiness as the dependent variable, and you could use logistic regression with chocolate consumption as a predictor. Some people may be generally happier or less happy independently from chocolate consumption. This can be modelled by including subject id as a random effect categorical predictor. Ag... | https://stats.stackexchange.com |
21,097 | [
"https://dba.stackexchange.com/questions/21097",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10228/"
] | I've gone over many DBaaS solutions, including Xeround (limited to 50G, in memory), NuoDB (currently in beta 7), DrawnToScale (not out yet), MongoDB (in memory), RavenDB (for ASP.NET, but NoSQL) and many others, DynamoDB (costly for real-time web app and doesn't offer backup/restore).
I find everyone lacking in some w... | Barry Morris here from NuoDB. Answers below:
<blockquote>
1) DBaaS (can be self hosted too) the can easily scale to terabytes of
data (ie. big data)
</blockquote>
<ul>
<li>NuoDB is a downloadable product that runs anywhere (laptop, rack, public cloud). We have not announced DBAAS at this point. NuoDB uses Key/... | The only backends that I am aware of that can scale to <em>hundreds</em> of TB are Hadoop and Bigtable. There are absolutely no backends that support hundreds of TB that supports easy backup and restore. That's nearly an impossibility with that quantity of data.
For "a few" TB, you can use PostgreSQL, MySQL, SQL Ser... | https://dba.stackexchange.com |
165,768 | [
"https://security.stackexchange.com/questions/165768",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/141144/"
] | I took a look at google and here and I coudn't find the answer to this question:
Let's say that I have a Webservice and an Android app. They communicate over HTTPS. Should I encrypt traffic or I can assume that the communications are relatively secure?
I'm not considering cert pinning here. In this case, cert pinnin... | If the systems are running Windows 10, it's that feature that allows you to download updates from your peers.
Port 7680 is the listener for the peer service that Windows 10 uses to transmit the update files. If the other employee has their host name set to their last name, that's what will appear on the connection. Wi... | This will show the PID the Process is associated to:
<pre><code>netstat -a -o
</code></pre>
This will show the .exe responsible for creating the socket:
<pre><code>netstat -a -b
</code></pre>
| https://security.stackexchange.com |
1,964 | [
"https://quant.stackexchange.com/questions/1964",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1404/"
] | Are there any "standard" VaR calculations run in a batch?
For example, testing a VaR calculation with a lag of 1,2, 5 or 10 days over 2 years?
Same question for the percentile, 1%, 2.5%, 5% etc.
| Standard (read: regulators will accept it) could be a one day, 99% VaR calculated with two years of historical data. A minimum of one year of history is needed although this is not the norm. Typically the one-day VaR is transformed into a 10-day VaR by scaling the calculation by sqrt(10). However, the new market ris... | Usually when it is for (market) risk management purposes it is quite standard to have 1 day horizon with (allegedly ;-) ) 99% confidence level.
As far as I know when it is for regulatory or economic capital requirement and/or Asset Liability Management then horizons might be much longer up to one year and confidence l... | https://quant.stackexchange.com |
484,330 | [
"https://electronics.stackexchange.com/questions/484330",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/240182/"
] | For example, an MCU (stm32, esp32, Pic18f .. etc) with CAN embedded, sends logic level signals through pins Tx and Rx.
They only need a signal converter. (example: MCP2551).
My question: Why can't any MCU with tx and rx pins use just one signal converter? Why does this also need an adapter? (Example MCP2515).
| The CAN protocol requires a specific collision detection mechanism that is difficult to implement in software, because all stations that have outgoing data start sending at the same time and then one after the other drop out as they determine that a station with a higher priority is also sending.
Having a CAN controll... | You can avoid a lot of confusion if you get your terminology right.
To access CAN bus the MCU needs two things: CAN Controller and CAN Transceiver.
Controller has Tx and Rx pins. Transceiver converts these pins into CANL and CANH bus signals.
When you say "MCU with CAN embedded" what you really mean is that CAN <stro... | https://electronics.stackexchange.com |
97,253 | [
"https://dba.stackexchange.com/questions/97253",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6383/"
] | I have my "customer" data in a normalized sql server database.
Getting out the customer data in my app is taking too long. This is because I have to go to 10+ tables to get all the data I need.
My company has an installation of SOLR that I thought about storing a Json object that contains all the data I need for a s... | Many NoSQL products have sharding built-in. The DBMS itself looks after storing a particular key range on a certain server and keeping redundant copies for high availability. Client connections are routed within the DBMS rather than in the application. Multi-server scale out becomes easy, at the cost of CAP compromi... | As an alternative, if you have Solr already set up, you can have it index your document and return it to you in multiple formats (JSON, XML, even Python dictionaries).
Solr offers a way to search through your information really fast as well as allowing you to do faceted queries as well.
While creating your own den... | https://dba.stackexchange.com |
136,114 | [
"https://security.stackexchange.com/questions/136114",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/92437/"
] | I have the requirement of configuring all of our applications to use only PFS ciphersuites where possible.
I have an application (HP Network Automation), which supports DHE key exchange (although not ECDHE), but when I limit it down to only the following two suites:
TLS_DHE_RSA_WITH_AES_128_CBC_SHA256,
TLS_DHE_RSA_WI... | I can confirm that I have tested hardened web servers for compliance and had no issues with IE or FF negotiating these ciphers. The only hiccup is that default configuration of FF, unlike other browsers, is configured to accept AES128-based suites over AES256-based suites if both enabled.
| If you look at the supported ciphers of IE11 and Firefox 47 on Qualys, they actually don't support these two ciphers, which was a surprise to me.
I got round it by enabling TLS_DHE_RSA_WITH_AES_128_CBC_SHA (no SHA256) for Firefox, and TLS_DHE_RSA_WITH_AES_128_GCM_SHA256 for IE11
| https://security.stackexchange.com |
27,221 | [
"https://dsp.stackexchange.com/questions/27221",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/14863/"
] | I'm doing some MIR related work with stereo audio and am a little unsure on how to proceed with some basic tasks. All my academic work prior to this has involved forcing audio to "mono" to perform analysis, and I'm trying to avoid that as much as possible here.
So, for example, I have a crest factor function in pytho... | Conceptually you can think of it as creating one mono signal by concatenating the left and the right channel signals, and then computing the RMS and the Crest factor of that mono signal. With $N$ the number of samples in the current frame, and $x_l[n]$ and $x_r[n]$ the left and right channel signals, respectively, you ... | This answer averages the two RMS values for each channel. But when a stereo signal is played over two loudspeakers the overall acoustic RMS value will increase (by something like +3dB) - not average. Thus I think the 1/2 multiplier term in xrms equation should not be applied.
Then what to do with the peak for a ster... | https://dsp.stackexchange.com |
1,775,383 | [
"https://math.stackexchange.com/questions/1775383",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/337221/"
] | So I was given the following problem :
ABC is a right angled triangle with the sides $a,b,c$ . Find the area of this triangle, given that $$a+b+c = 22$$ $$a^2+b^2+c^2 = 200$$
I've tried to do a lot of things withose two, and using the pythagore theorem I got :
$$a + b = 12$$
$$a^2 + b^2 = 100$$
Sure, I can turn i... | As noted, we have $$a+b=12$$$$a^2+b^2=100$$
As you mentioned, this can be turned into a polynomial. However, notice that $$(a+b)^2-a^2-b^2=2ab=44$$Thus $$ab=22$$ and by taking the half of this we can find the desired area. Sure, there are two solutions. Namely that $$a=6-\sqrt{14}, b=6+\sqrt{14}$$ or $$a=6+\sqrt{14}, b... | If you assume that the sides have been labelled so that $a^2 + b^2 = c^2$, then $2c^2 = 200$ becomes $c = 10$ and $a + b = 12$
So $144 = (a+b)^2 = a^2 + b^2 + 2ab = 100 + 2ab$. So $ab = 22$
the area of the triangle is $\dfrac 12 ab = 11$.
| https://math.stackexchange.com |
44,188 | [
"https://dba.stackexchange.com/questions/44188",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24784/"
] | I've a multi-tenant DB setup, and need to add some columns. I'm using schemas (and search_path) to partition my users, so I'm looking for a ubiquitous way to apply a DDL-schema change to all my databases. Initially, I'd thought I might be able to do it as a single query (cursor on pg_catalog), but thinking a command-... | I would prefer the latter solution. You can collect the schema names into a file (one schema per line) in <code>psql</code>:
<pre><code>\o change_schema.sql
\t on
SELECT n.nspname
FROM pg_catalog.pg_namespace n
WHERE n.nspname !~ '^pg_' AND n.nspname <> 'information_schema';
-- reset the output
\o
\t off
</co... | Just for completeness, another approach is to loop over all schemas and run the change with dynamic SQL in PL/PgSQL, eg:
<pre><code>DO
$$
DECLARE
schemaname name;
BEGIN
FOR schemaname IN SELECT nspname FROM pg_namespace WHERE nspname NOT LIKE 'pg_%' AND nspname <> 'information_schema' LOOP
EXECUTE ... | https://dba.stackexchange.com |
109,171 | [
"https://security.stackexchange.com/questions/109171",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/92643/"
] | My parents have a vacation home out in the country and are looking to setup a home surveillance system for remote viewing. I've heard that there can be serious vulnerabilities in these products. What are some guidelines I could use to help evaluate these products?
I have a software development background, so I'm comf... | Like most embedded hardware (routers, etc), their firmware often sucks, and unless you have unlimited time I'm afraid there is no way to thoroughly check every single camera out there. And even if you do find one that's <em>currently</em> secure, what guarantees that you'll get updates for vulnerabilities that will be ... | This started off as a comment on Andre's answer, but it got a bit long.
USB is fine as long as none of the cameras are more than 16 foot from the host :)
Since you need to run power out to the cameras anyway, just run a wired ethernet connection to the LAN (or use POE if you can find cameras which support it). On an ... | https://security.stackexchange.com |
781,781 | [
"https://math.stackexchange.com/questions/781781",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/5418/"
] | I found on the net the following excerpt
<img src="https://i.stack.imgur.com/IvgyY.png" alt="enter image description here">
Could someone help me giving the title, author(s) of this book?
| First ignore the restriction concerning the first office. The number of ways to distribute the $15$ identical computers is $C(17,2)$.
Now any distribution in which the first office gets $5$ computers or more should not have been included. To count these distributions, put $5$ computers into the first office, then de... | Number of ways will be coefficient of $x^{15}$ in
$$f(x)=(1+x+x^2+x^3+x^4)(1+x+x^2+\cdots+x^{15})^2=(1-x^5)(1-x^{16})^2(1-x)^{-3}=(1-x^5-2x^{16}+2x^{21}
+x^{32}-x^{37})(1+\binom{3}{1}x+\binom{4}{2}x^2+\cdots)$$
Thus number of ways is $\binom{17}{2}-\binom{12}{2}=70$
| https://math.stackexchange.com |
322,495 | [
"https://electronics.stackexchange.com/questions/322495",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/137286/"
] | I need to create a high pass filter to attenuate frequencies below 50KHz, I intend to use an RC circuit with an operational amplifier.
My question is: How do I set my cutoff frequency? I know that if I set a cutoff frequency of exactly 50K Hz I will get losses in my signal, how do I find the ideal cutoff frequency? Do... | I don't see any obviously bad solder joints on those pictures. However, these pictures aren't great for inspecting the solder joints. To get pictures of small things, you need to use a macro lens, good lighting, and proper exposure.
The main thing to look for is that the solder flowed. That is best seen in the top ... | If you use leaded tin then <em>none</em> of them should look matte. (ROHS tin is another story, such joints tend to look rather bleak even when properly soldered.) This wouldn't pass a professional examination, but might work (for a while) for indoors hobbyist purposes.
Overall looks like you use far too much tin and ... | https://electronics.stackexchange.com |
34,875 | [
"https://electronics.stackexchange.com/questions/34875",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7661/"
] | I am looking to make something that takes a pulse of floating voltage (say from a feedback coil of on a transformer), and maintain a differential output voltage depending on the sign of the amplitude of the pulse. Then when another pulse comes along with a different sign, the output would change signs as well. I natura... | If I understand your question right, a simple centre tapped rectifier like this should do:
<img src="https://i.stack.imgur.com/rv5Pq.png" alt="PulseCatcher">
L1 is the primary winding, L2 and L3 are the secondary windings. OUT1 and OUT2 are to your FFs (or whatever you are capturing with) Ignore the 1Meg R3, it's jus... | As close as I can get to understanding what you're asking for, you might want something like this:
<img src="https://i.stack.imgur.com/d1W0n.png" alt="enter image description here">
XFMR1 provides isolation from your inputs. If your input is actually single-ended, "IN-" will be the reference (ground) of the source ci... | https://electronics.stackexchange.com |
252,852 | [
"https://softwareengineering.stackexchange.com/questions/252852",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53493/"
] | C/C++ implicit conversions can cause bugs. Here's one example:
<pre><code>int foo, bar;
scanf("%d", &foo);
scanf("%d", &bar);
float foobar = foo / bar;
</code></pre>
If I input <code>7</code> and <code>2</code>, it's not <code>3.5</code> as expected - it's <code>3</code> -> bug (let's ignore the buffer overfl... | It goes kind of like this.
<ol>
<li>The ability to use unsigned values and variables and real numbers of different precisions
are not particularly common features in programming languages, but are critical in order for C/C++ to do its job. </li>
<li>Mixing arithmetic types like these is a major cause of bugs in real... | With GCC you'll find alot of the important warnings are already grouped together under <code>-Wall</code> and <code>-Wextra</code>, its also useful to use <code>-Werror</code> to turn warnings into errors.
| https://softwareengineering.stackexchange.com |
15,696 | [
"https://stats.stackexchange.com/questions/15696",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5344/"
] | I'm pretty new to statistics and I need your help.<br />
I have a small sample, as follows:
<pre class="lang-r prettyprint-override"><code> H4U
0.269
0.357
0.2
0.221
0.275
0.277
0.253
0.127
0.246
</code></pre>
I ran the Shapiro-Wilk test using R:
<pre class="la... | No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes from a population which has a normal distribution".
In fact the sample does not have a normal... | Considering that you are pretty new to statistics, I suspect that you are thinking about this because these are residuals of an estimate of a mean and you want to know whether the assumption of normality is valid for confidence estimates using a $t$-distribution.
$t$-tests are quite robust to violations of this assump... | https://stats.stackexchange.com |
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