qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
14,697 | [
"https://stats.stackexchange.com/questions/14697",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5946/"
] | I have some experience with both FLD and LR for classification.
On most data sets, I get very similar results, which raises the question - are FLD and LR related in some why?
An idea, for example, if I assume a normal distribution on the likelihood function instead a of a logistic function, does the maximization co... | Just (maybe redundant) elaborate on Frank's answer. LDA is based on assumptions of multivariate normality and equality of covariance matrices of the 2 groups (in population); it is also irritable to outliers and to unbalanced <em>n</em>'s; the predictors should normally be interval scale. All that is not required by L... | For many reasons, classification is not a good goal for most problems; prediction is. Logistic regression (LR) is a more direct probability model to use for prediction, with fewer assumptions. Linear discriminant analysis (LDA) assumes that X has a multivariate normal distribution given Y. Using Bayes' rule to get P... | https://stats.stackexchange.com |
263,079 | [
"https://physics.stackexchange.com/questions/263079",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52363/"
] | Given a sinusoidal signal with a frequency $\omega$, the Fourier transform ought to simply be a delta function at $\omega$. However, what happens to multiples of these? MATLAB's FFT shows nothing at $\omega/2$ for example but I'm wondering how this distinction is made.
EDIT: Clarifying a little, perhaps talking about ... | To keep things mathematically both precise and simple, let's stick with the discrete Fourier transform. Signals are vectors of $N$ complex points, where $N$ is the dataset's length. The dimension of this vector space is $N$.
In this setting, the Fourier transform is simply a resolution of a signal, thought of as a vec... | A sine wave at $\omega$ is periodic in $\omega /2$, but that does not mean that a sine at $\omega $ has frequency components at $\omega /2$. Another way of looking at it is noting that you cannot synthesize a sine at $\omega $ as the sum of sines of other frequencies.
| https://physics.stackexchange.com |
505,289 | [
"https://physics.stackexchange.com/questions/505289",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1638/"
] | <strong>Premise:</strong>
A friend and I were discussing the concept of a heater operating in a closed space (by this I mean an isolated area with no thermal conduction in or out) and how a given wattage will (eventually) heat the space the same. For example, consider two 1kW heaters, one with a fan and one without. I... | <blockquote>
I know that if an object is on an incline, there is friction as a
reaction to the component of the object's mass that is parallel to the
surface.
</blockquote>
It is more accurate to say that there is static friction acting up the plane that is equal and opposite to the component of the gravitationa... | Friction is a self-adjusting force that opposes relative contact motion between two surfaces. If a surface is not perfectly smooth, friction will always be there. If a block is on a flat surface, friction adjusts itself to zero as there is no tendency for the block to rub against the flat surface. If you were to apply ... | https://physics.stackexchange.com |
40,780 | [
"https://security.stackexchange.com/questions/40780",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/28535/"
] | <em>The Question</em>
I was reading a forum last night discussing the idea of emailing a user a login link, much like a password reset link, so they don't require a password. Their email address is already verified on sign up using a similar such link and I see them as being fairly similar in principle to a reset pass... | If you're relying on the email address to verify the original user's identity, whether for login or password reset, then a compromise of the email account means a compromise of the website's account. Therefore, I don't see any elevated security risk in this login scheme. In fact, this is essentially like using a third ... | A user might want to visit your website from a computer where they have no access to their e-mail account or do not want to access it. Your process would limit the computers where the user can access your site.
| https://security.stackexchange.com |
87,615 | [
"https://dba.stackexchange.com/questions/87615",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44545/"
] | When I am using setParameter in mongod config, I start mongod with error:
<pre><code>Unrecognized option: setParameter = enableLocalhostAuthBypass=1
</code></pre>
How can I use setParameter from config file ?
P/S: I am using YAML config file format.
| Here's a working example that I just tested using 2.6.6 - I specified two parameters just to show how it is done for reference:
<pre><code>storage:
dbPath: "/data/db/test"
systemLog:
destination: file
path: "/data/db/test/mongodb.log"
processManagement:
fork: true
setParameter:
enableLocalhostAuthB... | to set without mongod restart you can use like this example:
<pre><code>db.adminCommand( {
setParameter: 1,
logComponentVerbosity: {
verbosity: 1,
query: { verbosity: 2 },
storage: {
verbosity: 2,
journal: {
verbosity: 1
}
}
}
} )
</code></pre>
| https://dba.stackexchange.com |
110,558 | [
"https://security.stackexchange.com/questions/110558",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/32378/"
] | For a network offering webservices, I have had recommendations to blacklist a couple of common incoming DESTINATION ports, such as UDP 53, to combat the increasing load from DDoS. I'm wondering if it makes sense to blacklist attackers SOURCE ports as well. What's the industry practice?
| I've tested on Wireshark, from an attacker's point, of outgoing source ports and they are random high ports. Both legit web requests and malicious scans originate from random source ports, so I don't think the defender can block based on attackers' source ports.
| In terms of security, it is better to have a whitelist approach rather than a blacklist. As Neil has clearly pointed out, you should only allow ports for incoming connections in your firewall that corresponds to the services that you are providing and need to accessed from the outside.
Hope my answer helps you better ... | https://security.stackexchange.com |
190,330 | [
"https://softwareengineering.stackexchange.com/questions/190330",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/72591/"
] | I know this is a place where people ask advice for designing code.
I am at a bit strange side on my coding quest, on one side people send me design stuff.
Special graphics and ideas on how they should be shown in a program workflow.
(i think the marketing designers are a bit to powerfull in this project
They tend to ... | If you use Windows Presentation Foundation, it is a core part of the .NET framework from version 3.5. In short, it allows you to pretty much do all the things in flash, including tweening and rotating as you've said.
The other alternative is to embed the Flash ActiveX component and load an SWF.
EDIT to add: I just sa... | If you want to use Flash, you can pull in an ActiveX component of it into a .NET Form (though IIRC you need to get the ActiveX Flash installer to get that component and the installer is somewhat difficult to find on Adobe's website) then you could program things in Flex (if you don't have Flash handy). There's not much... | https://softwareengineering.stackexchange.com |
133,506 | [
"https://softwareengineering.stackexchange.com/questions/133506",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/46295/"
] | I'm self-learning iOS development through the iTunes U CS193p course, and I often find myself stuck. I've been trying to get unstuck myself, but it might take me hours and hours to figure out what I'm doing wrong, be it missing a method or not really getting a whole concept like delegation.
I'm worried that I might b... | When I am working with new developers, I encourage them to come ask questions after five or ten minutes where they are not making progress.
That has two benefits: the first is that they can get help without too much time spent staring at a problem, but they only ask when they are not getting somewhere. If they are le... | My only addition to everyone else's great answers:
TYPING UP your question into the StackOverflow question interface is a great way to make sure you're thinking through it fully. I can't begin to tell you how many questions I've answered for myself in the process of laying it out clearly enough to ask it properly. The... | https://softwareengineering.stackexchange.com |
110,140 | [
"https://mathoverflow.net/questions/110140",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27402/"
] | Hallo,
I am reading the paper "Hyperkaehler structures on the total space of holomorphic cotangent bundles" by D.Kaledin and I am asking if it is possible to embedd a real-analytic Kähler manifold, isometrically, as a special Lagrangian in a Calabi-Yau manifold. Acctualy what I am looking for is the following: Start w... | <strong>Disclaimer:</strong> I am not sure what kind of "explanation" you are looking for. I would guess that you are after the observation (due to Hitchin), that complex Lagrangian submanifolds become special Lagrangian after rotating the complex structure.
<strong>Observation:</strong>
Let $X$ be a hyperkaehler m... | How can you show then that, after a rotation, it satisfies the Calabi-Yau equation?
| https://mathoverflow.net |
222,492 | [
"https://physics.stackexchange.com/questions/222492",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/77178/"
] | An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not ?
| The Maxwell's equation: $$\nabla \cdot E=\frac{\rho}{\epsilon}$$
If this has to hold true $E$ must be differentiable at all points, so it has to be continuous (except at boundaries of surface charge)
| I can help you with some logic.The field lines are made by joining the forces, which is in the direction of the field line.These forces are actually produced by waves generated from the source charge in test charge and you know that these waves are generated continuously so we do not find breaks.<br>
If certainly it we... | https://physics.stackexchange.com |
418,404 | [
"https://physics.stackexchange.com/questions/418404",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/193317/"
] | Suppose I have a two masses attached with a spring on ei either side and one of the masses is kept in contact to the wall like in this diagram with friction neglected everywhere.
<img src="https://i.stack.imgur.com/N9Sl9.jpg" alt="enter image description here">
Now when the wall is removed after equilibrium is set ... | Based on the Nashwan's last clarification that he is simply removing air (and assuming no heat transfer involved) I suggest the following answer:
Since temperature is a measure of the average translational kinetic energy of the air molecules in the system, if we remove some of the molecules we also remove the kinetic ... | Nashwan, upon further reflection I believe the temperature will remain the same. Although removing air molecules lowers the total internal (kinetic) energy of the remaining molecules, there are also fewer molecules sharing that energy. Thus the average translational kinetic energy per remaining molecule should be the s... | https://physics.stackexchange.com |
67,510 | [
"https://chemistry.stackexchange.com/questions/67510",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/40630/"
] | In p-block elements, higher oxidation states are less stable down the group due to the inert pair effect. This is not the case for transition metals.
Why do heavier transition metals show higher oxidation states than lighter ones? Is the inert pair effect not valid for transition metals also?
| The inert pair effect is based on the fact that main group elements’ oxidation states depend on s and p orbitals (and only them). When going down the periodic table, the energy difference between s and p orbitals changes leading to some elements losing their valence s electrons more easily than others.
Transition meta... | The sum of the total ionaisation energies for achieving the highest oxidation state in a particular group is less for the heavier elements than for the lighter elements.Therefor stability of higher oxidation states increases down the group.
| https://chemistry.stackexchange.com |
470,114 | [
"https://physics.stackexchange.com/questions/470114",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/227129/"
] | In an automotive "radiator", with the fan blowing air through it, what is the primary means of heat transfer. And the 2nd and 3rd means.
| The mechanism of convection heat transfer in car radiator operation is not exactly what you are alluding to in your comment to @Ole Krarup. You are alluding what we call "natural convection," which is the result of density gradients in a gas. But, a much more important heat transfer mechanism, dominant in a car radia... | The answer is "convection". The air immediately surrounding the engine is heated up and quickly transported away by the fan. It pushes the hot air away and replaces it with new, cold air. This is then heated up and the cycle continues.
Whether conduction or radiation take the second place will depend on the temperatur... | https://physics.stackexchange.com |
472,431 | [
"https://physics.stackexchange.com/questions/472431",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/176553/"
] | I approach these expansion problems like so:
The gas and the surroundings(piston+outside) are at the same pressure at first. We heat the gas. The pressure rises inside the syringe <em>a bit</em>. The gas expands so the pressure remains constant. Then I use P(the constant pressure of the gas) *dV. What I want to confir... | Determining the shape of the Earth is not something you describe with any completeness in this forum. Which shape are you talking about? The topography or the gravity field? Each is a separate field of research, with many different methods.
First, the Earth is not a sphere. While a sphere is the lowest energy solution... | As has been mensioned in Solomon Slow's comment the scale of missing crater you have in your sketch is not acceptable for various reasons.
-Structurally the materials earth is made of can not support themselves under their own weights and will be crushed and collapse to a round shape which will fill the huge canyons. ... | https://physics.stackexchange.com |
511,329 | [
"https://physics.stackexchange.com/questions/511329",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246223/"
] | Say you are driving down the road and and jam on the brakes in a car with no ABS, at what point does the wheel stop spinning and stop causing a skid.
I suspect it is when the friction between the brake disk and brake pad become greater than the friction between the tyre and the road?
Just want to make sure I am think... | <blockquote>
. . . . at what point does the wheel stop spinning and stop causing a skid?
</blockquote>
If the wheels are not rotating and the car is moving then the car will be in a skid.
The condition that there is no relative movement at the point of contact between the road and the tyre is that <span class="m... | It is the static friction between the bottom of the tire and the road surface that keeps the tire from slipping or skidding (kinetic friction). Even though the tire is rotating, the bottom of a non slipping tire is in static contact with the road. When applied force is greater than static friction the wheel will slip. ... | https://physics.stackexchange.com |
595,493 | [
"https://stats.stackexchange.com/questions/595493",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/372803/"
] | I have a dataset of observations of hawks foraging. I am trying to examine the relationship between height of perch used (continuous independent variable, integers of 0 through 10) and outcome of a foraging attempt (binary: success or fail). I'd like to answer the question, are hawks more successful at shorter or talle... | It is not true. A simple counterexample is letting <span class="math-container">$X \sim N(0, 1)$</span>. Then <span class="math-container">$\max(E(X), 0) = 0$</span>, whereas
<span class="math-container">\begin{align}
& E(\max(X, 0)) = \int_{-\infty}^\infty \max(x, 0)\phi(x)dx = \int_0^\infty x\frac{1}{\sqrt{2\pi... | No, it's not. If <span class="math-container">$E[X] > 0$</span> then
<span class="math-container">$$
max(E[X], 0) = E[X]
$$</span>
so you would need
<span class="math-container">$$
E[X] = E[max(X, 0)]
$$</span>
That can easily be disproved with simple counterexamples.
If <span class="math-container">$E[X]\le0$</span... | https://stats.stackexchange.com |
14,325 | [
"https://physics.stackexchange.com/questions/14325",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5129/"
] | I've got two questions for you.
<ol>
<li>Electric current is the flow of electrons across a conductor.Why has it always got to do with electrons and not with protons? (I know neutrons are not eligible for electricity as they carry no charge.)</li>
<li>Sometimes my computer starts properly after I disconnect all the ca... | Well for 1), when a voltage is applied across a conductor all the charges in the material will feel a force. So yes the protons also feel a force. But in a typical metal conductor the protons will be fixed within a lattice structure and will be unable to move under low voltages. The electrons however will be bonded ... | i think protons are heavier than electrons so they can not move easily at a low voltage
| https://physics.stackexchange.com |
203,354 | [
"https://softwareengineering.stackexchange.com/questions/203354",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1936/"
] | I was writing some test code as an example where I had a washing machine class. It has a door state that should be open or closed, and also a running state, either on or off. I want to prevent the running state from changing from 'off' to 'on' when the door is 'open', and also prevent the door from being set to 'open' ... | What you are experiencing is called 'Code Smell' and is a good indicator that you might be doing something wrong. Luckily though, you saw the problem and already came up with a great solution, so there's not much for me to say here. A state machine works perfectly for what you're doing here.
Drawing it out might also... | You could implement your washing machine as a state machine, but there's just as much potential for state proliferation as there is for <code>if</code> statements if you don't do things carefully.
Working in states requires a different mindset where you think in terms of states (where you are), stimuli (what you get f... | https://softwareengineering.stackexchange.com |
298,248 | [
"https://mathoverflow.net/questions/298248",
"https://mathoverflow.net",
"https://mathoverflow.net/users/58541/"
] | Let <span class="math-container">$m \in \mathbb{N}\setminus \{0,1\}$</span>, <span class="math-container">$\alpha \in ]0,1[$</span>.
Let <span class="math-container">$\Omega$</span> be a bounded open subset of <span class="math-container">$\mathbb{R}^n$</span> of class <span class="math-container">$C^{m,\alpha}$</span>... | No. Let $A$ be the free abelian group generated by the $r_a$s. We can view this as a lattice in the real vector space $A \otimes \mathbb R$. Let $n$ be the rank of this group / the dimension of this vector space.
There is a natural evaluation map $f: A \otimes \mathbb R \to \mathbb R$ from this vector space to $\mathb... | No choice is needed.
First, assuming such a paradoxical decomposition, we get another one in a large circle $C=\mathbf{R}/k\mathbf{Z}$. Now we have, on the subgroup $\Gamma$ generated by the $r_i$ (and by $x\mapsto x+1$), an explicit sequence of Følner subsets, and corresponding normalized $\ell^1$-functions $f_m$.
... | https://mathoverflow.net |
375,888 | [
"https://physics.stackexchange.com/questions/375888",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/179170/"
] | If electric field is what is applying the force then how can they be in different directions? Eg: -q has an electric field inwards but it exerts force outwards on another charge -q1...... Doesn't make sense how they can be in opposite direction....
| Positron capture is not possible, and here is why: The "capture" part refers to the fact that the electron is taken from its atomic orbit around the nucleus containing the proton with which it reacts. Since a positron cannot for a bound state with a nucleus--it can't be captured.
Nevertheless, $e^+p(n, \bar{\nu}_e)$, ... | "Positron capture" does not normally happen. However if temperatures are high and pressures are high(like in the sun) it is possible for positron capture to occur. This could be a way that occasionally neutrons turn into protons.
| https://physics.stackexchange.com |
107,516 | [
"https://chemistry.stackexchange.com/questions/107516",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/58497/"
] | Consider simply aqueous solutions of <span class="math-container">$\ce{H2S}$</span> and <span class="math-container">$\ce{HCl}$</span> . It is pretty much known that <span class="math-container">$\ce{HCl}$</span> is stronger than <span class="math-container">$\ce{H2S}$</span> in water. The reason behind that first is ... | You are right that electronegativity is an important consideration but another factor that is also very important is size of the atom. Although there is a decrease in electronegativity from <span class="math-container">$\ce {O}$</span> to <span class="math-container">$\ce {S}$</span>, the size of the atom which the cha... | It is not just electronegativity. You also have to look at how strongly the atom bonds to hydrogen. If a strong bond forms, it might convince the atom to act as a base even if it would be grumpy based on its electronegativity. If only a weak bond forms, even an atom with relatively low electronegativity might balk a... | https://chemistry.stackexchange.com |
68,606 | [
"https://dba.stackexchange.com/questions/68606",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25307/"
] | I'm looking for direction here. I need to automate a process that will import several different file types into SQL Server. They are all text based files (no excel) but the internal format of the files is different. Some are comma delimited, others are tab delimited. They all contain the same base information (cust... | How many is "several"? If it's three or four, I'd start by writing a simple .NET script in SSIS which sorts out the files into separate directories. Use several foreach loops, each working in its own directory, with the files in that directory having a consistent format.
If there are a <em>lot</em> of formats, it'd ... | If header names are same across all the delimited files, then you can use Script Task/Script component inside Foreach Loop Container. You can put the logic ( by hard-coding header names) - First check file's delimited type (Comma/Tab etc) and then extract data for only those columns you are interested from that flat ... | https://dba.stackexchange.com |
1,850,991 | [
"https://math.stackexchange.com/questions/1850991",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Does the analogue of Schroder-Bernstein hold for finite topological spaces ? i.e. Let $X,Y$ be finite topological spaces such that there exist continuous injections from $X$ to $Y$ and $Y$ to $X$ , then are $X$ and $Y$ homeomorphic ? I know that it isn't true for arbitrary topological spaces ( even metric spaces , take... | You have a continuous injection from $f:X\hookrightarrow Y$ and a continuous injection $g:Y\hookrightarrow X$.
Since $f$ is injective $|X|\le |Y|$ and since $g$ is, $|Y|\le |X|$. So $|X|=|Y|$ and both are finite. We therefore can conclude that both $f$ and $g$ are bijections.
Let $h = g\circ f : X\to X$. It's a conti... | If $X$ and $Y$ are finite, then the assumed continuous injections $X\to Y$ and $Y\to X$ are in fact bijections. Therefore, given a continuous bijection $f:X\to Y$, its inverse maps open subsets of $Y$ <em>injectively</em> to open subsets of $X$, so $X$ has at least as many open subsets as $Y$ does. The other way around... | https://math.stackexchange.com |
136,796 | [
"https://mathoverflow.net/questions/136796",
"https://mathoverflow.net",
"https://mathoverflow.net/users/37150/"
] | Searching left me hanging. One of my professors told me the definition using the topological properties was the first one but I cannot find any resources. Is that true? If not, how was it originally defined? References would be lovely.
Best regards
| Profinite groups were first called "Groups of Galois type", see J.P. Serre's book "Cohomologie Galoisienne" of $1964$. The term "profinite" comes from Serre (if I am not mistaken).
Of course, some profinite groups have a much older history, e.g.,
already Hensel defined in $1910$ the $p$-adic integers during his studie... | Tate was the first to study the cohomology of profinite groups. In his unpublished 1958 article (reprinted as Chapter VII of Lang's notes "Topics in the Cohomology of Groups"). He writes: "We introduce a new category of groups and a cohomological functor, obtained as limits from finite groups. A topological group G wil... | https://mathoverflow.net |
646,922 | [
"https://physics.stackexchange.com/questions/646922",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/259324/"
] | I'm having some trouble understanding what is going on in <em>Mathematical methods of classical mechanics (Arnold, 2nd edition)</em> in the rigid body mechanics section (chapter 6). I don't know any other book that deals with rigid body mechanics like this. After introducing two frames of reference: the "stationar... | It seems the confusion is coming from thinking that in the body <span class="math-container">$\mathbf{V}$</span> equals <span class="math-container">$\dot{\mathbf{Q}}$</span>. This is however not true. The position vector <span class="math-container">$\mathbf{Q}$</span> of a point that rotates with the body is constant... | Angular momentum of a rigid body is a vector that is non-zero when the body is in rotation with respect to absolute space (or later, with respect to distant stars). This vector can be represented by coordinates in the frame of the absolute space (inertial frame), or by coordinates in the frame of the body.
| https://physics.stackexchange.com |
1,040,620 | [
"https://math.stackexchange.com/questions/1040620",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/195250/"
] | <blockquote>
Let $X$ and $Y$ be independent geometric random variables. What is the distribution of $Z=\min(X,Y)$?
</blockquote>
The probability mass functions are $\operatorname{Pr}(X=k)=(1-p)^{k-1}p$ and $\operatorname{Pr}(Y=k)=(1-q)^{k-1}q$. And the event $(Z=k)$ is the union of
<ul>
<li>$(X=k)$ and $(Y\ge k)$<... | Let $X\sim\mathcal{Geo}(p), Y\sim\mathcal{Geo}(q), X\perp Y$
$\begin{align}
\Pr(X\geq k) & = (1-p)^{k-1} & \impliedby X\sim \mathcal{Geo}(p) \tag{1}
\\[2ex]
\Pr(Y\geq k) & = (1-q)^{k-1}& \impliedby Y\sim \mathcal{Geo}(q)\tag{2}
\\[2ex]
\Pr(\min(X,Y)\geq k) & = \Pr(X\geq k,Y\geq k)
\\[1ex] & = \... | Let the parameters of the two geometrics be $\alpha$ and $\beta$. So these are the probabilities of "success," and the geometrics give the number of trials until the first success. Let $Z=\min(X,Y)$.We have $Z\ge z$ if and only if $X\ge z$ and $Y\ge z$.
The probability that $X$ is $\ge z$ is the probability of $z-1$ "... | https://math.stackexchange.com |
744,423 | [
"https://physics.stackexchange.com/questions/744423",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/355223/"
] | So,In my book it is written that -
<strong>Translational motion</strong> is the motion when all the particles of a moving body move the same distance in the same same in the same direction.It is of two types-1)Rectilinear and 2)Curvilinear
Now, my question is that to have translational motion doesn't need to have unifo... | If the mass m is constant and the tank volume V is constant, then <span class="math-container">$v_{avg}=\frac{V}{m}$</span> is constant for any changes that occur within the tank. So any changes in temperature and/or pressure will be accompanied only by changes in the relative masses of liquid and vapor.
| Specific volume is really just the inverse density. Since mass is conserved and the total volume is fixed, the total density remains fixed even though it's a sum of two different densities whose ratio changes with temperature.
This is what allows for the calculation of quality. The equation below expresses it as a cons... | https://physics.stackexchange.com |
24,283 | [
"https://stats.stackexchange.com/questions/24283",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9677/"
] | I've made replicate measurements of a parameter (fluorescence) which is expected to increase with time, and I'm having a hard time understanding how to test for significance of the slope of the parameter vs. time (using a linear least squares model).
Intuitively, it makes sense to me to combine all time-fluorescence p... | It's not legitimate to just fit a line through the whole thing for two reasons:
<ul>
<li>even if you had only one replicate, you will have autocorrelation in the residuals over time. Observation at $t_n$ is related to the observation at $t_{n-1}$ so you can't treat them as independent. There is actually less informa... | If you want to include a different intercept for each of the three sequences of values, you can try
<pre><code>n <- factor(rep(1:3, each=10))
lm( c(f1, f2, f3) ~ c(t1, t2, t3) + n )
</code></pre>
| https://stats.stackexchange.com |
612,636 | [
"https://physics.stackexchange.com/questions/612636",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/288142/"
] | I have what I think is a very simple question, basically, what does the notation "<span class="math-container">$\langle \rangle$</span>" stand for?
My background is in math and I am not familiar with physics notations. I am reading the following:
<blockquote>
"we assume that <span class="math-container"... | <span class="math-container">$\langle x\rangle$</span> refers to the expectation value of <span class="math-container">$x$</span>.
<span class="math-container">$\delta_{jk}$</span> is the Kronecker delta, defined as:
<span class="math-container">$$\delta_{jk}=\left\{\begin{align}0 && j\ne k \\ 1 && j=k\... | It looks like it is the mean of the product of two components. Whatever these are.
The relationship you show could mean that the noise in the components is not correlated so that the average of the noise in the products of different components cancel out whereas for the square of the components itself you get the stand... | https://physics.stackexchange.com |
210,820 | [
"https://dba.stackexchange.com/questions/210820",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/154273/"
] | I am relatively fresh to SQLServer's use of <code>ROWVERSION</code>/<code>TIMESTAMP</code> data, and normally just query for required rows based on modified dates.
How is the <code>ROWVERSION</code> assigned to a new row in a database? Does every new row start with the same rowversion, or is it a unique value? In othe... | You can't randomize them, the order is important. Maybe you can see it clearer if we add a few parenthesis between the joins.
<pre><code>SELECT
c.id
FROM
customers c
JOIN (sales s JOIN saleitems si ON s.id = si.saleid)
ON c.id = s.customerid
</code></pre>
What this query is doing is joining first ... | The JOIN syntax in most cases requires both JOIN and ON to be present (unless some specific situations like CROSS JOIN for which ON would not make any difference).
Consider this to be similar to <code>BEGIN..END</code> statements - they have to be the <code>END</code> statement relates to the nearest previous <code>BEG... | https://dba.stackexchange.com |
3,543,773 | [
"https://math.stackexchange.com/questions/3543773",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/546142/"
] | <blockquote>
<strong>The Problem is:</strong> For any <span class="math-container">$n \geq 1$</span>, define
<span class="math-container">$$P_n(x)= \frac{d^n}{dx^n}(x^n(1-x)^n)$$</span>
Show that
<span class="math-container">$$m \neq n \Rightarrow \int_0^1 \!\!{P_n(x) P_m(x)dx} =0$$</span>
</blockquote>
<stro... | Your answer is incorrect. While it is true that there are positive odd integers less than or equal to <span class="math-container">$200$</span>, what you have actually calculated with the expression
<span class="math-container">$$\left\lfloor \frac{200}{2} \right\rfloor$$</span>
is the number of even integers less th... | In this simple case you don't really need the Inclusion/Exclusion principle <span class="math-container">$-$</span> you can do it 'by hand'.
First, count the even numbers between <span class="math-container">$1$</span> and <span class="math-container">$30$</span> that are divisible by <span class="math-container">$3$<... | https://math.stackexchange.com |
106,014 | [
"https://mathoverflow.net/questions/106014",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24965/"
] | Let $G$ be a real semisimple Lie group (say $SL(2,\mathbb{R})$) and $H$ be its Cartan subgroup (say torus or diagonal subgroup of $SL(2,\mathbb{R})$).
My questions is: it is always true that we have a natural symplectic structure on the quotient space $G/H$?
If it is not true, could we consider this weaker version: L... | To add to Robert Bryant's answer, the coadjoint orbits of a Lie group always have a natural symplectic structure, the (Lie-)Kirillov-Kostant(-Souriau) form. These are the symplectic leaves of the natrual Lie-Poisson structure on $\mathfrak{g}^\ast$. For $x \in \mathfrak{g}^\ast$, we can identify the coadjoint orbit $\m... | Actually, the issue is that there is usually more than one 'natural' symplectic structure on $G/T$, where $T$ is a Cartan subgroup. The space of $G$-invariant closed $2$-forms on $G/T$ has dimension equal to the rank of $G$ (which is the dimension of $T$), and the generic one is nonsingular, so you might have trouble ... | https://mathoverflow.net |
361,247 | [
"https://math.stackexchange.com/questions/361247",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $(\Bbb R,\tau)$ be the Sorgenfrey line. Why $\Bbb R^2$ is not normal?
| $\mathbb{R}^2$ in this topology is separable (as witnessed by $\mathbb{Q}^2$) and has a closed and discrete (in itself, so discrete as a subspace) subspace $D = \{ (-x, x) : x \in \mathbb{R} \}$, where discreteness is witnessed by the fact that $[-x, -x+1) \times [x, x+1)$ intersects $D$ in $(-x,x)$ only.
Now all for ... | Let $\Delta=\{(x,-x)|x\in\mathbb{R}\}$. For an accessible example of a pair of closed subsets that can't be seperated by open neighbourhoods, use the closed subsets $A=\{(x,-x)|x\in\mathbb{Q}\}$ and $\Delta\setminus A$.
Showing that $A$ and $\Delta\setminus A$ are closed does require some fiddling with the basis eleme... | https://math.stackexchange.com |
2,800 | [
"https://robotics.stackexchange.com/questions/2800",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/4249/"
] | I'm developing/tuning a software PID for a quadcopter. For now I'm only trying to stabilise the pitch angle using the front and back motors, and I'm only looking at Kp. The motors have a control resolution: input variations need to reach a threeshold to have any effect at all.
The process output does reach the setpoin... | Since posting the question I tried to tune the 3 PID parameters a lot but I never reached any acceptable result. I didn't try to modify the error curve as I suggested in the question, but I found an alternative solution which works reasonably well. There might be other good solutions.
I was using a PID as follows:
<u... | It sounds like the problem stems from your motors. The motors are fine, but they have a threshold that prevents you from setting their speed to exactly the value you want. This is a problem because you are attempting to map your PID directly to their output, which has a minimum value.
You need to alter your motor ... | https://robotics.stackexchange.com |
134,743 | [
"https://physics.stackexchange.com/questions/134743",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/58785/"
] | Suppose the centre of mass of 2 bodies coincide , then how will we calculate the gravitational force between the 2 bodies ??
| Suppose you have two densities of mass $\rho_1$ and $\rho_2$. The two centers of mass coincide if
$$
\vec R_{CM_1} = \frac{\int_{\mathbb{R}^3} \vec r \rho_1(\vec r) \, d^3r}{\int_{\mathbb{R}^3}\rho_1(\vec r) d^3r} \quad \vec R_{CM_2} = \frac{\int_{\mathbb{R}^3} \vec r \rho_2(\vec r) \, d^3r}{\int_{\mathbb{R}^3}\rho_2(\... | You do this the same way that you always do it: you compute the integral of the forces of each element on each other element. When both objects are spheres (or have spherical symmetry) the math gets easier - but in general just knowing the location of the center of mass of an object is not sufficient to determine the f... | https://physics.stackexchange.com |
215,610 | [
"https://security.stackexchange.com/questions/215610",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/214669/"
] | I worked today with our teacher who logged me into a computer as admin. We had a task that required admin rights. A few seconds later he was talking to other students in our classroom, but I was able to reset the administrator password with lusrmgr.
<ol>
<li>Was the teacher right to do this (is it a critical problem)?... | <h1>Was the teacher right to do this?</h1>
Yes and no. One might be tempted to say that giving a student administrative rights is highly problematic, and leaving them unattended even more so. And to some degree, I even agree with it. You may have added a new administrative user, changed the admin credentials, installe... | <h3>The teacher logged me in as administrator for doing a short task, is the whole system now compromised?</h3>
No.
<h3>but I was able to reset the administrator password with lusrmgr.</h3>
Now it is, congratulations, you have performed a criminal activity.
<h3>Was the teacher right to do this (is it a critical... | https://security.stackexchange.com |
3,121,858 | [
"https://math.stackexchange.com/questions/3121858",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/405590/"
] | I'm having a hard time understanding why
<span class="math-container">$\theta = \frac{s}{r}$</span>
and
<span class="math-container">$s = \theta r$</span>
where <span class="math-container">$s$</span> is the arc length, <span class="math-container">$r$</span> is the radius, and <span class="math-container">$\thet... | Keep in mind that, although we can assign a length to a circular arc as though it were a straight line segment, it is not a straight line segment. It bends through a certain angle with respect to the circle upon which it lies.
When we assign a measure to the arc (and thereby to the associated angle) by dividing its l... | As is well known <span class="math-container">$\pi$</span> is defined as the ratio between the perimeter of a circle and its diameter or 2 times the radius which is the same, so <span class="math-container">$\pi = \frac{p}{2r}$</span>. So <span class="math-container">$p = 2\pi r$</span>. So as <span class="math-contai... | https://math.stackexchange.com |
53,168 | [
"https://stats.stackexchange.com/questions/53168",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/22462/"
] | I'm having a hard time understanding how to use confidence intervals for hypothesis testing. I've seen examples to reject a null hypothesis, but don't understand how to use a one-sided confidence interval to show significance.
If you have two samples, x and y, how you would you use a one sided confidence interval to ... | One sided confidence intervals are dual to one tailed hypothesis tests just as regular two sided CIs are dual to two tailed tests.
If $\theta$ is a parameter, and we say that $(a,\infty)$ is a one sided CI for $\theta$, then this means that $a$ was found by a process that will yield a value below the true value of $... | Rejecting a null is the same thing as achieving significance. If you understand "how to use confidence intervals to reject a null hypothesis", you've already done the other thing.
In short, if the interval for $\mu_x-\mu_y$ doesn't include zero, your reject the null; equivalently you have achieved significance, thereb... | https://stats.stackexchange.com |
324,994 | [
"https://mathoverflow.net/questions/324994",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16702/"
] | For <span class="math-container">$p \in \mathbb{R}$</span>, consider the function
<span class="math-container">$$F_p(\lambda_1, \dots, \lambda_n) = \lambda_1^p + \dots + \lambda_n^p.$$</span>
My goal is to maximize this function under the constraints that
<span class="math-container">$$ \lambda_1^2 + \dots + \lambda_n... | Proof for the case <span class="math-container">$p$</span> odd:
The Lagrange-multiplier equation yields
<span class="math-container">$$
p\lambda_i^{p-1}+a\lambda_i+b=0
$$</span>
for some <span class="math-container">$a,b \in \mathbb{R}$</span>. If <span class="math-container">$p>1$</span> is odd the LHS is a strict... | Too long for a comment. No simple answer is expected in view of the results of math experiment done with Mathematica:
<pre><code>Maximize[{x1^4 + x2^4 + x3^4 + x4^4, x1 + x2 + x3 + x4 == 0 && x1^2 + x2^2 + x3^2 + x4^2 == 1},
{x1, x2, x3, x4}] // ToRadicals
</code></pre>
<blockquote>
<span class="math-co... | https://mathoverflow.net |
245,370 | [
"https://softwareengineering.stackexchange.com/questions/245370",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/117422/"
] | I had a loop through object <code>Process</code>, each <code>process</code> instance can be of a different type, derived from <code>Process</code> base class (e.g.: <code>Process1</code>, <code>Process2</code>,...). Each derived type of <code>Process</code> has different properties. For instance: some <code>Process</co... | Below is an example using an interface and two implementations in a console application:
<pre class="lang-cs prettyprint-override"><code>using System;
using System.Collections.Generic;
namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
var processes =... | Use a hash which contains as key the name of the Process and as value the Object containing the process. That way you get just one line of code:
Note: the following is in perl since I don't know C#, but the logic is the same
<pre><code>$hashContainingProcesses{processName}.doSomething();
</code></pre>
Depending on h... | https://softwareengineering.stackexchange.com |
107,682 | [
"https://math.stackexchange.com/questions/107682",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/19821/"
] | It's probably a very silly question.
I could only show though that
$$
\sum_{k \geq 2} \frac{(-x)^{k}}{k!} = \sum_{k \geq 0} \frac{(-x)^{k}}{k!} -1 +x= e^{-x}-1+x
$$
which tends to infinity as $x \to \infty$. And also taking the ration of consecutive terms
$$
\frac{a_{k+1}}{a_{k}} = -\frac{x}{k+1}
$$
for positiv... | Consider the function $u:x\mapsto\mathrm e^{-x}-1+x$. Its derivative is $u':x\mapsto-\mathrm e^{-x}+1$. Since $\mathrm e^0=1$ and the exponential is an increasing function, $u'(x)\lt u'(0)=0$ if $x\lt0$ and $u'(x)\gt u'(0)=0$ if $x\gt0$. Thus, for every $x$, $u(x)\geqslant u(0)=0$.
This proves that... | If $f(x) \to +\infty$ as $x \to \infty$, then certainly $f(x) \ge 0$ for sufficiently large $x$. It's <strong>not</strong> dominated by the first term: e.g. the third term $x^4/4!$ is greater than the first term when $x$ is large.
| https://math.stackexchange.com |
674,422 | [
"https://physics.stackexchange.com/questions/674422",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/311011/"
] | Suppose a box of mass <span class="math-container">$m$</span> is thrown at angle <span class="math-container">$\theta$</span> with velocity <span class="math-container">$v$</span>. At the topmost point,the box explodes into two identical smaller boxes. One of the boxes falls straight to the ground at that point.
I have... | It is true that momemtnum is conserved only if external force is zero. But here as in written in photo:
<span class="math-container">$$2m(v_0 \cos\theta)=m(0)+mv_2$$</span>
This equation represents momentum conservation only in <em>horizontal/x</em> direction, where there is no external force (if mentioned no air resis... | The horizontal component of momentum is conserved since there are no forces that act in this direction.
The same cannot be said in the vertical direction since gravity is acting on the boxes.
So there will be conservation of momentum in the x-direction. You can see this mathematically in the equation <span class="math-... | https://physics.stackexchange.com |
196,630 | [
"https://physics.stackexchange.com/questions/196630",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87029/"
] | I have a freezer with -25°C temperature and Soda with +30°C.
What is the ice-cube-sized material I can put in the freezer that can bring my glas of soda to the lowest temperature?
Are e.g. saltwater icecubes better than pure water cubes?
extra points for not waterifying my soda :)
| <blockquote>
From a perspective on the spaceship, the radar beam travels away from me at the speed of light, so I might imagine that I would have ample warning of an object positioned at rest one light-hour away.
</blockquote>
One light-hour away in which frame? If that one light-hour away is from the perspective of... | Per Bort's comment, this is easier to think about from the spaceship's frame rather than the debris's frame. A rock is traveling toward your spaceship at .99 times the speed of light. You send out a pulse of light that intercepts the rock when it's one light-minute away from the ship. The pulse bounces back and arri... | https://physics.stackexchange.com |
625,409 | [
"https://electronics.stackexchange.com/questions/625409",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/286188/"
] | I need to connect capacitor bank to a 240VAC supply. I understand at the instance of switching on the capacitor bank there will be an inrush current since capacitor act like a short to ground. I'm thinking of just connecting an inductor in series with the capacitor to reduce the current. Will this practically work? If ... | Using a current limiting resistor burns off the energy that is otherwise held in the inductor and potentially turned into an unwanted surge voltage across the capacitor bank. You have to be careful of this; the peak voltage across the capacitor bank could be nearly double the supply voltage.
I recommend that you simula... | You can use a resistive network to control the magnitude of the inrush current and to distribute the power dissipation over several resistors. But you don't want that network to stay in series with the power supply once inrush is complete. You can use a MOSFET in parallel with the network, letting it block current dur... | https://electronics.stackexchange.com |
143,304 | [
"https://security.stackexchange.com/questions/143304",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1844/"
] | Given:
<ul>
<li>A web application</li>
<li>Some active administrator accounts.</li>
<li>Some inactive administrator accounts.</li>
<li>No existing "audit" mechanism to keep old accounts for.</li>
<li>Inactive administrators cannot log in.</li>
</ul>
Is it more beneficial or less to periodically delete inactive admini... | I'll argue to delete them. The only thing that prevents these accounts from being used is:
<blockquote>
Inactive administrators cannot log in.
</blockquote>
And that is a defense against brute forcing (or fooling) an authentication, yet it does not defend against privilege escalation.
OWASP guidelines for web app... | The moment I come across a question like this, I am always compelled to say "Yes, please delete the inactive accounts". Why? Because it is "good practice" to remove old accounts that are no longer in use. Some use cases that are borderline applicable to this scenario:
<ul>
<li>Username reuse: If the usernames are "gcl... | https://security.stackexchange.com |
153,297 | [
"https://electronics.stackexchange.com/questions/153297",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66333/"
] | In the Mutex description page of the FreeRTOS website the following sentence can be find:
<blockquote>
Priority inheritance does not cure priority inversion
</blockquote>
From what I know I thought that priority inheritance was a cure for priority inversion. If the high priority task A is blocked by the low priorit... | What is meant is that there are situations that can occur that are priority inversion and are not solved by priority inheritance.
An example:
The normal situation used is that task <strong>A</strong>, <strong>B</strong>, <strong>C</strong> are in decreasing priority. <strong>C</strong> takes a mutex, then <strong>B</... | If task C needs task B to complete a work so task C can relase the first mutex, then there must be a second lock/mutex connection between tasks C and B which priority inheritance could use to rise the priority of task B, allowing task B to finish the work needed by Task C so it can release the first mutex.
| https://electronics.stackexchange.com |
183,384 | [
"https://physics.stackexchange.com/questions/183384",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | We know that life is almost 4 billion years old on Earth.
We also know that time contracts as we approach the event horizon of the massive black hole at the center of the Milky Way galaxy.
Now the question is that how can we compute the radius of the orbit close to that event horizon for which the whole four billion ... | You seem to be asking for a distance above the event horizon at which time dilation due to the gravitational acceleration of the black hole would convert 4 billion years to 1 second. As all time is relative, what you really are asking for is the distance above the event horizon at which it would APPEAR to someone on E... | A few things:
1) time dilation is only a relative effect. A clock on earth would tick differently than one far from the milky way, but people on Earth would notice no abnormal effect.
2) To first order, time dialation effects are governed by the gravitational potential energy at a point. It turns out that the time ... | https://physics.stackexchange.com |
355,460 | [
"https://mathoverflow.net/questions/355460",
"https://mathoverflow.net",
"https://mathoverflow.net/users/153260/"
] | In the paper "Hilbert's inequality", Montgomery and Vaughan proved that a generalization of the discrete Hilbert transform is bounded in <span class="math-container">$\ell^2$</span>. The inequality reads as follows
<span class="math-container">$$ \Big| \sum_{k\neq n}\frac{a_k \overline{b_n}}{\lambda_k-\lambda_n} \Big| ... | One can transfer the continuous <span class="math-container">$L^p$</span> theory to this discrete setting without difficulty.
Let's normalise <span class="math-container">$\sum_k |a_k|^p = \sum_n |b_n|^q = 1$</span>. Consider the two quantities
<span class="math-container">$$ X_1 := \sum_{k \neq n} \frac{a_k \overli... | Let me deal with a continuous situation. Let <span class="math-container">$\lambda:\mathbb R\rightarrow\mathbb R$</span> be an increasing <span class="math-container">$C^1$</span> diffeomorphism and let <span class="math-container">$u,v$</span> be in <span class="math-container">$L^2(\mathbb R)$</span>. We have with <s... | https://mathoverflow.net |
180,274 | [
"https://electronics.stackexchange.com/questions/180274",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/53792/"
] | I'm following the wiring diagram for a digitech fs3x guitar pedal footswitch.
For the third SPST switch, it's wired from the other two switches connected by 2 diodes, both in the same direction. Can anyone explain why a single diode wouldn't work here (with both wires connected to it)
<img src="https://i.stack.imgur.... | The two diodes are preventing a high potential on EITHER the Ring or Tip from generating a current flow into the Tip or Ring respectively, when none of the momentary switches are depressed. A single diode, say for example the diode between the Tip and the Up button, would not prevent a potential on Tip from generating ... | The two diodes are to that the UP switch actuates both lines, while still allowing those lines to act independently and prevent the other switches on those lines to have the same affect as the UP switch.
| https://electronics.stackexchange.com |
2,262,642 | [
"https://math.stackexchange.com/questions/2262642",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/42344/"
] | How many license plates can be made using 4 digits followed by 3 letters or 4 letters followed by 3 digits?
My attempt is the following. First, there are $9^4 \times 26^3$ license plates using 4 digits followed by 3 letters. Second, there are $26^4 \times 9^3$ license plates using 4 letters followed by 3 digits. Thus,... | Since there are 10 digits (0-9) and 26 letters (a-z), the total number of valid combinations equals:
$$10^4 \cdot 26^3 + 26^4 \cdot 10^3 = 458,803,904$$
| I suppose there is a slight error
The first digit is not zero hence 9 ways but for the rest there should be 10 ways
Hence correct answer will be
9×10^3×26^3+26^4+9×10^2
| https://math.stackexchange.com |
168,417 | [
"https://chemistry.stackexchange.com/questions/168417",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/9473/"
] | Na - Sodium - Natrium
K - Potassium - Kalium
W - Tungsten - Wolfram
Sb - Antimony - Stibium
and so forth.
[English only] Why do we not use the names that match the symbols?
| In the <span class="math-container">$18$</span>th and <span class="math-container">$19$</span>th century, there was a strong rivalry between chemists of France, Germany and England, specially about giving a symbol to newly found elements. If a French chemist had discovered and given a name to a new element, the German ... | There are several reasons for this, one of which is the pigeon-hole effect. The English language consists of only 26 letters, while nature contains more than 90 elements. The letters would become repetitive if only English names were used. Secondly, English is a latecomer as a global language of science. It is a recent... | https://chemistry.stackexchange.com |
334,849 | [
"https://softwareengineering.stackexchange.com/questions/334849",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/204519/"
] | We're developing an app that has slightly different requirements for each business market (countries and states) that it's available from. It seems like a common situation but I can't seem to find a good article about structuring code/modules for this scenario.<br>
It's a C# app and we're debating between Strategy vs ... | <strong>Have a single app and design the appropriate configuration solution.</strong>
JacquesB hints at this, but I want to state it more strongly. You <em>must</em> do this by configuration rather than developing 50+ versions of the codebase. Anything else will be insanely unmanageable.
If there are complex requir... | It really depends on <em>what</em> is different. Is it something which can be expressed purely by configuration (eg. tax rates), or do you really need separate code logic for each state? The more you can handle purely by configuration the better!
You <strong>most likely</strong> does not need separate code by state. F... | https://softwareengineering.stackexchange.com |
352,994 | [
"https://mathoverflow.net/questions/352994",
"https://mathoverflow.net",
"https://mathoverflow.net/users/35959/"
] | Let us consider <span class="math-container">$$f(z):=\sum\limits_{j=1}^{j=n}a_j\sin(\lambda_jz) $$</span>
where all <span class="math-container">$a_j$</span> and <span class="math-container">$\lambda_j$</span> (of course, <span class="math-container">$\lambda_j$</span> are distinct) are real numbers and <span class="ma... | Note that <span class="math-container">$\sinh$</span> is a strictly increasing positive unbounded function on <span class="math-container">$(0,\infty)$</span> so for say <span class="math-container">$n \ge 3$</span>, the equation <span class="math-container">$\sinh 1+ \sinh 2+...\sinh (n-1) =\sinh x$</span> has a uniqu... | Proof of the existence of a complex root in the general case, expanding Oleg's remark:<br>
Think of the <span class="math-container">$n$</span> complex numbers <span class="math-container">$\sin(\lambda_j z)$</span> as vectors in the 2D plane; for <span class="math-container">$n\geq 3$</span> and fixed <span class="mat... | https://mathoverflow.net |
443,986 | [
"https://physics.stackexchange.com/questions/443986",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/192690/"
] | If I have a Langevin Equation with an external force term (which may be time dependent), is it possible for me to apply the standard 4th order Runge Kutta algortihm to solve it numerically?
Edit:
I would like to mention the use case for the question asked! I am trying to simulate the motion of a Brownian Particle, wh... | After Hawking wrote "The three-dimensional space is flat", he explained what that means: "That is to say it obeys Euclidean geometry." And as an example of what it means to obey Euclidean geometry, he gives the example "The angles of a triangle add up to 180 degrees". In a non-flat space, the angles of a triangle can a... | The term “flat” in this context does not mean 2 dimensional. It means “Euclidean”. A flat manifold is one where the interior angles of a triangle sum to 180 degrees, parallel lines never converge or diverge, and if you parallel transport a vector in a loop it lines back up on top of itself.
In contrast, the surface o... | https://physics.stackexchange.com |
197,079 | [
"https://security.stackexchange.com/questions/197079",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/94833/"
] | I sent a password reset request, to reset an account of mines and after having some talk with a rep I told him I forgot the email to the account which he told me to just provide the IP address that I used to login to the account doing so I gave it to him and I got back access.
But, I can see some problems with this fo... | It's not a safe way to verify you are the same person as the one who owns an account. It could be a relatively safe way to identify which account you (potentially) own if you have forgotten the username. (Or if your email address functions as your user name.)
If your IP address has only been used with one account rec... | <blockquote>
Is this a safe way to verify identity for an account password reset?
</blockquote>
No.
However, when joined with other things, it might have been considered enough for the representative to consider that you indeed are who you claim to be and reset the password for you.
| https://security.stackexchange.com |
741,360 | [
"https://physics.stackexchange.com/questions/741360",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/350173/"
] | Incompressible Navier-Stokes in vector notation is written as
<span class="math-container">$${\partial U \over \partial t}+(U\cdot\nabla)U =-\frac{1}{\rho} \nabla P + \nu \nabla^2(U),$$</span>
where <span class="math-container">$U$</span> is velocity vector field <span class="math-container">$U=(u,v)$</span>, <span cl... | Differentiating by the product rule: <span class="math-container">$$\frac{\partial (u_iu_j)}{\partial x_j}=u_j\frac{\partial u_i}{\partial x_j}+u_i\frac{\partial u_j}{\partial x_j}$$</span>But, for an incompressible fluid, the continuity equation reduces to <span class="math-container">$$\frac{\partial u_j}{\partial x... | The two forms are strictly equivalent in the incompressible case:
<span class="math-container">$$
\nabla \cdot (u\otimes u) = (u\cdot \nabla)u+(\nabla\cdot u)u
$$</span>
where <span class="math-container">$\nabla\cdot u=0$</span> when the fluid is incompressible.
The reason why this formulation is also natural is due t... | https://physics.stackexchange.com |
626,356 | [
"https://physics.stackexchange.com/questions/626356",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98822/"
] | The Higgs field is responsible for the masses of all elementary particles. Including the Higgs particle. But doesn't this transfer the question of mass, or inertia, to the Higgs field itself? Why has the Higgs field inertia which can be transmitted to the massless elementary particles?
| <blockquote>
from this we can write centripetal acceleration as:
<span class="math-container">$$ \ddot{r_c} = \frac{| \hat{j}|^2}{ |\vec{r}|}$$</span>
by the formula:
<span class="math-container">$$ \vec{\ddot{r_c} } = \frac{|\vec{\dot{r} }|^2}{|\vec{r}|^2}$$</span>
</blockquote>
These formulas are not general formulas... | Your initial equation assumes a particular coordinate system. If you move to a different system, all of your relations will change.
| https://physics.stackexchange.com |
25,064 | [
"https://electronics.stackexchange.com/questions/25064",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3632/"
] | I need resourceful information's on how to implement the serial protocol via an RS485 interface. As regards to my area of application, I simple want to communicate with my micro-controller via an RS485 port. How do I go about this? Any useful links with useful steps will be appreciated.
EDIT:
I am designing an energy... | <blockquote>
I want to know if there is anyway I can combine the serial protocol communicating via the RS485 interface
</blockquote>
RS485 doesn't have any defined serial protocol -- it's just the physical layer for specifying a multidrop differential signaling network, + a UART data link layer for encoding bytes vi... | Covert the sensor output by using controller to UART (Rx/Tx) standard. Feed the same UART signal into the input of RS485 electrical level converter and inject into your transmission medium.
i.e, transmission medium will carry UART-RS485 differential signal.
| https://electronics.stackexchange.com |
304,711 | [
"https://softwareengineering.stackexchange.com/questions/304711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/207104/"
] | I've been reading Scrum Guide and one part is missing for me.
<strong>What happens if Sprint Goal is not met at all?</strong>
Let's say the Sprint Goal is a big part of a functionality which cannot be broken into parts further so devs have, say 2 weeks (the Sprint duration) to accomplish it or not, but they fail to do... | The sprint goal should be placed back into the backlog and then reevaluated along with all the other stories in the backlog. In most cases, this will mean it will be prioritized to the top of the backlog and pulled into the next sprint. In theory, if business needs have changed since the backlog was last prioritized,... | I think this should be discussed and post mortem'ed in the Sprint Retrospective. Conclusions regarding the sprint goal will obviously vary, but ultimately the decision to give it up or carry it over to the next sprint should belong to the Product Owner.
| https://softwareengineering.stackexchange.com |
75 | [
"https://cs.stackexchange.com/questions/75",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/5/"
] | Is there any evidence suggesting that time spent on writing up, or thinking about the requirements will have any effect on the development time? Study done by Standish (1995) suggests that incomplete requirements partially (13.1%) contributed to the failure of the projects. Are there any studies done which show that ti... | I could be wrong, but I view smoothed analysis as a way to <em>explain</em> the in-practice behaviour of algorithms that have bad theoretical guarantees (simplex, k-means, and so on). I'm not sure what it would mean to <em>use</em> smoothed analysis in practice, except to justify the use of a particular heuristic with ... | The way people analyze algorithms in the real world is vastly different from academia. While in academia the goal is to find a provably-correct upper bound on the running time, in real life the goal is to understand how the algorithm works, and what tweaks can improve the running time. There are two main methods that a... | https://cs.stackexchange.com |
26,483 | [
"https://chemistry.stackexchange.com/questions/26483",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/14530/"
] | I was reading about concentration terms like molarity, molality, etc. and then I came across a question: which concentration is more:
<ul>
<li>1M(molar) of solute x dissolved in water vs.</li>
<li>1m(molal) of solute x dissolved in water </li>
</ul>
When I Google it, I did not find exact answers but did find some rel... | To convert from molal to molar, one generally needs to know the density of solution as well as the formula weight of solute. Suppose there is a single solute <span class="math-container">$x$</span> in water, and that <span class="math-container">$x$</span> has a formula weight of <span class="math-container">$f_x$</sp... | Molality is defined as the number of moles of solute per kilogram of solvent.i.e we have to weight 1kg of water (solvent) before adding solute. so 1 molal will be less concentrated.
| https://chemistry.stackexchange.com |
186,709 | [
"https://softwareengineering.stackexchange.com/questions/186709",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81222/"
] | This website is supposed to be a game where the players have some 'buildings' and these buildings produce resources. E.g. an iron mine may produce 30 pieces of iron ore per minute and automatically add it to the user's inventory. It doesn't matter whether the user is online or not, it should be running 24/7. So when th... | <pre><code>Need to save some state
Put it in the database
Retrieve on next login
</code></pre>
Actually, when the user logs in again, what you'll need to do is figure out how many pieces of iron ore <em>should have been mined</em> while the user was gone, and update the database with that knowledge the next time ... | It should not be your {whatever technology} website that should be doing this processing at all.
A background process of some sort should be doing the processing, and persisting it to the database intermittently.
That way other users can interact with the data whenever it needs to.
When you login to your website, i... | https://softwareengineering.stackexchange.com |
113,326 | [
"https://datascience.stackexchange.com/questions/113326",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/138987/"
] | I am working on a project where I need to train a model with a data set of 250 images. My <code>epochs</code> count is 500. Is that too much? Will it overfit?
I did this because I was following project with a data set of 40 images and the tutor used 500 <code>epochs</code>.
| Vanishing & Exploding Gradient problem happens in case of deep neural network. In NN when we have to update weights & biases for each layer we calculate the partial derivate with respect to y_hat at each layer <strong>(Back Propogation Algorithm)</strong>. Because in this case weights are multiplied in chain wi... | There's no problem using the sigmoid function in the final layer. Vanishing/exploding gradients only become a issue when the sigmoid function is used across multiple layers.
Sigmoid is used "behind the scenes" when you use the softmax function for multi-class classification. A sigmoid function is used for eac... | https://datascience.stackexchange.com |
126,058 | [
"https://electronics.stackexchange.com/questions/126058",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51770/"
] | I made a simple program in Visual C# which communicates with AVR via FT232RL chip.
PC <-> FTDI <-> MCU.
I am using FTD2XX_NET.dll for direct access to USB Device.
I'm wondering, what's the difference between a pair of FTDI-AVR and a single AVR with built-in USB Controller? I think there must be some difference... | There are quite some reasons, but they are, at least for most people, fairly niche.
The reasons that I see and have experienced
<ul>
<li>The choice in USB enabled AVRs is quite limited, especially the TINY family. If for some reason an AVR is required that does not have a combination of USB and some other peripheral,... | There are advantages in using a separate USB chip, and letting the AVR communicate via its UART.
A USB stack has to respond to polling from the host PC. This happens <em>at least</em> every millisecond. That means that it is even more difficult to guarantee hard real-time response to events, as the MCU might get inter... | https://electronics.stackexchange.com |
266,834 | [
"https://dba.stackexchange.com/questions/266834",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105539/"
] | DBMS_SCHEDULER is occupying all of my SYSAUX tablespace. I ran <code>dbms_scheduler.purge_log</code> which deleted 100 million rows from <code>dba_scheduler_job_run_details</code>, however <code>v$sysaux_occupants</code> and the data file size remain unchanged. Is there some additional action I need to take to clear th... | To release space to SYSAUX tablespace you can try:
<pre><code>alter table sys.scheduler$_event_log enable row movement;
alter table sys.scheduler$_event_log shrink space;
alter table sys.scheduler$_event_log disable row movement;
</code></pre>
| <pre><code>truncate table sys.scheduler$_event_log drop storage;
</code></pre>
| https://dba.stackexchange.com |
232,010 | [
"https://electronics.stackexchange.com/questions/232010",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37745/"
] | Here's my problem:
I have a power supply rated at 5V, 2.1A
I need this to feed two devices, both running at 5V
<ul>
<li>Device one is a single-board computer that can consume anything between 0.5A and 1.5A depending on what it's doing.</li>
<li>Device two is a battery charger, which is happy to take anything it can... | First, some clarification. There are two loads for one power supply: load A and load B. Load A needs to get power at 5 V with (at most) 10% tolerance. It can take any current in range from 0 (or 0.5 A, it does not matter) to the maximum capacity of the power supply. Load B must get "what remains".
There is no common s... | You can build a circuit that behave as you say. Basically, you need a small shunt resistor that measure the total current consumed by both device, a P-channel mosfet that will limit the power provided to device two, and an opamp inbetween that adjusts the gate voltage of the mosfet depending on the total current (i.e. ... | https://electronics.stackexchange.com |
778,479 | [
"https://math.stackexchange.com/questions/778479",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/107628/"
] | I'm stuck in solving the integral of $\dfrac{1}{\sin(x-a)\sin(x-b)}$. I "developed" the sin at denominator and then I divided it by $\cos^2x$ obtaining $$\int\frac{1}{\cos(a)\cos(b)\operatorname{tan}^2x-\cos(a)\sin(b)\operatorname{tan}x-\sin(a)\cos(b)\operatorname{tan}x+\sin(a)\sin(b)}\frac{1}{\cos^2x}dx$$
Then I made... | Here is another approach to join the 'party' using a simple trigonometric technique.
$$
\begin{align}
&\int \frac{1}{\sin(x-a)\sin(x-b)} dx\\&=\frac{1}{\sin(a-b)}\int \frac{\sin(a-b)}{\sin(x-a)\sin(x-b)} dx\\
&=\frac{1}{\sin(a-b)}\int \frac{\sin((x-b)-(x-a))}{\sin(x-a)\sin(x-b)} dx\\
&=\csc(a-b)\int \fr... | <strong>Hint</strong> for the original problem $\int\frac{1}{\sin(x-a)\sin(x-a)} \mathrm{d}x$:
$$\frac{1}{\sin(x-a)\sin(x-a)}=\csc^2(x-a) \; \mathrm{and} \, \int{\csc^2u \,\mathrm{d}u}=-\cot u+C$$
| https://math.stackexchange.com |
132,839 | [
"https://mathoverflow.net/questions/132839",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5239/"
] | Let $n$ be a positive integer and $A$ be a commutative ring. The ring $A$ is said to be of Bass stable range $\mathrm{sr}(A)\leq n$ if for $a, a_1, \dots, a_n \in A$ one has the following implication:
$$1 \in \langle a, a_1, \dots, a_{n}\rangle \implies \exists \ x_1, \dots, x_n \in A, 1 \in \langle a_1+x_1a,\ \dots... | Sorry for putting this in a separate answer, but I think it will be cleaner this way.
<blockquote>
The stable range of $\mathbb{Z}[x]$ is equal to 3.
</blockquote>
I believe I now understand Vaserstein's intended argument that it's $\ge 3$:
(1) There are rings of the form $A={\mathbb Z}[x]/(h)$ such that $SK_1(A)... | There's a comment at the top of page 993 of
L N Vaseršteĭn, A A Suslin, "Serre's problem on projective modules over polynomial rings, and algebraic K-theory", Math. USSR Izv., 1976, 10 (5), 937–1001,
to the effect that one of the authors had proved that the stable rank of $\mathbb{Z}[X]$ is 3, but unfortunately witho... | https://mathoverflow.net |
215,691 | [
"https://security.stackexchange.com/questions/215691",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/215068/"
] | My company ships very large, very heavy products to the homes of everyday consumers (think big home renovation materials). Currently, we provide the customer's name, shipping address, and phone number to the factory. The factory then provides that information to a freight company who will then provides it to a final-mi... | <blockquote>
my concern is that providing this email address to other businesses in
our manufacturing and delivery pipeline will have PCI compliance
consequences.
</blockquote>
No, PCI does not care about email address at all. The only time it's mentioned in the DSS is to state you can't send unencrypted PAN vi... | PCI compliance is about payment data. An email address on it's own is not payment data, so it's nothing you have to worry about with regards to PCI compliance.
Generally speaking, the email address is not more or less important than the "customer's name, shipping address, and phone number". So if that was cleared to ... | https://security.stackexchange.com |
29,140 | [
"https://datascience.stackexchange.com/questions/29140",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/47675/"
] | I understand that the models are only as good as the data you get, and bad design can generate really bad data. Nonrandom sampling, unbalanced/incomplete designs, confounding, can make data analysis really hard.
At what point should one be confident that they ran a <em>useful</em> model? Do you just do a cross-valida... | Hey Welcome to the Site!
What you are saying is right, Data Science din't reach to the stage where it has some standard methods for achieving this(standard procedures, don't know we would be able to reach that stage in near future). But we have some general standards like:
<ol>
<li>Forecasting: ETS,ARIMA,SARIMA etc <... | <blockquote>
What makes you confident in your results?
</blockquote>
The appropriate method to evaluate whether you have modeled a real signal or noise is completely dependent on the question you are asking and the modeling approach you've used to address it. Many very thick books have been written on this topic, of... | https://datascience.stackexchange.com |
40,172 | [
"https://mechanics.stackexchange.com/questions/40172",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/24696/"
] | I have an 2013 Opel Astra J, recently noticed that the seat belt warning chime for the passenger seat doesn't work (I don't have any other indication except for that chime), driver's seat chime and dashboard indicator are working.
also, after ignition, the yellow indicator for armed passenger airbag is on for 60 secon... | Yes, the passenger seat belt warning chime and the passenger present systems are linked.
I can't speak about Opel directly, I'm familiar with Mazda and Honda. The way the passenger present systems works, is by using a weight sensor in the seat. The weight sensor senses below 20 kilos and above 40 kilos. If something ... | The "seatbelt buckled" sensor is not the ultimate decision on airbag deployment strategy. In fact, an unbuckled setbelt in some systems sets a condition for GREATER airbag deployment force on some systems - the logic being that the airbag is now solely responsible for an impact ride-down, and the task is not shared by... | https://mechanics.stackexchange.com |
179,568 | [
"https://mathoverflow.net/questions/179568",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10893/"
] | Given an operator $A \in \mathcal L(B)$, $B$ being a Banach space, I came across the following question: assume $\mathrm{dom}(A)=\mathrm{range}(A)$, $\mathrm{dom}(A)$ dense in $B$.
Under which conditions is it possible to obtain the boundedness of $A$ from the boundedness of $A^2$. It is clear that "in most" cases thi... | Your first query has been answered, but not the second. We make the simple remark that it is the case when $A$ is a self-adjoint (even normal) operator on Hilbert space by the spectral theorem. Presumably this can be extended to operators on general Banach spaces with good spectral properties (spectral operators, ope... | I can give a counterexample where $A:H\to H$ is a linear, bijective, unbounded self map of a Hilbert space with $A^2=\text{id}$.
Something similar can probably be done for many other Banach spaces as well, but I hope this gives a flavor of what might happen.
It might be that no counterexamples exits in somehow reasonab... | https://mathoverflow.net |
843,634 | [
"https://math.stackexchange.com/questions/843634",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I am wondering whether for any two lines $\mathfrak{L}, \mathfrak{L'}$ and any point $\mathfrak{P}$ in $\mathbf{P}^3$ there is a line having nonempty intersection with all of $\mathfrak{L}, \mathfrak{L'}$, $\mathfrak{P}$. I don't really know how to approach this, because I was never taught thinking about such a problem... | The polynomial $x^2+x$ is always divisible by 2, but as polynomials $x^2+x\not\equiv0\pmod2$ -- for one thing, the degree on the left is different from the degree on the right.
Similarly, even though $x^p-x$ is zero mod $p$ for any $x$, <em>as polynomials</em>, $x^p$ and $x$ are different.
Basically "are equivalent a... | You have to make a distinction between (more concrete) functions from $\Bbb Z / p \Bbb Z$ to $\Bbb Z/p \Bbb Z$ and (more abstract) polynomials with coefficients in $\Bbb Z/ p \Bbb Z$.
For each polynomial, there is an associated polynomial function. And as you have just discovered, it is NOT true that if the polynomia... | https://math.stackexchange.com |
50,965 | [
"https://security.stackexchange.com/questions/50965",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/39521/"
] | Is it possible to extract userid from GPG public key?
I got public key only and want to know to whom it might belong. I find one possible workaround — to publish this information on keyserver — it decodes information and reveals it to public. But I'm not sure, I should do this.
Is it possible to extract userid using ... | Use <code>gpg --list-packets [filename]</code> to list all data packets, then grep for user IDs. For example:
<pre><code>$ gpg --export 0xDED9B508F4E10DB2 | gpg --list-packets | Egrep '^:user ID packet'
:user ID packet: "John Doe <john@example.org>"
</code></pre>
An alternative would be to use <code>pgpdump</co... | The following will emit the "username < email >" field from the UID packet, without requiring regexes:
<pre><code>$ gpg --with-colons --list-keys 0xDED9B508F4E10DB2 | awk -F: '$1=="uid" { print $10 }'
blah <a@b>
</code></pre>
| https://security.stackexchange.com |
75,484 | [
"https://electronics.stackexchange.com/questions/75484",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24239/"
] | I have building a device that will use a solenoid. The solenoid will be used such that it will be mounted in the floor and when a stick is put over it, it will start vibration. That vibration needs to be felt by the person holding the stick. I learned of late that solenoids are are of two type i.e. Pull an Push.
Can ... | First, don't confuse the interface (multiplexing the address lines) with the internal arrangement (laying things out in a matrix).
All RAM chips use a matrix a the the lowest (single bit cell) level, most use a less regular layout at the higher level (for instance two separate banks).
Multiplexing the address lines ... | The architecture is different. Dynamic devices store a bit per device, so you see 8 or 16 chips in a line (or on a SIMM) to store a byte or word. (Plus one or two more, if parity bits are needed.) Static devices store a full byte, so you usually see one or two of them on a board. It's only if the data bus is wide (... | https://electronics.stackexchange.com |
4,957 | [
"https://quantumcomputing.stackexchange.com/questions/4957",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/2832/"
] | Once a state is measured, but we don't look at the result, is the state now written as a density matrix, that is, the probability that it could land on a measurement operator multiplied by the operator applied on the state, this summed up for every measurement operator that it could land on contained in the measurement... | Suppose you have a state <span class="math-container">$\rho$</span>, and a random process that changes this to a state <span class="math-container">$\rho_j$</span> with probability <span class="math-container">$p_j$</span>. If you know what the value of <span class="math-container">$j$</span> is, your knowledge of the ... | In the Copenhagen interpretation, there are only two kinds of <em>things</em> that one can do, one is <strong>evolution</strong> and other is the <strong>measurement</strong>. Measuring but <em>not looking</em> is equivalent to measuring the system and hence projecting it to one of the possible eigenstates. (Or maybe y... | https://quantumcomputing.stackexchange.com |
528,497 | [
"https://physics.stackexchange.com/questions/528497",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | As you would know that <span class="math-container">$\text {Force}= \text {mass} \times \text {acceleration}$</span>. So <span class="math-container">$\text {mass}= \text {force}\div{\text {acceleration}}$</span>.
Now both force and acceleration are vectors. But their is no such thing as vector division. So how can we... | From <span class="math-container">$\vec F= m\vec a$</span>, we know that direction of <span class="math-container">$\vec F$</span> and <span class="math-container">$\vec a$</span> are same.
Let's define a unit vector such that <span class="math-container">$$\vec u = \frac{\vec F}{|\vec F|} = \frac{\vec a}{|\vec a|}$$... | Since <span class="math-container">$\vec F= m\vec a$</span> this would imply <span class="math-container">$| \vec F|= m|\vec a|$</span>. And since magnitude of a vector is scalar, we can say <span class="math-container">$$m=\frac{|\vec F|}{|\vec a|}$$</span>
| https://physics.stackexchange.com |
104,442 | [
"https://mathoverflow.net/questions/104442",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25641/"
] | Hi all. I have a linear programming problem where I need to find both maximum and minimum values of the objective function. The optimal points are not relevant.
Is there an efficient way to do so?
| You can certainly construct problems where the active constraints for the maximum are disjoint from the active constraints for the minimum, so this is as hard as separately solving for max and min.
| Probably not much more efficient than finding the max and min solutions separately.
| https://mathoverflow.net |
40,956 | [
"https://biology.stackexchange.com/questions/40956",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/17473/"
] | It seems in electrophoresis, agrose gel always runs horizontally, and SDS-PAGE gel always runs vertically, why?
| When you stand general agarose gel vertically, the gel is slippery coming out from the bottom; although, some run vertically.
To polymerize acrylamide, it is good idea to avoid air because oxygen inhibits polymerization of acrylamide. You would get an air tight condition, pouring acrylamide between glass plates, but ... | Generally, one would want to run all the gels vertically to save the space. The gel slab has to either support itself or be enclosed in a supporting structure, like between glass plates. Simple agarose electrophoresis wouldn't benefit from enclosure into a precisely defined glass enclosure, and agarose is not strong en... | https://biology.stackexchange.com |
47,870 | [
"https://mathoverflow.net/questions/47870",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2191/"
] | Suppose that a triangulated category $C$ contains a full additive subcategory $B$ of (strong) generators (i.e. there does not exist a proper strict triangulated subcategory $C'\subset C$ that contains $B$) such that: there are no non-zero $C$-morphisms between $B_1$
and $B_2[i]$ for any $B_1,B_2\in Obj B$ and $i\neq 0... | Mikhail, if you assume more generally that $C$ is topological (in an appropriate sense) then your claim is also true. As Matthias suggests above, this is a tilting-like theorem, Theorem 5.1.1 in '<em>Stable model categories are categories of modules</em>' by Schwede and Shipley. This assumption may comprise all example... | It follows that $C \cong D^b(mod-B)$. I don't think the latter is equivalent to $K^b(B)$ (by the way, what does $K^b$ denote?) unless in very special situation, like when the homological dimension of $B$ is zero. For example, if $X = Spec A$ is a smooth affine variety and $C = D^b(coh-X)$, then you can take $B = \{O_X\... | https://mathoverflow.net |
235,811 | [
"https://softwareengineering.stackexchange.com/questions/235811",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/40410/"
] | In my earlier days of programming, I was using Visual Basic for learning. It taught me many concepts, and I was able to make some cool programs (in my opinion, anyways...). I have expanded my horizon to basic C/C++, PHP, and MySQL.
One of my most favourite projects, I want to turn into a multi-platfrom (for x86/x64) w... | It depends primarily of what platforms you're aiming at.
If you target <strong>only PC platforms</strong> (which none of is very exotic), then you have many options regarding language (C++, Java, Python, Go, etc.) and cross-platform GUI framework (Qt, GTK, SWT, Swing, wxWidgets, etc etc). Portability shouldn't be main... | Each OS uses its own file formats for executable files and shared libraries and each OS also has its own API for applications to interact with it. This means that generally, binaries built for OS A can not be used on OS B.
There are two ways to write applications that can be used on multiple platforms:
<ol>
<li>You u... | https://softwareengineering.stackexchange.com |
355,164 | [
"https://physics.stackexchange.com/questions/355164",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167499/"
] | I know that when two particles are collided some new particles come into existence and i know that the new particles weren't inside of the original particles. I understand that the energy of the collision can vibrate other fields to make particles.
What I don't understand is "were those other fields nearby the colli... | I presume you are talking about Quantum Fields. Particles are basically disturbances in fields. When particles collide, they can release energy. This agitates quantum fields, leading to a particle. (The disturbance in the field is the particle). There is a new disturbance in the field, and so, a new particle is created... | Think of tangled up wires on top of each other. Sometimes when you move one of them the right way it moves the other. Now let us say this movement is a vibration. You vibrate one and it vibrates the other. This is a cartoon picture of the mathematics. A disturbance in some field (particle A) can cause a disturbance in... | https://physics.stackexchange.com |
494,261 | [
"https://stats.stackexchange.com/questions/494261",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/296098/"
] | Suppose we have the standard simple linear regression model:
<span class="math-container">$$
Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i,
$$</span>
with <span class="math-container">$E[\varepsilon_i|X_i] = 0$</span> and <span class="math-container">$\text{Var}[\varepsilon_i|X_i] = \sigma^2$</span>.
I'm trying to show t... | Following from the third line, <span class="math-container">$E[Y_i-\bar Y|\mathbf X]=(\beta_0+\beta_1X_i)-(\beta+\beta_1\bar X)=\beta_1(X_i-\bar X)$</span>. When substituted that back, we have
<span class="math-container">$$\begin{align}E[\hat \beta_1|\mathbf X]&=\sum_{i} \beta_1g_i(\mathbf X)(X_i-\bar X)=\beta_1\s... | You can see it as
<span class="math-container">$$
\hat{\beta}=(X^tX)^{-1}X^ty = (X^tX)^{-1}X^t(X\beta+\varepsilon) =(X^tX)^{-1}X^tX\beta + (X^tX)^{-1}X^t\varepsilon
$$</span>
So you have that
<span class="math-container">$$
\hat{\beta}=\beta + (X^tX)^{-1}X^t\varepsilon
$$</span>
And then, it is straightforward to see t... | https://stats.stackexchange.com |
259,436 | [
"https://mathoverflow.net/questions/259436",
"https://mathoverflow.net",
"https://mathoverflow.net/users/103514/"
] | Can somebody explain why the cumulative binomial equals an integral expression?
Thanks!${}$
$$
\sum_{j=0}^{k-1}\binom{n}{j}\theta^j(1-\theta)^{n-j} = 1- \binom{n}{k}k\int_0^\theta t^{k-1}(1-t)^{n-k}dt\,.
$$
| <strong>Key players:</strong> $m\binom{n}m=n\binom{n-1}{m-1}$, derivative $\frac{d}{d\theta}$ and re-indexing $j-1\rightarrow j$.
Denote the LHS by $f(\theta)$ and the RHS by $g(\theta)$. Take derivatives w.r.t. $\theta$ to get
$$g'(\theta)=-k\binom{n}k\theta^{k-1}(1-\theta)^{n-k}=-n\binom{n-1}{k-1}\theta^{k-1}(1-\the... | This is essentially the same as the solution by T. Amdeberhan, but I find that it is sometimes easier to prove such identities simultaneously for all $k$. I'll use the standard formula
$$ \sum_{k=0}^n k\binom{n}{k}U^{k-1} = n(1+U)^{n-1}\quad(*) $$
obtained by differentiating the binomial formula. Let
$$ I(k) = \binom{n... | https://mathoverflow.net |
87,049 | [
"https://stats.stackexchange.com/questions/87049",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/40508/"
] | I've got a question and I have done several experiments in R, yet couldn't figure out why.
The question is for a data set of N*D, N for number of data points and D for dimension, the maximum number of principal component is max(N, D).
Then I discovered a fact that, when N is larger than D, by using D principal compon... | I think you have some mistaken notions about PCA. The maximum number of principal component is D. Principal components are orthogonal to each other, so once you have D of them, you span the entire space. You wouldn't be able to find a D+1 principle component in a space of D dimensions, regardless of N>D.
The first par... | @mt0 provided a nice answer (+1), the only thing missing there is an illustration. So in an attempt to win the Worst CrossValidated Illustration Contest here is my drawing captured by a laptop camera:
<img src="https://i.stack.imgur.com/ICWQb.jpg" alt="PC">
Here in both cases $D=2$. On the left $N>D$, so there are... | https://stats.stackexchange.com |
136,420 | [
"https://mathoverflow.net/questions/136420",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23204/"
] | I am looking for references on the following: <strong>Spin structures on surfaces, and particularly the spin mapping class group.</strong>
<strong>What is known about generating the spin mapping class group? Has anybody found a finite set of generators?</strong>
| The answer of course depends on the spin structure chosen. The paper
Johnson, Dennis,
Spin structures and quadratic forms on surfaces.
J. London Math. Soc. (2) 22 (1980), no. 2, 365–373.
proves that the set of spin structures on a closed surface $\Sigma_g$ of genus $g$ can be identified with the set of quadratic ... | In the following paper, explicit finite generating set of the spin mapping class group for the spin structure with Arf invariant 0 was obtained
On diffeomorphisms over surfaces trivially embedded in the 4–sphere,
Algebraic & Geometric Topology 2 (2002) 791–824
for the spin structure with Arf invariant 1:
Surf... | https://mathoverflow.net |
629,491 | [
"https://electronics.stackexchange.com/questions/629491",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/283858/"
] | Basically I am making a reflow plate, that requires mains voltage for the heating plate. I have a basic knowledge of mains voltage and am just trying to make the product as safe as possible, by adding fuses, grounding any metal parts, having isolation between high voltage and low voltage.
But I am not sure if it matter... | So long as the switch is specified for 240V AC use and the contact current rating is greater than that drawn by the plate it shouldn't matter what switch you use.<br />
Since you are in the UK make sure it has British Standard (BS) marking. Try to make sure it's a genuine part from a reputable manufacturer and supplier... | You can't use any switch.
The switch must have safety approvals your electrical code requires for mains voltage.
In addition, the switch must be rated for local mains voltage with some margin , it must be rated to handle the rated current, and it must be rated to handle any inrush current as the heater will draw a surg... | https://electronics.stackexchange.com |
215,886 | [
"https://electronics.stackexchange.com/questions/215886",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52628/"
] | Consider that the hardware team will take 2 months to develop some hardware, but by that time I will need to have the software ready.
My question is that how can I write the software and test it without having the hardware?
Is there any standard/s to be followed? How do you do it?
| Not having hardware during the initial stages of firmware development happens. Common strategies to deal with this are:<ol>
<li>Spend time up front architecting the system carefully before you write any code. Of course you should do this anyway, but in this case it's even more important than usual. It's much easier... | Without any insight into what it is you're developing, or which family of microcontrollers your hardware will eventually be based on, most families of microcontrollers have low cost development systems available that have a suite of common peripherals on them, which may allow you to simulate at least some of your event... | https://electronics.stackexchange.com |
24,327 | [
"https://dba.stackexchange.com/questions/24327",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11628/"
] | I need to query an SQL database to find all distinct values of one column and I need an arbitrary value from another column. For example, consider the following table with two columns, key and value:
<pre><code>key value
=== =====
one test
one another
one value
two goes
two here
two al... | The easiest query to write is for MySQL (with not strict ANSI settings). It uses the non-standard construction:
<pre><code>SELECT key, value
FROM tableX
GROUP BY key ;
</code></pre>
In recent version (5.7 and 8.0+) where the strict settings and <code>ONLY_FULL_GROUP_BY</code> are the default, you can use the <code>AN... | <strong>For MS-SQl Server:</strong>
<pre><code>;with FinalDataset as
(
select *,
row_number() over(partition by key order by value) as rownum
from YourOriginalTable
)
select
key,
value
from FinalDataset
where rownum = 1
</code></pre>
Likewise, you could have rownum = 2 for your second result s... | https://dba.stackexchange.com |
163,583 | [
"https://stats.stackexchange.com/questions/163583",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/24515/"
] | I am trying to derive the covariance of two sample means and get confused at one point. Given is a sample of size $n$ with paired dependent observations $x_i$ and $y_i$ as realizations of RVs $X$ and $Y$ and sample means $\bar{x}$ and $\bar{y}$. I try to derive $cov(\bar{x},\bar{y})$.
I am relatively sure the result s... | <blockquote>
Covariance is a <em>bilinear</em> function meaning that
$$
\operatorname{cov}\left(\sum_{i=1}^n a_iC_i, \sum_{j=1}^m b_jD_j\right)
= \sum_{i=1}^n \sum_{j=1}^m a_i b_j\operatorname{cov}(C_i,D_j).$$
There is no need to mess with means etc.
</blockquote>
Applying this to the question of the covarianc... | I think the algebra issue is resolved with the following:
${1 \over n^2}E(\sum_{i=1}^n x_i \sum_{i=1}^n y_i)={1 \over n^2}E(\sum_{i=1}^n x_i y_i +\sum_{i\ne j}x_i y_j)$
$={1 \over n^2}(n(Cov(x_i,y_i)+\mu_X \mu_Y)+n(n-1)\mu_X \mu_Y)$
$={1 \over n^2}(n Cov(x_i,y_i)+n^2 \mu_X \mu_Y))=Cov(x_i,y_i)/n+ \mu_X \mu_Y$
| https://stats.stackexchange.com |
1,294,585 | [
"https://math.stackexchange.com/questions/1294585",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/242617/"
] | My hypothesis is that $\mathbb{R \times R}$, the set of all pairs $(r_1, r_2)$, of real numbers is uncountable. I understand that the set of all pairs of natural numbers is countable. But could someone explain why the set of all pairs of real numbers uncountable? I am having trouble proving it using diagolization
| Notice that $\Bbb R \times \{0\} \subset \Bbb R \times \Bbb R$ has the same quantity of elements that $\Bbb R$¹. So if you prove that $\Bbb R$ is uncountable, you're done.
¹ Actually $|\Bbb R| = |\Bbb R^n|$ for every $n$.
| Real numbers are uncountable, hence the Cartesian product of real numbers is uncountable.
| https://math.stackexchange.com |
19,749 | [
"https://dba.stackexchange.com/questions/19749",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/9587/"
] | Normally when I create a stored procedure I use the following as a template of sort
<pre><code>Create procedure <procedurename>
<@param1 <type>, @param2 <type>, etc..>
as begin
<procedure>
end
</code></pre>
Is there a way to include granting execute permission on only that stored pro... | <pre><code>GRANT EXECUTE ON dbo.procname TO username;
</code></pre>
| truncate table Setting permission on objects like stored procedures can be accomplished with:
<pre><code>GRANT EXECUTE ON <schema>.<object> to <user>;
</code></pre>
However, you may also want to grant security rights at both the login and user level. You will want to determine and grant ONLY the nec... | https://dba.stackexchange.com |
28,318 | [
"https://chemistry.stackexchange.com/questions/28318",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/15414/"
] | While calculating the adiabatic flame temperature for the following combustion reaction:
$$\ce{\Phi\, C2H6 + $3.5$\,(O2 + $3.76$\,N2) -> $a$\,CO2 + $b$\,CO + $d$\,H2O + $e$\,H2 + $f$\,O2 + $g$\,N2}$$
Where $\Phi$ is the equivalence ratio.
To determine the product composition ratios $a$, $b$, $d$, $e$, $f$ I need ... | Short answer (After some trials): <strong>It does not matter which dissociation reaction you use</strong>, The system of equation will be solved anyway since the reactions are not independent.
However, using the first reaction as a dissociation mechanism would generate a Kp equation that's a lot easier to solve than t... | We should use only those equations which are linearly independent. For example, of the three equations specified eqn.(1) can be written by linearly combining eqn(2) and eqn(3).
So use eqn (2) and (3) only.
| https://chemistry.stackexchange.com |
540,802 | [
"https://electronics.stackexchange.com/questions/540802",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/272895/"
] | For a jump height measuring device to have feedback of what training works.
| This is a generic method. The ubrr is an unsigned int which makes it 16 bits wide (2 bytes).
To break this into discrete bytes like in the example, you need to shift the bits right by 8 to get the high byte.
In your specific example it doesn't matter because the high byte is empty anyway, but what if you need a ubrr o... | For 3,096 then
UBRRH = decimal 12 OR binary 1100
UBRRL = decimal 24 OR binary 0001 1000
| https://electronics.stackexchange.com |
3,896,953 | [
"https://math.stackexchange.com/questions/3896953",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/814866/"
] | Let <span class="math-container">$p$</span> be a prime. Find all nonzero integers <span class="math-container">$k$</span> such that <span class="math-container">$\sqrt{k^2 − pk}$</span> is a positive integer.
<hr />
I first let <span class="math-container">$k^2 - pk = x^2,$</span> where <span class="math-container">$x$... | Let <span class="math-container">$A$</span> be abelian group. Apply <span class="math-container">$U$</span> to get <span class="math-container">$U(A)=A$</span>. Now apply <span class="math-container">$F$</span> to get <span class="math-container">$FU(A) = A/A'$</span>. Now, since <span class="math-container">$A$</span>... | Claim 1 holds, because for every group you can find a (natural) isomorphism between <span class="math-container">$FU(G)$</span> (the abelianization of <span class="math-container">$G$</span>, that was already abelian and has just been regarded as a mere group, forgetting abelianity: the commutator subgroup <span class=... | https://math.stackexchange.com |
58,437 | [
"https://mechanics.stackexchange.com/questions/58437",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40031/"
] | I failed a smog test in CA (1992 Corvette) and the results came back that the EGR valve is not holding pressure. It failed on nitric oxide emissions measured at 989 ppm at 15 mph and 1329 ppm at 25 mph.
The repair for that is cheap, but the mechanic is also saying my cats are bad, which are mondo expensive as you well... | I bought a car that had 3 previous owners and recently sold it. All it means is that each owner had a reason for selling the car. Maybe it was too small for a growing family, maybe it was a fun weekend car that no longer fits in the budget.
Can you see how long each owner kept the car? If it's been through 3 owners i... | A long time ago, I bought a car with 2 owners, both of them having approximately equal ownership time. It had piston slap, which the second owner probably removed temporarily by pouring oil or diesel into the spark plug holes immediately prior to my arrival to the test drive. Although this is just one data point, it pr... | https://mechanics.stackexchange.com |
261,728 | [
"https://electronics.stackexchange.com/questions/261728",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/124335/"
] | I just carried out an experiment in my college to study the attenuation of fibre optic cable versus length and type of cable.
This experiment was carried out with an LED light source and a power meter connected at the other end.
The wavelength is set to 1300nm and the results obtained as follows:
<pre><code>Single M... | This is where the measurement scientist has to go into full sceptical and investigative mode.
First thing. Fibre, as a passive material, is lossy. It absorbs power. Therefore the power arriving at the end of a length of fibre will be less than was launched. Period. No arguments. We don't do over-unity here.
So what ... | The other answers have suggested some ways your experiment might have gone wrong. Let me tell you how to do a fiber attenuation measurement correctly.
The standard technique is called a <em>cut-back measurement</em>.
This means you set up your source feeding a long piece of fiber (say, 10 m). You then direct the ou... | https://electronics.stackexchange.com |
172,294 | [
"https://electronics.stackexchange.com/questions/172294",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/75891/"
] | I have successfully wired everything together and the LCD powers up fine. Its a 16x2 display.
The one problem i see is that when the LCD gets power, one of the rows is visibly darker than the other one. Someone told me that i needed to initialize the LCD screen first in order for me to use it.
I have the datasheet av... | You can't just ignore the RS, RW & E lines.<br>
RS & RW <em>must</em> be driven correctly - for sending commands to the LCD, both must be low as the datasheet indicates.<br>
E <em>must</em> be toggled from low to high and back to low again for <em>each and every</em> initialisation command byte.<br>
Depending o... | As given in the datasheet, the delays are not identical. The first few delays <em>must</em> be longer since you need to allow for the LCD controller to fully initialize before sending it further commands.
Also, you need to strobe the E input each time, as shown in the timing diagrams.
| https://electronics.stackexchange.com |
204,313 | [
"https://softwareengineering.stackexchange.com/questions/204313",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/95996/"
] | I want to build a website that will contain a lot of images. I don't want users who visit the website to be able to save the images.
I have blocked the right click option, but is there any other way to keep users from saving the images?
| A common solution to this sort of problem is watermarking images. Stock photo sites which require membership or payment in order to download photos show sample photos with watermarks. In order to see the larger photo, <em>you must already have access</em>. You'll notice that you will never be able to see the large p... | There is nothing you can do. If the browser can download an image, other non-browser tools can download it too. If somebody wants to save one of your images to their computer, they can find a way.
| https://softwareengineering.stackexchange.com |
3,286 | [
"https://electronics.stackexchange.com/questions/3286",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/927/"
] | I'm using a TMS320F2812 and want to drive LEDs of some of the pins. I couldn't figure out what the safe levels of current were which could go in or come out of the IO pins from the datasheet. What is the safe range or how could I find out? What are normal values for these levels? Thanks.
| If you google TMS320F2812, the 2nd link is to a PDF file tms320f2812.pdf; if you look in this document at table 6.2, "Recommended Operating Conditions", you can find the numbers you need.
If you plan to connect the LED from the pin to ground (through a resistor, of course), so that a '1' output lights the LED, the nu... | See page 90 of the data sheet. It's 4 mA for some pins, 8 mA for others. You could drive high-brightness LEDs from them, but you might be better off using drivers.
| https://electronics.stackexchange.com |
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