qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
1,324,804 | [
"https://math.stackexchange.com/questions/1324804",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/248078/"
] | The normal to the ellipse $b^2x^2+a^2y^2=a^2b^2$ is passing through the x-axis in point $A$ and through the Y-axis in point $B$.
Point $P$ is the midpoint of $AB$.
Need to find the locus of $P$.
My attempt :I tried to use the fact of the tangent to the ellipse $n^2=a^2m^2+b^2$ and to use slopes but I didn't succeed... | i will parametrize the ellipse by $$x = a \cos t, y = b \sin t $$ the slope of the tangent is $$\frac{dy}{dx} = -\frac{b\cos t}{a \sin t} $$ therefore the slope of the normal is $$\frac{a\sin t}{b \cos t}.$$ the equation of the normal line is $$(y-b\sin t)b \cos t = a \sin t(x -a \cos t) $$ the $x$-intercept is given... | Hint.
$x(t)= a \cos t$, $y(t)=b \sin t$ is a parameterization of your ellipse.
Then for $t \in [0, 2 \pi]$, find the normal to the ellipse at point $(x(t),y(t))$ and the intersection points with the coordinates axis. Then you'll get the midpoint as a function of $t$.
| https://math.stackexchange.com |
244,538 | [
"https://electronics.stackexchange.com/questions/244538",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59353/"
] | I'm trying to understand how transformers work. I understand the primary/secondary stepping down/up voltage or current, but why do they use oil (in oil tank) with transformers?
| Transformers are oil filled for two reasons:
<h2>Cooling</h2>
The transformer windings dissipate waste heat, which needs to be removed. Transformer oil absorbs this heat from the windings and conducts it to the outside of the transformer, where it can be dissipated to the outside air.
It is possible to build an air-... | High power transformers often have the core and windings immersed in a liquid (not always oil, poly-chlorinated byphenol used to be popular). These transformers usually have fins sticking out from the core. One purpose of the liquid is to convect heat from the core to the fins, where it can be more easily dissipated ... | https://electronics.stackexchange.com |
51,302 | [
"https://physics.stackexchange.com/questions/51302",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12615/"
] | I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is <span class="math-container">$ \vec {A}= B/2 (-y, x, 0)$</span>.
I know that <span class="math-container">$$H=\sum_i p_i \dot q_i -L$$</span> where <span class="math-container">$p_i$</span> is conjugated momentum, ... | 1) We start writing the <strong>Lagrangian</strong>
$$L=\frac{1}{2}mv^2+q\vec{v}\cdot\vec{A}=\frac{1}{2}m(v_x^2+v_y^2+v_z^2)+q\frac{B}{2}\left(-yv_x+xv_y \right)$$
2) We find the <strong>momenta</strong>
$$p_{x}=\frac{\partial L}{\partial v_{x}}=mv_{x}-\frac{qBy}{2}$$
$$p_{y}=\frac{\partial L}{\partial v_{y}}=mv_{y... | The potential of a charged particle in an electromagnetic field is:
$$U(r,v,t)=q\phi -q\mathbf{v}\cdot A$$
Being $\phi$ the electric potential, $v$ the speed of the particle, $q$ the charge of the particle, and $A$ the vector potential of the magnetic field. Make sure su haven't made any mistakes calculating the lagr... | https://physics.stackexchange.com |
106,847 | [
"https://electronics.stackexchange.com/questions/106847",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40433/"
] | I'm uncertain of the term "fat" when referring to NMOS and PMOS. Tried google and nothing. Could I get a little clarification?
| Microchip designer here...
I've never heard of a "fat" MOS transistor, but there is such a thing as a "thick oxide" MOSFET transistor, sometimes referred to as just "thick" transistors.
Typically, a MOSFET transistor is designed such that the electrical performance is good for a particular voltage range. For example,... | The first thing that comes to mind when referring to MOSFETs as fat is the channel width. The larger the channel the more current can flow when the FET is on. So a "fat" MOSFET would be able to source or sink more current than a thin one.
| https://electronics.stackexchange.com |
119,000 | [
"https://physics.stackexchange.com/questions/119000",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4016/"
] | Thought experiment: what happens if we measure momentum of a particle so precisely, that the uncertainty of its position becomes absurd?
For example, what if the uncertainty of the position exceeds 1 light year? We know for a fact that the particle wasn't a light year away from the measuring device, or else how could... | You assume that you can instantly measure the momentum to arbitrary precision, and this isn't the case.
Let's consider a plane light wave to keep things simple, and suppose you want to measure the momentum so precisely that the position uncertainty becomes exceedingly large. How precisely do we have to measure the mom... | Consider a measurement apparatus (M.A.) of characteristic size $d$, the uncertainty about the momentum of the measurement apparatus is then $\Delta p_{M.A.} \approx \dfrac{\hbar}{d}$
Now, if the measurement apparatus is measuring the momentum of a particle, the uncertainty about the measured particle momentum is nece... | https://physics.stackexchange.com |
483,647 | [
"https://electronics.stackexchange.com/questions/483647",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/214898/"
] | In my university lectures I have generated an FM signal (for instance with carrier frequency of 2GHz, frequency deviation equal to 100kHz, and modulating frequency equal to 100kHz.)
In order to perform the demodulation, my teacher has followed these steps:
<ol>
<li>Choosing a high resolution bandwidth in order to inc... | The trick here is that the RBW filter is placed so that its transition band (on one side) spans the frequency range that the modulated signal covers, so the attenuation of the filter is dependent on the modulation signal.
The RBW must be selected so that the transition band is wide enough that the entire signal fits i... | 1 is to view outside the normal bandwidth to look for intermeodulated distortion (IMD) or other spurious emissions. PIM and such.
| https://electronics.stackexchange.com |
1,931,280 | [
"https://math.stackexchange.com/questions/1931280",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/173262/"
] | <blockquote>
Let $\varphi:G\to G'$ be a group homomorphism. Is $\varphi(G)$ a normal subgroup of $G'$?
</blockquote>
I dont know how to prove that the statement is false.
Without lose of generality suppose that $G$ is a subgroup of $G'$ and $\varphi$ is the inclusion map, then the problem is reduced to prove that ... | This is wrong in general. For instance, let $G=\langle (1 \; 2)\rangle$, which is a non-normal subgroup of $G'=S_3$
(let $g=(1 \; 3) \in G'$, and show that $g^{-1}(1 \; 2)g \not \in G$),
and just take $\phi : G \to G'$ the inclusion.
However, if $H$ is a normal subgroup of $G$, and if $\phi : G \to G'$ is a surjective... | For (counter) example:
$$G=\{\,(1),\,(12)\,\}\;,\;\;G'=S_3\;,\;\;\phi:G\to G'\;,\;\;\phi(12)=(12)\;,\;\;\phi(12)=(1)$$
In fact, you can choose <strong>any</strong> group $\;G'\;$ which has at least one non-normal subgroup $\;G\;$ , and then take the inclusion homomorphism $\;G\to G'\;$ and you get a counter example.
| https://math.stackexchange.com |
3,697 | [
"https://mechanics.stackexchange.com/questions/3697",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1887/"
] | I bought a battery today for my scooter. The mechanic fitted the battery into the scooter and it seems to be running fine. But when I noticed the battery's box later on, it said "Dry Charged" and on further reading in the manual, I figured out that the battery would have needed some sort of "electrolyte" and also an "i... | I don't think you'll have any issues. If you continue to be worried about it, you should be able to pull the caps off of the top of the battery to check the fluid level within. You should be able to see the electrolyte at almost the top. If you don't, then I would take it back to the shop where you had it fitted and ge... | My grandson installed a dry charged 6v battery in his Honda CT 90 6 months ago. The electrolyte remained in the box never added and eventualy discarded when the box was destroyed by leaking acid.
The battery worked all summer and was showing 6.8 v when the bike failed to start this October.
When I discovered it dry,I a... | https://mechanics.stackexchange.com |
146,996 | [
"https://stats.stackexchange.com/questions/146996",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/73854/"
] | I know very little of Probability and Statistics, and am wishing to learn. I see the word "distribution" used all over the place in different contexts.
For example, a discrete random variable has a "probability distribution." I know what this is.
A continuous random variable has a probability density function, then ... | The following is for $\mathbb R-$valued random-variables. The extension to other spaces is straight forward if you are interested. I would argue that the following slightly more general definition is more intuitive than separately considering density, mass and cumulative distribution functions.
I include some mathemat... | Let $(\Omega,\mathscr{F},P)$ be a probability space, let $(\mathscr{X},\mathscr{B})$ be a measurable space, and let $X:\Omega\to\mathscr{X}$ be a measurable function, which means that $X^{-1}(B)=\{\omega:X(\omega)\in B\}\in\mathscr{F}$ for every $B\in\mathscr{B}$. The <strong>distribution of</strong> $X$ is the probabi... | https://stats.stackexchange.com |
113,379 | [
"https://softwareengineering.stackexchange.com/questions/113379",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/38347/"
] | There is always a debate over the topic - "Whether to put the business logic in Stored Procedure or Not?". If we decide not to use the ORM Tool and not to put the Business Logic in Stored Procedure then where would we put the Business Logic?
In my previous applications I have always preferred putting all of the Busine... | I would adopt a pragmatic approach - historically the primary 'benefit' of keeping business logic in stored procs is for performance reasons (2.5 tier architecture), whereas separating the business logic into a BLL tier (3/N tier) is generally cleaner from a maintenance perspective, and easier to test (Mock / Stub out ... | Being a java developer my preference was to put business logic in the BLL (nice and easy source control, familiarity etc etc etc).
However, after working for a large enterprise with many distributed applications using different technologies (C#, Java, Pick (don't ask)) one significant benefit of using stored procedur... | https://softwareengineering.stackexchange.com |
52,824 | [
"https://electronics.stackexchange.com/questions/52824",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17495/"
] | I'm trying to use an LCD (DEM16101) from a uC.
At some point I've connected it's power input to a 6V battery (above its 5.5 V max rating).
I can't initialize it properly so at this point I'm wondering - how can I tell if I've fried it?
| <em>Edit: There is some argument over Maximum and Absolute Maximum values in the comments. Personally, I would still not trust the device to operate correctly, even though it has not reached or exceeded the Absolute Maximum rating. A couple comments have been made that I am incorrect in my interpretation of the datashe... | You can't tell whether you fried it, that would be proving a negative. However, you should <i>assume</i> you fried it, especially since it doesn't appear to work anymore. You violated a absolute maximum spec, so really shouldn't be surprised. Violating such a spec is no <i>guarantee</i> of damage, but you can no lon... | https://electronics.stackexchange.com |
7,153 | [
"https://mathoverflow.net/questions/7153",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1107/"
] | I'm not sure whether this is non-trivial or not, but do there exist simple examples of an affine scheme $X$ having an open <strong>affine</strong> subscheme $U$ which is not principal in $X$? By a principal open of $X = \mathrm{Spec} \ A$, I mean anything of the form $D(f) = \{\mathfrak p \in \mathrm{Spec} \ A : f \not... | Let X be an elliptic curve with the identity element O removed. Let U=X-P where P is a point of infinite order. Then U is affine by a Riemann-Roch argument. Now suppose that U=D(f). Then on the entire elliptic curve, the divisor of f must be supported at P and O only. This implies that P is a torsion point, a contradic... | For a simple, really concrete example you can also look at:
$A=k[x,y,u,v]/(xy+ux^2+vy^2)$, $X =Spec(A)$, $I=(x,y)$, $U = D(I)$.
Then the functions $f=\frac{-v}{x}=\frac{y+ux}{y^2}$ and $g=\frac{-u}{y}=\frac{x+vy}{x^2}$ are defined on $U$. But $yf+xg=1$, so $U$ is affine!
Cheers,
| https://mathoverflow.net |
2,707,189 | [
"https://math.stackexchange.com/questions/2707189",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/517532/"
] | Show that if n is a power of 3, then $\sum_{i=0}^{\log_3n} 3^i = \frac{3n-1}{2}$
$\sum_{i=0}^{\log_3n} 3^i =3^0+3^1+3^2+3^3...+3^{log_3n}$
This is a geometric sequence, so I used the geometric sum formula: $S= \frac{a_1 \cdot (q^n-1)}{q-1}$.
The first element is : $ 3^0 = 1$,
The ratio is : $q=3$,
The number of el... | Make a change: $n=3^m$. Then:
$$S=\sum_{i=0}^{m} 3^i=\frac{1\cdot (3^{m+1}-1)}{3-1}=\frac{3\cdot 3^m-1}{2}=\frac{3n-1}{2}.$$
| $$\sum_{i=0}^{\log_3 n} 3^{i}
=\frac{3^{\bbox[yellow]{1+}\log_3 n}-1}{3-1}
=\frac{3 \cdot 3^{\log_3 n}-1}{2}
=\frac{3n-1}{2}.$$
| https://math.stackexchange.com |
134,861 | [
"https://softwareengineering.stackexchange.com/questions/134861",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25945/"
] | Working on a problem that uses the percent change formula:
<pre><code>percent change = 100 * [(new value - old value) / old value]
</code></pre>
How would I explain the difference if <code>new value or old value = NULL</code>, rather than <code>0</code> to someone who might not be a programmer?
My boss is wondering... | To explain to a boss the difference between "zero" and "null":
"Zero" is a value. It is the unique, known quantity of zero, which is meaningful in arithmetic and other math.
"Null" is a non-value. It is a "placeholder" for a data value that is not known or not specified. It is only meaningful in this context; mathema... | Boss-speak is always tough...
Zero is a number so you can do things with it.
Null is a unicorn. It doesn't exist so you can't do anything at all with it.
| https://softwareengineering.stackexchange.com |
148,622 | [
"https://physics.stackexchange.com/questions/148622",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65222/"
] | I'm trying to get a hold of the idea of gravity in general relativity and spacetime. I've seen plenty of demonstrations of the rubber mat analogy to describe gravity and spacetime curvature. Is this curvature a deformation of 3 dimensional space or a deformation of time, or a combination of the two?
If it's a curvatur... | In a certain sense (regime) acceleration is caused by the <em>curvature of time</em> more than the <em>curvature of space.</em> Actually, the curvature is of the spacetime so that, making rigid distinctions has no much sense. However, if you consider the motion of a particle free falling in a region of spacetime, the e... | I'm hardly a GR expert, so if you want a more technical analysis I'm sure others will be able to give you one. However, the answer to your apparent questions is fairly straight forward.
It is not the curvature of space <em>or</em> the curvature of time that causes accelerations, it is the curvature of <strong>space-t... | https://physics.stackexchange.com |
2,086,439 | [
"https://math.stackexchange.com/questions/2086439",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/401774/"
] | I was given the next question: How many options are there to hand to two people 4 green apples, 3 red apples and 5 yellow apples.
I thought about using the partition method by multiplying each case. Is it the right way of looking at the problem and solving it?
I'm sorry, English isn't my first language and I couldn'... | I'd do it differently: since $A$ and $B$ are not both zero, we can divide by $-\sqrt{A^2+B^2}$, getting
$$
\frac{-A}{\sqrt{A^2+B^2}}x+\frac{-B}{\sqrt{A^2+B^2}}-\frac{C}{\sqrt{A^2+B^2}}=0
$$
and we can choose $\alpha$ so that
$$
\begin{cases}
\cos\alpha=-\dfrac{A}{\sqrt{A^2+B^2}}\\[6px]
\sin\alpha=-\dfrac{B}{\sqrt{A^2+B... | $$
{p\over C } = { \cos \alpha\over -A} = { \sin\alpha\over -B}
\\
\implies \frac{p^2}{C^2}=\frac{\cos^2(\alpha)}{A^2}=\frac{\sin^2(\alpha)}{B^2}
$$
If
$$
\frac{a}{b}=\frac{c}{d}=k
\\
\implies a=bk, c=dk
$$
So the value of :
$$
\frac{a+c}{b+d}=\frac{bk+dk}{b+d}=\frac{k(b+d)}{b+d}=k=\frac{a}{b}=\frac{c}{d}
$$
Simply ... | https://math.stackexchange.com |
541,282 | [
"https://physics.stackexchange.com/questions/541282",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/137908/"
] | consider a bipartite state on two Hilbert spaces <span class="math-container">$\rho_{AB}$</span>. Usually, I think of a channel <span class="math-container">$\mathcal E$</span> as acting only on <span class="math-container">$A$</span> if
<span class="math-container">$$\mathrm{Tr}_A(\mathcal E(\rho_{AB}))=\mathrm{Tr}_A... | The torsion is indeed defined from the connection, independently of the manifold and metric. By synedoche, people sometimes refer to the structure composed of the manifold, the differential structure, the metric and the connection, <span class="math-container">$(M, \mathfrak{A}, g, \nabla)$</span>, as "the manifol... | Formally what you do is the following. Spacetime is a set of data <span class="math-container">$(M,\mathcal{O},\mathscr{A},\nabla,g)$</span> where <span class="math-container">$(M,\mathcal{O},\mathscr{A},g)$</span> is a smooth Lorentzian manifold and <span class="math-container">$\nabla$</span> is a connection. Let <sp... | https://physics.stackexchange.com |
8,048 | [
"https://scicomp.stackexchange.com/questions/8048",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4833/"
] | Specifically, ode15i. I have ode15i solving a system of 5 first order implicit odes in 5 variables with an initial condition (made consistent by decic). It's great for what I need, except I need to add a final condition as well. Is this possible? I think (but am not sure) ode15s works too.
Edit: -
Edit 2: I think I f... | The MATLAB routines starting with 'ode', like ode15i, are for solving initial value problems. If you want to solve a boundary value problem, use bvp4c or bvp5c.
| I assume that you want to solve $$f(t,y',y)=0 \text{ on } (0,T)$$ with two-point boundary values $$y(0)=\alpha \text{ and } y(T)=\beta.$$
You cannot simply apply ODE solvers to this problen unless you take the heuristic approach of forward-backward iteration (see the list below).
There is no general approach to thes... | https://scicomp.stackexchange.com |
87,723 | [
"https://softwareengineering.stackexchange.com/questions/87723",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29299/"
] | I am in need of some help with philosophy and design of a continuous integration setup.
Our current CI setup uses buildbot. When I started out designing it, I inherited (well, not strictly, as I was involved in its design a year earlier) a bespoke CI builder that was tailored to run the entire build at once, overnigh... | Although I haven't faced a situation as bad as you describe, I have been maintaining a CI configuration with tens of components, between which there are some 'simple' dependencies. I hope that my approach may give you some hints with which to proceed. The problem is definitely not related only to the choice of CI ser... | What has worked in similar situations for me:
<ul>
<li>App-level abstraction by shunting some parts of the build into dedicated build apps (in our case these are PHP scripts called from the main build). This can reduce a few dozen lines of build steps into one build step.</li>
<li>Build-level abstraction by making sub... | https://softwareengineering.stackexchange.com |
220,282 | [
"https://electronics.stackexchange.com/questions/220282",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/86919/"
] | is there any way how theoretically determine the current consumption of ultrasound piezo transducer?
I only know impedance for res freq = 50 ohms and excitation voltage around -170 V.
Does the Ohms law work in this case?
Thank you.
| It depends on what kind of signal you are driving it with. Ultrasonic transducers are pulsed, how much you pulse it is up to the designer, which you are going to want to keep minimize, 1) Not to waste power and 2) Not to dissipate large amounts of power into the thing you are measuring. A piezoelectric transducer is ca... | If you're driving the transducer at resonance, the reactive terms will cancel and all you'll be left with is the resistance.
In this case, if the impedance looks like a pure resistance, then Ohm's law applies and the transducer will draw
$$ I = \frac {E}{Z} = \frac{170V}{50\Omega} = 3.4 \text { amperes}$$
and dissi... | https://electronics.stackexchange.com |
303,521 | [
"https://physics.stackexchange.com/questions/303521",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4075/"
] | Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$
and then set $\mu=\phi$
(for example), is it acceptable to then write $x^{\phi}$
or should I just write $\phi$? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$
as $$\frac{\partial g_{\phi\nu}}{\partial ... | I think that there is some problem with your notation.
Disclaimer: what follows are conventions, so they could be not universally respected, although I think this is what is mostly followed.
Reading
$$ \frac{\partial g_{\mu\nu}}{\partial x^\mu} = \partial_\mu g_{\mu \nu} $$
in its <em>literal</em> sense, it is not a... | Yes of course that is completely acceptable. You can say $x^\mu=x^\nu=(ct,r,\theta,\phi)$ The $\mu, \nu$ or whatever else are at your discretion as long as you are consistent. With respect to your derivative the first two make sense. The third derivative is a legitimate expression but it means that you are taking the d... | https://physics.stackexchange.com |
2,676,703 | [
"https://math.stackexchange.com/questions/2676703",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/499560/"
] | In information theory, the joint entropy $H(X,Y)$ of a pair of discrete random variables $(X,Y)$ is defined as:
$$
H(X,Y) = -\sum_{x\in \mathcal X}\sum_{y\in \mathcal Y}p(x,y)log_2p(x,y)\tag{1}\label{eq1}
$$
And the conditional entropy $H(Y \mid X)$ of the same $(X,Y)$ as:
$$
H(Y \mid X) = -\sum_{x\in \mathcal X}\su... | Without having looked at the details of your proof, I suggest the following alternative argument.
Instead of seeing $X$ and $Z$ as two distinct discrete random variables, we pair them up and interpret $A := (X,Z)$ as a single random variable. Clearly, all information that is contained in $X$ and $Z$ is also contained... | <span class="math-container">$H(X,Y) = -\sum\limits_{x\in \mathcal X}\sum\limits_{y\in \mathcal Y}p(x,y)\log_2p(x,y)$</span>
<span class="math-container">$H(X,Y∣Z)=−\sum\limits_{x\in \mathcal X} \sum\limits_{y\in \mathcal Y}\sum\limits_{y\in \mathcal Z}p(x,y,z)\log_2p(x,y∣z)$</span>
<span class="math-container">$H(X,... | https://math.stackexchange.com |
95,693 | [
"https://stats.stackexchange.com/questions/95693",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14163/"
] | Say I have data that I'd like to cluster that has different dimensions that are of different data types. For example:
<ol>
<li>ordinal: You mood today: Very happy, happy, neutral, sad, very sad</li>
<li>Ratio: Age: ...</li>
<li>Interval: Weight: 100-120, 121-180, 181-200, 201-600</li>
</ol>
Is there an accepted step ... | Handling mixed type of data is unfortunately not well supported in tools.
There are two common approaches:
A) encode the data numerically. E.g. red -> (1,0,0), blue -> (0,1,0), green -> (0,0,1)
B) use a method that can work with arbitrary distance functions (e.g. hierarchical clustering, DBSCAN, OPTICS), and use a d... | For most cluster algorithms you have to use a proper metric that cover your data. It does not matter the type of the data if you have an appropriate metric.
Something you can do is to represent each feature as a real number and then use the L2 metric, but you have to calibrate if you want a linear progression or not.
... | https://stats.stackexchange.com |
64,572 | [
"https://softwareengineering.stackexchange.com/questions/64572",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/10282/"
] | i was working on a website with FF4 and while resizing an element with Firebug, FF4 just crashed my nVidia Display Driver. Fortunately Windows 7 was able to help me by recovering from this serious error and i was able to completely recover my work again.
So my question is, should those browser developers get into low ... | First of all, when a driver crashes, that's a security risk, and so drivers should never, ever, crash. Others have pointed this out. It's an OS or driver bug you ran across, not a firefox one.
Now, to the other question: why does only firefox trigger this bug? There's a multipast answer to that:
<ul>
<li>Most apps us... | I think that more and more, browsers are becoming first-class citizens in today's systems. Chrome OS is the promise of a future where the browser will replace the OS as the user's primary interface. Among software standards, HTML seems to be the most widely implemented as well as one of the most flexible and powerful. ... | https://softwareengineering.stackexchange.com |
111,550 | [
"https://physics.stackexchange.com/questions/111550",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35952/"
] | I am pretty much confused with this notation I believe. The Heisenberg states are denoted by <span class="math-container">$\left|x,t\right>$</span> and the Schrodinger states are given by <span class="math-container">$\left|x(t)\right>$</span>. It seems like both of these are parameterised with time, but the Schr... | An electron is not a spinning ball of charge and the intrinsic spin of particles cannot be understood in such terms. Not only is it difficult to make sense of what it means for a pointlike particle to spin, but also when treating the electron as a spinning ball of charge one finds a value of the ratio between the magne... | Lets take the rotating "spherical ball" analogy seriously (actually a torus below).
The electron is modeled as a tiny stationnary torus rotating at an angular velocity <span class="math-container">$\omega$</span> around the symmetry axis passing through its center of mass. The material on the torus is moving... | https://physics.stackexchange.com |
122,725 | [
"https://physics.stackexchange.com/questions/122725",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10456/"
] | The standard lore in relativistic QFT is that poles appearing on the real-axis in momentum-space Green's functions correspond to particles, with the position of the pole yielding the invariant mass of that particle. <em>(Here, I disregard complications tied to gauge-fixing and unphysical ghosts)</em>
Schematically, I... | For simplicity, take <span class="math-container">$\hbar=1$</span> and consider a Hermitian scalar, renormalized field <span class="math-container">$\phi(x)$</span>; other fields are treated analogously. Then (for simplicity ignoring the necessary smearing since the field is a distribution only)
<span class="math-conta... | Particles are very rarely eigenstates of the Hamiltonian.
In particle physics, only (dressed) electrons (and protons?) might be eigenstates. All the other particles have a finite life-time, implying that they decay, which means that they are obviously not eigenstates.
What we want to call a particle is something whi... | https://physics.stackexchange.com |
59,639 | [
"https://electronics.stackexchange.com/questions/59639",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17602/"
] | If you had a variable resistor connected between a lamp and the wall, could it be dimmed with a variable resistor?
Would it be practical, i.e. would it waste much energy? And would it affect both current and voltage or only one?
| Yes; this was how it was done before triac dimmers became available. Usually known as a "rheostat".
The sum of energy dissipated in lamp + dissipated in resistor is then constant, so you need a 60W resistor.
Both voltage and current would be affected together; the lightbulb is an ohmic resistor.
| As pjc50 mentioned, in past resistive regulators were used to control dimming and speed regulation of fans.
Although a rheostat can be used to regulate a mains device but it was expensive and brought up the costs. To lower the cost, a multi tap resistor was used.
This resistive setup is not practical these days as tr... | https://electronics.stackexchange.com |
171,974 | [
"https://mathoverflow.net/questions/171974",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5152/"
] | In a finite distributive lattice $L$ one has $height(L) = |J(L)|$ i.e. the size of the largest chain equals the number of join-irreducible elements.
Briefly, this follows by arranging the subposet $J(L) = \{x_1,\dots,x_n\} \subset L$ so that $j > i \implies x_j \nleq x_i$, and then observing that $0 < x_1 < x... | Join semi-distributive lattices don't have this property because weak order on $S_n$ is join semi-distributive and doesn't have this property. (Eg, for $n=3$.)
Lattices satisfying the property you are interested in are called "join-extremal" by George Markowsky, in a paper Primes, irreducibles and extremal lattices. ... | I shall prove a result allows one to effortlessly construct precisely the finite lattices $L$ such that $height(L)=|J(L)|$.
A closure system is a pair $(X,C)$ such that $C\subseteq P(X)$ and $C$ is closed under arbitrary intersection ($X\in C$ by taking the empty intersection). If $(X,C)$ is a closure system, then $C$... | https://mathoverflow.net |
215,045 | [
"https://dba.stackexchange.com/questions/215045",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/158595/"
] | I am joining two tables <code>HR</code> and <code>UserDefined</code> based on the <code>Employee_ID</code>:
<strong>HR Table</strong>
<pre><code>First Name Last Name Employee_ID
---------- --------- -----------
Joe Smith 456654
</code></pre>
<strong>User Defined Table</strong>
<pre><code>Area ... | Join to <code>User Defined Table</code> twice, once with <code>Area = 1</code> and once with <code>Area = 2</code>.
<pre><code>from [HR Table] as HT
inner join [User Defined Table] as UT1
on HT.Employee_ID = UT1.Employee_ID and
UT1.Area = 1
inner join [User Defined Table] as UT2
on HT.Employee_ID = ... | Took the cte code from @Aduguid, another alternative is
<pre><code>;WITH
hr_table
AS
(
SELECT tbl.* FROM (VALUES
( 'Joe', 'Smith', 456654)
) tbl ([First Name], [Last Name], [Employee_ID])
)
,
user_defined_table
AS
(
SELECT tbl.* FROM (VALUES
( 1, 'ABCD1234', '31-Aug-2018', 456654)
, ( 2, ... | https://dba.stackexchange.com |
19,706 | [
"https://stats.stackexchange.com/questions/19706",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2817/"
] | Lets assume we only have 2 variables, <code>x</code> and <code>y</code>, and our model (in R code) is <code>lm(y~x)</code>. Given that any 2 points can be used to form a line, I know it doesn't make much sense to try to fit this model if I only have 2 observations.
What about the case where I have 3 observations? Wo... | I think the question is how usefull the model will be.
You probaly wont be able to describe the real world, makeing a model that will have a high chance to be at least poor to describe the world.
If you are useing R, you could play and figure what your model with 3 points will look like.
for example:
<pre><code>#lets... | If the data points are aggregates (for example state or country level averages) then it might not be a bad idea to fit a regression with just three points, since they'd represent many more underlying observations. Weighted least squares would probably be a better strategy than just OLS, but it would depend on the situ... | https://stats.stackexchange.com |
278,629 | [
"https://mathoverflow.net/questions/278629",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10333/"
] | I hope this is a suitable MO question. In a research project, my collaborator and I came across some combinatorial expressions. I used my computer to test a few numbers and the pattern was suggesting the following equation for fixed integers $K\geq n>0$.
$$\dfrac{K!}{n!K^{K-n}}\sum\limits_{ \begin{subarray}{c} k_1... | This is the answer to the first question, I wrote a long answer to Question 2 as a separate answer.
Note that $A:=\sum_{k_i>0,k_1+\dots+k_n=K}\frac{K!}{n!k_1!\dots k_n!} \prod k_i^{k_i-1}$ is a number of forests on the ground set $\{1,2,\dots,K\}$ having exactly $n$ connected components and with a marked vertex in ... | Here's another proof. We first rewrite the identity (by setting $k_i=j_i+1$) as
$$
\sum_{j_1+\cdots +j_n=K-n}\prod_{i=1}^n \frac{(j_i+1)^{j_i-1}}{j_i!}
= n\frac{K^{K-n-1}}{(K-n)!}. \tag{1}
$$
Let $F(x)$ be the formal power series satisfying $F(x)= e^{xF(x)}$. It is well known (and easily proved, e.g., by Lagrange i... | https://mathoverflow.net |
516,371 | [
"https://physics.stackexchange.com/questions/516371",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/144045/"
] | <span class="math-container">$$\vec{B}\cdot\frac{\partial \vec{B}}{\partial t}=\frac{1}{2}\frac{\partial}{\partial t} (B^2)$$</span>
Griffiths states this result in his derivation of the Pontying vector, but I have absolutely no idea where it came from or how to go about deriving it myself. Any help is appreciated.
| It's just an application of the product rule.
<span class="math-container">\begin{align}
\frac{1}{2}\frac{\partial}{\partial t}(B^2)&=\frac{1}{2}\frac{\partial}{\partial t}(\vec{B}\cdot\vec{B})\\
&=\frac{1}{2}\left(\frac{\partial\vec{B}}{\partial t}\cdot\vec{B}+\vec{B}\cdot\frac{\partial\vec{B}}{\partial t} \r... | It is a result of the chain rule:
<span class="math-container">$$\frac{1}{2} \frac{\partial({f}^2)}{\partial t} = \frac{1}{2} \underbrace{\frac{\partial f}{\partial t}}_\text{inner derivative} \ \ \ \ \underbrace{ \frac{\partial (f^2)}{\partial f}}_\text{outer derivative} = f \frac{\partial f}{\partial t}.$$</span>
... | https://physics.stackexchange.com |
85,540 | [
"https://mathoverflow.net/questions/85540",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5710/"
] | What are the groups $X$ for which there exists a group $G$ such that $G' \cong X$?
My considerations:
<hr>
$\bullet$ If $X$ is perfect we are happy with $G=X$.
$\bullet$ If $X$ is abelian then $G := X \wr C_2$ verifies $G'=\{(x,x^{-1}): x \in X\} \cong X$.
$\bullet$ If $X$ satisfies the following properties:
(1) ... | A complete answer seems not to be known. Let me give you the following two nearly-contemporaneous references from the mid-70s:
Robert Guralnick, <em>On groups with decomposable commutator subgroups</em>
Michael Miller, <em>Existence of Finite Groups with Classical Commutator Subgroup</em>
Both Guralnick and Miller ... | Let me quote some well-known results and perhaps related problems which may be illuminating!
Let $G$ be a non-abelian finite $p$-group having cyclic center. Then, there is no finite $p$-group $H$ such that $G$ is isomorphic to a normal subgroup of the derived subgroup $[H,H]$ of $H$. In particular, $G$ cannot be isomo... | https://mathoverflow.net |
218,301 | [
"https://dba.stackexchange.com/questions/218301",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/127579/"
] | I tried to check what is consumming my Disk Space on Centos 7, I found these 2 database file:
<blockquote>
/var/lib/mysql/pub/vues.ibd: 8.1G
/var/lib/mysql/pub/log.ibd: 8.6G
</blockquote>
I would like to delete them. pub is the name of my database.
And log and vues are tables.
| That would be most unwise. Never fiddle with MySQL files directly.
If you want to delete those tables use SQL:
<pre><code>DROP TABLE pub.vues, pub.log
</code></pre>
| As @danblack pointed out it's not the best idea. However to formally answer your question - if you delete the <code>vues.ibd</code> and <code>log.ibd</code> files the InnoDB dictionary will still keep entries about them. If you ever decide to create tables with same name the <code>CREATE TABLE</code> statement will fai... | https://dba.stackexchange.com |
4,629,045 | [
"https://math.stackexchange.com/questions/4629045",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1144868/"
] | How would you compare <span class="math-container">$O((\log n)^k)$</span> in relation to <span class="math-container">$O(n^c)$</span>, <span class="math-container">$n,c \in \mathbb{N}*$</span> ? I'm very stuck on how to go about this.
I specifically need to see how <span class="math-container">$O((\log n)^{2021})$</spa... | Your approach directly yields the GF <span class="math-container">$$(z^2 + z^4 + \ldots)( z+z^2 +\ldots)(z+z^2 + \ldots)(z+z^2 + \ldots) = \frac{ z^5}{(1-z^2)(1-z)^3}.$$</span>
Do you see why?
We have <span class="math-container">$ 2x_ 1 + (x_2 - x_1) + x_3 + x_4 = n$</span>, with no restriction other than each term be... | The number of solutions with <span class="math-container">$x_1<x_2$</span> is the same as the number of solutions with <span class="math-container">$x_1>x_2$</span>. So take the generating function without restrictions, <span class="math-container">$(z+z^2+\cdots)^4$</span>, subtract the generating function for ... | https://math.stackexchange.com |
76,607 | [
"https://dba.stackexchange.com/questions/76607",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/47449/"
] | I have a somewhat complicated query consisting of many joins on an issue tracker/project management database in MySQL. <br>
My issue is that my query was doing OK while I was in the process of building it up, but after the addition of one final join, the query performance (duration) is no longer tolerable.
The query b... | Looking at the EXPLAIN and examining the indices did not help me (maybe I did not try hard (or correctly) enough).
My final solution was to not JOIN together so many instances of large tables (in this case, the "issues" tables). In effect, I split up the query into two queries and now my querying performance is much l... | You have forgotten the join criteria <code>and ist.id = i_team_2.status_id</code>.
If you had used the modern JOIN syntax this would have stood out like a sore thumb.
| https://dba.stackexchange.com |
9,213 | [
"https://quant.stackexchange.com/questions/9213",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/2114/"
] | I am working on an improvement of my company's order allocation system. We run a central Order Management System (OMS) but currently performance attribution from filled orders leaves room for improvement.
I look to understand how other systems handle order and trade allocation.
Example: Asset 'A'
<pre><code>Fill1; ... | Approaches like FIFO and LIFO are most useful for tax accounting. If you don't have a tax accounting reason to do them, I'd recommend avoiding them, as they don't reflect actual realized gains (it's very rare for a position accounting system to move cash in and out of your account based on FIFO or LIFO).
I'm going to... | I'll add my own experience here based on what we do at our firm, simply to provide more support for what Brian said in his answer.
Fills that move a position further away from 0 contribute to the average price of the position.
Fills that move a position closer to 0 "book profits" against the average price of the posi... | https://quant.stackexchange.com |
358 | [
"https://quant.stackexchange.com/questions/358",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/106/"
] | I am starting to work with options data from optionmetrics. I use data frames, but it seems like xts or zoo objects are the way to go for features and speed. I can't figure out the best work-around to get 1 row per date. Should I be doing a list of xts objects with one object per optionid?
Here's my current approach: ... | I haven't seen a framework for options specifically, however...
The way I have done this in the past is to essentially setup a timeseries(xts or zoo) for each option(underlying,type,strike,expiry). Obviously doing this via code is important because it is intensely error prone.
We use a build function to put those int... | FWIW, here's the approach I used. I keep the dates as an integer in YYYYMMDD form and merge the calls and puts in to a data frame <code>both</code>. Then I use <code>ddply</code> to operate on each matched call and put to find the future SPX close and call/put bid-offer average <code>boa</code>.
<pre><code>library(ply... | https://quant.stackexchange.com |
245,921 | [
"https://softwareengineering.stackexchange.com/questions/245921",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/113977/"
] | Everything I've read says to pass parameters to a REST service in the URI, whether by template, or query string:
<pre><code>https://www.myapp/my/login/api/authenticate/ganders/mypassword
</code></pre>
or
<pre><code>https://www.myapp/my/login/api/authenticate?user=ganders&password=mypassword
</code></pre>
But ob... | I'd structure it by moving it inside the json fields if HTTP basic auth isn't an option.
For example:
<pre><code>POST https://my.server/login
{ "username": "user",
"secret": "someSecureHashAndNotThePlaintextPasswordSeriouslyDontDoThat" }
</code></pre>
| <blockquote>
Everything I've read says to pass parameters to a REST service
in the URI, whether by template, or query string:
</blockquote>
Nobody that understands REST would recommend that.
URL (uniform resource locator) is a subtype of URI (uniform resource identifier). A URL is meant to be a string representi... | https://softwareengineering.stackexchange.com |
37,705 | [
"https://cs.stackexchange.com/questions/37705",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/27131/"
] | Let:
<ul>
<li>$2EQ$ - The language of all binary ($\mathbb{Z}_2$) equation sets that have a solution in $\mathbb{Z}_2$, where each multiplication is of at most two $x_i,\, x_j$. Meaning a set of equations of the form: $\Sigma a_i \cdot x_i + \Sigma \, \Sigma \, a_{i,j} \cdot x_i \cdot x_j = b $.</li>
<li>$3EQ$ - Same ... | Hint: You can add a variable $x_{ij}$ whose value is always $x_ix_j$ by adding the equation $x_{ij}-x_ix_j=0$. This allows you to reduce cubic equations to quadratic ones.
| They're both NP-hard, and both in NP, so they are both NP-complete. Therefore, there is a reduction between them.
Hint: Try proving that Independent SET $\le_P$ 2EQ. Once you prove that, you should be able to take it from there, as the desired result follows immediately.
| https://cs.stackexchange.com |
560,840 | [
"https://electronics.stackexchange.com/questions/560840",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/283282/"
] | I need to power an SG90 servo but am having trouble with erratic behavior when using a phone USB charger of 5V 1A or when trying to use the MB102. The MB102 voltage regulator also overheats within a few seconds.
Is there an explanation for this and a solution? Do I need a voltage regulator?
| <ol>
<li>The MB102 <strong>has</strong> a voltage regulator.</li>
<li>The 5V USB "charger" <strong>has</strong> a voltage regulator.</li>
</ol>
No, you don't need to add a regulator to either of those two.
Since you mention the MB102, it seems you have everything wired to a breadboard.
That's generally <stron... | Link specs to all parts and don’t use 12V on LDO.
Only 6.5 if driving 2 servos, if only 1 servo, they have a 350 mA stall current.
I suspect if you use a low ESR cap 100uF near Servo, It should perform better with a 1A supply. But the MB102 is rated for 700mA and heat rise depends on voltage drop with 6.5V min input fo... | https://electronics.stackexchange.com |
44,206 | [
"https://datascience.stackexchange.com/questions/44206",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/59446/"
] | I am building a binary classifier, which classifies numerical data, using Keras.
I have 6992 datapoints in my dataset. Test set is 30% of the data. And validation set is 30% of the training set.
When evaluating the model, I get these values:
<pre><code>recall: 0.8914240755310779
precision: 0.7006802721088435
f1_... | You have imbalanced classes. Notice that your accuracy is very close to your precision, and quite dissimilar to your recall. This means that your precision (accuracy of positive predictions) is dominating the overall accuracy measure - nearly all of the cases in your data are classified as positive, so the accuracy amo... | F1-score is equal to:
2*((recall*precision)/(recall+precision))
If your model was catching more true negatives (TN) it would lower the F1-score. While your model is probably good at predicting true positives, it is likely predicting true negative at a lower rate.
| https://datascience.stackexchange.com |
248,845 | [
"https://mathoverflow.net/questions/248845",
"https://mathoverflow.net",
"https://mathoverflow.net/users/54552/"
] | Given <span class="math-container">$g\in L^2(\mathbb{R}^3)$</span>, consider the following function ( defined for <span class="math-container">$r>0$</span> ):
<span class="math-container">$$c(r):=\int_{\mathbb{R}^3}\frac{g(x)}{|x|^2+r}dx$$</span>
I'm interested in the behavior of <span class="math-container">$c(r)$<... | Once you asked, here goes. Let $h(r)=c(r^2)$. Then you need to look at the operator
$$
\Psi: f\mapsto \int_0^\infty f(\rho)\frac{\rho}{\rho^2+r^2}\,d\rho.
$$
Note two things:
1) The kernel is positive and dominated by $1/(r+\rho)$ (just consider the cases $\rho\le r$ and $\rho\ge r$ separately. Hence, it is not worse... | Let $h(s)$ be the average of $g(x)$ over the sphere $|x|=s$. Thus
$$c(r) = \int_0^\infty \dfrac{4 \pi s^2 h(s) \; ds}{s^2 + r}$$
where $$ \int_0^\infty 4 \pi s^2 h(s)^2 \; ds \le \|g\|_2^2 < \infty$$
So Cauchy-Schwarz says
$$ c(r) \le 4 \pi \|s/(s^2+r)\|_2 \|s h(s)\|_2 \le \dfrac{\pi}{r^{1/4}} \|g\|_2 $$
with eq... | https://mathoverflow.net |
601,127 | [
"https://physics.stackexchange.com/questions/601127",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/195949/"
] | Normally I don't care about units in the derivations on relativity or QM. Just set <span class="math-container">$\hbar = c = 1$</span>.
But learning about the energy momentum tensor for the Klein Gordon equation, I couldn't make <span class="math-container">$T^{00}$</span> for example have units of energy density, tha... | Assuming that spacetime is four-dimensional, your result is correct. When <span class="math-container">$\hbar=c=1$</span>, it reduces to the statement that <span class="math-container">$\phi$</span> has mass dimension <span class="math-container">$1$</span>, which is often stated in the literature about relativistic qu... | As mentioned in the comments, with <span class="math-container">$c$</span> and <span class="math-container">$\hbar$</span> set to 1. Energy has the unit of <span class="math-container">$L^{-1}$</span> and the 4D integral of the Lagrangian density is dimensionless as <span class="math-container">$\hbar$</span>. It means... | https://physics.stackexchange.com |
2,006 | [
"https://engineering.stackexchange.com/questions/2006",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/844/"
] | I have got a spinning top from a Canadian manufacturer, and I am deeply amazed by how neatly it spins.
My interest in physics has led me to try to find out at what top speed I can spin the top and how that compares to other tops made from other materials and other shapes.
I have glued a little sticker to it and recor... | There are several ways.
The most direct is to paint half of the top white and the other black, then point something with a light sensor at it. AC amplify the output a little, then determine the frequency. This could be with a deliberate frequency counter, a scope that displays frequency directly, or a microcontrolle... | Probably the easiest practical method to measure the frequency of a spinning top with everyday equipment is to analyze the sound created by the motion and look for the characteristic frequency. This can be done with a spectrum analyzer app that should be available for free for most smartphones.
Place the spinning top ... | https://engineering.stackexchange.com |
12,884 | [
"https://mechanics.stackexchange.com/questions/12884",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/7332/"
] | I have a 2009 Chevrolet Aveo that I bought new from the dealer.
Today I was running errands around town and just as I was about the get on the highway to head home, the battery light and emergency brake light turned on. As I was driving home, the electrical components in the car started going out one-by-one. First the... | <strong>This sounds like an alternator problem to me</strong>. If you have the means, pull the alternator and take to an AutoZone, Pep Boys, or the like. They will test it for free for you. The reason I suggest an alternator, is this is typical behavior when the alternator is dieing, where your electrical components st... | When testing your battery, you must check the voltage across the actual battery posts. The posts are the lead posts coming out of the casing of the battery. Do not measure using the leads coming off of the battery. If, using the posts, your voltage is below 12.+ volts, and you have a known good voltmeter then you have ... | https://mechanics.stackexchange.com |
99,095 | [
"https://electronics.stackexchange.com/questions/99095",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20216/"
] | Apart from the register structure what is the difference between GPIOx_ODR and GPIOx_BSRR?<br>
Is GPIOx_BSRR an abstraction layer for GPIOx_ODR? I know that a change in GPIOx_BSRR "will" change the GPIOx_ODR but how and what are the diferences?
More info:
<ul>
<li>registers description page-162 of STM32F0advanced ARM... | The BSRR has bitfields that allow you to set and clear bits in a port atomically--without a read-modify-write operation. Instead of reading the ODR value, ORing it with the bits to set, and writing it back, you simply perform a single 32-bit write to the BSRR to set or only the relevant bits.
This often means you don... | ODR gives you complete control of the output state of the entire port. If you know what all the port's pin's values should be at in any given moment, you can write directly to ODR. This will overwrite the values of each pin, where 1 sets and 0 resets. This may be more desirable than BSRR if you know what the output pin... | https://electronics.stackexchange.com |
254,865 | [
"https://electronics.stackexchange.com/questions/254865",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41037/"
] | We all know energy cannot be formed from nothing.
So how does a bipolar junction transistor (BJT) — for example — amplify the base current by beta and outputs it to collector current?
Where is the “catch?” Is there somewhere else where were losing energy?
| The base current in a transistor <em>controls</em> the collector current. The energy comes from the power supply. It is not generated within the transistor.
| The 'catch' is that a transistor only controls the flow of current; it does not itself generate power. The power would come from some other part of the circuit, perhaps from the electric company via a power supply or from a battery.
Now, one possible point of confusion is that transistors can be represented as equi... | https://electronics.stackexchange.com |
54,668 | [
"https://stats.stackexchange.com/questions/54668",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/23683/"
] | I want to know if it is possible for a library in R to evaluate the association of independent variables and create a formula? I am trying to come up with a model to predict power consumption of a machine, using some hardware counters and performance attributes. When I use linear regression, I have no problem since I c... | Look at using linear regression but with a polynomial (poly) function or spline function on the predictors that you think may have a non-linear relationship. Then plotting and further examination of those results may suggest the form of a non-linear function (or the linear model may be sufficient for your purposes).
... | A nonlinear regression function is never going to decide the functional form for you.
You might want to stick with a linear model and use a transformation of the variable with the nonlinear relationship. For example, check the correlation between power $a4^2$, $ln(a4)$, or some other transformation and use which ever ... | https://stats.stackexchange.com |
313,254 | [
"https://softwareengineering.stackexchange.com/questions/313254",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/217255/"
] | I have some problems understanding the concept of a <code>runtime library</code>, especially the Python one.
So I have written some a hello world python program and intend to execute it, so I write <code>python ./hello_world.py</code>.
What steps happens between me hitting the Enter button and the machine code generat... | For as diverse as they are, there are a handful of common concepts that all serious, modern programming languages share. Two of them are the core of the answer for your questions above.
<blockquote>
What steps happens between me hitting the Enter button and the machine code generated from my python code being execu... | The standard Python implementation is a byte code virtual machine. This means that the <em>machine code</em> (opcodes from your processor's opcode set) is <strong>not</strong> generated from your program. The opcodes are only <em>selected</em> from the opcodes that are already compiled into the virtual machine while th... | https://softwareengineering.stackexchange.com |
2,319,025 | [
"https://math.stackexchange.com/questions/2319025",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/355736/"
] | A fair coin is flipped successively at random until the first head is observed. Let the random variable X denote the number of flips of the coin that are required. Then the space of x is S={x: x=1,2,3,4, ....}. Later we learn that, under certain conditions, we can assign probabilities to these outcomes in S with the f... | We need the following:
$$
\require{AMScd}
\begin{CD}
A @>>> B \\
@VVV @VVV \\
C @>>> D
\end{CD}
$$
This is pullback iff $0\rightarrow A \rightarrow B\oplus C \rightarrow D$ is exact.
| Let $0\to A_1\to A_1\oplus A_2\to A_2\to 0$ be exact and $T:Ab\to Ab$ be left exact.
$0\to TA_1\to T(A_1\oplus A_2)\to TA_2$. The point is to show at $T(A_1\oplus A_2)\to TA_2$ is surjective. Since $A_2$ is a direct summand of $A_1\oplus A_2$, I got a retraction $\pi_2:A_1\oplus A_2\to A_2,i_2:A_2\to A_1\oplus A_2$ wh... | https://math.stackexchange.com |
117,758 | [
"https://softwareengineering.stackexchange.com/questions/117758",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3692/"
] | I've agreed to build an iPhone app for a client that was referred to me. I'm a full-time software engineer by day, but this is only my 2nd iPhone app and I agreed to do it without upfront funding as it would give me a project to further learn the API as well as increase my portfolio of iPhone apps.
The client suggeste... | I had exactly the same situation.
<ol>
<li>You are the developer and more important - a 50% partner. there is no reason in the world to register the app on their name. </li>
<li>You can open a new user in iTunes connect with permissions to view financial reports on the app and a different bank account.</li>
<li>reque... | If you think there might be a decent possibility of significant revenue, do a contract, incorporate with both of you as shareholders, and put the app under a company account.
If not, does it really matter whose account? (consider admin work, bank fees, tax reporting, branding, who will do the marketing, the extra $99... | https://softwareengineering.stackexchange.com |
500,871 | [
"https://physics.stackexchange.com/questions/500871",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/38312/"
] | In Arnold's Classical Mechanics of Classical Mechanics, he refers to Lyapunov stability in many of the problems in the second chapter.
E.g. on page 20: "Problem: Consider a periodic motion along the closed phase curve corresponding to the energy level <span class="math-container">$E$</span>. Is it stable in the sense... | let say you have this vector differential equations:
<span class="math-container">$$\vec{\ddot{x}}=-\vec{f}(\vec{x},\vec{\dot{x})}\tag 1$$</span>
and you want to check the stability at a stable point <span class="math-container">$\vec{x}_0$</span>
according to Lyapunov theory, you have to linearized equation (1) an... | Partial answer
I know Lyapunov stability better from chaotic systems in one dimension like the logistic map and I can confirm that one can calculate the Lyapunov constant for non-stable points.
The key thing we test with Lyapunov is whether two points close together move together or apart in a dynamical system. If t... | https://physics.stackexchange.com |
16,358 | [
"https://mechanics.stackexchange.com/questions/16358",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1602/"
] | On my car (2005 Dodge Grand Caravan) when I fill up my gas tank, almost immediately afterwards pulling out of the gas station my van sputters, misses, hesitates, call it what you will. The past couple of times the engine has actually stalled as well.
This is very short term. After this quick event it is then fine for ... | This sound similar to what I have experienced when there is rust or other "crud" in the bottom of the gas tank. Letting it get VERY low then filling it will stir up the "crud" and allow it to temporarily clog things up until it settles back down.
To confirm if this is whats happening, try filling up before the fuel le... | When the tank is going to be completely filled the proper procedure is to allow the pump to shut off automatically. Add no more fuel after this initial shut off. Over filling the tank by filling to "the brim" can cause the evaporative emissions system to be damaged or rendered inoperative. The system is designed to con... | https://mechanics.stackexchange.com |
3,804 | [
"https://stats.stackexchange.com/questions/3804",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6/"
] | Suppose I'm modeling a set of processes using a beta-binomial prior. I can build parameterized beta-binomial models that average over large groups of the processes to give reasonable, although coarse, priors.
$p_i \sim \beta B(n, \alpha_i, \beta_i)$ (roughly)
I know how to update those priors using observed partial ... | Lets see if I understand Harlan's (and Srikant's) formulation correctly.
$$\pi_1 \sim beta(\alpha_1,\beta_1)$$
$$\pi_2 \sim beta(\alpha_2,\beta_2)$$
Say, $\pi_1$ corresponds to the set of data for which you have less information <em>apriori</em> and $\pi_2$ is for the more precise data set.
Using Srikant's formulati... | Assume that prior2 is a beta random variable and set $\alpha$ and $\beta$ as needed subject to the constraint that $\frac{\alpha-1}{\alpha + \beta -2} = 6$.
In response to your comment:
<ol>
<li>Getting to prior2:
<ul>
<li>Fix either $\alpha$ or $\beta$ at the same value as prior1 and tweak the other to match the d... | https://stats.stackexchange.com |
149,851 | [
"https://cs.stackexchange.com/questions/149851",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/58827/"
] | I am trying to analyze a series that I found, in the analysis of an algorithm. And I was wondering if the following was true:
<span class="math-container">$$\log_{2}{\left(\frac{1}{2}n\right)} + \log_{2}{\left(\frac{1}{4}n\right)} + \log_{2}{\left(\frac{1}{8}n\right)} + \cdots + \log_{2}{\left(\frac{1}{2^{log_{2}(n)}}n... | Using <span class="math-container">$\log a + \log b = \log (ab)$</span>, we get:
<span class="math-container">$$\sum\limits_{k=1}^{\log_2 n}\log_2\left(\frac1{2^k}n\right) = \log_2\left(\prod\limits_{k=1}^{\log_2 n}\frac{n}{2^k} \right) = \log_2\left(\frac{n^{\log_2 n}}{2^{\sum\limits_{k=1}^{\log_2 n}k}}\right) = \log_... | Let <span class="math-container">$k:=\log_2 n$</span> then
<span class="math-container">$\sum\limits_{j=1}^{\log_2 n}\log_2(\frac{1}{2^j} \cdot n) = \sum\limits_{j=1}^{k}(\log_2(\frac{2^k}{2^j})) =
\sum\limits_{j=1}^{k}\log_2(2^j)
= \sum\limits_{j=1}^{k} j = \frac 1 2 k(k+1)$</span>
so
<span class="math-container">$\s... | https://cs.stackexchange.com |
23,615 | [
"https://cs.stackexchange.com/questions/23615",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16607/"
] | I don't know the proper mathematical expression for for-loops, especially those that carry two distinctly behaving variables with each iteration.
For example, assuming <code>n</code> is previously defined and holds some positive integer, how I would I represent the set printed by this for-loop in mathematical notation... | You attempt is basically correct, assuming that the <code>for</code>-loop is short for nested loops. You'd usually write it like
$\qquad\displaystyle\{ (n-j)(n-k) \mid j \in \{n, \dots, 2n\}, k \in \{n, \dots, 0\}\}$.
Now we note that we can write
<ul>
<li>$k$ instead of $n-k$ (in the code, reverse the direction of... | If you go and execute the program you wrote you will get the sequence $0, -1, -4, -9, -16, \dots$. The program prints the first $n+1$ squares negated. In set theory, one would write $$\{-x^2:0\le x \le n\}$$.
| https://cs.stackexchange.com |
43,864 | [
"https://mathoverflow.net/questions/43864",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4745/"
] | <strong>Could one describe the subsets of the integers closed under the binary operation Ax+By
where A and B are arbitrary fixed integers ?</strong> That is, describe the subsets S
of the integers such that if $x,y\in S$ then $Ax+By\in S$. Or just the minimal such subsets
containing 1.
Do I guess correctly that th... | I think the problem is pretty much solved in a series of papers by Klarner et al;
David A Klarner and Karel Post, Some fascinating integer sequences.
A collection of contributions in honour of Jack van Lint.
Discrete Math. 106/107 (1992), 303–309, MR 93i:11031
D G Hoffman and D A Klarner, Sets of integers closed u... | Some trivial observations.
If $A=1, B=-1$ we get subgroups of $\mathbb{Z}$.
If $A=1, B=1$ we get positive cones (sets closed under positive linear combinations).
If $A=k, B=0$ we get sets closed under multiplication by $k$.
If $A=2, B=-1$ and $1, 2 \in S$, then $S=\mathbb{Z}$. To see this, let $n \in \mathbb{N... | https://mathoverflow.net |
212,415 | [
"https://dba.stackexchange.com/questions/212415",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4628/"
] | I had a master-slave set up working fine until a power outage on the slave. Now I get
<blockquote>
error connecting to master 'repl@10.0.0.1:50000' - retry-time: 60<br />
maximum-retries: 86400<br />
message: Access denied for user 'repl'@'localhost' (using password: YES)
</blockquote>
The password has not changed and ... | Odd.
The fix seemed to be to change the password.
<ol>
<li>stop slave</li>
<li>change password for <code>repl</code> user at master.</li>
<li>on slave: <code>change master to master_password = 'new pass'</code></li>
<li>start slave</li>
</ol>
| Mariadb 10.5 seems to store passwords in another table mysql.global_priv as well as in mysql.user. I didn't have my users in global_priv which was causing the login issues. Setting the password again fixed the issue.
It seems that global_priv is not being replicated, from master and it contains old values before the da... | https://dba.stackexchange.com |
57,645 | [
"https://cs.stackexchange.com/questions/57645",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/51436/"
] | Can a problem (described by a set of inputs and accepted answers) be designed such that for all programs which produce an answer in finite time for a (countably) infinite number of inputs, at least one of those outputs is incorrect.
That is, the program need not terminate for all outputs, but the outputs it does gene... | A simplified example can be the following:
$$T( n ) = \begin{cases}
\max \{ M(n) \mid |M| \leq n \} + 1 & \text{if such max exists}\\
0 &\text{otherwise.}
\end{cases}$$
In other words the "unprogrammable" (uncomputable) task $T$ (or better <em>uncomputable function</em> $T$) simply picks all program... | The halting problem can be solution to your question.
You are saying that the algorithm for halting problem never terminates (or it terminates for a finite number of inputs) when the input is a "non-terminating" program. But this is not quite right. Because, you can actually devise an algorithm for halting problem th... | https://cs.stackexchange.com |
287,950 | [
"https://physics.stackexchange.com/questions/287950",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/133801/"
] | By definition, the wave function can be obtained by acting the position eigenstate to a state of the system, e.g., $\langle x\vert \psi \rangle$. For the wave function of an electron travelling in one-dimensional space, we can calculate the wave function of an electron by the way mentioned above, $\psi(x)=\langle x \ve... | Not a true answer, but too long for a comment. A 1-particle probability theory runs into certain difficulties when we add relativity into quantum mechanics, but we can't help but do that for a speed-$c$, zero-rest-mass particle such as a photon.
A non-relativistic quantum model of one particle has a probability densit... | The Quantum Mechanics people use to deal with electrons is a non-relativistic theory. It is, in great part, based on the quantization of the Hamiltonian (there's also the spin part which is added by hand in that setting),
$$H = \dfrac{P^2}{2m}+V$$
And the resulting theory has proved to be not Lorentz invariant, so, i... | https://physics.stackexchange.com |
1,903,585 | [
"https://math.stackexchange.com/questions/1903585",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/363822/"
] | <blockquote>
Write down a system of three equations in three unknowns with exactly three solutions.
</blockquote>
I have absolutely no idea how to go about answering this question. Can someone please explain it to me?
| Consider the following system (assuming not every equation needs to have all of the three variables in it):
$$
(x-1)(x-2)(x-3)=0 \\
y=0 \\
z=0
$$
This system has exactly three solutions: $(1,0,0),(2,0,0),(3,0,0)$.
| The first thing you should realize is that it cannot be a linear system of equations, because a linear system has either one unique solution, no solution, or infinitely many solutions.
| https://math.stackexchange.com |
9,652 | [
"https://electronics.stackexchange.com/questions/9652",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I'm considering using a chip which outputs 8-bit data on a 27 MHz clock. The data will go from the chip to a FPGA, a distance of a few cm max. Do I need to be concerned about timing differences between traces on a PCB, and if so, how can I mitigate these? I've often seen motherboards with traces in small coil shapes, p... | Leon is right, it probably doesn't matter for 27MHz signals on traces that are only a few cm long.
However, you can mitigate skew by making the trace lengths equal. If you've got the time to ask a question about it, and you have the board space, why wouldn't you want to do this? There's very little reason to build ... | At 27 MHz any differences in track length over a few cm will have a negligible effect. Try doing some calculations involving the speed of light, allowing for the velocity factor.
| https://electronics.stackexchange.com |
70,946 | [
"https://mathoverflow.net/questions/70946",
"https://mathoverflow.net",
"https://mathoverflow.net/users/112114/"
] | I'm an REU student who has just recently been thrown into a dynamical system problem without basically any background in the subject. My project advisor has told me that I should represent regions of my dynamical system by letters and look at the sequence of letters formed by the trajectory of a point under the iterati... | Intuitively this should happen for a large class of dynamical systems, but I don't know the right necessary and sufficient conditions.
A class of examples satisfying this is given by polyhedral billiards, where you assign a symbol to each face and correspond orbits to sequences in the obvious manner. It is a result o... | I think symbolic dynamics is the study of what you get <em>after</em> you've introduced your partition and coded points by their itinerary. Your question is essentially "when is the symbolic dynamics a faithful representation of the original dynamical system?".
As Vaughn says, the thing you're looking for is expansive... | https://mathoverflow.net |
146,697 | [
"https://physics.stackexchange.com/questions/146697",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59679/"
] | I have the following question regarding an ideal rigid body.
Firstly, is it always true without any exceptions that the angular velocity of any point about any other point on a rigid body is always the same?
If so, what happens in case of precession, in which two different angular velocities are predefined?
| Think of rotation as a manifestation of a change in coordinate direction. Affix a coordinate system at <em>any</em> point on a rigid body and it is going to change direction <em>at the same rate</em> regardless of the point location (even at the rotation axis). This is why angular velocity is shared among the entire ri... | I think when a rigid body rotating about any point , the point of rotation remains fixed and all other points of the rigid body always rotate about that fixed point with same angular velocity. <img src="https://i.stack.imgur.com/jZCzP.png" alt="enter image description here">
Let us suppose a disk rotating about its ce... | https://physics.stackexchange.com |
317,642 | [
"https://physics.stackexchange.com/questions/317642",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/148058/"
] | From what I have read, a quantum state of a quantum object contains all the properties of the quantum object. But I have read that the Pauli Exclusion principle states that two identical particle in a system cannot have the same quantum state simultaneously.
But since the quantum state is the combination of <em>all</e... | A quantum state is an element of a projectivized complex Hilbert space. A quantum object has (at any given moment) one state, and that state is a complete description of the object.
In practice, we often simplify matters by choosing to ignore certain observables in order to be able to work with a more manageable Hilb... | I think that your problem is semantics, as the phrase
<blockquote>
But since the quantum state is the combination of all the properties of the quantum object and that due to a quantum object's wave nature its position can be infinitely different,why does the PEP work?
</blockquote>
suggests.
First, it is not true... | https://physics.stackexchange.com |
139,873 | [
"https://electronics.stackexchange.com/questions/139873",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52754/"
] | I have built the circuit below and have been using a 7 segment display which is meant to be designed to work with the circuit. However there is no clear diagrams showing which wire on the display connects to what pin on the chip. So I painstakingly worked out where each wire should go, but the display does not work. Wo... | I think there should not be problems with this circuit. Everything is written here For connection. In the LM8560 it's written something like in Pin7 a&f, a=>segment a, f=>segment f. MIN=>Minutes digits, HR=>Hour digits.
Choosing your Display, i think that you can you can look at any duplex display but it just use t... | You can certainly wire a display that is not internally multiplexed in any way you want, including duplexing, however I don't see why it would be any better than a display that is designed to work with that chip.
There are single, dual and quad digits (at least) that are so wired, but check before buying to make sure... | https://electronics.stackexchange.com |
58,644 | [
"https://stats.stackexchange.com/questions/58644",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/23681/"
] | I have used software before to do linear regression and factor in/out the confounding variables, but what I would like to do is generate a new data set which is adjusted for the confounding variables. How would I go about this?
Further explanation:
I have 1 dependant variable, multiple interesting independant variabl... | In the context of multiple linear regression, "adjusting" for a covariate simply means including it as an explanatory variable.
There is an equivalent way of understanding multiple linear regression that provides insight into this question. To regress, say, $Z$ on $X$ and $Y$, we may (arbitrarily) select one of the e... | This project will take an excellent understanding of statistics. This is not really a software question.
Briefly, it is not useful to think of adjusting variables to produce new variables. You need to adjust for variables in the context of a statistical model. Only in the very special case of ordinary regression wi... | https://stats.stackexchange.com |
744,980 | [
"https://physics.stackexchange.com/questions/744980",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228212/"
] | In linearized gravity, where we take a general background metric <span class="math-container">$g$</span> with perturbation <span class="math-container">$h$</span>, the linearized Einstein equations become
<span class="math-container">$$-\square h_{\alpha\beta}+\nabla^{\delta}\nabla_{\alpha}h_{\beta\delta}+\nabla^{\delt... | It's the second option, otherwise your equations of motion wouldn't be diffeomorphism-invariant. On the flat space-time background these options coincide.
| The second option is correct.
Notice that, in your first development of the D'Alembertian operator, you implicitly assume that <span class="math-container">$$\nabla_\mu h_{\alpha\beta} = \partial_\mu h_{\alpha\beta}. $$</span> You have rightly identified this only holds in a Minkowski background.
| https://physics.stackexchange.com |
23,580 | [
"https://security.stackexchange.com/questions/23580",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15672/"
] | I'm using nmap and I am having trouble finding which ports are dangerous and pose the greatest security risks.
Which ports are potential security risks for nmap?
I was thinking samba, telnet, vnc and ftp will pose security risks but I'm unsure.
| It doesn't really work like that.
Ports don't pose a security risk in themselves; it's the <em>application listening on a port</em> that has the risk attached.
And, how vulnerable any given application might be depends on many factors - is the application well patched? Is it well configured? So you can't just say "V... | <strong>All open ports providing services are a potential security risk.</strong> The nature of the security risk depends on nature of the service that a program provides. Services providing Samba, VNC, FTP, SSH, HTTP, ... protocols all pose a risk to your security, each in its own (but not unique) way.
| https://security.stackexchange.com |
55,931 | [
"https://mathoverflow.net/questions/55931",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12259/"
] | Let <span class="math-container">$\mbox{Rings}$</span> be the category of commutative rings with <span class="math-container">$1$</span>.
Is there an equivalence of categories <span class="math-container">$F: \mbox{Rings} \to \mbox{Rings}$</span> such that
<span class="math-container">$$F(\mathbb{Z}[x])\not\cong \ma... | The category <span class="math-container">$\mbox{CRing}$</span> of commutative rings is <em>rigid</em>, i.e. every equivalence <span class="math-container">$\mbox{CRing} \to \mbox{CRing}$</span> is isomorphic to the identity,
Proof: Let <span class="math-container">$F : \mbox{CRing} \to \mbox{CRing}$</span> be an equ... | Here is a new, short proof, that the category <span class="math-container">$\text{CRing}$</span> of commutative rings is rigid:
Lemma: Let <span class="math-container">$R,S$</span> be commutative rings, such that <span class="math-container">$\text{CAlg}(R), \text{CAlg}(S)$</span> are equivalent as categories. Then <... | https://mathoverflow.net |
570 | [
"https://mathoverflow.net/questions/570",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1/"
] | For an algebraic group G and a representation V, I think it's a standard result (but I don't have a reference) that
<ul>
<li>the obstruction to deforming V as a representation of G is an element of H<sup>2</sup>(G,V⊗V<sup>*</sup>)</li>
<li>if the obstruction is zero, isomorphism classes of deformations are para... | A representation of G on a vector space V is a descent datum for V, viewed as a vector bundle over a point, to BG. That is, linear representations of G are "the same" as vector bundles on BG. So the question is equivalent to the analogous question about deformations of vector bundles on BG. We could just as easily a... | The statements about the group and Lie algebra in the question are special cases of a more general fact.
Namely, if $A$ is an associative algebra and $V$ an $A$-module, then obstructions to deformations of $V$ lie in the Hochschild cohomology group $HH^2(A,{\rm End}(V))$,
freedom of deformation in $HH^1(A,{\rm End}(... | https://mathoverflow.net |
3,902,836 | [
"https://math.stackexchange.com/questions/3902836",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/677426/"
] | There're similar questions already, but I somewhat struggled to apply their reasoning to this particular statement.
I wanted to ask if my proof is correct (and clarify several things which I've seemingly figured out when writing it here). Here's the proof:
<span class="math-container">$$\mbox{(1) }\lim_{x \to 0^-} f\le... | WA Don nailed it, but I feel compelled to add an answer.
I'm going through Spivak myself and when first encountering problems like this, I tried approaches very similar to super.t's.
It took a while to absorb what was going on. Initially I found it a bit confusing trying to keep straight which conditions are fixed, whi... | The proof you give becomes a bit unwieldy and it does not make clear that <span class="math-container">$N$</span> must be negative.
I think it can be shortened as follows:
<hr />
Assume <span class="math-container">$\lim_{x\to0^-} f(1/x)$</span> exists and equals <span class="math-container">$\ell$</span>. Then take a... | https://math.stackexchange.com |
182,507 | [
"https://softwareengineering.stackexchange.com/questions/182507",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/78393/"
] | I've heard people saying usage of JDBC (Java Database Connectivity) isn't recommended in Java applets. All I they say is: 'because of the security reasons'. What 'security reasons' do they mean? What would a potentially 'bad person' do when he/she found out about JDBC used in an applet, placed somewhere on a website? ... | At the most basic level, the database server ought not be opened up to the public internet. If you want random users running a Java applet to access the database directly, that implies that the database is configured to accept connections from anyone on the internet. If that's the case, an attacker can attack your da... | <ol>
<li>because you'd need to expose your database to the internet</li>
<li>you need to let the applet have access to the password used to connect to the database, a hacker can easily pull that password out of a debugger</li>
<li>most people don't think to use different DB accounts with different privileges</li>
<li>y... | https://softwareengineering.stackexchange.com |
47,253 | [
"https://dba.stackexchange.com/questions/47253",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/23528/"
] | When I connect to my local server, I get this message
<pre class="lang-none prettyprint-override"><code>A network-related or instance-specific error occurred while establishing a connection to
SQL Server. The server was not found or was not accessible. Verify that the instance name
is correct and that SQL Server i... | Go to SQL Server Configuration Manager
Start->all program->SQL Server 2008 R2->Configuration Tools->SQL Server Configuration Manager
Explore "SQL Server Network Configuration" and then select "Protocols For MSSQLSERVER".
Check your TCP/IP Protocols in right side pane. If it is disabled then enabled it and Restart t... | Are you sure about your installation is successful?.If yes, then ckeck whether your server is
<ol>
<li>configured for remote access</li>
<li>exception in firewall </li>
<li>check all protocols whether they are enabled or not accoding to your requirement.</li>
<li>whether the instance is started or not.</li>
</ol>
| https://dba.stackexchange.com |
20,051 | [
"https://electronics.stackexchange.com/questions/20051",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I'm still new to all this stuff, but I'm slowly trying to understand. I'm getting most of my information from "Getting Started in Electronics" (Forrest Mimm's book)
Okay, so MOSFETs allow current to pass through the source and drain if positive current is flowing through the base. Am I correct?
FETs do the same thing... | Now you know why I don't like this book.
<blockquote>
Basic differences between a MOSFET and a FET
</blockquote>
A MOSFET <em>is</em> a type of FET. It stands for "metal oxide semiconductor field effect transistor". All MOSFETs are FETs, not all FETs are MOSFETs. But the term is so common that things that are no... | No, you are confused. FETs are controlled by <em>voltage</em> on the <em>gate</em>. The gate does not draw current, which is to say it is high impedance. In a MOSFET there is actually a layer of silicon dioxide beteen the gate and the channel. In other FETs the gate is a reverse biased junction to the channel.
Bip... | https://electronics.stackexchange.com |
438,568 | [
"https://electronics.stackexchange.com/questions/438568",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/222051/"
] | I want to connect Arduino to 3 phase 10 hp ac motor. I just want basic functionality that is I should be able to turn it on or off using the code.
Is it possible to do with 3 phase solid state relay?
if yes, can I use 3 relays instead of a 3 phase solid state relay?
If no, how to do it?
| Better use three phase contactor with 230VAC coil. Supply 230V to coil by simple arduino relay.
| Since Arduino is limited to 5VDC (or 3.3) you will need an output to a switching transistor to drive the motor contactor of your choice.
| https://electronics.stackexchange.com |
12,629 | [
"https://mathoverflow.net/questions/12629",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2672/"
] | Is the category of groups with group-homomorphisms the same as the category of models of group theory with elementary maps?
If not so: why?
| The Categories will be fundamentally different. The category of groups with group homomorphisms, (even with monomorphisms) enjoys a directedness property: any two groups can map monomorphically into their direct sum.
But in the category of models of group theory under elementary maps, the finite groups map elementari... | I'm not sure if my answer is to the question you're asking (perhaps you can rephrase/extend it? e.g. by providing definitions that you do know, so it's clear which ones your asking about?).
Consider the category $\mathbb G$ with categorical products freely generated by an object called $G$, a distinguished morphism $e... | https://mathoverflow.net |
2,818,482 | [
"https://math.stackexchange.com/questions/2818482",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/435689/"
] | This should be really simple, I'm baffled by the fact that I just cannot get it to work. I'm either overthinking it, or just tired.
I'd like to compute the Fourier Transform of the following function:
<blockquote>
$$ f(x) =
\begin{cases}
1-|x|, & \text{If $|x|\leq 1$} \\
0, & \text{If $|x|>1$}
\end{ca... | To verify your intuition (without doing integral "now"): By $\text{Rect(t)}*\text{Rect}(t)=\text{Tri(t)},$ $$\mathscr{F}(\text{Tri(t)})=\mathscr{F}(\text{Rect(t)}*\text{Rect}(t))=\mathscr{F}(\text{Rect}(t))\cdot\mathscr{F}(\text{Rect}(t))=\text{sinc}(f)\cdot\text{sinc}(f)=\text{sinc}^2(f)$$
The second equality follows... | \begin{align}
\hat f(k) &= \int_{\mathbb R}e^{-2\pi ikx}f(x)\ \mathsf dx\\
&= \int_{-1}^0 (1+x)e^{-2i\pi kx}\ \mathsf dx + \int_0^1 (1-x)e^{-2i\pi kx}\ \mathsf dx\\
&= \frac{1+2 i \pi k-e^{2 i \pi k}}{4 \pi ^2 k^2} + \frac{1-2 i \pi k-e^{-2 i \pi k}}{4 \pi ^2 k^2}\\
&= \frac{2-e^{2 i \pi k}-e^{-2 i... | https://math.stackexchange.com |
567,608 | [
"https://stats.stackexchange.com/questions/567608",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/174716/"
] | I have 50 data points each with 7 variables.
<pre><code> v1 v2 v3 v4 v5 v6 v7
data point 1
data point 2
...
data point 50
</code></pre>
These 50 data points are divided into two groups, with label <code>a</code> or <code>b</code>. Each group has 25 data points. I need to compute a final score usin... | The summary variable has mean zero by construction, so the issue is what happens when you compare the two groups.
A short answer is that this isn't always true. It will be true if the number of observations is equal in two subsamples, which itself implies an even number of observations <span class="math-container">$n$<... | The variable v* all have zero mean already (because of the standardization). So a linear combination of them will still have a zero-mean. That's why the means of the two (equal size) groups add to 0.
| https://stats.stackexchange.com |
281,888 | [
"https://electronics.stackexchange.com/questions/281888",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/135916/"
] | I'm trying to build an AM transmitter to remotely listen to sounds within a fairly small distance from the microphone (<30m). One thing I wanted to try was to use the microphone jack on my laptop to pick up the signal. The idea is that I could pick up all signals (my laptop can record up to 192,000 samples per secon... | No, it is not practical to transmit audio nor any other information at such low frequencies. The passive antenna would have to be much bigger than the very distance you want to transmit. When I am saying bigger I am talking about a dipole hundreds of meters long.
An alternative would be to use an active antenna but w... | Perhaps FM modulate a tone, which drives a piezo tweeter above the audio range.
Use your laptop microphone to capture the acoustic energy.
| https://electronics.stackexchange.com |
476,101 | [
"https://physics.stackexchange.com/questions/476101",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/127780/"
] | For an atomic form factor <span class="math-container">$F(\textbf q)$</span>, the corresponding charge density distribution is given by
<span class="math-container">$$ \rho(\textbf r) = \frac{1}{(2\pi)^3}\int\text{d}^3 \textbf q \,F(\textbf q)\,\text{e}^{-\text{i}\textbf q\cdot \textbf r}.\tag{1} $$</span>
where <span... | The answer is 1, as you have found - the water surface remains parallel to the incline. As to how to get the answer without writing all the equations, draw a diagram showing the acceleration vectors.
There will be gravitational acceleration (vertically down), acceleration parallel to the surface of the inclined plane ... | The only effect a plane would have on that glass of water would be if the plane would accelerate. Assuming that the plane travels at constant speed perfectly perpendicular to earth's centre, the water's surface will behave just the same as on ground.
| https://physics.stackexchange.com |
38,921 | [
"https://security.stackexchange.com/questions/38921",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/20829/"
] | I've noticed that there are a lot of different payloads to choose from in MetaSploit, and the choice (assuming there's enough room in the target) usually depends on what you're trying to do.
However, from what I understand the payloads vary in size greatly. How can I determine the size of each payload so that I'll kn... | The <strong>msfvenom -s</strong> or <strong>generate</strong> command is useful for individual payload sizes. Sometimes you will want to know all the payloads within a certain payload size constraint. For example if you are developing an exploit, you know you have limited space to carry a payload of say 100 bytes and y... | You could either use the <code>msfpayload</code> command and watch for the line <code>Total size:</code>
<pre><code>msfpayload PAYLOAD O
</code></pre>
Or use the <code>generate</code> command inside the MetaSploit console and watch for the first line
<pre><code>use payload/PAYLOAD
payload(PAYLOAD) > generate
</co... | https://security.stackexchange.com |
11,664 | [
"https://security.stackexchange.com/questions/11664",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6838/"
] | I just ran nMap against my IP address and got the following result:
<ul>
<li>PORT STATE SERVICE</li>
<li>21/tcp open ftp</li>
<li>22/tcp open ssh</li>
<li>23/tcp open telnet</li>
<li>80/tcp open http</li>
<li>443/tcp open https</li>
<li>3389/tcp open ms-term-serv</li>
</ul>
Which of these are ok to... | Assuming you scanned from outside your network, nmap is showing you what you're listening on. It only affects inbound. You can close the ports.
| Like the other answers, it depends on what you scanned and where you scanned it from.
If this is your personal computer and you scanned it from your local network or scanned localhost from your own machine, then you shouldn't probably have any of those open unless you are serving on those ports.
If this is some sort... | https://security.stackexchange.com |
401,239 | [
"https://electronics.stackexchange.com/questions/401239",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/189277/"
] | in core_cm4.h header file defined some thing like this:
<pre><code>#ifdef __cplusplus
#define __I volatile /*!< Defines 'read only' permissions */
#else
#define __I volatile const /*!< Defines 'read only' permissions */
#endif
#define __O ... | "I" means: Input
"O" means: Output
"IO" means: Input and Output
As Long Pham notes, it is a naming convention, but also it is normal to use meanings to a type. Like an integer can be a counter, a timestamp, a date etc.
There are some reasons to use this:
<ul>
<li>It is good for readability... | Since this is for the definition of a hardware register map:
I think the reason is that C, unlike C++, allows the declaration of <code>const</code> qualified variables without providing an initializer:
<pre><code>volatile const uint32_t REG; // Ok in C, invalid in C++
</code></pre>
Similarly, C++ doesn't allow <code>co... | https://electronics.stackexchange.com |
696,747 | [
"https://physics.stackexchange.com/questions/696747",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/279008/"
] | Consider a tensor of arbitrary rank (2 for this case) <span class="math-container">$A_{ij}$</span>, and dimension one. Granted there are two indices to specify a component, but since each index can only take one value, there is only one component in this entire tensor: <span class="math-container">$A_{11}$</span>. So, ... | Perhaps an example is in order. Consider e.g. a 1D charge density <span class="math-container">$\rho$</span> in a 1D world. It transforms as a covariant (0,1) tensor <span class="math-container">$\rho^{\prime}=\frac{\partial x}{\partial x^{\prime}}\rho,$</span> so it is not a scalar.
| Tensors of rank <span class="math-container">$k$</span> over a vector space <span class="math-container">$V$</span> form the space <span class="math-container">$\otimes^k V$</span>. When the vector space is 1d, then we may as well take it to be the ground field <span class="math-container">$\mathbb{K}$</span>.
But <sp... | https://physics.stackexchange.com |
666,098 | [
"https://physics.stackexchange.com/questions/666098",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | I've recently started reading about the random walk, from different sources across the internet, and there is this small detail that I'm not being able to wrap my head around.
Suppose we have, a symmetric random walk in <span class="math-container">$1$</span> dimension. The walker has an equal probability of going to t... | In general, we can say that <span class="math-container">$C=AB$</span> will have real, imaginary and complex eigenvalues (complex of the form <span class="math-container">$z=a+ib$</span> where and <span class="math-container">$\{a,b\in \mathbb{R}\mid a,b \ne 0\}$</span> as shown in the comments by Mark and Qmechanic's ... | TL;DR: Assuming that <span class="math-container">$A,B$</span> are self-adjoint, the product <span class="math-container">$AB$</span> does not need to be diagonalizable. And if <span class="math-container">$AB$</span> is diagonalizable, the eigenvalues need not be real or imaginary.
Example 1: <span class="math-contain... | https://physics.stackexchange.com |
14,206 | [
"https://mathoverflow.net/questions/14206",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2672/"
] | Sorry for not knowing the answers to these elementary questions:
Is the property of formulas of the first-order language of Peano arithmetic of "defining a finite set of natural numbers" goedelizable?
If so: Is the set of formulas with this property decidable, semidecidable or non-decidable?
| The set of (Gödel codes for) PA provably bounded formulas $\phi(x)$ is computably enumerable (c.e.). By provably bounded, I mean PA $\vdash \exists b\forall x(\phi(x)\to x \leq b)$. Indeed, you can enumerate all consequences of PA and when you find one of the shape $\exists b\forall x(\phi(x)\to x \leq b)$ then enumera... | Francois has fully answered the question about the formulas phi(x) that PA proves to define a finite set, and I agree completely with what he said.
It is also natural, however, to consider which formulas phi(x) define a finite set in the standard model of arithmetic.
Here, the situation is even worse. The set of (c... | https://mathoverflow.net |
131,993 | [
"https://dba.stackexchange.com/questions/131993",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/89417/"
] | Excuse the long question, this is my first on the board.
I have just joined an organisation that is running a mission critical SQL server 2012 on a VMWare host along with another 9 (at least) VM's (web servers and batch processing servers mainly) on the same physical box.
The Physical box has 6 CPU's with 64GB of Mem... | There is nothing inherently wrong with the current configuration however you have not included info that would be relavent, such as whether the host is overcommitted on RAM/CPUs. What problem are you trying to solve - performance and/or HA/DR? Assuming you are not overcommitted:
<ul>
<li>Make sure the SQL Server insta... | Here are a few things to consider:
<ul>
<li>How old is the current hardware? You need to remember that PC hardware gets updated by Intel and its OEMs every 18 months or so. Meaning that if you don't buy new hardware every 3 years, your old hardware will fall behind more than 1 or 2 generations very quickly. (At the ti... | https://dba.stackexchange.com |
228,765 | [
"https://softwareengineering.stackexchange.com/questions/228765",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/14409/"
] | <strong>Short version</strong>
My boss wants me to store <em>user</em> passwords for an ASP.NET Web Forms web app we're developing in clear text, so that a user with admin rights can click a button and get back the current passwords for the accounts she controls.
<em>I don't want to do that</em>, because I deeply car... | If you must do this because you aren't being given an option, you might encrypt the passwords with a password that is not stored in the code or in the database. Make the recovery 'by request' of the customer (they have to call you for it), and someone on your end would have to enter the password to re-generate the use... | Store them in a file, and encrypt it with a key linked to the logged in user's account. Windows then manages the encryption and the security of being allowed to decrypt the file.
This way the password will <em>always</em> be in clear text... if you've logged on as the user that's allowed to read that file. You may nee... | https://softwareengineering.stackexchange.com |
176,405 | [
"https://math.stackexchange.com/questions/176405",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26103/"
] | A couple has $3$ kids, and $1$ of them is known to be male.
What is the probability that $1$ (only $1$) of the other $2$ kids is male?
| in generally,if we consider $3$ child,and we know that only $1$ is male,then probability of being any choosen child male is $1/3$,but if our space is consisted by two child then possibility of all combination is,let choose male as $M$,and female $F$,so
$(F,F)$,$(F,M)$,$(M,F)$,$(M,M)$ probability is $2/4=1/2$
| I'll give the answer for a slightly easier variation and let you work out the rest for yourself.
<em>Question : A family has two kids, at least one of which is a boy. What is the probability that the other kid is also a boy ?</em>
Let <em>A</em> be the event "at least one of the kids is a boy" and <em>B</em> the eve... | https://math.stackexchange.com |
276,242 | [
"https://physics.stackexchange.com/questions/276242",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/34342/"
] | As far as I know, current cosmological models predict an infinite universe. This leaves me wondering, given our current understand of cosmology:
<blockquote>
Can a hypothetical cosmological-scale computer keep expanding it's memory and perform an unlimited amount of operations?
</blockquote>
By expand I mean the d... | The universe may or may not be infinite, we don't know yet. We know it is alsmot flat, but may be spherical. Maybe it is infinite, maybe not. But irrelevant. The universe we are part of, or anybody anywhere in it, is expanding and has a cosmological horizon. Outside that we never reach, going at c or lower. Thus you on... | The fundamental limit on information that can be stored in a region of space is given by the Bekenstein bound. This bounds occurs when you have a black hole.
This bound can be seen in the following way. An observer in a Rindler wedge measures radiation with temperature
$$
T~=~\frac{\hbar c}{2\pi gk},
$$
for $g$ the ... | https://physics.stackexchange.com |
3,912,929 | [
"https://math.stackexchange.com/questions/3912929",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/775699/"
] | In my topology quiz this question was asked and I couldn't do it right. So, I am posting it here.
<blockquote>
Let A be any set . Let P(A) be the power set of A, that is the set of all subsets of A, Then how is the statement" P(A)=<span class="math-container">$\phi$</span> for some A" a false statement?
</blo... | The powerset of a set <span class="math-container">$X$</span> has <span class="math-container">$2^{|X|}$</span> elements.
So the powerset of any set has at least one element (as <span class="math-container">$2^0=1$</span>), and therefore can not be empty.
| Assume <span class="math-container">$\exists A$</span> such that <span class="math-container">$\mathcal P(A)=\emptyset$</span>. This means that there is no <span class="math-container">$B$</span> such that <span class="math-container">$B\subseteq A.$</span> But we know that <span class="math-container">$A\subseteq A$</... | https://math.stackexchange.com |
278,954 | [
"https://math.stackexchange.com/questions/278954",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/58288/"
] | Given $a,b,n\in \mathbb{N}$. What is the easiest route to find a pair of integers $x,y$ such that $(a^2+b^2)^n = x^2 + y^2$?
| Compute $(a+bi)^n$ and take the real and imaginary parts.
Why it works: The squared norm $\|a+bi\|^2 = a^2+b^2$ is completely multiplicative, so $$\|(a+bi)\|^{2n} = (a^2+b^2)^n = \|(a+bi)^n\|^2.$$
| The easiest is to observe that if $n=2m$ is even, we can use $x=(a^2+b^2)^m$, $y=0$. If $n=2m+1$ is odd, we can use $x=a(a^2+b^2)^m$, $y=b(a^2+b^2)^m$.
| https://math.stackexchange.com |
85,758 | [
"https://mathoverflow.net/questions/85758",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10898/"
] | In Heath-Brown's 2002 paper, "Rational points on curves and surfaces", he states
"We may observe that if $d \geq 3$, the surface $$x_1^d + x_2^d - x_2^{d-2} x_3 x_4 = 0$$
is absolutely irreducible, and contains no lines other than those in the planes $x_2 = 0, x_3 = 0$, and $x_4 = 0$."
I am wondering how he is able... | A line is given by a pair of equations:
\begin{equation*}
a_1 x_1 +a_2 x_2+a_3 x_3 + a_4 x_4=0, \qquad
b_1 x_1 + b_2 x_2 + b_3 x_3 + b_4 x_4=0.
\end{equation*}
Suppose this line is on $X$.
If the minor $a_3 b_4-a_4 b_3$ is non-zero, then we may rewrite the equations of the line as
\begin{equation*}
x_3=a x_1+ b x_2, ... | Any line on $X$ has at least one point in common with the plane $x_2=0$. Thus, any line on $X$ contains a point whose first two coordinates vanish. In particular, one of the equations of a line in $X$ can be chosen to be of the form $\lambda x_1+\mu x_2=0$ for a non-zero pair $(\lambda,\mu)$. From here, the result i... | https://mathoverflow.net |
25,900 | [
"https://electronics.stackexchange.com/questions/25900",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7814/"
] | When computing the N-point FFT of some signal, the result is always divided by N. I can understand why this is the case for a summation over the N points, but often the result of the FFT operation is a vector of length N rather than a summation. Why then is the length-N vector that is the output of the FFT scaled by th... | The difference is that the digital Fourier transform (and FFT as well) gives a vector of size N (or M in some cases) that contains sums of N samples.
So, basically, each point of the FFT transform is the result of a sum over a certain time interval of the time-based samples. That's why you divide by N.
You can consid... | The 1/N scaling factor is almost arbitrary placed. An unscaled FFT followed by an unscaled IFFT using exactly the same complex exponential twiddle factors multiplies the input vector by scaler N. In order to get back the original waveform after an IFFT(FFT())round trip (thus making them inverse functions), some FFT/... | https://electronics.stackexchange.com |
541,928 | [
"https://electronics.stackexchange.com/questions/541928",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/170897/"
] | I'm somewhat new to electrical engineering, I've been messing around with Raspberry Pi and I'm trying to use a 18650 battery pack (2 batteries) to power a Raspberry Pi (and some other things such as a Fan HAT).
I'm trying to convert that 7.1volt 15Amp battery pack to something around 5volt 4Amp. How should I go about d... | First, when you see a power supply rated at <span class="math-container">\$V\$</span> volts and <span class="math-container">\$A\$</span> amps, it usually means that it'll produce <span class="math-container">\$V\$</span> volts at <strong>up to</strong> <span class="math-container">\$A\$</span> amps. If you present th... | 7.1V and 15A implies that the power of the battery is 106W. What you are asking is if you can transform that into 20W. That is not a good way of looking at it. Your total power (aside from converter losses when you lower the voltage) will not change. In this case you want to manipulate just voltage, and there are sever... | https://electronics.stackexchange.com |
52,131 | [
"https://electronics.stackexchange.com/questions/52131",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16966/"
] | How can we say an Intel i7 processor is a microprocessor? It has got:
<ul>
<li>internal cache memory</li>
<li>RAM</li>
<li>BIOS memory</li>
<li>ROM. </li>
</ul>
Only thing left would be I/O pins. If it has got that too, how come that is a microprocessor?
| The terms microprocessor and microcontroller are most often defined by marketing people -- a certain sub-genus of Homo Sapiens that does not tend to follow common literary convention.
The terms microprocessor and microcontroller (and the related terms CPU and MCU) are often used incorrectly (or some might claim that t... | There's a major misunderstanding there: an i7 doesn't have RAM, ROM or BIOS memory - they're provided by the motherboard.
Actually, as was noted in a comment, the i7 does have a small amount of RAM (the cache can be used as RAM) and ROM (for the boot ROM). But even then, for the CPU to be useful, you still need exter... | https://electronics.stackexchange.com |
1,284,289 | [
"https://math.stackexchange.com/questions/1284289",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/18373/"
] | Let $X \subset \mathbb{P}^{N}$ be a non-degenerate smooth variety with positive dimension. Take $x_{1}, \ldots, x_{n}$ general points on $X$, with $\mathrm{codim}(X) \geq n - 1$. Denote by $P$ the $(n - 1)$-plane generated by the points $x_{1}, \ldots, x_{n}$. It seems that, if the intersection $P \cap X$ is a curve, t... | First, if $\mathrm{codim}(X) > n - 1$, then by the Trisecant Lemma $P \cap X = \{ x_{1}, \ldots, x_{n} \}$, and therefore, $P \cap X$ is not even a curve.
Assume $\mathrm{codim} = n - 1$. In this case, we can apply the Trisecant Lemma only for $(n - 2)$-planes generated by $n - 1$ of the general points $x_{1}, \ldo... | The Segre threefold in $\mathbb{P}^5$, given by the image of $\mathbb{P}^1\times\mathbb{P}^2$ under $([a:b],[x:y:z]) \mapsto [ax:ay:az:bx:by:bz]$, is a counterexample.
It has codimension $2$, but it meets the $2$-plane $T_0=T_1=T_3=0$ in the union of two lines, $T_0=T_1=T_2=T_3=0$ and $T_0=T_1=T_3=T_4=0$.
At this tim... | https://math.stackexchange.com |
423,065 | [
"https://softwareengineering.stackexchange.com/questions/423065",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/42918/"
] | I have a legacy service written in a procedural style which I am rewriting. I
want to improve the maintainability first and foremost; the code gets tweaked
often as the business rules change over time. Hence, I want to decouple a lot of
things, encapsulate as much of the logic in their own objects as possible, and
make... | I think OO is fine for this, as are other approaches. As written, it seems like only two things drive ALL your logic:
<ul>
<li>Someone taking an action (bid, retraction, price change, etc.)</li>
<li>Time (auction ending)</li>
</ul>
As such there is no need to constantly run a procedural loop (the equivalent of polling)... | I don't think this is a good application for applying OO. Whether it is or not, I don't think you'll get a lot of assistance with top-level OO design patterns.
The existing system is super complicated, with parallelism and complex logic, and has evolved into an approach that probably no one fully understands: 100 reco... | https://softwareengineering.stackexchange.com |
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