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
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|---|---|---|---|---|---|
89,981 | [
"https://mathoverflow.net/questions/89981",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5069/"
] | Is there any reasonable geometric meaning of the L-genus for smooth manifolds? or perhaps easier, for complex algebraic surfaces?
The question came up after a friend and I realized that we don't understand why one would expect to have such a formula for the signature in terms of Pontrjagin classes (i.e. the signature ... | Let $S$ be a smooth algebraic complex surface. Then, there is the following relation: $$p_1=c_1(S)^2-2c_2(S)=K_S^2-2\chi_{top}(S)=3L$$ where $p_1$ is the first Pontryagin class and $L$ the L-genus.
On the other hand, cobordism theory says $p_1[S]=3\tau$ where $\tau$ is the signature of $S$.
Now (by Hodge theory)
$... | Hirzebruch himself has a very nice paper explaining (if I remember correctly) how he came up with the signature theorem and why the formulas arise in a fairly reasonable way. Here's the reference:
MR0368023 (51 #4265) Hirzebruch, F. The signature theorem: reminiscences and recreation. Prospects in mathematics (Proc. Sy... | https://mathoverflow.net |
385,524 | [
"https://softwareengineering.stackexchange.com/questions/385524",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/121757/"
] | From general observation I've come across the standard to be 36. I was looking to incorporate a uuid in my urls but didn't want it that long. Is there a minimum where I can still keep the uuid unique?
| These days it's common for an application to create and/or destroy multiple files per second. As long as you're sure you can't get into some sort of loop that creates/destroys files at high speed, and there's no chance that a partially-written file will give your app trouble (e.g. if someone yanks the power cord at an ... | The question cannot be answered without a specific use case. In your case I do not see an immediate technical problem with it but it is a very ad hoc hap-snap solution of which you do not want many more. User settings should be saved in a user settings file in an appropriate store (like the registry or a file in My Doc... | https://softwareengineering.stackexchange.com |
71,574 | [
"https://dsp.stackexchange.com/questions/71574",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/35245/"
] | ***Still need help in 2021 - not fully clear still on Jan 20th ***
I am confused about the relation between Sinc and Rectangle transform pair and how that relates the Bandwidth of Pulses, Bandwidth of Zero-ISI Filter and the Symbol Rate.
Using :
<ul>
<li><span class="math-container">$T_s$</span> = Symbol Time Period</l... | The reason is very simple in the context of the DFT and Sampling Theorem.<br />
In that context the sampling duration is about the duration you have full knowledge of and able to reconstruct under the assumption of proper sampling.
For discrete signals, in the context of the DFT, the model is about the signals being pe... | You are right, the <em>duration associated with taking <span class="math-container">$N$</span> uniform samples</em> of a signal is
<span class="math-container">$$ D = (N-1) \cdot T_s$$</span>
where <span class="math-container">$T_s$</span> is the <strong>sampling period</strong>.
A concrete example is sufficient; assum... | https://dsp.stackexchange.com |
591,050 | [
"https://physics.stackexchange.com/questions/591050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278670/"
] | I am trying to find an alternative way of calculating the electric field inside and outside of a sphere with charge density σ, all of it in its surface. The sphere has a radius R.
I am trying to fin this field (inside and outside) by superposing the electric field of several circular loops.
Do you have any idea how to ... | <blockquote>
If a mass has nothing to do with gravity on falling objects, why it here?
</blockquote>
Its true mass of body has nothing to do with gravitational acceleartion but it has to do with the gravitational force.
We defined the gravitational energy to be the work done by a particle to travel from infinite to tha... | <em>If a mass has nothing to do with gravity on falling objects, why it here?</em>
Not true. Mass has nothing to do with the speed at which an object falls - a small mass, m, and a larger mass, M, when released at the same time from the same height, will hit the ground at the same time (ignoring air resistance). But th... | https://physics.stackexchange.com |
355,243 | [
"https://physics.stackexchange.com/questions/355243",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/168122/"
] | In the slit experiment , you find dark fringes ,since wave energy potentials are canceled, can you say that it is in one way the creation of 'nothingness'?Similar to heating due constructive interference, does cooling (reduction of entropy) happens due to destructive interference?
| "not shining light on something" is not the creation of negative entropy. It does mean that that point on the screen is receiving less energy - but it will still receive blackbody radiation from every other component in the system that is in direct line of sight. As such, the point on the screen and the rest of the sys... | To answer your title question: not at all, indeed in many ways the opposite.
The fact that dark fringes can arise betokens a pure light state and <em>lack</em> of, or zero entropy.
Mixed light states, <em>i.e.</em> ones which are classical mixtures of pure quantum states, almost always give rise to interference patte... | https://physics.stackexchange.com |
395,016 | [
"https://electronics.stackexchange.com/questions/395016",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2629/"
] | Is it possible to charge a lead acid car battery with a lab bench power supply?
I am thinking of hooking it up to 13.8 Volts and 1 Amps. Will this work?
| I do this all the time, make sure you put it on constant current. (the faster the better time but you can always trickle charge). I usually do somewhere around 13-14V and about 1A.
Make sure you have good cables, I had some bad chinese cables (bad alligator clips), I measured an 0.75V drop across them so a higher gauge... | Everything is great until you turn the power supply off with the battery attached... and the supply decides to self-destruct. Some lab power supplies - even a few made by respected brands - are infamous for being absolutely intolerant to back-feeding from low impedance sources such as lead-acid batteries.
I would <stro... | https://electronics.stackexchange.com |
422,310 | [
"https://physics.stackexchange.com/questions/422310",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/187604/"
] | We know that in circular motion the position vector is $r\hat{r}$. Then the velocity is the time derivative of it. So it gives $$dv/dt = r d\hat{r}/dt + \frac{dr}{dt} .\hat{r}.$$ now I can't understand why $dr/dt$ isn't zero. The $r$ or radii isn't changing throughout the circle. So should the velocity be only $rd\ha... | Saying that the position is $r\hat r$ does not only describe circular motion. This is just a general position vector.
Therefore, your time derivative is just a general velocity vector. The first term represents velocity tangent to the position vector, the second parallel to it. Therefore, if you are undergoing circula... | You are indeed right to say that the term $\frac{dr}{dt}$ is <em>zero</em>. Indeed the velocity vector is given just by $r\frac{d\hat{r}}{dt}$.
You can see why this is true too if you consider the dot product of the velocity vector and the radius vector. Consider the displacement or position vector to be $r\hat{r}=r(... | https://physics.stackexchange.com |
664,983 | [
"https://physics.stackexchange.com/questions/664983",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/313241/"
] | Does potential energy only happen when the work done is by a conservative force? Or does work done by non-conservative forces also create potential energy?
| Forces can be conservative or non-conservative. But conservative forces do work where this work is equal to the change in potential energy. Conservative forces are also characterized by the fact that the work done by the force that moves an object from one point to another is <em>independent</em> of the path taken betw... | For a conservative force the following property is true
<span class="math-container">$$\oint_C \vec F \cdot \vec {dl}=0$$</span>
Using stokes theorom:
<span class="math-container">$\oint_C \vec V \cdot \vec{dl}=\iint_S (\vec \nabla \times \vec V)\cdot \hat ndA$</span> where <span class="math-container">$\hat n$</span> ... | https://physics.stackexchange.com |
2,332,357 | [
"https://math.stackexchange.com/questions/2332357",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/424197/"
] | Let $V$ be a finite-dimensional inner product space and $W$ be a subspace of $V$. Recall that any $v \in V$ can be written as $x+y$ with $x\in W$ and $y \in W^\perp$; and that the projection $\mathrm{proj}_{W}v$ is equal to $x$ by definition.
Prove that the function $T:V\rightarrow V$ defined by $T(v)=\mathrm{proj}... | By definition of the projection onto $W$ we have
$$
\DeclareMathOperator{proj}{proj}
\proj_W v = \proj_W (x + y) = x
$$
For two arbitrary scalars $\lambda_i$ and two vectors $v_i \in V$ we have individual
splits $v_i = x_i + y_i$ with $x_i \in W$ and $y_i \in W^\perp$.
We can combine them into
$$
\lambda_1 v_1 + \lamb... | If $\langle\cdot,\cdot\rangle$ is your inner product and if $(e_1,\ldots,e_k)$ is an orthonormal basis of $W$, then$$(\forall v\in V):T(v)=\sum_{j=1}^k\langle v,e_j\rangle e_j.$$This expresses $T$ as a sum of linear maps. Therefore, $T$ is linear.
| https://math.stackexchange.com |
26,129 | [
"https://scicomp.stackexchange.com/questions/26129",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/22811/"
] | I have to minimize a function $f(\mathbf{x})$, where the vector $\mathbf{x}\in\mathbb{R}^n$ satisfies $|\mathbf{x}|=1$. So I tweaked the code of $f$ so that it renormalizes $\mathbf{x}$ as the first step, and this allows me to <em>avoid</em> adding the constraint to the minimization algorithm. At the end of the optimiz... | Based on your current optimization strategy, it is likely you cannot get away with just the gradient of $f(\cdot)$ evaluated at $\frac{\boldsymbol{x}}{\left| \boldsymbol{x}\right|}$ since normalization isn't linear wrt. $\boldsymbol{x}$. However, you could try using chain rule by first assuming that $f(\boldsymbol{u}(\... | <ol>
<li>Does your optimization guarantee that $|\mathbf{x}|=1$ all the time? If not you have to renormalize at each step and actually your function changes.</li>
<li>If you are always on the L1-ball, then simply treat $\mathbf{x}_{new}=\mathbf{x}/|\mathbf{x}|$ and optimize $f(\mathbf{x}_{new})$. This will not change y... | https://scicomp.stackexchange.com |
44,527 | [
"https://mechanics.stackexchange.com/questions/44527",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/28722/"
] | A friend of mine has a car (Opel Corsa 2004). In morning he woke up and only one (right wheel) of his tires were flat. The day before he drove on the highway for a couple of hours and after that he had to go through the woods on a forest road for 1 mile, because a street was closed. In the evening all tires were ok. Bu... | Recently had to deal with flat tire myself. Here is what I would recommend you to do:
<ol>
<li>If the car is already at home, then partially reinflate the tire and spray some soap water to locate the leak. You actually don't have to take off wheels to do this. Also, it is very hard to locate slow leaks without using s... | Flat tires happen. Inspect the tire carefully. This probably more easily done by jacking the car up and removing the entire wheel. Look carefully and slowly at the entire tread, especially in the grooves. Odds are you will find a nail or a screw.
The first car I bought, the left-rear would loose 2 PSI of pressure ever... | https://mechanics.stackexchange.com |
3,393,074 | [
"https://math.stackexchange.com/questions/3393074",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/713891/"
] | <blockquote>
Find integers <span class="math-container">$a$</span>, <span class="math-container">$b$</span>, and <span class="math-container">$c$</span> such that <span class="math-container">$$m^3=a{m\choose3}+b{m\choose 2}+c{m\choose 1}$$</span> <span class="math-container">$\forall$</span> <span class="math-containe... | <span class="math-container">$$m^3=a {m \choose 3} +b {m \choose 2}+ c{m \choose 1} = a\frac{m(m-1)(m-2)}{6}+b \frac{m(m-1)}{2} +c m.$$</span>
<span class="math-container">$$m^3=a \frac{m^3-3m^2+2m}{6}+b\frac{m^2-m}{2}+cm=\frac{a}{3}m^3+(\frac{a}{2}-\frac{b}{2}) m^2+(\frac{a}{3}-\frac{b}{2}+c) m.$$</span> On comparinc ... | HINT: Expanding and collecting like terms we get
<span class="math-container">$$m^2(a-6)+m(-3a-3b)+2a+3b+6c=0$$</span>
| https://math.stackexchange.com |
303,793 | [
"https://softwareengineering.stackexchange.com/questions/303793",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/129869/"
] | I'm currently setting up integration testing for my company. I haven't done it before. We are developing a Java web application which uses MySQL as datasource.
I know it is very common to use an in-memory database like H2 or HyperSQL for development.
My question is, is it best practice to use a separate in-memory DB ... | <blockquote>
Do you have to use an in-memory database?
</blockquote>
No, you don't <strong>have to</strong>. But depending on what kind of application you are developing, and depending on what kind of tests you are going to implement, it can have some benefits.
Pros:
<ul>
<li>tests may probably run faster than on... | <ul>
<li>What happens when all the code is right, but the database is down?</li>
<li>What happens when all the code is right, but the data in the database (or the time) has changed (<code>select count(1) from table where date > sysdate - 1</code>)?</li>
<li>What happens when two unit tests run at once?</li>
<li>What... | https://softwareengineering.stackexchange.com |
280,677 | [
"https://softwareengineering.stackexchange.com/questions/280677",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/176554/"
] | I've developed a data acquisition system for a scientific experiment. An FPGA buffers the scientific data in a FIFO and a C# program empty this FIFO at a rate of ~45MB/s.
Because the duration of the experiment suddenly changed from seconds to days, the data now needs to be stored as binary data.
Not being a programme... | Forget my earlier answer. I actually implemented it now and it works. Not spoiling the whole thing but just answering your question, here's part of my code:
<pre><code>def Fun(I):
lo, hi = 0, len(I) # We'll search I[lo:hi], i.e., excluding index hi
while lo < hi:
check middle index
adjust... | Don't slice your list, pass start and end indices instead
<pre><code>def Fun(I):
def Inner(I, L, R):
for i in range(L,R):
if i==[i]:
return i
elif I[len(I)/2-1]>len(I)/2-1:
return Inner(I, L, L + (R/2))
else:
return Inne... | https://softwareengineering.stackexchange.com |
21,539 | [
"https://cs.stackexchange.com/questions/21539",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/13257/"
] | Is there a way to figure out what the following CFG accepts?
$\qquad\begin{align}
S &\to S \vee T \mid T \\
T &\to T \wedge F \mid F \\
F &\to p \mid\; \thicksim p
\end{align}$
I'm confused by the boolean algebra symbols. I know the first is S or T, the second is T and F and the third is not p but ... | A grammar <em>generates</em> a language, it doesn't accept it. Automata accept languages.
The whole point of gramars is that they are easily able to generate quite complex languages. Even regular languages (accepted by finite automata or denoted by regular expressions) can be very hard to describe in simple terms.
In... | This accepts all the expressions involving 1 variable, sum of products (minterms) expressions.
This grammar makes the priority of $\thicksim$ greater than $\wedge$ which is in turn greater than $\vee$, in this grammar, because if you generate the parse tree, $\thicksim$ will be at the leaves.
| https://cs.stackexchange.com |
151,269 | [
"https://stats.stackexchange.com/questions/151269",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/75025/"
] | I'm working on a paper and I have some problems explaining some of my findings. I have four independent variables, let's call them A,B,C,D. And i have one dependent variable, let's call it Y.
In my correlation analysis I have these correlations between the dependent variable (Y) and the four independent (A,B,C and D).... | It appears that your predictors share a particular type of multi-colinearity known as suppression. Suppression refers to a pattern of multi-colinearity that results in a larger or reversed effect in multiple regression compared to simple regression. Since the partial correlation of D is larger (and sig.) in the multipl... | Are the results that you show for the multiple regression really correlations? or are they the coefficient estimates?
With your check on multicolinearity, what did you see? was there some relationship, just not enough to worry you? or was there really no relationship?
Remember that correlations and simple linear reg... | https://stats.stackexchange.com |
5,299 | [
"https://chemistry.stackexchange.com/questions/5299",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1794/"
] | The boiling point of water is $\pu{100^\circ C}$. However, we find that even at room temperature, water can evaporate into gas.
Therefore, water vapor can exist at temperatures of, say, $\pu{50^\circ C}$.
At what temperature, can you say for certain that all water vapor will turn into liquid?
In other words, what is ... | You're right - water vapor can exist at temperatures such as $\pu{50^\circ C}$. This is a phenomenon known as evaporative cooling, where molecules of water with higher kinetic energies tend to "release" themselves from the system, and as a result, less and less water molecules are held within that system.
Temperature ... | From a chemical engineering perspective (where we do a lot with steam), the answer is dependent on if you're in a closed system or not. If I put some water in a closed container, it would evaporate only enough such that the gaseous water would reach the vapor pressure at that specific temperature. All temperatures abov... | https://chemistry.stackexchange.com |
131,196 | [
"https://mathoverflow.net/questions/131196",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21870/"
] | Hello,
I consider a compact and connected (smooth) Riemannian manofold $(M,g)$. I'm interested in the eigenfunctions of the Schrödinger Operator $L=-\Delta+ V$ acting on (smooth) functions. Do you know for what kind of potentials $V:M\rightarrow \mathbb{R}$, the eigenfunctions will be smooth?
Explicitly:
<ul>
<li>Ar... | If the first (lowest) eigenfunction $f_0$ is smooth, then $V$ is smooth. Indeed, assuming $M$ connected, it is a classical fact that $f_0$ doesn't vanish (it is the first case of Courant's nodal theorem for instance), and obviously $V=\lambda_0 +\Delta f_0/f_0$.
With boundary and Neumann condition, the same argument a... | If you know that the eigenfunction is nowhere vanishing -- which holds e.g. for the first eigenfunction -- then your question is a local question, i.e. you can write it in coordinates. Then it follows from regularity theory for elliptic equations as explained e.g. in the book by Gilbarg and Trudinger that the eigenfunc... | https://mathoverflow.net |
267,080 | [
"https://electronics.stackexchange.com/questions/267080",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/126710/"
] | In my electronics class, we just saw the principles of a linear regulator (like the LM140L or uA78LXX). But I didn't understand why we are controlling a common collector with the differential amplifier.
If we use a common emitter or common base, we will have a really big gain…
Can you help me to understand that little... | Besides the excellent answer by Neil_UK, I'll add another point of view.
The differential amplifier (a.k.a. the error amplifier) is the stage that provides the "signal processing" needed to keep the output voltage at the required level. The CC stage, a.k.a. <em>emitter follower</em>, acts as a buffer, i.e. a power st... | When you're designing a feedback circuit, you don't necessarily need the biggest gain from each component in the loop, just sufficient gain. More important than gain is stability. A good way to design an unstable system is to have several high gain stages, each rolling off at a similar frequency.
In the case of the ol... | https://electronics.stackexchange.com |
138,396 | [
"https://chemistry.stackexchange.com/questions/138396",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/84903/"
] | In whatever resources I have consulted to study <em>reversible thermodynamic processes</em>, a common statement seems to be :
<blockquote>
The system and surroundings (if the boundary allows) are in mechanical (<span class="math-container">$P_{sys}=P_{surr})$</span> and thermal <span class="math-container">$(T_{sys}=T_... | In a cases where where the temperature is changing during the reversible process, instead of just using a single reservoir at a constant temperature, what you do is use a continuous sequence of reservoirs, all at slightly different constant temperatures (over the range from the beginning to the end of the process), wit... | With regard to question 2, the correct equation to describe the entropy change during a finite reversible process is
<span class="math-container">$$\Delta S_{\text{surr}} = \int\dfrac{-dq_{sys}}{T_{surr}} \tag{1}$$</span>
which follows from the statement <span class="math-container">$$dS_{\text{surr}} = \dfrac{-dq_{sys... | https://chemistry.stackexchange.com |
40,082 | [
"https://mathoverflow.net/questions/40082",
"https://mathoverflow.net",
"https://mathoverflow.net/users/321/"
] | I'm not teaching calculus right now, but I talk to someone who does, and the question that came up is why emphasize the $h \to 0$ definition of a derivative to calculus students?
Something a teacher might do is ask students to calculate the derivative of a function like $3x^2$ using this definition on an exam, but it ... | This is a good question, given the way calculus is currently taught, which for me says more about the sad state of math education, rather than the material itself. All calculus textbooks and teachers claim that they are trying to teach what calculus is and how to use it. However, in the end most exams test mostly for t... | I'm teaching Calc 1 this semester, and I've stumbled onto something that I like very much.
First of all, I start (always) by having my students draw bunches of tangent lines to graphs, compute slopes and draw the "slope graphs" (they also do "area graphs", but that's not relevant to this answer). They build up a bit ... | https://mathoverflow.net |
3,409,070 | [
"https://math.stackexchange.com/questions/3409070",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/718748/"
] | Let <span class="math-container">$p$</span> be a prime number and let <span class="math-container">$V$</span> and <span class="math-container">$W$</span> be <span class="math-container">$\Bbb{F}_p$</span> vector spaces of dimensions <span class="math-container">$2$</span> and <span class="math-container">$3$</span> res... | <strong>Hint</strong>:
Denote <span class="math-container">$v_1$</span> and <span class="math-container">$v_2$</span> two basis vectors in <span class="math-container">$V$</span>.
To define a linear map from <span class="math-container">$V$</span> to <span class="math-container">$W$</span>, you first have to map <spa... | This is not an answer. It is a series of hints. If you get stuck, update your question, showing your work, then comment to this post asking for more detail in that step.
Can you count the number of points in <span class="math-container">$V$</span>? in <span class="math-container">$W$</span>?
Can you find a basis of... | https://math.stackexchange.com |
216,810 | [
"https://softwareengineering.stackexchange.com/questions/216810",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/79698/"
] | Conventionally, which of the above documents is deemed to hold the most weight when it comes to system acceptance?
I recently had a conversation along these lines:
It was argued that the initial requirements / tender documentation should be used to determine system acceptance. It was said that the solution design onl... | Passing acceptance testing is an indication that the system meets the users' requirements acceptably. As such, the requirements document is generally considered the source of truth for acceptance criteria.
There will almost always be further elaboration of requirements during design. If these are truly an expansion ... | System acceptance should be against the customer's requirements. You are correct that analysis and derivation is performed against the customer's initial set of requirements. Often, customer requirements aren't enough to design and implement against, so it's necessary to elaborate on the needs of the customer, refine t... | https://softwareengineering.stackexchange.com |
406,590 | [
"https://physics.stackexchange.com/questions/406590",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/164488/"
] | The sum of two 3-momenta $\vec{p}_1$ and $\vec{p}_2$ can be zero if their magnitudes are equal and they are directed opposite to each other.
What about the sum of two 4-momenta $p_1^\mu$ and $p_2^\mu$?
Let's assume that the sum can be zero which implies that their individual components must add up to zero. In parti... | This is a common source of confusion because many folks figure that a uniform distribution would be very ordered.
The thing's that things <em>aren't</em> becoming uniformly distributed; that's just a macroscopic view! What's actually happening is that the macroscopic view is becoming increasingly less informative, i.... | No, it's not a contradiction. Entropy is not a measure of disorder. The entropy $S$ is a measure of the number of ways to arrange a system,
$$ S = k\ln\Omega. $$
The energy is becoming more "evenly spread" <em>because</em> the entropy has to increase, for this is the most probable macrostate.
There are more ways to ... | https://physics.stackexchange.com |
788,613 | [
"https://math.stackexchange.com/questions/788613",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/7867/"
] | How can I solve $f(x)f'''(x)=f'(x)f''(x)$ when f(x) is a function from reals to reals? I figured by trial and error that exp(ax) and sin(ax) are solutions, but I don't know a method to find these solutions without guessing.
| As it stands, your key equation is false for noncommutative rings.
<hr>
With respect to your second question, the quotient of a topological ring is always a topological ring, no further assumptions needed. The fundamental observation is the following:
<blockquote>
Suppose $X,Y$ are topological spaces with equival... | We need to start also with the hypothesis that addition is continuous.
Assume that left and right multiplications are continuous and multiplication is continuous at $(0,0)$. We want to see that multiplication is continuous at $(a,b)$, for all $a,b\in R$.
Let $V$ be a neighborhood of $0$; we need to find a neighborho... | https://math.stackexchange.com |
146,473 | [
"https://security.stackexchange.com/questions/146473",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/36050/"
] | If we buy a VPS, the admin of the enclosing server can always steal our data, right?
Is using a dedicated server a solution? (We can't afford our own datacenter in any case.) But it seems that stealing from a dedicated server is harder, as one needs to plug into it physically.
If nevertheless using a VPS, does orderi... | When ordering cheap VPS's this is certainly true.
However, the largest cloud service providers are a different matter. If this is a genuine risk, you should look at the likes of Azure and AWS which have very significant certifications for security.
Azure, for example, can offer customer lock keys and provide very sig... | Dedicated or virtual, when you lease a server from a third party, you're trusting that provider to not monkey with your business. Colocation (particularly if they give you a locked cabinet) gets you a bit more privacy, but you're still implicitly trusting the the people who run the facility to keep their hands to thems... | https://security.stackexchange.com |
82,969 | [
"https://stats.stackexchange.com/questions/82969",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/22314/"
] | So I have fundamental confusion about graphical models. Suppose the following graphical model is given:<img src="https://i.stack.imgur.com/L0C2D.png" alt="enter image description here">
Now the question is do we have the following equality?:
$$p(m_2|\alpha,\beta,y_3)=p(m_2|\alpha,\beta)$$
If so, why exactly and could... | Yes, this is because the $\alpha, \beta$ node $d$-separates $m_2$ and $y_3$. See <em>Probabilistic Reasoning in Intelligent Systems</em> for an explanation of $d$-separation.
| Another intuitive example of why two sibling nodes are independent given their parent:
<ul>
<li>Imagine $A$ and $B$ are two guys living in the same city. </li>
<li>Whether A gets wet or not depends on whether it rains or not. Same for B.</li>
</ul>
Now, if don't know whether it rained or not but we observed that $A$... | https://stats.stackexchange.com |
55,853 | [
"https://stats.stackexchange.com/questions/55853",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17590/"
] | I want to difference a nonstationary time series to fit an ARIMA model with X(t)=X(t)-X(t-1) formula (using <code>diff</code> function in MATLAB) but I can not figure out what should I use for first value since the is no value before the first one? Should I use zero or the same value as X(1)?
Thanks
| It should be "missing", and you will need to drop it from the analysis.
| If we look at statistical software in general, the 0th value should be "missing value". You should remove the 0th value in the fitted value and in the original data when plotting or calculating the RMSE unless RMSE would be bigger than it should be.
| https://stats.stackexchange.com |
1,753,722 | [
"https://math.stackexchange.com/questions/1753722",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/227967/"
] | Let G be a group and suppose <span class="math-container">$g \in G$</span>.
<span class="math-container">$\varphi:G\rightarrow Aut\left ( G \right )$</span>
<span class="math-container">$g \mapsto i_{g}$</span>
is a Homomorphism with image <span class="math-container">$Inn\left ( G \right )$</span>
where <span class="m... | Suppose $i_{g}$ is the identity map on $G$, i.e. $g \in \ker(\varphi)$. Then $i_{g}(h) = g^{-1}hg = h$ for each $h \in G$, so $hg = gh$ for all $h \in G$. Hence, $g \in Z(G)$. On the other hand, suppose $g \in Z(G)$. Then $i_{g}(h) = g^{-1}hg = g^{-1}gh = h$, so $i_{g} = \mathrm{Id}_{G}$.
| Note that for any $g$, saying $gx=xg$ is equivalent to saying $gxg^{-1}=x$. So if $g$ is in the center then $gxg^{-1}=x$ for all $x\in G$, i.e. $i_g$ is the identity map.
| https://math.stackexchange.com |
496,375 | [
"https://electronics.stackexchange.com/questions/496375",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/247982/"
] | <strong>I'm new to the electronics world</strong>, and I came to know that electronics companies (As Fairchild) provide datasheet for the components they produce (As IGBT, Triac, etc.).
<strong>Do electronics companies (As Samsung, LG, Sony, etc.) provide a datasheets & a diagrams for the electric boards in their ... | If the manufacturer provides a <strong>service manual</strong>, it would be there. In the very old days it was common to have the schematics inside the manual or sometimes even glued to the inside of the case on old television sets, but those days are long gone. For test and lab equipment sometimes the schematics are p... | It's hard to believe all circuits are public. Maybe here and there you can find some. They used to be maybe 40 years ago, I saw once schemes of tv sets- for technicians who were able to fix them, which is a sort of a lost skill.
But the question is, why would you need it. Obviously not to fix. If you need a reference ... | https://electronics.stackexchange.com |
19,286 | [
"https://math.stackexchange.com/questions/19286",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/6331/"
] | Let $R$ be the relation defined on $\mathbb{Z}$ where $a\; R\; b$ means that $a + b^2 \equiv 0\pmod{2}$.
How would I go about finding the equivalence class $[-13]$?
| You would find all $a \in \mathbb{Z}$ such that $a+(-13)^2 = 0 \pmod{2}$ since $[-13] = \{a \in \mathbb{Z}: aR -13 \}$.
| $a+b^2=0\ (2)$ is the same as "$a$ and $b$ have the same parity", so the set of odds is $-13$'s class.
| https://math.stackexchange.com |
128,701 | [
"https://mathoverflow.net/questions/128701",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14976/"
] | I have a Hilbert space of quantum density matrices written in the Glauber-Sudarshan P representation - ie. we have coherent states $|\alpha \rangle$ and we write density matrices as
$$ \rho = \int d^2\alpha \ P(\alpha) |\alpha\rangle \langle\alpha|.$$
The states $|\alpha\rangle$ form an overcomplete set and are not a... | <blockquote>
Can we construct a linear projection operator P onto C?
</blockquote>
No. The range of any linear operator will be a linear subspace.
<blockquote>
If not, is there a nonlinear projection operator and if so how would one construct it?
</blockquote>
Yes, if $K$ is a closed convex subset of a Hilbert s... | H there is a standard "projection" map P: H \to K defined by letting Pv be the closest element of K to v.
| https://mathoverflow.net |
46,648 | [
"https://mathoverflow.net/questions/46648",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2031/"
] | I have a few really basic questions about minimal surfaces. Does a smooth or piecewise smooth injection $S^1$ into $\mathbb R^3$ always give a unique minimal surface or are there instances with discrete distinct solutions? Can it not be the case that a 1-parameter family of minimal surfaces exists for a given "frame"... | In $\mathbb{R}^3$ there is always some minimal surface spanning a given connected simple curve (assuming the curve is not too horrible, say Lipschitz). Here surface needs to be broadly understood as being possibly immersed and of arbitrary topology. This can be seen using the machinery of geometric measure theory and... | There is a simple answer to your first question. Imagine two circles of the same radius lying in parallel planes so that the segment joining their centers is perpendicular to the planes.
There are two minimal surfaces that bound this configuration. One consists of two disks,
one in each plane, and the other is a sectio... | https://mathoverflow.net |
200,227 | [
"https://physics.stackexchange.com/questions/200227",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/58610/"
] | Peskin and Schroeder, equation 3.28, states that the Klein-Gordon equation $$(\partial^2+m^2)\psi=0 \tag{3.28}$$ is a valid choice of equation for a Dirac spinor field. Their explanation makes sense (the spinor transformation matrices obviously commute with differentiation and scalars and it was verified earlier that t... | Formally, the meaning you assign is just the usual meaning of the derivative.
$$\partial_\mu \psi(x^\nu) = \lim_{h \to 0} \frac{\psi(x^\nu + h\delta^\nu_\mu) - \psi(x^\nu)}{h}$$
You can indeed compute it componentwise, because you can subtract two spinors, as in the equation above, just by subtracting their component... | Basically your confusion is caused by a bias about what a vector is.
Everyone agrees that you can add two vector and get another.
Everyone agrees you can scale a vector and get another vector.
Sometimes we square a vector and get a scalar, but some people say that is "merely" an abuse of notation. But that is just a... | https://physics.stackexchange.com |
5,735 | [
"https://electronics.stackexchange.com/questions/5735",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I've seen several microcontrollers rated to operate from 2.97V to 3.63V. Others I've seen rated from 3V to 3.6V.
What's with the extra 30mV on either end of the scale? It doesn't seem like it would make any difference, but maybe I'm missing something.
| So that is 3V (with a 1% tolerance) to 3.6V (again with approx 1% tolerance)
OR
as Thomas O commented 3.3V +/- 10%
| I am assuming that is just a precaution or tolerance. Stating that if you run it at 3V its not the bottom of the scale, and you are safe there.
| https://electronics.stackexchange.com |
160,041 | [
"https://mathoverflow.net/questions/160041",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $Q\cong\mathbb{P^{1}_{1}}\times\mathbb{P^{1}_{2}}\subset\mathbb{P}^{3}$ be a smooth quadric surface. We have the following two actions on $Q$:
$$S_2\times Q\rightarrow Q,\; (\sigma,(x,y))\mapsto\sigma(x,y)$$
where $S_2$ is the symmetric group of order $2$, and
$$Aut(\mathbb{P^{1}_{1}})\times Aut(\mathbb{P^{1}_{2}})... | Yes, it is true. This is easily seen by looking for example at the Picard group, generated by $C$ and $D$, the two fibres of the projections. Since $C^2=D^2=0$ and$C\cdot D=1$, the only curves of self intersection $0$ are multiple of $C$ or $D$, and the irreducible ones are equivalent to $C$ or $D$. Composing an automo... | Here is another way to see this. The automorphism group of <em>any</em> quadric hypersuface $$Q(x) = 0 \subset \mathbb{P}^n,$$ is exactly the projective orthogonal group $\textrm{PO}(Q)$ of $Q$.
The key point now is that we have the coincidence that $\textrm{SL}(2) \times \textrm{SL}(2)$ is a double cover of $\textrm... | https://mathoverflow.net |
313,930 | [
"https://electronics.stackexchange.com/questions/313930",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11074/"
] | I've ran into quite a few engineers from unrelated backgrounds that put unpopulated components on the BOM. Some will do a section clearly labelled DNP at the bottom, others will leave them dispersed throughout the BOM, but highlight the rows.
Having a DNP section seems like the way to go if you must do this, the only... | If you don't explicitly document that these components are not to be placed, you will inevitably have your manufacturing team notice that there is a location on the board with no corresponding line in the BOM, and delay the build to send an engineering query asking what is supposed to be placed there.
Explicitly docum... | This practice is not necessary. But when there is a QC worker checking the board assembly, and she finds an unpopulated component, she will wonder, is it a mistake or not. So she will go to BOM and chem with the DNP section.
It's true that this method can be messed up, just like any other method.
| https://electronics.stackexchange.com |
81,461 | [
"https://electronics.stackexchange.com/questions/81461",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22282/"
] | Oscilloscope shows a sinusoid V(RMS)=1.67V and V(MAX)=2.48V. I have a GW INSTEK GPS-3303 power supply and a RIGOL DS1052E oscilloscope. The supply is in series tracking mode, with the probe directly connected to the negative CH1 and ground of the probe connected to ground of the supply. The "output" button of the suppl... | You have noise in your system, plain and simple. How you handle it is the same ways that you handle any other noise: remove the source of the noise, or filter out the noise. Some things to consider are:
<ul>
<li>Long cables can cause noise. Shorten them, or use shielded cables</li>
<li>Use differential measurements... | From memory, the ADC input on this PIC requires the "signal" to be a "low" output impedance (22kohm pot would be too high) and this means having a capacitor across the input pin. The ADC type on these devices are "successive approximation" and they will cause noise on the input pin - this will be seen as a measurement ... | https://electronics.stackexchange.com |
364,529 | [
"https://electronics.stackexchange.com/questions/364529",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/167127/"
] | I am trying to understand a topic on limits of performance.
So there is a delay of tau between input and output so the transfer function becomes G(s)*e^-(tau *s).
I am unable to understand the statement "The phase contribution of delay is negative and at crossover frequency is -(tau * omega_c) ,where omega_c is cross... | \$e^{-\tau s} \rightarrow e^{-j\omega \tau}=cos(\omega \tau)-jsin(\omega \tau) = 1\angle( -\omega \tau) \$
This means unity gain, and a phase lag proportional to angular frequency. At the cut-off frequency of the other the component of the TF, the phase angle contributed by the delay will be found by setting \$\omega... | The phase shift due to a time delay, measured as a fraction of a cycle of the signal frequency, is equal to the time delay divided by the period of the signal frequency. Since the period is the reciprocal of the frequency, the phase shift can be expressed as the product of the time delay and the signal frequency. This... | https://electronics.stackexchange.com |
121,877 | [
"https://dba.stackexchange.com/questions/121877",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/75651/"
] | Currently, I am transitioning a server from a company to another.
They want to keep SQL Server installed on the server so we are wiping clean all the databases, maintenance plans and jobs.
I'm trying to delete a bunch of SQL Server Agent jobs but even though they are disabled they are still on "IDLE" mode so it raise... | You have maintenance plans. Try to follow these steps:
Find the maintenance plan name and id that you want to delete.
Write down the id of the one you want to delete.
<pre><code> SELECT name, id FROM msdb.dbo.sysmaintplan_plans
</code></pre>
--Place the id of the maintenance plan you want to delete into the below qu... | The problem appears to be that you have a maintenance plan that has created these jobs. As such you will not be able to delete them simply by deleting the job.
What you will need to do is identify which maintenance plan is associated with the jobs and then delete the maintenance plan all together. This should then eit... | https://dba.stackexchange.com |
203,146 | [
"https://softwareengineering.stackexchange.com/questions/203146",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/93050/"
] | I think I have a decent grasp of what Dependency Inversion principle (DIP) is, my confusion is more around dependency injection.
My understanding is the whole point of DI is to decouple parts of an application, to allow changes in one part without effecting another, assuming the interface does not change.
For exampl... | In your example, you haven't gained anything. Your intuition is correct. If you have only one class implementing an interface, there is no gain, because it may always stay that way. There is no limit to the degree to which we can add interfaces and clutter the code.
| In this example, I would not call using a DI container "better practice". However, code bases tend to grow and become more complicated. Imagine we have a dependency graph like this:
<pre><code> A
/ \
/ \
B C
\ /
\ /
D
</code></pre>
The code to construct this graph without a DI container woul... | https://softwareengineering.stackexchange.com |
276,035 | [
"https://dba.stackexchange.com/questions/276035",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/216171/"
] | We are currently researching our case of storing the road distances between cities. Right now we have 6 billion of those distances.
Our structure right now in SQL Server is that we have a <code>float</code> which represents the relationship between cities. For example if we have a city with <code>Id</code> 1 inside th... | My assumption here is using <code>FLOAT</code> in place of the actual composite key is slowing the query engine's ability to create the proper estimates.
So instead of using the "clever" column, just use a composite primary key:
<pre><code>CREATE TABLE Country
(
CountryCd CHAR(3) NOT NULL --ISO Count... | SQL is a relationnal database. If you want this to perform well in SQL, you will have to review the design so that it is normalized.
Otherwise, SQL will have to read all row in order to find the "id"s which will not perform well.
If you had a table with "From", "to" and "distance"... | https://dba.stackexchange.com |
51,434 | [
"https://electronics.stackexchange.com/questions/51434",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16819/"
] | I have a circuit which requires a PNP transistor.
I only have an NPN transistor.
Is there a way to convert one to the other given that they have the same characteristics (apart from the npn/pnp part?)
And for others after me... can the reverse also be done? e.g. how does one convert a PNP transistor to its NPN equiv... | If it's the only type of transistor in the circuit, the translation is straightforward; build the circuit as designed, reverse the power connections and any other polarised components (diodes, electrolytic caps).
If you need one PNP in a mostly NPN circuit, there is no general solution.
There may be solutions, depend... | If you have the exact NPN equivalent you only need to mount the circuit as it is drawn, so that the base, collector and emitter terminals of the NPN are connected where base, collector and emitter of the PNP should go, and then reverse the power supply polarity. This trick works in most cases, but it depends on the cir... | https://electronics.stackexchange.com |
319,037 | [
"https://stats.stackexchange.com/questions/319037",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/188710/"
] | If I have two different symmetric (with respect to the median) distributions $X$ and $Y$, is the difference $X-Y$ also a symmetric (with respect to the median) distribution?
| Let <span class="math-container">$X \sim f(x)$</span> and <span class="math-container">$Y \sim g(y)$</span> be PDFs symmetric about medians <span class="math-container">$a$</span> and <span class="math-container">$b$</span> respectively. As long as <span class="math-container">$X$</span> and <span class="math-container... | This is going to depend on the relationship between $x$ and $y$, here is a counter example where $x$ and $y$ are symmetric, but $x-y$ is not:
$$x=[-4, -2, 0, 2, 4]$$
$$y=[-1, -3, 0, 1, 3]$$
$$x-y = [-3, 1, 0, 1, 1]$$
So here the median of $x-y$ is not the same as the difference in the medians and $x-y$ is not symmetr... | https://stats.stackexchange.com |
115,320 | [
"https://security.stackexchange.com/questions/115320",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/102070/"
] | I have a lab machine that I have been practicing some SQL injection on.
I know that the POST parameter that I am trying to exploit is vulnerable as I was able to extract the user DB manually.
I then went to do this with SQLmap with the below command.
<pre><code>sqlmap -u 192.168.1.50/base-login.asp --dbms="Microso... | To be sure of your syntax, you can intercept a regular request of your post by burp for example. You save it in a file and you can inform sqlmap to use this request for testing an injection.
For that the option in sqlmap is <code>-r</code>.
<pre><code>Target:
At least one of these options has to be provided to set... | Is this just a typo?
<pre>
<b>--data"=</b>txtLoginID=admin&txtPassword=test&cmdSubmit=Login"
</pre>
should be
<pre>
<b>--data="</b>txtLoginID=admin&txtPassword=test&cmdSubmit=Login"
</pre>
| https://security.stackexchange.com |
408,163 | [
"https://physics.stackexchange.com/questions/408163",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Conductors are opaque because, when hit by a Maxwellian wave, the free charges on their surface create another wave which destructively interferes with the former in the region of space beyond said surface. This doesn't happen in dielectrics; why then are some of them, say, wood or rubber, opaque still?
I would very m... | Just because the material doesn't conduct currents on a macroscopic scale, does not mean it doesn't contain any movable charges at all. In fact, as the very name “dielectric” suggests, such a material contains charges which can be to some degree separated – electrons move a bit to one side or the other, never actually ... | You cannot totally avoid quantum mechanics, but it may suffice to say that reflections by free electrons are not the only way to prevent transmission. Any situation where light can promote an electron from a low energy state to a higher one will cause absorption, regardless of DC conductivity. Or even with little absor... | https://physics.stackexchange.com |
184,683 | [
"https://softwareengineering.stackexchange.com/questions/184683",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/46461/"
] | The app I'm developing needs to display lists of items. Simple enough, but there are a number of things which can change based on user input:
<ul>
<li>Items can be added to/removed from the list.</li>
<li>The items in the list can be updated. Multiple items can be updated simultaneously!</li>
<li>The filters can be up... | <ol>
<li>As the lists are the model (and the items are only parts of them), I would suggest the following process:
<ul>
<li>When changed, items raise events to the list in which they are placed.</li>
<li>When changed (directly or via a change in the items), lists raise events to the depending views.</li>
<li>Lists fil... | As you will be continually adding and removing items from the list I'd suggest you use a LinkedList as this provides more efficiency by simply removing reference from the removed item to the next available in the list - thus preventing the need to move all elements forward. In the case of filtering you could implement... | https://softwareengineering.stackexchange.com |
96,777 | [
"https://mathoverflow.net/questions/96777",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11765/"
] | Q1: What is the simplest example of two non-isomorphic fields $L$ and $K$ of characteristic $0$ such that $L(x)\simeq K(x)$ (here $x$ is an indeterminate)?
Q2: Do we have a sufficient criterion for a general field $K$ of characteristic $0$ which guarantees that if $K(x_1,\ldots,x_n)\simeq L(x_1,\ldots, x_n)$ (here $L... | I don't think that there are any really easy examples. In the famous paper of Beauville, Colliot-Thélène, Sansuc and Swinnerton-Dyer "Variétés stablement rationnelles non rationnelles" they construct surfaces $S$ over $\mathbb Q$ that are not rational, but such that the products $S \times \mathbb P^3$ are rational. You... | An answer to Q2, generalizing Ralph's comment: "$K$ is algebraically closed" is a sufficient condition. Indeed, you can characterize $K$ inside $K(x_1,\dots,x_n)$ as the set of elements having $m$-th roots for infinitely many integers $m$. More generally, it is enough to assume that for some $m>1$, the $m$-th power ... | https://mathoverflow.net |
17,174 | [
"https://chemistry.stackexchange.com/questions/17174",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5424/"
] | <img src="https://i.stack.imgur.com/1nX2j.gif" alt="enter image description here">
As you can see, the first step is the slowest, but by using the rate-determining step approximation you wouldn't arrive at the correct rate law which is:
$r=k\ce{[HCOO^{−}]}^{1/2} \ce{[S2O8^{2−}]}$.
The first reaction is very slow, so... | The rate of the third reaction affects the rate of the first reaction, i.e. they are competitive reactions and in that case the rds method can't be applied.
The rate of the first reaction is $r=-\mathrm{d}\ce{[S_2O_8^{2-}]}/\mathrm{d}t$, but the change of the concentration of the peroxydisulfate depends on the third r... | In this answer, I will attempt to explain using chemical principles, rather than detailed mathematics.
As has been said already, reactions 1 and 3 both consume $\ce{S2O8^{2-}}$. Now, for the rate determining step to dominate the decay of this species, there would necessarily be very little consumption of it in any oth... | https://chemistry.stackexchange.com |
68,376 | [
"https://mathoverflow.net/questions/68376",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13825/"
] | I would like to know what is known about the spectrum of the Laplace-Beltrami operator on 2-dimensional negatively curved surfaces of constant curvature.
For instance,
<ul>
<li>What is the spectrum of the Hyperbolic plane of constant curvature $-k$? </li>
<li>What is the Laplace-Beltrami operator and its spectrum fo... | Probably you should try the following:
Chavel, "Eigenvalues in Riemannian geometry"
Buser "Geometry and spectra of compact Riemann surfaces"
and if you can read french: Berger, Gauduchon, Mazet "Le spectre d'une variete riemannienne"
| Question #3: No lower bound.
There are metrics on surface of genus 2 (or more)
with constant curvature $-1$ and arbitrary big diameter;
then diameter goes to infinity, the surface looks more and more like two surfaces with cusps.
On such a surface the second eigenvalue can be arbitrary small (if the surface is not con... | https://mathoverflow.net |
4,142 | [
"https://mechanics.stackexchange.com/questions/4142",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/252/"
] | I have a aging (y2k) motorcycle with not too many Ks on the clock. I have been told by a mechanic that I need to replace my sprockets and chain. This seems reasonable since the chain has been poorly maintained.
Normally, if the sprockets were worn, you'd replace them to prevent damage to the chain. Given both are wor... | Chain maintenance is critically important for motorcycle safety.
If this old chain has not been properly maintained throughout its life, you may be at higher risk of seized links or chain breakage.
Best case scenario with a broken chain is that it comes off the bike cleanly and you coast safely to a stop, avoiding an... | A worn chain doesn't have to break to be a hazard. As the chain and sprockets wear the chain gets longer and the sprockets get smaller. This makes tensioning the chain difficult if not impossible as the jacking/tug bolts will not be long enough. If the teeth are worn bad enough the chain may not roll off the sprocket a... | https://mechanics.stackexchange.com |
432,840 | [
"https://softwareengineering.stackexchange.com/questions/432840",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/250257/"
] | Sometimes there are elaborate discussions about a subject, and while finally developing the program, you want to refer to a mail ... but then people still continue mailing about the subject, so the mail chain continues.
How do you refer to a particular mail in the comment of the source code?
There are two obvious ways:... | I would recommend creating an issue in a defect tracking tool like Jira and referring to the Jira issue rather than the originating email in your code comments. This will pick up any work that has been done to resolve/ignore the issue plus possibly multiple opinions from developers.
| Bad idea overall. Email is ephemeral. People not in the recipient list would have no idea what is being referred to, and in time the mail archives are gone from servers and peoples' computers, losing all information.
If it's relevant enough to need to be referenced, place the information somewhere where it's reasonably... | https://softwareengineering.stackexchange.com |
157,228 | [
"https://mathoverflow.net/questions/157228",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10265/"
] | Consider a complex Banach space $X$ with a real subspace isometric to $\ell^1_{\mathbb R}$. What is the best constant $c$ such that $X$ contains a complex subspace $c$-isometric to $\ell^1_{\mathbb C}$?
I guess this is a very classical question, but I could not find an answer.
In this question, $\ell^1_{\mathbb R}$ (... | Schechtman and I discussed your question this morning and have these comments.
You can get $1+\epsilon$. The usual argument for improving the constant works in the complex case as well as the real case; i.e., if a complex Banach space contains a subspace complex isomorphic to $\ell_1$, then for all $\epsilon >0$ i... | I think that $c$ arbitrarily close to $1$ can be realized. From Dvoretzky's theorem we now that given any $\varepsilon>0$, there is some finite $N$ such that the $N$-dimensional space with the $\ell^1$ norm, denote it by $\ell^1_{\mathbb{R}}(N)$, contains a $2$-plane $H$ which is $(1+\varepsilon)$-isometric to Eucl... | https://mathoverflow.net |
116,274 | [
"https://stats.stackexchange.com/questions/116274",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/56206/"
] | I'm relatively new to statistics, and am currently working some data collected as a part of an interview survey. I have a response variable in ordinal form, which mostly looks into people's perceptions of an animal, and a range of predictor variables that include discrete numeric, ordinal and binary variables. I have a... | An identity covariance matrix, $\Sigma=I$ has variance = 1 for all variables.
A covariance matrix of the form, $\Sigma=\sigma^2I$ has variance = $\sigma^2$ for all variables.
A diagonal covariance matrix has variance $\sigma^2_i$ for the $i^\text{th}$ variable.
(All three have zero covariances between variates)
| An identity matrix is by definition a matrix with 1's on the diagonal and 0's elsewhere. If you choose to use an identity matrix as your covariance matrix, then you are totally ignoring the data for calculating the variances. Is that really what you mean to do? The only way that could make sense is if you had already s... | https://stats.stackexchange.com |
16,831 | [
"https://datascience.stackexchange.com/questions/16831",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/28753/"
] | I had no idea how to explain this in the title but anyway... Let's say I have a data points like this:
<pre><code>John, Happy | Greedy | Smart | Funny, 0.8
Ann, Smart | Sad | Funny, 0.6
Joel, Greedy | Prideful | Stupid, 0.2
</code></pre>
Where the first part is the name the second is there characteristics and the thi... | It's a regression machine learning problem. Assuming you have 30 characteristics, one-hot encoded into 30 columns. And your target is the character score, min-max scaled into $[0, 1]$.
So we have <code>X.shape=(None, 30)</code>, <code>Y.shape=(None,)</code> (just like what ncasas has stated), thus we can train a regre... | The typical way to address this is to transform those <em>characteristics</em> into a representation where you compose a vector with one component for each possible characteristic, with a $1$ in the position of each characteristic owned by the individual, or zero otherwise.
This way, you would have:
<pre>
name | gree... | https://datascience.stackexchange.com |
129,982 | [
"https://dba.stackexchange.com/questions/129982",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/87769/"
] | I have this query generated by <code>Django</code> where a user has <code>orders</code> and <code>jobs</code> as related tables. <code>jobs</code> are of two types: <code>clean</code> and <code>wash</code>. I want to count for each user shown the number of orders, clean jobs and wash jobs.
One of the users has 3 clean... | You have two joins from the base table (<code>auth_user</code>) and both joins are to tables with 1-to-many relationship with the base table. That creates the multiple rows. If for example, an auth_user has 3 orders and 7 jobs, the join (before any group by) will result in 21 rows.
When you then <code>GROUP BY</code>... | This construction:
<pre><code>FROM `auth_user`
LEFT OUTER JOIN `order`
ON ( `auth_user`.`id` = `order`.`user_id` )
LEFT OUTER JOIN `job`
ON ( `auth_user`.`id` = `job`.`user_id` )
</code></pre>
return as many rows as many rows child table has with same id
an... | https://dba.stackexchange.com |
67,695 | [
"https://mathoverflow.net/questions/67695",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11016/"
] | I am afraid to continue to ask trivial things but really I do not know how to proceed, so I ask the experts:
A specially multiplicative function, is a function
$f$ from positive integers to complex numbers,
that satisfies:
$$
f(n)f(m) = \sum_{d \mid \gcd(m,n)} f(\frac{mn}{d^2})g(d)
$$
for all $m,n$, where $g$ is a com... | I don't understand your definition of "specially multiplicative"; if $m$ and $n$ are coprime, it gives $f(m)f(n)=mn$, which is not true of the sum of divisor function...
However, the Ramanujan $\tau$-function satisfies $\tau(m)\tau(n)=\sum_{d\mid (m,n)}{\mu(d)\tau(mn/d^2)}$, which might be what you mean?
In any case,... | Paul McCarthy states in the notes of chapter 1 of his book "Introduction to Arithmetical Functions" that the completely multiplicative functions $g_1,g_2$ such that $\tau=g_1*g_2$ are defined on primes in the following way:
$$g_1(p)=\frac{1}{2}\left(\tau(p)+\sqrt{\tau(p)^2-4p^{11}}\right)$$
$$g_2(p)=\frac{1}{2}\left(\t... | https://mathoverflow.net |
14,588 | [
"https://mechanics.stackexchange.com/questions/14588",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4339/"
] | Last time I got new tyres I was advised that as they were out of stock of the particular size I was after (195/60/R15) and since they were part used tyres, I should be OK going with a slightly smaller tyre (185/60/R15) and that this would have "no effect" on anything.
Since if it really had "no effect" on anything th... | In theory, your tire size of 195/60/R15 is broke down like this:
<ul>
<li>195 - Tread width in millimeters</li>
<li>60 - Sidewall height as a percentage of tread width</li>
<li>R - Radial tire</li>
<li>15 - Rim width in inches</li>
</ul>
I say, in theory, because each tire manufacturer doesn't measure their tire... | I have been using one size up tires on my sub-compact car for 21 years. (Nearly 300,000mi)
While they do have more rolling resistance and cost $10~20 more per tire, there are some real advantages. Improvements in Ride Smoothness, Snow Traction, Highway Mileage, Cornering and Emergency Handling. Yes my Spedo/Odometer ... | https://mechanics.stackexchange.com |
12,128 | [
"https://physics.stackexchange.com/questions/12128",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4444/"
] | I've had a discussion with my father today, about the fuel usage of a vehicle at the same rpm, but a different gear.
He claims that the following situations have the same fuel usage:
<pre><code>Gear: 2
rpm: 2000
fuel usage: 5.1l/100km
Gear: 5
rpm: 2000
fuel usage: 5.1l/100km
</code></pre>
I say it should be somethi... | <blockquote>
I've had a discussion with my father
today, about the fuel usage of a
vehicle at the same rpm, but a
different gear.
</blockquote>
The fuel injector system does not always inject a constant amount of fuel into the engine.
If you are driving down a hill and remove your foot from the gas pedal (a l... | What anyone failed to acknowledge is that to spin the engine faster requires more work, so you would end up using way more fuel in 2nd gear than 5th. We upshift to save fuel at lower RPM, and the engines would explode if you had them spinning too fast. Engines also have accessories, such as water pumps, compressors, ... | https://physics.stackexchange.com |
52,895 | [
"https://mechanics.stackexchange.com/questions/52895",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/36485/"
] | I had my ac belt and my serpentine belt chaged on my 2007 M35 now my car is making a horrible noise.When I start my car then after a few minutes it stop.But I notice if my ac is on it makes this noise also what could that be?
| When belts are installed, they need to be adjusted (depending on the vehicle) or they can slip causing a squealing sound.
In some cases, the new belt is not stretched like the old one. This puts added pressure on the idler pulley. That can create a lot of noise if the pulley is going bad. They should have checked it.... | Had to have a different set of belts put on the one they replaced them with was cheap thats why they made the nosie.Thanks
| https://mechanics.stackexchange.com |
84,396 | [
"https://softwareengineering.stackexchange.com/questions/84396",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/21497/"
] | So, I just started an internship, and I'm worried that I'm asking too many questions. My mentor assigns me projects and helps me learn all the company's technologies and methodologies. However, there's so much new material for me to learn while doing this project that I have a lot of questions. I generally ask quest... | Be respectful of your mentor's time by keeping a list of questions and asking them in batches, to the extent possible. Don't actually interrupt your mentor until you literally cannot make any forward progress without help.
A lot of times you'll learn a lot by struggling to find the answer yourself, even in cases where... | As a senior who has seen juniors asking all kinds of questions, I would say it's <strong>not a matter of how often you ask, but what you ask</strong>.
You need to feel it yourself, but generally the rule is: <strong>Show your interest</strong> and ability to think and <strong>work independently</strong>.
It's OK to ... | https://softwareengineering.stackexchange.com |
127,205 | [
"https://dba.stackexchange.com/questions/127205",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/52232/"
] | My requirement wholly depends on the <code>QUERY</code>.
I am filtering my gridview on the basis of <code>three parameters</code>.
<ol>
<li><code>Project_name</code> (Always required)</li>
<li><code>Date</code> (Not always)</li>
<li><code>Vehicle_No</code> (Not always)</li>
</ol>
So, what my requirement is,
<block... | The problem is with the below bind variable substitution:
<pre><code>AND ( sv.project_id = DECODE(:' 1368','0', project_id, :'1368')
AND TO_CHAR (date_in, 'dd-MM-yyyy') = DECODE(:' ', '0', date_in, :' ')
AND vehicle_no = DECODE(:' GJ-06-0Z-9202', '0', vehicle_no, :' GJ-06-0Z-9... | If you want to restrict the resultset based on the <code>vehicle_no</code>, then use <code>AND</code> instead of <code>OR</code>.
<pre><code> WHERE (gd.good_type_code(+) = sv.good_type)
AND ( sv.project_id = '1368'
AND TO_CHAR (date_in, 'dd-MM-yyyy') = '26-11-2015'
---> OR vehi... | https://dba.stackexchange.com |
18,360 | [
"https://ai.stackexchange.com/questions/18360",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/16521/"
] | I am currently studying <em>Deep Learning</em> by Goodfellow, Bengio, and Courville. In chapter <strong>5.2 Capacity, Overfitting and Underfitting</strong>, the authors say the following:
<blockquote>
Typically, when training a machine learning model, we have access to a training set; we can compute some error measu... | <blockquote>
The language used here is confusing me, because it is discussing a "distribution", as in a "probability distribution", but then refers to inputs, which are data gathered from outside of any probability distribution. Based on the limited information my studying of machine learning has taught me so far, my... | For illustration, I use the dog/cat classification task. Suppose, the training data of cat and dog follows the Gaussian distribution(for simplicity) and we trained a model which gives an accuracy as below.
<ul>
<li>train - 98.2% </li>
<li>val - 97.7% </li>
<li>test - 97.2%</li>
</ul>
The model is neither overfitting ... | https://ai.stackexchange.com |
418,435 | [
"https://stats.stackexchange.com/questions/418435",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/215131/"
] | I'm trying to predict <code>fantasy_points</code> for individual Basketball players in upcoming games. The formula to calculate a player's <code>fantasy_points</code> is:
<code>fantasy_points = (1 * points_scored) + (1.5 * assists)</code>
So if Player A scores 10 points and 4 assists:
Player A <code>fantasy_points<... | Here's a perspective: the two model approach is <em>more</em> constrained, hence is always going to result in an inferior model. Consider the 2m (two-model) model - it looks like:
<span class="math-container">$$ f_{2m}(\mathbf{x}) = 1.5 (\mathbf{c_1} \cdot \mathbf{x}^T) + 1.0 (\mathbf{c_2} \cdot \mathbf{x}^T)$$</span>... | <blockquote>
Impossible that one predictive model is better than two?
</blockquote>
Rather than getting into the weeds on your specific models, let's just step back and view this question in a more general setting. If we consider an arbitrary series of observable values, then it is possible that a model could give ... | https://stats.stackexchange.com |
656,270 | [
"https://physics.stackexchange.com/questions/656270",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/306551/"
] | I just studied about Momentum. So I thought of an experiment. If a body is moving with a constant velocity, it has a constant momentum. But as soon as a force is applied on the body, it accelerates and hence, the momentum also changed. Is this experiment violating Law of Conservation of Momentum ? If not, please tell h... | Newton's 3rd Law say that 'for every force there is an equal and opposite force'.
When the force is applied to the body an opposite force acts on a different body and gives it an equal change of momentum, but in the opposite direction.
When adding up the new total momentum it'll come to the same total as before, as one... | Considering a single body, conservation of momentum is valid until there is no external force.
Momentum is given by <span class="math-container">$p=mv$</span>. If you exert an external force, <span class="math-container">$v$</span> of the object increases (or decreases if it was an opposing force), according to <span c... | https://physics.stackexchange.com |
131,031 | [
"https://physics.stackexchange.com/questions/131031",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57296/"
] | Question: I have a pipeline that is tilted. I know the length of the pipeline, and the pressure (90psi) that is felt at the very bottom. I'm trying to find out how much liquid has leaked out if the pressure at the bottom decreases to 80psi.
Is the pressure felt at the very bottom directly proportional to the amount of... | The most common explanation for the "matter-antimatter asymmetry of the Universe" is $\rm CP$ violation in interactions involving leptons. This scenario is usually called leptogenesis because it generates a net excess of leptons compared to anti-leptons. This $\rm CP$ violation is currently unconfirmed by experiment (t... | CPT does exchange particles with their antiparticles, so if there were a time direction associated with particles then it might make sense to say that, by CPT, the antiparticles would have to have the opposite time direction.
But there's no time direction associated with particles. It doesn't even make sense to say th... | https://physics.stackexchange.com |
8,960 | [
"https://quant.stackexchange.com/questions/8960",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/6116/"
] | I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis.
If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if added another asset has some correlation with them two, the efficient frontier would be pushed to the left of these three... | You have a good point there. Adding an asset will not increase the minimum variance. If the assets are uncorrelated, the minimum will decrease (move left) towards zero. If they're positively correlated, it will decrease towards some minimum above zero.
Consider the case of uncorrelated assets, <span class="math-contain... | In mean-variance analysis, you combine different assets to minimize variance and maximize expected return. The hyperbola is not a function of the number of assets, but of their mean and variance. If the efficient frontier where a tangent to the y-axis (which can't be) or nearly a tangent, that would mean you would have... | https://quant.stackexchange.com |
74,744 | [
"https://mathoverflow.net/questions/74744",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17481/"
] | I have been computing eigenvalues of adjacency matrices for several directed (not necessarily strongly connected) graphs and one remarkable property seemed to hold (each graph that I have examined contained at least one cycle, but this need not to be a necessary condition):
"If $\lambda$ is an eigenvalue of an adjacen... | Let $D$ be the Paley tournament on seven vertices. Its vertices are the integers mod seven
and there is an arc from $i$ to $j$ is $j-i$ is a non-zero square mod seven. The characteristic polynomial of the adjacency matrix is $(x-3)(x^2+x+2)^3$. The only real eigenvalue is 3, the remaining eigenvalues are equal to $(-1\... | If $k$ is the greatest common divisor of the cycle lengths of the digraph, then the spectrum is invariant under rotation around the origin by $2\pi/k$. This is an application of the Perron-Frobenius theorem (see the Wikipedia article of that name).
On the other hand, the set of eigenvalues of digraphs is closed under ... | https://mathoverflow.net |
56,355 | [
"https://dsp.stackexchange.com/questions/56355",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/19259/"
] | So I have a digital linear chirp signal:
<span class="math-container">$$ x[n] = \sqrt{\frac{2}{N}} \cdot \cos\Big( 2 \pi \frac{f_{0}}{f_{s}}n + \pi \frac{B}{N} n^{2}\Big) $$</span>
Where <span class="math-container">$f_{0}$</span> is the initial frequency, <span class="math-container">$f_{s}$</span> is the sampling f... | You need to resample the signal to simulate the Doppler induced dilation. The resampling factor is <code>I=Td/Ts</code>
where
<code>Td</code> = Duration of the signal after dilation
<code>Ts</code> = Actual duration of the transmitted signal
In Matlab you can use the function <code>resample()</code>, but you need to f... | Rather than re-sampling, this is best accomplished by re-creating the signal after it is Doppler shifted. This allows any arbitrary waveform to have Doppler imparted on it. See Mark A. Richards, "Fundamentals of Radar Signal Processing," section 2.6.1. and in particular equation 2.90 for details on why this... | https://dsp.stackexchange.com |
570,789 | [
"https://physics.stackexchange.com/questions/570789",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/198210/"
] | From Leonard Susskind's book <em>The Theoretical Minimum</em>.
<blockquote>
"A particle in two dimensions, x and y, has mass m equal in both directions. It moves in a potential energy <span class="math-container">$V = \frac{k}{2(x^2+y^2)}$</span>. Work out its equations of motion. Are there circular orbits? If so,... | One way to approach this problem is using the effective potential formalism. If you are in a central potential (one that only depends on <span class="math-container">$r$</span>, where <span class="math-container">$r^2 = x^2+y^2$</span>, which you have) then there are some tricks you can use to simplify your problem. Wr... | The general orbit is not going to have an analytic solution. Just focus in the circular orbits and ask what their period is.
Good luck with your A-Levels!
| https://physics.stackexchange.com |
129,091 | [
"https://softwareengineering.stackexchange.com/questions/129091",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44688/"
] | I work for a small company that has had a product development department for quite a while. What we haven't had, however, is a QA/testing group.
We are looking to add a testing group, but are struggling to determine where best to put them in the organizational structure of the company. Specifically, we are going to hi... | <strong>Yes and no</strong> :)
Both developers and QA people should have the same goal (and their performance measured against that): deliver a quality product in time and on budget. You get to define "quality product", but it has to be the same for both groups. Why? Because if it isn't the same, you will get two grou... | It really depends on how serious your firm is about QA. For example will you be doing test driven development?
You mention a "testing group", this would suggest multiple people. If it is in fact a group of several people it should probably be a separate department. What puzzles me however is do you currently have at l... | https://softwareengineering.stackexchange.com |
171,649 | [
"https://security.stackexchange.com/questions/171649",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/161645/"
] | I just made a very simple batch virus that runs itself and runs on startup. I want to test it because I want to send it to a YouTuber who films himself running these viruses on a Virtual Machine.
The question is, how can I make the Virtual Machine safe for running this without going to my actual computer? Also, since ... | The default settings for most VMs will be sufficient for keeping everything isolated, that's what they're designed for.
The specific settings might be a little different depending on what software your're using, but here's a few things you can check in your VM's settings to keep your computer safe:
<ul>
<li>Disable ... | To prevent the virus from escaping the VM's virtualized hard disk, you'll need to make sure you don't connect the VM and host file systems (no "shared drives" or "shared files" or anything). You should also make sure the VM has not mapped any network drives with write access.
RAM usage is not a concern. The RAM a VM u... | https://security.stackexchange.com |
1,271 | [
"https://quant.stackexchange.com/questions/1271",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/954/"
] | Back in the "old days" (ie 5-10 years ago) when we wanted to be long or short an emerging currency (say the ZAR, BRL, or TRY) we simply did everything against the pre-eminent currency of the day, the dollar. So for example to be long the Turkish Lira, we sold USDTRY. Short the rand, we bought USDZAR. Most of the return... | Short answer - Use the betas from a multiple regression to create a hedged portfolio.
In a single factor model (i.e. hedging with only one other currency), you can interpret the Beta as the proportion of the factor that you would need to short. So if Beta = .5 then for every 1MM you are long, you would go short $500K ... | It depends on what aspect of ZAR you are trying to take a position on.
As A K pointed out, if your book is in USD and you want to take a position on the spot rate itself, then just have a USDZAR position. Yes, it is correlated with EURUSD because of both EUR-ZAR correlations and because of USD variations, but that's p... | https://quant.stackexchange.com |
634,151 | [
"https://math.stackexchange.com/questions/634151",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/120501/"
] | I am confused about this question, i dont know where to start.
If $A$ is countably infinite and $A - B$ is finite. What is the Cardinality of $A\cap B$?
Can you please give me a hint how to start and the receipe how i can solve such kind of questions.
| It is actually a geometric series that you posted here.
so for a Geometric series(GP series) we have a closed formula.
so now let us have a look: if we have a series such as...
a + ar + ar^2 + ar^3 + ... + ar^n (note that all the powers are only for 'r' not for 'a')
if anyone ask for the sum for this series then we ... | <em>Hint:</em> Multiply your sum with $m-1$, and see what you get. :-)
| https://math.stackexchange.com |
456,619 | [
"https://physics.stackexchange.com/questions/456619",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208138/"
] | My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: <span class="math-container">$$a = vdv/dx.$$</span>
It says acceleration vector equals velocity (as a function of <span class="math-container">$x$</span>) times <span class="math-conta... | The statement <span class="math-container">$a = v (dv/dx)$</span> only holds in that form for one-dimensional motion, where the quantities <span class="math-container">$v$</span> and <span class="math-container">$x$</span> are just numbers rather than vectors. It follows from the chain rule, if we view <span class="ma... | Your expression doesn't make sense for (non-trivial) vectors, only for scalars (which are one-dimensional, a.k.a. "trivial" vectors).
The expression <span class="math-container">$a=v\frac{dv}{dx}$</span> only makes sense if <span class="math-container">$v$</span> and <span class="math-container">$x$</span> are both f... | https://physics.stackexchange.com |
126,209 | [
"https://cs.stackexchange.com/questions/126209",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/119997/"
] | I have problem in determine whether it is decidable or not, can somebody help me please
| A language over <span class="math-container">$\{0\}$</span> is any subset of the set S of all strings consisting of a finite number of 0s. S is countable, the set of all subsets of S is uncountable.
Any decidable language must be decided by some algorithm. The set of algorithms, no matter how you describe it, is coun... | No. Consider any undecidable language <span class="math-container">$L$</span> (for example, take the language <span class="math-container">$Halt = \{(M,x): \text{ M halts on x}\}$</span>), we can encode each string of this language in unary (by writing the binary number representing <span class="math-container">$(M,x)... | https://cs.stackexchange.com |
387,400 | [
"https://electronics.stackexchange.com/questions/387400",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/193870/"
] | I am trying to measure capacitances using an Arduino UNO.
<img src="https://imgur.com/CiAtGGF.png" alt="Schematic">
The C pin charges the capactitor through a 10K resistor (I have also tried 100K and 220), and the G pin discharges it.
V_A and V_B are measurement points across the 10K resistor.
The program does the ... | A 470 uF will be likely an electrolytic type and this will have a leakage current in the order of 1 to 10 uA per microfarad, Assuming 1 uA is the figure then the total leakage will be 470 uA and this will cause a volt drop (irrespective of capacitance value) across the 10 kohm resistor of 4.7 volts and your algorithm w... | You are testing at v_b < 4V, so I assume you are using an NFET with Vt<1V.
Vt is often defined as the 1mA conduction threshold, when you want the top FET to conduct much faster, its gate voltage should be greater than supply or drop Vd by 2 diode drops and test at a lower threshold.
Or better yet, change stat... | https://electronics.stackexchange.com |
417,973 | [
"https://mathoverflow.net/questions/417973",
"https://mathoverflow.net",
"https://mathoverflow.net/users/69681/"
] | It is known that if a finite group <span class="math-container">$G$</span> admits a faithful <em>topological</em> action on the 3-sphere <span class="math-container">$S^3$</span>, then <span class="math-container">$G$</span> admits a faithful action on <span class="math-container">$S^3$</span> by <em>isometries</em>. (... | I believe (though have not checked carefully) that the argument in my paper proves:
<blockquote>
If <span class="math-container">$\Gamma$</span> (discrete) acts continuously and properly discontinuously on a smooth three-manifold <span class="math-container">$M$</span>, then that action can be uniformly approximated by... | My earlier attempt at an answer was a bit of a mess -- let me have another go.
The hypotheses of the question introduce several technical difficulties, but I'm unsure which are crucial and which can be relaxed. Certainly, if we're willing to relax them slightly then we can get a positive answer, so I'll give an answer ... | https://mathoverflow.net |
173,160 | [
"https://physics.stackexchange.com/questions/173160",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/38593/"
] | For many operators, their adjoint can be expressed as a function of other known operators, for example $$\hat{T}_a^\dagger = \hat{T}_{-a} \\ \hat{p}_x^\dagger = \hat{p}_x$$ where $\hat{T}_a \psi (x) = \psi (x+a)$ and $\hat{p}_x \psi(x)= -ih \frac{\partial \psi(x)}{\partial x}$.
But if we consider the operator $\hat{K}... | The operator <span class="math-container">$K$</span> on the Hilbert space <span class="math-container">$H$</span> is antilinear and satisfies
<span class="math-container">$$(\eta,K^*\psi)=\overline{(\eta,K\psi)},\qquad\forall \eta,\psi\in H,$$</span>
which is not what you would expect for self-adjointness.
You can con... | $\hat{K} \Psi = \Psi^*$ is not a well defined operator at all. On the one hand it is clear that $\hat{K^2} = 1$ and $\hat{K}$ is therefore real. On the other hand by your definition
$$
<\Psi| K |\Psi> = \int \Psi^{*2} d^3r \not\in \mathbb{R}
$$
It is ill defined because it does not map from the space of the Kets ... | https://physics.stackexchange.com |
140,392 | [
"https://softwareengineering.stackexchange.com/questions/140392",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32945/"
] | In development, I would normally have my own test scripts that would document the data, scenarios and execution steps that I plan to test; this is my dev test plan. When the functionality has been deployed to Test, testers test it using their own test script that they wrote. In UAT, the business user then tests using t... | Firstly QA is not Test. If your QA department are not involved in the entire development process, they are Test, not QA. QA when doing it's job, provides quality assurance, at best Test shows the lack of quality, but cannot prove quality exists - i.e. Test shows QA has failed, but cannot show they have succeeded, so T... | We use UATs from the start.
It acts as a universal reference and I think it works well. While there might be test scripts that are used only by the Devs or Testers for smaller components, the direction of the testing is always pointed towards one unified target. At the end of the day, the UAT is the only one that cou... | https://softwareengineering.stackexchange.com |
659,150 | [
"https://physics.stackexchange.com/questions/659150",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230396/"
] | Is centripetal force the correct terminology? Why is the resultant (orthogonal ) force component called "centripetal force"? In my view, it is just a component
| The terminology is correct. It doesn't have to be the resultant force. You are correct that it may only be a component. "The centripetal force" is just a name we give to the sum of all forces that point towards the centre (thus the name) because only these forces cause turning. Regardless of other forces bein... | Centripetal is the name given a force when that force acts to keep an object moving at constant velocity, moving in a circle. The actual force can be gravity, tension in a string, etc.
More generally, centripetal force refers to the component of the total force that is directed toward the center, and the total motion ... | https://physics.stackexchange.com |
30,717 | [
"https://stats.stackexchange.com/questions/30717",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11941/"
] | Pearson correlation coefficient is calculated using the formula $r = \frac{cov(X,Y)}{\sqrt{var(X)} \sqrt{var(Y)}}$. How does this formula contain the information that the two variates $X$ and $Y$ are correlated or not? Or, how do we get this formula for the correlation coefficient?
| What matter is $cov(X,Y)$. Denominator $\sqrt{var(X)var(Y)}$ is for getting rid of units of measure (if say $X$ is measured in meters and $Y$ in kilograms then $cov(X,Y)$ is measured in meter-kilograms which is hard to comprehend) and for standardization ($cor(X,Y)$ lies between -1 and 1 whatever variable values you ha... | If, in the formula that you display, you remove the 'dividedness' of all three terms, <em>cov(X,Y)</em>, <em>var(X)</em> and <em>var(Y)</em> by <em>n-1</em>, you get even more basic formula for <em>r</em>: $\frac{SCP(X,Y)}{\sqrt{SS(X)} \sqrt{SS(Y)}}$, where <em>SCP</em> is "sum cross-products" and <em>SS</em> is "sum o... | https://stats.stackexchange.com |
443,746 | [
"https://stats.stackexchange.com/questions/443746",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/23694/"
] | Suppose my observed data <span class="math-container">$y$</span> and <span class="math-container">$x$</span> is generated by the following relationship for each observation <span class="math-container">$i$</span>:
<span class="math-container">$$ y_i = h(y_i,\theta) + x_i + \varepsilon_i$$</span>
where <span class="ma... | Here is some rough code in R implementing the non-linear two stage least squares estimator under the assumption that <span class="math-container">$\mathbb E[\epsilon\lvert x] = 0$</span>. Just to see if it works ... it seems to be working up to the point of standard over-underflow issues there might be. But the non-lin... | <hr>
<blockquote>
<em>Or how else is such a non-linear relationship without closed-form
solution approached?</em>
</blockquote>
For maximum likelihood we want the density of <span class="math-container">$y$</span> conditional on <span class="math-container">$x$</span> (because this is our sample), <span class="ma... | https://stats.stackexchange.com |
132,314 | [
"https://softwareengineering.stackexchange.com/questions/132314",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/14294/"
] | I'm developing a web application with a strong focus on security. What measures can be taken to prevent those who work on the application (programmers, DBAs, quality assurance staff) from capturing user entered values that should be well-protected, such as passwords, social security numbers, and so forth?
| This is quite simple. Banks do it all the time.
You have three groups of people involved. These are security groups. With distinct authorizations.
Developers cannot assign security authorizations and cannot see production data.
Operators cannot assign security authorizations and cannot create software.
Security ... | The programmers don't have access to the production servers. But someone has to have access. There's no way around it. And there's always a chance that someone may go insane and abuse their access.
Data that is hashed/salted is theoretically secure even from the people who have full access to view it. But most data is... | https://softwareengineering.stackexchange.com |
32,216 | [
"https://cs.stackexchange.com/questions/32216",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/22957/"
] | When a computer OS supports multi-program, it needs to have a scheduling algorithm to handle which process will be run by the cpu.
If a process is in state 'blocked' waiting for IO, the scheduling causes another process to be taken by the cpu while the process in state 'blocked' is waiting for a response I/O. In this... | The scheduling algorithm is largely irrelevant. What is relevant is how the Operating System kernel saves information about requests it has made for which it is awaiting replies.
When we say that a process is in state "blocked" we don't really mean that there is a variable somewhere called <code>state</code> to which... | First of all, different environments need different scheduling algorithms.
This is mainly because different operating systems have different objectives according the needs. Then, what the scheduler is going to optimize will not be the same for every case.
There are Real time systems, batch processing, interactive sys... | https://cs.stackexchange.com |
572,664 | [
"https://physics.stackexchange.com/questions/572664",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/197434/"
] | Suppose that there is a system of two photons 1 and 2, each of which is in a mixed state <span class="math-container">$1/2|R\rangle\langle R| + 1/2 |L \rangle\langle L|$</span>, where <span class="math-container">$|R \rangle$</span> and <span class="math-container">$\langle L|$</span> are two orthonormal pure polarizat... | There is no difference for measurement outcomes in the <span class="math-container">$\{|R\rangle, |L \rangle\}$</span> basis. However, you will see a difference if you look at a rotated basis e.g. consider the axes:
<span class="math-container">$$|+\rangle = \frac{1}{\sqrt{2}} \left(|R\rangle + |L\rangle\right) \\
|-\r... | The thing is whether those two photons are independent or not.
A single photon can be <span class="math-container">$|L\rangle$</span> or <span class="math-container">$|R\rangle$</span>, which are pure states, or any linear combination of them (normalized).
However, whtn you have two photons as a compound system, you ca... | https://physics.stackexchange.com |
68,142 | [
"https://security.stackexchange.com/questions/68142",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/55343/"
] | These days there are several database technologies are available for data storage purpose.
<br>
While performing injection attacks, how do attackers actually identify the database used by a website?
<br>
If it is possible by any queries or commands through any application entry points, can someone
<br>
explain to me th... | There are three common ways to deal with the variety of databases out there:
<ol>
<li>Many web applications are tied to a specific database backend, rather than being able to use a variety of backends. For example, if someone's using MediaWiki, you know they're using either MySQL or MariaDB.</li>
<li>An attacker can ... | Even though noSQL databases are on the rise, the vast majority of web applications still use some kind of SQL database. The basic SQL features are standardized, so many simple SQL queries work on any SQL database. I doubt there is any database which calls itself SQL and doesn't understand <code>password = '' OR '1'='1'... | https://security.stackexchange.com |
192,386 | [
"https://dba.stackexchange.com/questions/192386",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/139919/"
] | If I am doing a SQL Update query that affects, for instance, 1000 rows, how do I check that the query worked as intended and didn't hit any strange edge cases, (short of examining each row visually myself)?
What is best practice for this ?
Additional info requested in comments
I was writing a SQL query to update any ... | You could query before and after looking for the particular conditions you are wanting to update.
For adhoc queries it's a good idea to run the query as a select statement using the same where clause <em>before</em> running as an update statement.
The update should update exactly the same rows select returned unles... | Script belong to <code>Sql Server</code>. but my above idea is for any DBMS.
Main goal should be <code>fullfilling requirement, error free Script and best performance.</code>
Why would I want to know everytime that whether those 1000 rows were updated sucessfully or not ? why would i want to know about each rows ?
w... | https://dba.stackexchange.com |
190,359 | [
"https://softwareengineering.stackexchange.com/questions/190359",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/84141/"
] | At the moment I am teaching myself iOS programming, and one concept I find really hard to wrap my head around is delegation. What is it? Why and how is it used? What is the advantage? The technical writing from the book I'm reading makes it hard to understand.
| To understand <code>delegates</code>, you have to understand <code>protocols</code>.
A <code>protocol</code> is like a service contract. When an object (most often a <code>UIViewController</code> subclass, but not always) signs that contract, it is saying "I am interested in providing logic to back the message you sen... | Delegates are objects that implement certain functions when it doesn't make sense to implement those functions on the normal object. It is a form of dependency injection.
For a concrete example, look at the UITableViewDelegate protocol. These methods don't make sense for a table view to implement directly, because act... | https://softwareengineering.stackexchange.com |
149,746 | [
"https://mathoverflow.net/questions/149746",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34538/"
] | Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then :
$$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$
<blockquote>
<strong>Question</strong> : Is it singly generated (as von Neumann algebra)? how ?
</blockquote>
<strong>Allowed operations</strong> : $() \mapsto I$ , $(A) \mapsto \lambda A$ ... | Pick distinct complex numbers $\lambda_1,\ldots,\lambda_k$ and consider the element
$$
X:=\Bigg(\,\underbrace{\begin{smallmatrix}
\lambda_1&1&0&0&0\\
0&\lambda_1&1&0&0\\
0&0&\ddots&\ddots&0\\
0&0&0&\lambda_1&1\\
0&0&0&0&\lambda_1\\
\end{sma... | For the sake of completeness, here are more general statements:
<strong>1) Every separable type I factor is singly generated.</strong> You take the weighted shift $S=\sum_j 2^{-j}E_{j,j+1}$. Then $W^*(S)$ contains $(S^*S)^{1/2}=\sum_j2^{-j}E_{jj}$ and now by using the characteristic function of $\{2^{-j}\}$ we obtain... | https://mathoverflow.net |
63,690 | [
"https://mathoverflow.net/questions/63690",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9833/"
] | Let $X\subset\Pi_1^0$ be the set of statements which are
provable in PA$+$Con(PA) but independent of PA.
Is $X$ recursively enumerable?
| The answer is no, and in particular, $X$ is $\Pi^0_1$-hard. Let $\sigma(x)=\exists v\,\theta(x,v)$ be a complete $\Sigma^0_1$-formula, where $\theta\in\Delta^0_0$, and find a formula $\pi(x)$ such that PA proves
$$\pi(x)\leftrightarrow\forall w\,(\mathrm{Proof_{PA}}(w,\ulcorner\pi(\dot x)\urcorner)\to\exists v\le w\,\... | Here's a proof that doesn't directly diagonalize but instead relies on well-known results, which in turn were proved by diagonalization. So ultimately, it isn't really easier than Emil's, but it may be easier to find and remember.
I claim first that, if a $\Pi^0_1$ sentence $\phi$ is provable in PA plus $\neg\text{Co... | https://mathoverflow.net |
308,151 | [
"https://mathoverflow.net/questions/308151",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31356/"
] | Let $X$ be a subset of $\{0,1\}^*$ with the following property: for every pair of distinct strings $x_1$, $x_2$ from $X$
$x_1$ is not a substring of $x_2$ and $x_2$ is not a substring of $x_1$.
How much can be the log-density of $X$,
i.e. $\lim \frac{ \log X_n}{n}$, where $X_n$ is the cardinality of all strings of... | I'm going to use $\log_2$ instead of $\log$ throughout; this only results in constant factor change (and the largest possible answer becomes $1$, which is convenient).
Fedor Petrov's answer implies that $\lim \frac{\log_2 X_n}{n} < 1$ for any $X$. We can, however, construct a family $X$ with $\lim \frac{\log_2 X_n}... | Even if we forbid one substring $a$, the density becomes 0: if $m$ is a length of $a$, then there exist at most $(2^m-1)^{\lceil n/m\rceil}$ strings of length $n$ without substring $a$.
| https://mathoverflow.net |
96,463 | [
"https://electronics.stackexchange.com/questions/96463",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6981/"
] | I have a AD 09 license from my school, and they said it would not work on a W8 pc. Now I am in process of getting a new laptop. Since most laptops come with W8, I am wondering if I will be able to run Altium if I upgrade it too. Does anybody here have any experience?
I tried searching, but "Altium designer windows 8" ... | I am using altium designer 14.1 and its working fine in windows 8.
| I can only say that 13.3.4 does. And I see no reason why it should be different for 14. I do NOT use the nanoboard or any other hardware so I cannot say about that.
| https://electronics.stackexchange.com |
428,567 | [
"https://electronics.stackexchange.com/questions/428567",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/110418/"
] | I wanted to make use of a single port RAM to be a single clock FIFO in verilog for an asic project , due to some constraints i can not use the dual port RAM. My confusion is when I have to perform read and write simultaneously, I thought about using a faster clock and give 1 cycle for read another cycle for write, but... | You need to define your requirements more carefully.
<ul>
<li>How many reads can occur on contiguous clock cycles?</li>
<li>How many writes can occur on contiguous clock cycles?</li>
</ul>
If the answer to both is "just one", then all you need is a simple aribter. Do the read when requested, and if a write happens at... | You can use 2 single port RAM to build a synchronous FIFO. All the even address goes to RAM0, and all the odd Address goes to the RAM1.
When you want to read and write at the same cycle, make sure the address 0 are not the same.
Else you have to give priority to Wite (or Read), and wait for the next cycle
| https://electronics.stackexchange.com |
365,925 | [
"https://mathoverflow.net/questions/365925",
"https://mathoverflow.net",
"https://mathoverflow.net/users/161287/"
] | I would be interested in recommendations for topological graph theory texts. I think Gross and Yellen has a great chapter on topological graph theory, and I find Mohar and Thomassen's <i>Graphs on surfaces</i> from 2001 a great reference as well.
<blockquote>
Could you recommend more current references, ideally with fo... | Maybe this is another useful reference for you, now I found the link:
Ralucca Gera, Stephen Hedetniemi, Craig Larson, Teresa W. Haynes (editors) (2018): <em>Graph Theory: Favorite Conjectures and Open Problems</em>
It is actually two volumes, and obviously more recent than the other reference I mentioned. It covers gra... | My recommendation, try Lando and Zvonkin (2004): Graphs on Surfaces and Their Applications.
I think it is a great book which applies graphs embedded on surfaces to solving problems from other fields of mathematics. The style is very refreshing, vivid, and lively, I would say. The style reminded me of Hatcher's chapter ... | https://mathoverflow.net |
251,677 | [
"https://electronics.stackexchange.com/questions/251677",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/120338/"
] | Okay, I'm a total noob and don't know if I'm even wording this question correctly, but I'll try.
My understanding is that the power supply (an USB power supply in my case) determines the current. I have a 2.5A 5V supply, and a USB-to-DC cable that connects that power supply to an USB hub (5V as well). Now that hub wou... | The power supply works as a <em>voltage</em> source up to 2.5A current. You cannot combine the current of the externals supply and the PC's port - that would require expensive adaptive circuitry.
| Your power supply can deliver <strong>up to</strong> 2.5 Amps at 5 Volts, but does not force 2.5 Amps into a load. Any load will only "ask" the power supply for the current it requires.
| https://electronics.stackexchange.com |
929,514 | [
"https://math.stackexchange.com/questions/929514",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/169916/"
] | For example, we're given a problem in which sin $\theta = \sqrt3/2$ and cos $\theta = -1/2$. To find out the angle $\theta$, I look at the unit circle and I get the answer. However, I was just curious whether there's an alternative to this, any idea? Because when I tried using cos(-$\theta$) = cos$\theta$, I get the wr... | They're not the same. If you have a topology (only the open sets) you get a Borel $\sigma$-algebra: the smallest one containing all open sets (so that contains the topology).
But this also contains all closed sets, all countable intersections of open sets (which need <em>not</em> be open, nor closed) etc. The Borel $\... | A $\sigma$ algebra needs to be closed under ${\bf countable}$ union and under complementation. Now, a topology is closed under ${\bf any}$ union and in general not closed under complementation.
This holds in general. Furthermore, you have that the Borel $\sigma$ algebra contains the topology (by definition), hence it ... | https://math.stackexchange.com |
629,550 | [
"https://math.stackexchange.com/questions/629550",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Investigate the convergence of $\sum a_n$ where $a_n = \displaystyle\int_0^1 \dfrac{x^n}{1-x}\sin(\pi x) \,dx$.
We have thought about using the dominated convergence theorem to find $\lim a_n$, but that would result in something like $\lim a_n = \lim \displaystyle\int_0^1 \dfrac{x^n}{1-x}\sin(\pi x) \,dx = \displaysty... | Though Sasha's solution is perfect, I'd like to suggest another approach (suitable to the [measure-theory] tag):
We note that
$$S_N = \sum_{n=0}^N a_n = \int_0^1 \frac{1-x^{N+1}}{1-x}\frac{\sin(\pi x)}{1-x}dx$$
Now, $f_N := \frac{1-x^{N+1}}{1-x}\frac{\sin(\pi x)}{1-x}\to\frac{\sin(\pi x)}{(1-x)^2}$ pointwise and monot... | Using $\sin(\pi x) \geqslant \pi x(1-x)$ for $0\leqslant x \leqslant 1$
$$
a_n = \int_0^1 \frac{x^n}{1-x} \sin(\pi x) \mathrm{d}x > \int_0^1 \pi x^{n+1} \mathrm{d}x = \frac{\pi}{n+2}
$$
it follows that $\sum_{n=0}^\infty a_n$ diverges.
| https://math.stackexchange.com |
109,366 | [
"https://dba.stackexchange.com/questions/109366",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/72345/"
] | I have a database table to store technicians (employees) which is structured like this:
<pre><code>| firstName | lastName | phone | alternatePhone | email | canadaTravel | canDrive | notes |
</code></pre>
In this table, only the first two columns are required. Any other values can be null. I would like to prevent aga... | There is no way to allow for two technicians with the same name and still prevent duplicate technician's from being entered without always providing an additional characteristic that will differentiate them to the DBMS as part of a unique constraint. The DBMS does not reflect reality but instead only what you have <st... | Perhaps you will solve this problem with little help from your UI person. Check for the presence of the name in the DB before making a new entry. If similar name is found in the DB, show some kind of warning in the UI that the user should be able to override.
Otherwise, as you perhaps realize, you can either have a un... | https://dba.stackexchange.com |
61,091 | [
"https://softwareengineering.stackexchange.com/questions/61091",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19431/"
] | So, I have a couple of projects that I have been working on and I am trying to decide if I want to open source them or provide them for free as closed source.
I have never "owned" an open source project before and I would love to hear thoughts on the pros and cons of both options. Any horror stories of deciding on ei... | The worst thing, that could happen to you if go open source is, that someone forks your code, and creates a project that is more successful. This requires the two of you to have fundamentally different oppinions about where the project should go.<br>
Firstly, this is not much of a risk, and secondly, I think not much i... | The big question you have to answer is what you think you gain by protecting them, because the gains from open-sourcing can be numerous.
If the product is good, you will build a community of people willing to maintain it for you. Bugs will be found and fixed before you even run into them yourself.
You can use it to p... | https://softwareengineering.stackexchange.com |
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