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 |
|---|---|---|---|---|---|
2,927,475 | [
"https://math.stackexchange.com/questions/2927475",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/545426/"
] | Consider the sequence <span class="math-container">$\left \{ z_{k} \right \}$</span> in <span class="math-container">$\mathbb{R}.$</span> Let the sequence <span class="math-container">$$\left \{ x_{n} \right \} = \sum_{k=1}^{n}z_{k}\ \ \ \ \text{and}\ \ \ \left \{ y_{n} \right \} = \sum_{k=1}^{n}\left | z_{k} \rig... | Take any <span class="math-container">$\epsilon>0$</span>. You assume the sequence <span class="math-container">$y_n$</span> is a cauchy sequence so you know that:
<span class="math-container">$\exists (n_0\in\mathbb{N})\forall(m,n\geq n_0)[|y_m-y_n|<\epsilon]$</span>
Well, so let's take <span class="math-conta... | Concerning your idea: no, it is not true in general.
Take <span class="math-container">$\varepsilon>0$</span>. Since <span class="math-container">$(y_n)_{n\in\mathbb N}$</span> converges, there is a natural <span class="math-container">$N$</span> such that<span class="math-container">$$m,n\geqslant N\implies\lvert ... | https://math.stackexchange.com |
1,066,105 | [
"https://math.stackexchange.com/questions/1066105",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/110071/"
] | Let $\omega$ be a <em>non-vanishing</em> (for clarification: nowhere vanishing) smooth $1$-form on a smooth manifold $M$, if $\mathrm{d}\omega \wedge \omega =0$, do we already have $\mathrm{d}\omega= \sum a_i \wedge \omega$ for some $1$-forms $a_i$?
| Extend the first line $AP_1$ through the hypotenuse till it reaches a point $D$ such that $\angle{ABD}$ is a right-angle. If you add every odd-numbered segment ($P_0P_1,\; P_2P_3,\;\ldots$) it is the same as length of $AD$.
Similarly, if you add every even-numbered segment ($P_1P_2,\; P_3P_4,\;\ldots$) it is the same ... | The triangles, $P_0P_1P_2$, $P_2P_3P_4$,...,$P_{2n}P_{2n+1}P_{2n+2}$,... are similar. Furthermore, the ratio of each triangle and the next one are always the same (can you find it with trigonometry?).
The lengths of the segments $\overline{P_0P_1}$, $\overline{P_2P_3}$,...,$\overline{P_{2n}P_{2n+1}}$,... form a geomet... | https://math.stackexchange.com |
433,031 | [
"https://stats.stackexchange.com/questions/433031",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/140835/"
] | Let <span class="math-container">$\mathbf{a} \sim \mathcal{GP}(\mathbf{m},\mathbf{C})$</span> where <span class="math-container">$\mathbf{a} \in \mathbb{R}^T$</span> is modeled as Gaussian process with mean <span class="math-container">$\mathbf{m} \in \mathbb{R}^T$</span> and prior covariance <span class="math-containe... | Yes, by definition a random variable is Gaussian if and only if all linear functionals are normally distributed. With <span class="math-container">$e_t$</span> the <span class="math-container">$t$</span>th standard Euclidean basis vector, we have <span class="math-container">$a_{t,k}=e_t'Ae_k=tr(Ae_ke_t')=\langle A, e_... | Maybe this is not the answer you were looking for but if we assume that <span class="math-container">$\mathbf{a}$</span> is i.i.d and that <span class="math-container">$p(\mathbf{a}(t) > 0\vert t_{0}) = \phi(m_{t}\,C_{t,t}^{-\frac{1}{2}})$</span> then for each <span class="math-container">$\mathbf{a}\in\mathbf{A}$</... | https://stats.stackexchange.com |
420,860 | [
"https://softwareengineering.stackexchange.com/questions/420860",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73722/"
] | I am working on implementing a database of sorts and am stuck wanting to make it <em>perfect</em> from the get go because I realize I don't know how to <em>migrate</em> the database engine from one data structure to another (as the data structure implementations evolve). I am afraid that if I pick a database data struc... | What you are dealing with is a change in the structure of the files that are used to persist information.
There are two main ways to deal with this:
<ol>
<li>Perform a conversion from the old format to the new format during installation of the software version that relies on the new format. The conversion tool would be... | Under the assumption that you have a new database/data structure that works and supports all that the old one supports… What follows is the solution that comes to mind.
Make an interface/façade/abstraction layer for what the software uses from the database/data structure. Then make three implementations: one uses the o... | https://softwareengineering.stackexchange.com |
563,404 | [
"https://stats.stackexchange.com/questions/563404",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/287171/"
] | I am comparing three regression models, simple linear regression, Lasso and Bayesian Lasso then the R-Square and RSME for them are
<pre><code>r2 score for Bays model is 0.10171034421952285
rmse score for Bays model is 0.7888288293573854
r2 score for regression model is 0.3303114752643104
rmse score for regression model... | Sure, it just means that the model with the best fit is the OLS model.
We like alternatives to OLS, such as regularized models, because they can achieve better fits than OLS, but that better fit is not guaranteed. Your situation is one where the regularized models are not as good as the OLS model.
A potential remedy is... | If these are fits on training data, Lasso and Bayesian regression models are <em>supposed</em> to not fit the training data as well as simple linear regression. This is to avoid overfitting. However, a negative r-squared value on training data indicates that something has gone wrong, although I can't say what from the ... | https://stats.stackexchange.com |
254,874 | [
"https://electronics.stackexchange.com/questions/254874",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/120200/"
] | I have an audio circuit which is supplied by a voltage of 9V dc and 12V dc. These voltages are produced by means of a conventional transformer which transforms the mains 230V ac 50Hz to 15V ac 50Hz. After the transformer there is a rectifier (diode bridge and capacitor) followed by two regulators, one for the 9V dc and... | 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 |
88,758 | [
"https://security.stackexchange.com/questions/88758",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/30546/"
] | I’m researching a possibility of implementing KEK and DEK servers compliant with PCI-DSS requirements.
PCI Tokenization Guidelines states:
“The tokenization solution should include a mechanism for distinguishing between tokens and actual PANs.”
The document doesn’t specify for which type of token the requirement abov... | <blockquote>
Am I right thinking that it is NOT relevant for the tokens based on
mathematically reversible cryptographic functions?
</blockquote>
<strong>You're right. But you may not want to do it that way.</strong>
Tokens are <em>generally</em> isomorphic to card numbers (15-16 digit numeric) because they are ... | You are right. However, mathematically reversible tokens (aka encrypted data) have a much smaller reduction in PCI compliance scope than a real, randomly generated token. Also, if you are set on the mathematically reversible route, you can also use format-preserving encryption (FPE). FPE produces ciphertexts that can h... | https://security.stackexchange.com |
27,316 | [
"https://mathoverflow.net/questions/27316",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4177/"
] | I have no intuition for field theory, so here goes. I know what the algebraic and separable closures of a field are, but I have no feeling of how different (or same!) they could be.
So, what are the differences between them (if any) for a perfect field? A finite field? A number field?
Are there geometric parallels? (... | Geometrically there is a very big difference between separable and algebraic
closures (in the only case where there is a difference at all, i.e., in positive
characteristic $p$). Technically, this comes from the fact that an algebraically
closed field $k$ has no non-trivial derivations $D$; for every $f\in k$ there is
... | First of all, there is not <em>the</em> algebraic/separable closure. Choices have to be made. However, if an algebraic closure $k^{\mathrm{alg}}$ of $k$ is fixed, inside it there is a unique separable closure $k^{\mathrm{sep}}$ of $k$, namely the subfield consisting of the separable elements over $k$.
Ignoring the fai... | https://mathoverflow.net |
203,921 | [
"https://electronics.stackexchange.com/questions/203921",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/93329/"
] | Is there a specific way Outrunners are normally wound? (Wye or Delta)
What are the pros/cons to winding the motor a certain way?
| A Wye connected BLDC motor will have a \$K_t\$ that is \$\sqrt3\$ larger than a delta connected motor (assuming they are wound exactly the same. This means that delta connected motors will run faster for a given voltage and produce less torque for a given current.
The only issue you may run into with delta connecte... | Motor is wound always the same, you then connect windings in wye or delta. you can cobine two voltage levels like 230/400V (delta/wye) in wye you have more losses in copper, also it is more expensive due to more copper used. Idealy you would connect in delta connection if it is possible.
| https://electronics.stackexchange.com |
3,534 | [
"https://physics.stackexchange.com/questions/3534",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1483/"
] | The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half—the halves clearly don't fall more slowly just from having been sliced into two pieces.
However, I believe the a... | Using your definition of "falling," heavier objects do fall faster, and here's one way to justify it: consider the situation in the frame of reference of the center of mass of the two-body system (CM of the Earth and whatever you're dropping on it, for example). Each object exerts a force on the other of
$$F = \frac{G... | <h2>Inertial Reference Frames</h2>
The paradox appears because the "rest frame" of the Earth is not an inertial reference frame, it is accelerating. Keep yourself in the CM (center of mass) reference frame and, at least for two bodies, there is no paradox. Given an Earth of mass <span class="math-container">$... | https://physics.stackexchange.com |
300,029 | [
"https://mathoverflow.net/questions/300029",
"https://mathoverflow.net",
"https://mathoverflow.net/users/95838/"
] | I am trying to evaluate the integral
$$
I_k(x)=\int_1^x \log^k t \frac{\sqrt{t-1}}{t^2} dt
$$
with $x$ tending to infinity.
In fact, I wish to have an estimate
$$
\sum_{k=0}^\infty \frac{1}{\log^k x} \int_1^x \log^k t \frac{\sqrt{t-1}}{t^2} dt = C+E(x),
$$
where $C$ is explicit and $E(x) \to 0$ as $x \to \infty$.
The... | First of all, your series diverges for any $x>1$, because we always have
$$I_k(x)\geq \int_{\sqrt{x}}^x \log^k t\sqrt{t-1}t^{-2}dt\geq \frac{\sqrt{\sqrt{x}-1}}{x}\int_{\sqrt{x}}^{x} \frac{\log^k t}{t} dt=\frac{\sqrt{\sqrt{x}-1}}{x}\frac{(\log^{k+1} x)(1-2^{-k-1})}{k+1}.$$
If you want to get the asymptotics for $I_... | In view of the output of the Mathematica code
<pre><code>Table[Series[Integrate[Log[t]^k*Sqrt[-t^2+1],{t, 1/x^2, 1},Assumptions->x> 1],{x,Infinity,2}],{k,1,3}]
</code></pre>
$$O\left(\left(\frac{1}{x}\right)^3\right)+\frac{2 \log (x)+1}{x^2}+\left(-\frac{\pi }{8}-\frac{1}{8} \pi \log (4)\right), $$
$$\frac{1}{... | https://mathoverflow.net |
19,838 | [
"https://physics.stackexchange.com/questions/19838",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7253/"
] | If the electric potential is 220V and some device needs 1500watts then how does it suck exactly that amount of electrical energy from outlet?
| If it's a light bulb or heater, it's just a resistor.
First, forget that it's alternating current, just to simplify things.
Think of the power source as a really big 220 volt battery.
If it's drawing 1500 watts, divide that by 220, and that will tell you the current I in Amperes.
(That just measures how many electron... | It is not the most straightforward viewpoint to say that a device "needs 1500 watts". This is more a consequence than a condition. What happens is that you create an electric circuit by plugging in a device into the outlet. That circuit follows Ohm's law: $$V = I R$$ So for a given voltage and resistance a certain curr... | https://physics.stackexchange.com |
41,545 | [
"https://electronics.stackexchange.com/questions/41545",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/13365/"
] | I'm designing a system with a master board and a variable number of identical daughter boards that I would like to connect in a chain. The master board contains a microcontroller but the daughter boards don't contain anything intelligent. The master board will only connect to one daughter board, and each daughter boar... | The simplest way to create a generic "board select" signal is to create a distributed shift register, as shown below. This is similar to what you do when you use a 74xx595 as an I/O expander, and also similar to how JTAG works.
<img src="https://i.imgur.com/iadjQ.png" alt="board select block diagram">
The microcontro... | If the daughter boards are just supposed to output signals received from the master, a common approach is to cascade 74HC595 or 74HC4094 shift register chips; each board has "register latch", "shift clock", and "data" inputs which are fed to the first shift register, and passes on the "register latch" and "shift clock"... | https://electronics.stackexchange.com |
70,947 | [
"https://chemistry.stackexchange.com/questions/70947",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/42783/"
] | My teacher said that we always used indicators such as methyl red, methyl orange, litmus, phenolphthalein, etc. rather than universal indicator. I don't understand why, though, would not universal indicator serve the same function, but for essentially all titrations rather than select few?
| The thing with universal indicators is that you have 6 different colors or so differentiating certain pH-ranges.
Now if you want to titrate to a certain pH-Value, it is easier to have an indicator like phenolphtalein that changes from colorless to a color at a certain point (phenolphtalein being colorless from 0 to 8... | I'm a chemistry teacher. I quite like using universal indicator. It usually goes from red/orange to yellow in one drop, then to green in another drop, then to blue/purple after another drop. We stop at green (neutral). I like it because it's clearly green.
With phenolphthalein we stop when the pale pink persists for ... | https://chemistry.stackexchange.com |
455,145 | [
"https://physics.stackexchange.com/questions/455145",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/178763/"
] | I'm having problem with calculating the functional derivative of <span class="math-container">$F$</span> with respect to <span class="math-container">$\phi(x)$</span> while
<span class="math-container">$$F = \int d^{4}x \phi^2 \partial_{\mu}\phi\partial^{\mu}\phi.$$</span>
I want to obtain <span class="math-container... | Here is one argument:
<ol>
<li>Starting from Newton's 2nd law, the Lagrangian <span class="math-container">$L(q,v,t)$</span> is just one step away. </li>
<li>A Legendre transformation <span class="math-container">$v\leftrightarrow p$</span> to the Hamiltonian <span class="math-container">$H(q,p,t)$</span> is well-defi... | To describe the motion of bodies, it is enough to know two variables — the coordinates and velocitys, or the coordinates and momentums, then the initial conditions are determined. In the case of setting other variables, it is necessary to use boundary conditions, which is more complicated. It is necessary to set the in... | https://physics.stackexchange.com |
549,528 | [
"https://electronics.stackexchange.com/questions/549528",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/274810/"
] | Is this something that is possible? Is it a good idea? I would then have double the amp hours on one "set" of the batteries in series.
All batteries are the same brand and type.
| No this is not a viable idea at all.
If you have three batteries, there are only two ways to arrange them. All in series (3S) or all in parallel (3P).
If you want to add capacity to your battery bank, you should add two more batteries so that you have two in parallel and two in series (2P2S).
There are many details to ... | Not a particularly good idea.. you missed same age/useage? As batteries age their characteristics change, you will eventually over charge one set of batteries and under charge the other. This will shorten the life of all 3 batteries. Better to go 2 + 2 or keep the third separate.
But if you set up the charger(s) to ... | https://electronics.stackexchange.com |
91,782 | [
"https://electronics.stackexchange.com/questions/91782",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30723/"
] | A computer using a direct-mapped cache has \$2^{24}\$ words of main memory and a cache of 256 blocks. Each cache block contains 64 words.
<ol>
<li>How many blocks of main memory are there?</li>
<li>What is the format of a memory address as seen by the cache? (What are the sizes of the tag, block, and word fields?)</li... | Solutions:
<ol>
<li>B = Capacity (C) / block size (b)<br>
B = 2<sup>24</sup> / 2<sup>6</sup><br>
B = 2<sup>18</sup> blocks</li>
<li>2<sup>24</sup> = 24-bit address<br>
T = 24 - (8 + 6) = 24 - 14 = 10 bits<br>
B = 256 = 2<sup>8</sup> = 8 bits<br>
W = 64 = 2<sup>6</sup> = 6 bits<br></li>
<li>0x01BD36 = 0000000110 111101... | For X addresses, where 2^N+1 < X < 2^N, N address lines are not sufficient, N+1 is sufficient (but leaves some address space unused). Hence you have no other option than to use (at least) N+1 address lines.
| https://electronics.stackexchange.com |
286,864 | [
"https://dba.stackexchange.com/questions/286864",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/225655/"
] | Given a table sales, with item selled in two different currencies how to get the exchange in EUR
Sales Table:
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>item</th>
<th>currency</th>
<th>Amount</th>
</tr>
</thead>
<tbody>
<tr>
<td>A</td>
<td>USD</td>
<td>1000</td>
</tr>
<tr>
<td>A</td>
<td>E... | Room should have PK of (hotel_id,room_number).
Weak entities have compound keys with the strong entity key/foreign key as the leading column(s).
There are people who disagree with this approach, but they are wrong.
<blockquote>
How can i find the room belonging to specific hotel which has the different number of beds l... | The real question is <em>why is there no <strong>primary key</strong> for the <code>Rooms</code> table?</em> In most cases (except a few edge cases like <strong>staging tables</strong>) you should have a <strong>primary key</strong> on your tables.
Despite this, even without a <strong>primary key</strong> on the <code>... | https://dba.stackexchange.com |
482,024 | [
"https://physics.stackexchange.com/questions/482024",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231412/"
] | We know change in kinetic energy is equal to total work done by all the forces acting on the object.For work done there should be a force .What's that force.direction?
ex a parallel plate capicitor's dielectric is attached to a mass m which is pulling it downward .We need to find the vale of dielectric so that it stay... | For a dielectric being pulled into a high-E-field region, one cannot
make the usual 'E field is perpenducular to the parallel plates'
assumption, because the edge of the dielectric is a fringe region
with curved field lines. The polarization of the dielectric
makes the separated charges along that edge subject to th... | The correct relation is that the change in kinetic energy is equal to the total work done on a particle--not the change in mechanical energy. Or, another relation that holds true is that the work done on a particle by conservative forces is equal to the (negative) of the change in its potential energy.
For example, i... | https://physics.stackexchange.com |
441,689 | [
"https://physics.stackexchange.com/questions/441689",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206584/"
] | <blockquote>
I am considering a particle within a potential given by <span class="math-container">$$V(x)=mg|x|$$</span> and am attempting to find the energy eigenvalues of the system.
</blockquote>
Taking <span class="math-container">$V(x)$</span> to be defined piecewise, I've solved the Schrödinger equation in a pi... | You're over-complicating things.
The potential is even (i.e. <span class="math-container">$V(-x) = V(x)$</span>), which means that the eigenfunctions need to be either even or odd functions, and that means in turn that you can replace your problem with just the <span class="math-container">$x>0$</span> half, consi... | Apart from wave function continuity, there is a condition of its derivative continuity at <span class="math-container">$x=0$</span>. It follows from the Schrodinger equation integration from <span class="math-container">$x-\epsilon$</span> to <span class="math-container">$x+\epsilon$</span>. This will give you the nece... | https://physics.stackexchange.com |
228,964 | [
"https://mathoverflow.net/questions/228964",
"https://mathoverflow.net",
"https://mathoverflow.net/users/85560/"
] | I'm working on a model that would require to use vectorial functions of $\mathbb{R}^n \rightarrow \mathbb{R}^n$, such that $\forall x, y \in \mathbb{R}^n$, $\lVert \frac{df(x)}{dx}(y) \lVert_2 = \lVert y \lVert_2$, ie with an orthogonal Jacobian.
I can only think of trivial functions (like $f(x) = Ox + c$ for $O$ orth... | Such maps are conformal. A theorem of Liouville says that if $n\geq 3$,
the only conformal maps (defined in some region in $R^n$) are Mobius. A Mobius map is a composition of inversions
in spheres. For example $x\mapsto x/|x^2|$ is the inversion in the unit sphere.
Inversions in all spheres generate the Mobius group.
... | $\def\RR{\mathbb{R}}$A brute force approach shows that there are no other $C^2$ solutions. Let $F: \RR^n \to \RR^n$ have orthogonal Jacobian everywhere. We will show that the Hessian of $F$ vanishes everywhere, so $F$ is linear.
It is enough to show that Hessian vanishes at $0$, since there is nothing special about $0... | https://mathoverflow.net |
397,198 | [
"https://mathoverflow.net/questions/397198",
"https://mathoverflow.net",
"https://mathoverflow.net/users/164670/"
] | Let <span class="math-container">$G$</span> be a group acting highly transitively (and faithfully) on a set <span class="math-container">$S$</span>. Suppose that <span class="math-container">$G$</span> is finitely presented, and that every stabilizer in <span class="math-container">$G$</span> of a finite subset of <spa... | Yes. There is such a reason.
I will write a subset of <span class="math-container">$G$</span> is RE if the set of those words over the generators for <span class="math-container">$G$</span> which represent elements of the subset is recursively enumerable.
As IJL argued, since <span class="math-container">$G$</span> is ... | Is there an algorithm to distinguish the elements of the set <span class="math-container">$S$</span>? If so, here is a word problem algorithm. This doesn't seem to use any transitivity properties, just faithfulness.
Start with the positive integer <span class="math-container">$n=1$</span>. Given a word <span class="... | https://mathoverflow.net |
36,373 | [
"https://dba.stackexchange.com/questions/36373",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5544/"
] | Earlier I created a user :
<pre><code>SQL>create user suhail identified by password
SQL>User created.
SQL>Grant create session,create table to suhail;
SQL>Grant Succeeded.
</code></pre>
but when I login as <code>suhail</code> and try to create a <code>table</code> I get an error saying <em><code>ORA-01950... | This error says that the user doesn't have quota on tablespace <code>SYSTEM</code> which is set as the default persistent tablespace. You can assign a user the quota like this:
<pre><code>sql> alter user scott quota 50m on system;
</code></pre>
Here, <code>50m</code> means that the user quota on the <code>SYSTEM</... | You have to create one new tablespace into the database because for the <code>SYSTEM</code> tablespace access, <code>SYSDBA</code> privileges are required.
So, create one new tablespace and assign it as the default tablespace to all users. When you create any user, by default it will give assign particular tablespace.... | https://dba.stackexchange.com |
913 | [
"https://mechanics.stackexchange.com/questions/913",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/590/"
] | In general, where can one find information about the quantity of fuel that is left in the vehicle's tank when the warning light turns on?
More specifically, in a Suzuki Swift GLX (auto) 2010 model?
| Look up in your owner's manual how capacity your fuel tank has. Next time you fuel up, take note of the difference. In my car it's roughly 2 gallons (7.5 liters). However, realize that modern cars use fuel as a coolant for the fuel pump and running the tank dry often may damage the fuel pump over time.
| Look up in your owner's manual and it should tell you how much fuel is left when the light comes on. You can always confirm it by following Parker's answer too.
| https://mechanics.stackexchange.com |
431,931 | [
"https://math.stackexchange.com/questions/431931",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/42912/"
] | I'm having troubles with this definition:
<img src="https://i.stack.imgur.com/8sz3q.png" alt="">
<img src="https://i.stack.imgur.com/T9uFv.png" alt="">
My problem is with the <em>uniquely part</em>, for example the zero element:
$0=0+0$,
but $0=0+0+0$
or $0=0+0+0+0+0+0$.
Another example, if $m \in \sum_{i=1}^{1... | Well notice what the definition says. It says that for each $m \in M$, you need to be able to write $m= \sum\limits_{\lambda \in \Lambda} g_{\lambda}$ where this sum is over all $\lambda$. So for $0$, the only possibility is a sum of $0$ $\lambda$-many times.
| The collection of <strong>nonzero</strong> elements is unique. In the case of the element $0$ the set of nonzero elements summing to zero is the empty set.
| https://math.stackexchange.com |
192,387 | [
"https://math.stackexchange.com/questions/192387",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/38778/"
] | The <strong>proof</strong>: Let $\alpha= \sup X$. If $f$ is a bijective mapping of $\alpha$ onto some $\beta < \alpha$, let $\kappa \in X$ be such that $\beta < \kappa \le \alpha$. Then $|\kappa|=|\{f(\xi): \xi < \kappa\}| \le \beta$, a contradiction. Thus, $\alpha$ is a cardinal.
*An ordinal $\alpha$ is a ca... | (I will write $X \approx Y$ to denote that $X$ and $Y$ are equinumerous.)
Note the following simple fact: If $f : X \to Y$ is a bijection, then for every $A \subseteq X$ the restriction $f \restriction A$ is a bijection between $A$ and $f''A$, which gives us that $A \approx f''A$ for all $A \subseteq X$.
In the cont... | Let $X$ be a set of cardinals. Let $\alpha = \sup X$. Suppose that $\sup X$ is not a cardinal. Then there exists a $\beta < \alpha$ such that there exists a bijection $f : \alpha \rightarrow \beta$. Since $\alpha$ is not a cardinal and $X$ is a set of cardinals, you have that $\alpha \notin X$. Since $\alpha = \sup ... | https://math.stackexchange.com |
97,241 | [
"https://electronics.stackexchange.com/questions/97241",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/31060/"
] | I started writing firmware for my product and I'm a rookie here. I went through many articles about not using global variables or functions. Is there any limit for using global variables in an 8 bit system or is it a complete 'No-No'. How should I use global variables in my system or should I completely avoid them?
I ... | You can use global variables successfully, as long as you keep in mind @Phil's guidelines.
However, here are some nice ways to avoid their issues without making the compiled code less compact.
<ol>
<li>Use local static variables for persistent state that you only want to access inside one
function.
<pre><code>#includ... | The reasons you would not want to use global variables in an 8-bit system are the same you would not want to use them in any other system: they make reasoning about the program's behavior difficult.
Only bad programmers get hung up on rules like "don't use global variables". Good programmers understand the reason behi... | https://electronics.stackexchange.com |
142,220 | [
"https://mathoverflow.net/questions/142220",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38851/"
] | Fermat proved that <span class="math-container">$x^3-y^2=2$</span> has only one solution <span class="math-container">$(x,y)=(3,5)$</span>.
After some search, I only found proofs using factorization over the ring <span class="math-container">$Z[\sqrt{-2}]$</span>.
My question is:
Is this Fermat's original proof? If not... | Fermat never gave a proof, only announced he had one (sounds familiar?). Euler did give a proof, which was flawed, see Franz Lemmermeyer's <A HREF="http://www.fen.bilkent.edu.tr/~franz/ant/ant01.pdf" rel="noreferrer">lecture notes,</A> or see page 4 of David Cox's <A HREF="http://math.stanford.edu/~lekheng/flt/cox.pdf"... | Fermat did not prove this result; he claimed that the only solution is the obvious one and conjectured (in words that seem to suggest he knew how to prove it, but without explicitly saying so) that this can be proved by descent. I am sure that Fermat, if he really believed
to have a proof (in my opinion he did not), w... | https://mathoverflow.net |
340,996 | [
"https://softwareengineering.stackexchange.com/questions/340996",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/260680/"
] | I am writing a wrapper for a REST API and I have run into something I have never had to ask myself before.
This API is for E-Commerce transactions, it has SALE and RETURN endpoints (and some other endpoints that aren't critical to this discussion).
The SALE and RETURN requests are nearly identical, with the exception... | My favorite example of inheriting and adding nothing new is this:
<pre><code>public class LoginException : System.ApplicationException{}
</code></pre>
Why? Because I've said all I need to say with that wonderfully descriptive class name. Sure if I want to add a dynamic message I'll need to add a constructor. But if... | Yes, it's completely reasonable to have "empty" subclasses of a base class. A different but in some ways analogous situation is wrapping a type to enforce a type distinction even when representationally there is no difference. For example:
<pre><code>struct Seconds {
public Seconds(int v) { Value = v; }
publi... | https://softwareengineering.stackexchange.com |
640,871 | [
"https://electronics.stackexchange.com/questions/640871",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/143392/"
] | Can modern IT equipment with redundant SMPS handle AC input from two independent, unsynchronized AC inputs, or is it not recommended?
| It should be fine, since each SMPS is doing its own rectification and switching on the primary side of the transformer. It's the secondaries where they meet, and they all have DC.
| Yes. It's common practice to feed them from two different UPSes, often on separate phases. Personally, I have one supply on UPS and one directly from grid. I don't know if the UPS tries to match output phase with grid or not but this does not matter for SMPSes.
| https://electronics.stackexchange.com |
153,361 | [
"https://physics.stackexchange.com/questions/153361",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/63691/"
] | Suppose a wagon is moving at constant velocity on a friction-less surface, and rain begins to fill the wagon.
The net force on the wagon is zero, so momentum is conserved; as the mass of the wagon increases, the speed decreases. But if the velocity of the wagon changes, the net force can't be zero, right?
There has... | To deal with this type of problem, you must be careful to define exactly what <strong><em>system</em></strong> you are dealing with, and then not change that system part way through the problem. This definition allows you to be very clear about whether the "system" has any external forces acting, and thus whether the ... | When the raindrops hit the wagon's surface, they aren't moving relative to the tracks. Friction is required to accelerate the raindrops to the wagon's speed. By Newton's third law, there must therefore be a reaction force on the wagon surface by the raindrops.
| https://physics.stackexchange.com |
481,691 | [
"https://physics.stackexchange.com/questions/481691",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/205249/"
] | Let me specify beforehand that this question has been asked previously but I haven't been able to satisfy my curiosity.<br>I know a battery maintains a potential difference between it's terminals , let's say that the ground is at 0 potential for my question , then with respect to the ground both the terminals are at no... | <strong><em>I know a battery maintains a potential difference between it's terminals , let's say that the ground is at 0 potential for my question , then with respect to the ground both the terminals are at non-zero potentials.</em></strong>
This statement depends on what you mean by "ground". In electrical power syst... | Yes, according to me, there will be momentary current. Let's say you arranged the circuit in a way so that electrons are pushed into the Earth. Now there will be a force on electrons displacing them but as soon as the electrons are displaced positive charges develop, as the circuit is not complete and no electrons can ... | https://physics.stackexchange.com |
126,284 | [
"https://security.stackexchange.com/questions/126284",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/113699/"
] | As we know zip files supports a simple password-based symmetric encryption system and some vendors use other algorithms. I used the <code>zipinfo</code> command in Linux but it doesn't say what encryption algorithm is used. How can I find that out?
| 7Zip archiver (freeware) has an info button that among other useful things tell you the encryption type an archive is using.
As a general note, .Zips usually use something called "ZipCrypto Deflatte".
| If you're on Windows in Total Commander you can press Ctrl+PageDown to enter the archive. Right click > Properties on any file will tell you the encryption type.
| https://security.stackexchange.com |
164,974 | [
"https://math.stackexchange.com/questions/164974",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34801/"
] | I don't understand why in the definition of a topology, you require the union of an "arbitrary" collection of open subsets to be open and the intersection of a "finite" number of open subsets to be open. That is, I don't get why one of them is arbitrary and the other is finite.
Thanks!!
| So, I'm going to answer this question in two parts. Firstly, I will answer a question implicit in the original post: what is the purpose of definitions? Secondly, I will answer the explicit question in the original post: why does the definition of a topology involve an arbitrary union of open sets but only a finite int... | One motivation for topology in this formal sense is to capture what it means for a function to be continuous when there isn't a metric to which you can apply an $\epsilon - \delta$ approach. If you think about open sets on the real line and how these relate to continuity by the "metric definition" you will note that th... | https://math.stackexchange.com |
10,172 | [
"https://physics.stackexchange.com/questions/10172",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3653/"
] | Would the vast and seemingly diffuse clouds of dark matter floating around our galaxy (and most others) absorb gravitational waves? Is this perhaps why we haven't detected any yet?
| It is very difficult to detect gravitational waves because gravity is such a weak force. For the same reason though it's very difficult to dampen gravitational waves. We know that dark matter behaves similar to 'normal matter' for what its equation of state and coupling is concerned, so it won't be able to absorb gravi... | To start this discussion I present a few facts about gravity waves. A weak linear gravity wave is a perturbation on a background metric $\eta_{ab}$ with the total metric
$$
g_{ab}~=~\eta_{ab}~+~h_{ab}.
$$
The Ricci curvature to first order is
$$
R_{ab}~=~{1\over 2}\Big(\partial_c\partial_a{h^c}_b~+~\partial_c\part... | https://physics.stackexchange.com |
151,072 | [
"https://softwareengineering.stackexchange.com/questions/151072",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/62495/"
] | I was writing some tests in Gherkin (using Cucumber/Specflow). I was wondering how abstract should I get with my tests.
In order to not make this open-ended, which of the following statements is better for BDD:
<pre><code>Given I am logged in with email admin@mycompany.com and password 12345
When I do something
Then... | They're not really tests; they're scenarios or examples of how to use your code. If you avoid the word "test" you'll have an easier time, and it will become obvious that 2 is the way forward because you'll be able to discuss your scenarios with the business.
The business have no interest in tests phrased in the way yo... | Another key thing to think about when penning your features and scenarios is this: If we change X in the system, will I need to refactor my scenarios? If the answer is yes, I would say that it is getting to specific about the details. IMO features and scenarios should only change because of changes in requirements from... | https://softwareengineering.stackexchange.com |
541,931 | [
"https://physics.stackexchange.com/questions/541931",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249663/"
] | In the book <em>Quantum Field Theory for the Gifted Amateur,</em> the author stated that, having a field that transforms locally via <span class="math-container">$\psi(x) \rightarrow \psi(x)e^{i \alpha(x)}$</span> will destroy local symmetry -and he is right- but he said we can fix that right up by adding a field <span... | 1)The situation is similar to general relativity, where you cannot compare vectors in different tangent planes, and must supply a connection to 'transport' vectors between different planes. Here, once you allow gauge transforms, you cannot compare fields at 2 different points before and after the transform, since they... | I want to give you an initial argument and a point from where you can start to find the result yourself.
To have a symmetry in the lagrangian given by a local <span class="math-container">$U(1)$</span> transformation you should have that
<span class="math-container">$$\bar\psi e^{-i\alpha(x)}(i\not \partial - m) e^{i... | https://physics.stackexchange.com |
333,941 | [
"https://softwareengineering.stackexchange.com/questions/333941",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/197872/"
] | With pre-built CMS usually comes a lot of features that you do not need in your typical smaller project for small businesses and in the end you have to write a lot of your own functionality for said project anyways that is missing. So basically CMS in that scenario saves you initial time overhead of not having to desig... | The answer, as with many things, is it depends. Pre-built CMS tools and custom software each offer a lot, but also have their drawbacks. It's a matter of weighing the business needs vs. what you are getting.
Pre-built CMSs (especially those that have been around a while), are usually pretty easy to use. They allow ... | I'd say it's exactly the opposite.
One, writing custom software is extremely expensive. Small businesses won't be able to afford writing things that already exist from scratch, for large businesses that is less of an issue.
Two, pre-built CMSes that have been around for a long time have a LOT of functionality already... | https://softwareengineering.stackexchange.com |
108,958 | [
"https://cs.stackexchange.com/questions/108958",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/64608/"
] | Does anyone know when the list data structure was mentioned in computer programming/algorithms? Who gave birth to this list concept?
| Knuth gives a good overview on the history of lists and linked data structures. From <em>The Art of Computer Programming</em>, Volume I, Section 2.6:
<blockquote>
Linked memory techniques were really born when A. Newell, J. C. Shaw, and H. A. Simon began their investigations of heuristic problem-solving by machine.
... | List processing is simultaneously three things in the
development of computer science. (1) It is the creation
of a genuine dynamic memory structure in a machine
that had heretofore been perceived as having fixed
structure. It added to our ensemble of operations those
that built and modified structure in addition to tho... | https://cs.stackexchange.com |
544,690 | [
"https://physics.stackexchange.com/questions/544690",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/182305/"
] | I understand that non-newtonian fluid could become solid under high shear rate. What I can't find online, is could we control at which shear rate the NNF would solidify? Like when an electrical field with field strength A is applied to the NNF, the NNF would only start solidifying under shear rate X, but when the field... | Great question! I remember being mystified with the elusive nature of thermodynamics and its formalism. But the fact of the matter is that like most (if not all) of physics, at the core of it, they’re just differential equations.
To look at this the first and fundamental thing to note is that thermodynamics is a stud... | I guess most of the time you are interested in understanding how a system's, for example, internal energy change as you change the volume. On the other hand, some quantities such as internal energy or enthalpy are independent of the way you change the system so therefore like gravitational potential energy they only de... | https://physics.stackexchange.com |
463,636 | [
"https://physics.stackexchange.com/questions/463636",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/212614/"
] | If we were to throw some water on the floor then walk over it we may or may not slip but it wouldn't that be difficult to walk. If we repeat the same thing with oil we it would be harder to walk as me spread our legs and apply a force component of force tangential to the surface of the floor does this not mean that the... | The quality responsible for oil being "slippery" is called <em>lubricity</em> and it is very different from <em>viscosity</em>- although many oils that have high lubricity are also more viscous than water.
In very general terms, lubricity has to do with the ability of the lubricant to withstand being subjected to ext... | Firstly, friction is a resistive force which acts between two surfaces in contact. Viscosity is fluid friction; the frictional force that acts between the layers of fluid particles or between an object immersed in the fluid and the fluid particles. Scientifically, the frictional force that acts between the layers of oi... | https://physics.stackexchange.com |
163,513 | [
"https://chemistry.stackexchange.com/questions/163513",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/118083/"
] | I read this definition:
<blockquote>
reversible process is one which can be stopped at any stage and reversed so that the system and surroundings are exactly restored to their initial states. An irreversible process is one in which heat is transferred through a finite temperature.
</blockquote>
But I just don't get it ... | The difference is this: In a reversible process, when you restore the system to its original state, the surroundings are also restored to their original state (note that the entire cyclic process, including the movement away from the initial state, and the restoration to the initial state, must be reversible). Hence ... | In thermodynamics, we usually specify the demarcation between the system and the surroundings such that all irreversibility occurs within the confines of the system, while the surroundings are taken to be operated reversibly assuming ideal constant temperature reservoirs and mechanical equipment involving conservative ... | https://chemistry.stackexchange.com |
169,339 | [
"https://physics.stackexchange.com/questions/169339",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74961/"
] | For my final year project, I need to design a lab to generate a hysteresis loop. But I have no idea how to do it.
Is there any mathematical function or any code or any article which would help me to generate the shape of the curve?
Can anyone help me with this?
Thank You
| The dose that kills a tumor is deliberately aimed at that tumor. If, instead of using a collimated beam, you put a person in a wide beam for radio "therapy", you would be treating their entire body as a tumor and kill them.
The dose in RT is computed locally - "this" part of the body (these grams of tissue) absorbed (... | Radiographer working in radiation treatment here. (called MTRA in germany)
While I can't offer as much insight from a scientific standpoint I can offer a view from first hand treatment. If you speak about full body dosage it actually means full body dosage. If you reduce the area you can go a good deal over 5 Gy. For ... | https://physics.stackexchange.com |
491,109 | [
"https://physics.stackexchange.com/questions/491109",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/220584/"
] | Any linear function of the density matrix can be related to a proper observable, but is it not the case of entanglement and purity?
| It is not true that entanglement cannot be related to linear observables on the system: An <em>entanglement witness</em> <span class="math-container">$W$</span> is a linear operator such that
whenever the expectation value
<span class="math-container">$$
\mathrm{tr}[W\rho]<0\ ,
$$</span>
the state must be entangle... | One way to interpret your question is that you ask why there is no (linear) measurement which allows to see whether a given state <span class="math-container">$\rho$</span> is mixed, or how mixed it is. This relates both to the purity, and to the entanglement -- <em>if</em> by "entanglement" you mean "identifying if (... | https://physics.stackexchange.com |
138,480 | [
"https://electronics.stackexchange.com/questions/138480",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58264/"
] | It's fairly common now to see desktop computers in cases with large windows cut in the sides. I've always been under the impression that if unshielded, computer equipment will produce a lot of radio frequency interference. Given the ubiquity of cell phones/wireless routers, etc, I can only assume it's not radiating all... | Alongside the theory hopefully someone can confirm this to me
i had to sit for a while and read about how mosfets work, basically get activated by a voltage above 2.5v between Source and gate, this allows the current to flow from Source to Drain
in my circuits, using the PMOS for positive voltage and NMOS for negati... | Replace the PMOS with an NMOS and flip the LED around.
| https://electronics.stackexchange.com |
18,444 | [
"https://mathoverflow.net/questions/18444",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2361/"
] | Consider the structure $\langle HF,\epsilon\rangle$ (the hereditarily finite sets with the epsilon-relation). An ultrapower of this structure will have externally-infinite elements -- elements not generated by a finite number of applications of the (definable) singleton+binary-union operations.
Can anybody give me a ... | As I pointed out in the comments, $(HF,{\in})$ is biinterpretable with $\mathbb{N}$, which means that the corresponding ultrapowers are biinterpretable too. So you will find all you need in the vast literature on nonstandard arithmetic.
A nice interpretation of $(HF,{\in})$ in $\mathbb{N}$ is given by defining $m \in ... | Let me offer a counterpoint to François's informative answer and explain how one also can look upon the nonstandard ∈ relation on pseudo finite sets as very rich indeed.
I claim that every countable model of set theory, including every countable model of full ZFC and every countable model of ZFC + large cardinal... | https://mathoverflow.net |
8,033 | [
"https://chemistry.stackexchange.com/questions/8033",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/-1/"
] | Quite often (from my own experience anyway), one of the safety rules in a school (high school or university) laboratory is that the students must wear leather shoes.
I like to demonstrate some of the safety rules, so my question is, <strong>what is an effective and safe experiment to demonstrate the safety of wearin... | The simplest thing to do is to sacrifice two pairs of shoes, one with leather uppers and the other with canvas/cloth/whatever. Put something inside the shoes to represent "feet". Do something nasty to each pair, like pour concentrated acid over them (using secondary containment to avoid spills and splashes!). Then, ext... | Use directly shoes could be not so practical and reproducible. I will try to find first to figure out which experiment could be more convincing. So why don't take many little piece of leather, cotton and synthetic fiber and make some general test (maybe useful even for clothes). These are what is passing through my mi... | https://chemistry.stackexchange.com |
12,014 | [
"https://electronics.stackexchange.com/questions/12014",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1240/"
] | In a car battery charger, I found a strange rectifier. Can someone explain to me how does it work?
<img src="https://i.stack.imgur.com/VulyL.png" alt="Rectifier">
Here I have a transformer which is unmarked. By measuring resistance between its output terminals, I determined that the plus cable is connected to the cen... | Maybe these illustrations will help:
<img src="https://i.stack.imgur.com/QTyaU.png" alt="Phase 1">
<img src="https://i.stack.imgur.com/IWIY9.png" alt="Phase 2">
Let's assume that the start and end of the primary and secondary windings are such that the 'starts' are at the top of the picture and the 'finishes' are at ... | By center tapping you have just picked a reference that has two different sides that at any one point will oscillate in reference to it.
When the top side goes negative in reference to the center tap it will conduct from the load. The same applies for the bottom side. The number of turns on each side will determine wh... | https://electronics.stackexchange.com |
285,924 | [
"https://softwareengineering.stackexchange.com/questions/285924",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/113632/"
] | As I understand the purpose of DI is that I can easily swap a lower level implementation. But it forces the lower level abstraction to be defined inside the higher level.
A lower level becomes dependent on the abstraction defined in the higher level and can't be used without it. But what if I would ever want to reuse ... | Some time passed and now I think that I can answer myself.
<ol>
<li>There is no sense to make an adapter when two interacting classes are located in the same dll. For such case it makes the code more complicated and difficult for refactoring but does not provide any benefits. If you want to reuse some functionality yo... | You are very confused.
<blockquote>
A lower level becomes dependent on the abstraction defined in the higher level
</blockquote>
No it doesn't. It depends only on the abstraction that it has defined <strong>itself</strong>. For instance, a <code>TaxAuditImpl</code> might depend on the interface <code>TaxAuditor</co... | https://softwareengineering.stackexchange.com |
397,942 | [
"https://stats.stackexchange.com/questions/397942",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/58868/"
] | Everytime that I am making some predictive model and I have missing data I impute categorical variables with something like "UNKNOWN" and numerical variables with some absurd number that will never be seen in practice (even if the variable is unbounded I can take the exponent of the variable and make the unknown values... | One reason you may not want to use "insert impossible value" methods is that means that your predictive model works <strong>conditional on the distribution of the data missingness remaining unchanged</strong>. Thus, if after building your tree model, it is realized that we can start using certain features more often, w... | I disagree. You can use "missing" as an additional set of information, just as anything else. Imputation, in this case, emphasizes the lack of information along some dimension in your sample. That could have additional explanatory power.
The issue is more that "missing" will become a dichotomic variable and mixing it ... | https://stats.stackexchange.com |
10,453 | [
"https://math.stackexchange.com/questions/10453",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/272/"
] | This is a newbie question, but I would be grateful for any reference that you could give.
let $f(x) \in \mathbb{A}$, where $x \in \mathbb{A}$
Is there a symbol to indicate the repeated application of $f$ unto its results, in a manner similar to $\sum$ and $\prod$?
Thank you!
| The symbol $\circ$ is used for composition of functions: $g\circ h(x)$ means $g(h(x))$. For composing a function with itself, many people use $f^{\circ n}(x)$, defined inductively by
\begin{align*}
f^{\circ 1}(x) &= f(x),\\
f^{\circ(k+1)}(x) &= f\Bigl( f^{\circ k}(x)\Bigr).
\end{align*}
So $f^{\circ 2}(x) = f(f... | It is usually indicated by $f\circ f$ or if there are more than two repeated applications, simply $f^n(x)$
| https://math.stackexchange.com |
24,912 | [
"https://physics.stackexchange.com/questions/24912",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3415/"
] | Is there a possible explanation for the apparent equal size of sun and moon or is this a coincidence?
(An explanation can involve something like tide-lock effects or the anthropic principle.)
| It just happens to be a coincidence.
The current popular theory for how the Moon formed was a glancing impact on the Earth, late in the planet buiding process, by a Mars sized object. This caused the break up of the impactor and debris from both the impactor and the proto-Earth was flung into orbit to later coallesce... | Both the moon <em>and</em> the earth's orbits are eccentric, and so the ratio between the sun's and moon's apparent diameter varies with the time of year. When the moon is at perigee, and the earth at aphelion, the moon will seem larger than the sun than when the moon is at apogee and earth at perihelion.
However, the... | https://physics.stackexchange.com |
271,274 | [
"https://mathoverflow.net/questions/271274",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36688/"
] | Assume that we have a vector bundle $E$ over $S^n$.
<blockquote>
Is there a continuous family of invertible linear maps $T_x:E_x \to E_{-x}$?
</blockquote>
Here continuity has the obvious meaning as soon as we have trivialization for the bundle around $x$ and $-x$
There is an obvious affirm... | There is no such family of <em>complex</em> linear maps for the tautological bundle on $\mathbb CP^1$. The antipodal map is orientation reversing, hence the first Chern class changes its sign. The same argument should work for the positive complex spinor bundle on any even-dimensional sphere.
The same argument also wo... | You are asking if a real vector bundle of rank $k$ over $S^n$ is isomorphic to its antipodal image.
If $n$ is odd, the answer is always yes because the antipodal map is homotopic to the identity of $S^n$.
If $k=2$, the answer is easily seen to be yes, because the oriented $2$-bundles are classified by an integer, the E... | https://mathoverflow.net |
216,870 | [
"https://electronics.stackexchange.com/questions/216870",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/84456/"
] | From what I know so far (might be wrong), The ideal or unity power factor means that all the energy is consumed by resistive components and are converted to heat, light, etc. In this case apparent power and real power are equal.
On the other hand, if reactive power exist in the system we have stored energy that is no... | <blockquote>By correcting the power factor less energy is used in the circuit and hence less current is entering the circuit.This would result in lower electricity bill and less power lost since current has decreased</blockquote>
No. Assuming a fixed voltage (very low impedance) supply, like the power grid, low power... | For me correcting/improving power factor is very similar to the counter weight we find in elevators.
Just imagine how difficult it is for the elevator motor to handle the carriage weight without the counter weight.
Now power company is the elevator motor, the carriage is your load and correcting power factor is the ... | https://electronics.stackexchange.com |
78,123 | [
"https://cs.stackexchange.com/questions/78123",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/70743/"
] | I transformed the MNIST dataset as follows:(<strong>X (70000 x 784)</strong> is the <strong>training</strong> matrix)
<pre><code>np.random.seed(42)
def transform_X():
for i in range(len(X[:,1])):
np.random.shuffle(X[i,:])
</code></pre>
I had thought that <strong>shuffling the pixels in an image</strong> w... | I think that the first algorithms running time is actually $\mathcal{O}(x^4)$.
<ul>
<li>The outer for loop executes exactly $x$ times,</li>
<li>the inner for loop executes at most $x$ times during every one of these $x$ iterations of the outer loop</li>
</ul>
In fact, the inner loop executes exactly $\frac{x(x+1)}{2... | Algorithm 2 seems better in running time at first look, Provided that when your body inside loops takes same amount of time in iterations in both of the Algorithms. i.e. If I consider the asymptotic time as quadratic for the body of loop in each iteration for both algorithms, then Algorithm 1 will have O(x^4) time and ... | https://cs.stackexchange.com |
113,577 | [
"https://stats.stackexchange.com/questions/113577",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | I am looking at several dependant variables for which I created LMMs of the following kind:
<pre><code>DV ~ Group + (1|Subject) + (1|Time)
</code></pre>
Now I am struggling with how to interpret the output concerning the random effects, e.g. for DV1:
<pre><code>Random effects:
Groups Name Variance Std.Dev.... | I'd suggest centering the interpretation around intraclass correlations:
<ol>
<li>For DV1, the total random variation not explained by the <code>group</code> differences (the fixed factor) is $\hat\sigma^2_{tot} = 6.2 + 67.7 + 50.2 = 124.1$, so that the total SD is $\hat\sigma_{tot}=11.14$. For DV2, these figures are ... | A few things. First, be careful with the general term "variability." In a general context it is fine, but if you are referring to variance or standard deviation specifically, use the correct term. Also, as per my comment to your statement, remember that these are variances of the distributions of subject- and time-spec... | https://stats.stackexchange.com |
9,572 | [
"https://softwareengineering.stackexchange.com/questions/9572",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/86/"
] | What features are vital for good bug tracking software and why are they important? What in particular is necessary for you to consider these features done right?
| Simplicity.
If it's too complicated or too long to enter or sort bugs, nobody will want to use it.
| Integration with SCM, so that any fixes can be traced back to the code, and code changes can be traced back to an issue. This does require vigilance to check in only code related to the issue being promoted/checked in against. i.e. no "Added feature xyz, and fixed random bugs in 4 different locations and a quick refact... | https://softwareengineering.stackexchange.com |
477,952 | [
"https://electronics.stackexchange.com/questions/477952",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/240855/"
] | I'm thinking of getting an auto transformer and rectify it to make mains isolated 240V 8A DC power supply. I would like to know if its possible to rewind an old microwave transformer to 1:1 isolating transformer with maximum output of 2kW. I know that the waveform wouldn't be smooth so i'll be using beefy 450V 2000uF c... | The following is largely complementary to Dave Tweed's answer
<ul>
<li>The welds are generally along the surface and can be removed with an angle grinder "fairly easily". The laminations can be rebuilt using a clamp to hold the core together. Epoxy helps prevent lamination chatter but DO NOT introduce any additional a... | Possible, but not easy to rewind, because microwave oven transformers are welded shut.
a 1KVA transformer can be used as an autotransformer to step 120V 16A up to 240V 8A.
but then you say "isolated" - an autotransformer won't make isolated power.
and you say "240V DC" , you don't make 240V DC from 240V AC.
So, t... | https://electronics.stackexchange.com |
29,237 | [
"https://cstheory.stackexchange.com/questions/29237",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/282/"
] | I'm looking for a good reference, possibly a survey, on the different types of cryptography methods. As far as I understand, the security of a cryptographic method depends on some hardness assumptions, and I've heard of methods based on the hardness of factorization, discrete logarithm, NP-complete problems (such as th... | A good start would be Katz and Lindell's <i>Introduction to Modern Cryptography</i>.
Alternatively, you might want to take one of the crypto courses on Coursera: I recommend the ones taught by Jonathan Katz and by Dan Boneh (search for "cryptography" on Coursera). They are both free.
| You might like to look at Bernstein, Buchmann, Dahmen (editors): <em>Post-Quantum Cryptography</em>. The idea of the book is to study what will be available when current methods will become insecure. The book arose via a discussion at an IPAM/UCLA workshop.
| https://cstheory.stackexchange.com |
165,823 | [
"https://physics.stackexchange.com/questions/165823",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57434/"
] | For something to be a blackhole, it must have gravity and the radius must be smaller than the schwarzschild radius for its mass.
-Electrons have gravity
-Electron are theoretically believed to be infinitely small points
Since it has gravity it is capable of being a black hole. Since its radius is infinitely small, i... | There is no universally accepted quantum theory of gravity.
Quantumly, the "shape" of a fundamental particle is a very fuzzy notion - we know that states are often not localized, so it is wholly unclear what it means to say "the electron is pointlike". The proper formal interpretation of a "pointlike particle" is simp... | Electrons are very close to the energy of self-capacitance of a quantum of charge.
The size of the electron is very close to $r_e$, the energy supposed if one tries to charge a sphere of that radius with a single electronic charge, ie $mc^2 = e^2/4\pi\epsilon r_e$.
| https://physics.stackexchange.com |
144,913 | [
"https://softwareengineering.stackexchange.com/questions/144913",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3382/"
] | Ok, I've been teaching a buddy how to program for a while now. He's a very fast learner, and he's quite good at programming so far. However, he has one "issue" I keep trying to correct.
He jumps in and starts doing highlevel programming without learning some of the basics (He's created a full blown web application but... | Personally, I think it can be a great idea to sample different technologies and languages when learning to program. Focusing on one technology has the obvious benefit of making you very good at it, but the obvious downside of only knowing a single technology.
But I think the more important subtler downside is that lan... | There is good reasoning on both sides of this issue. Knowing "<em>enough</em>" about a lot of different technologies is certainly valuable. Knowing "<em>a little</em>" about a lot of different technologies? Not so much.
<em>Deep knowledge</em> of particular technologies can certainly be valuable - IF there's ongoin... | https://softwareengineering.stackexchange.com |
214,849 | [
"https://physics.stackexchange.com/questions/214849",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96757/"
] | I am trying to model the equation ruling the simple movement of a ball inside a circle structure (think of a 2D pendulum with no gravity looping on and on).
I assume the following equation of the movement:
$\theta(t) = c + b t + a t^2$ where $\theta(t)$ is the angle at time $t$. ($a,b,c$ are constant)
After some ca... | This is a bizarre question.
Newton's laws <strong>do</strong> include internal forces. However, Newton's third law happens to <em>cancel out their overall effect on a center of mass</em>. But, if you want to understand the motions of the constituent parts of the system, then you <em>do</em> have to understand their in... | I'm just going to give a couple of examples: cases where it is obvious the internal forces change the kinetic energy state of the whole system.
<hr>
<ul>
<li>Consider a system of two masses resting on a frictionless, horizontal surface with a light spring held between them but not connected to either mass. If the ini... | https://physics.stackexchange.com |
144,939 | [
"https://softwareengineering.stackexchange.com/questions/144939",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41038/"
] | We are building a Windows Mobile based application to interface with a customer's existing web application. We are reading and writing data to the customer's SQL server 2008 database.
The customer wants all reads to happen through SQL views, and all writes to happen through stored procedures.
But taking a look at the... | Its actually a pretty good design. Using views confers the following advantages:-
<ul>
<li>It insulates your application from any changes in the underlying physical tables.</li>
<li>A view can be regarded as the formal interface specification between client and server.</li>
<li>The view allows fine grained access cont... | While accessing the data through a view layer is a good idea, a separate view for every query is inevitably going to mean that you are going to repeat yourself quite a bit. Inevitably, there are going to be business rules that are going to be common across many views (i.e. whatever filters you need for an entity to ap... | https://softwareengineering.stackexchange.com |
736,270 | [
"https://math.stackexchange.com/questions/736270",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/136509/"
] | I'm having problem in getting the proof from Gallian text <em>in the higlighted region</em>:
<img src="https://i.stack.imgur.com/3z1Jr.png" alt="enter image description here" /><img src="https://i.stack.imgur.com/iX6Yh.png" alt="enter image description here" />
<blockquote>
Shouldn't the yellow marked <span class="math... | If all the letters denoted indeterminates, then you can easily feed the system into Macaulay2, for example.
It will then turn out that the ideal generated by the polynomials $f_i$ is $9$-dimensional, so there are certainly many (possibly complex) solutions. In particular, $0$ is in the solution set, so you always have... | This is probably doable without any software. Start by substituting the variables that you know are $0$. Then you've also got a bunch of equations of the form $xy = 0$; make case distinctions $x = 0$, $y = 0$ and see what you wind up with. It wouldn't surprise me if what remains (in each of the many cases) is easy enou... | https://math.stackexchange.com |
81,151 | [
"https://stats.stackexchange.com/questions/81151",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31420/"
] | Let $X$ and $Y$ be two independent random variables with respective pdfs:
$$f \left(x;\theta_i \right) =\begin{cases} \frac{1}{\theta_i} e^{-x/ {\theta_i}} \quad 0<x<\infty, 0<\theta_i< \infty \\ 0 \quad \text{elsewhere} \end{cases} $$
for $i=1,2$. Two indepedent samples are drawn in order to test $H_0: \... | If memory serves, it appears you have forgotten something in your LR statistic.
The likelihood function under the null is
$$L_{H_0} = \theta^{-n_1-n_2}\cdot \exp\left\{-\theta^{-1}\left(\sum x_i+\sum y_i\right)\right\}$$
and the MLE is
$$\hat \theta_0 = \frac {\sum x_i+\sum y_i}{n_1+n_2} = w_1\bar x +w_2 \bar y, ... | The likelihood function given the sample <span class="math-container">$\mathbf x=(x_1,\ldots,x_{n_1},y_1,\ldots,y_{n_2})$</span> is given by
<span class="math-container">\begin{align}
L(\theta_1,\theta_2)&=\frac{1}{\theta_1^{n_1}\theta_2^{n_2}}\,\exp\left[-\frac{1}{\theta_1}\sum_{i=1}^{n_1} x_i-\frac{1}{\theta_2}\s... | https://stats.stackexchange.com |
3,933 | [
"https://physics.stackexchange.com/questions/3933",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/104/"
] | In our Physics lab we have a 1 milliwatt (0.001W) helium neon laser. Despite the low power, we were cautioned not to even look at reflections of the beam as it could cause permanent eye damage - why is such a low power level hazardous? I have a 3W LED which I can look directly into which is more than 3,000x more powerf... | Dear Thomas, the diameter of the beams of these HeNe lasers is between 0.5 and 1 millimeter, so the power 1 mW is coming to $10^{-6}$ squared meters or so. The ratio of power and area is $10^{-3}/10^{-6} = 10^{+3}$ Watts per squared meter.
On the other hand, when a 3W LED is watched from the distance 0.1 meters, the p... | Because the light from the laser is collimated. This means that you have all this energy focused on a small spot. The larger power from a non collimated light source is spatially spread and the effective amount of energy that reaches your retina per time is much smaller.
| https://physics.stackexchange.com |
18,104 | [
"https://cs.stackexchange.com/questions/18104",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/5066/"
] | I need to implement TSP algorithm by brute force for learning purposes.
I've understood there's a set of cities, let's call it <strong><em><code>V</code></em></strong> and it's possible to get a matrix representation for the costs for going from a <strong><em><code>v1</code></em></strong> city to a <strong><em><code>v... | D. W. computes for each node $v \in S$ the number of paths $n(v)$ from $v$ to $t$. Using this information, it is easy to decode a number in the range $[0,n(s))$ to a unique path from $s$ to $t$ in $S$ (and so in the original graph). More generally, at each node $v$ we will come up with a procedure to map $[0,n(v))$ to ... | The answer is yes, if you'll grant me some reasonable assumptions.
Generate a random seed (uniformly at random), then use a cryptographically secure pseudorandom generator to stretch it to an arbitrarily long sequence of pseudorandom bits. Under reasonable cryptographic assumptions, that pseudorandom sequence will be... | https://cs.stackexchange.com |
536,596 | [
"https://physics.stackexchange.com/questions/536596",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | In Quantum Mechanics, 2nd Edition by Davies & Betts on page 78 it states that there is a symmetry implied by the following Hermitian operator equation:
<span class="math-container">$${\displaystyle \int \phi^{*}(A \psi)d \,\tau} = {\displaystyle \int \psi(A \phi)^{*}d \,\tau} \tag{1}$$</span>
in the way the Herm... | The notation here seems to have gone seriously awry. As taught to me at Cambridge by the students of Dirac, kets are vectors and bras are vectors in the dual space. I have never seen anyone write an operator inside a ket or a bra. That would not make sense as the symbol inside the ket is a label not a vector. E.g. one ... | I will neglect all rigorous description and just provide the usual physics arguments. Let <span class="math-container">$A$</span> be a quantum operator and <span class="math-container">$\psi,\phi$</span> arbitrary wave functions. Then using the inner product of the underlying Hilbert space <span class="math-container">... | https://physics.stackexchange.com |
155,695 | [
"https://electronics.stackexchange.com/questions/155695",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35366/"
] | Sensors need to be calibrated every so often, so that the voltage/current change due to the change in the conductance is always the same, and the signal conditioning of that voltage/current is always gives the same output for the same input. i.e, it needs to be calibrated to remove gain and offset error that occur over... | Here's the LTspice sim, edited a little so you can see what's going on without running the code:
<img src="https://i.stack.imgur.com/Gm3IN.png" alt="enter image description here">
<img src="https://i.stack.imgur.com/GxPZX.png" alt="enter image description here">
and here's the code:
<pre><code>Version 4
SHEET 1 2680... | Real diodes will allow some small leakage current even before they're 'properly' forward-biased.<br>
This leakage current is apparently enough to turn your transistor on.<br>
The 330 ohm resistor shunts this leakage to ground and so keeps the transistor off until you have a high enough voltage to properly forward-bias ... | https://electronics.stackexchange.com |
34,316 | [
"https://mathoverflow.net/questions/34316",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1587/"
] | OK, the title is opinionated and contentious, but I have a definite
question. I know that the title refers to the Bourbaki volume
<em>Groupes et Algèbres de Lie</em> (Chapters 4-6), published in 1968, but
<blockquote>
who said that it is the only great book that Bourbaki ever wrote?
</blockquote>
The only reference... | Google found this:<br>
Notices of the AMS, September 1998, p. 979:<br>
Bill Casselman's review of POLYHEDRA by Cromwell,<br>
we find the phrase "the one great book by Bourbaki"
| I've heard this sentence (almost literally, if I remember correctly) in 1980 from Vladimir Drinfeld.
He added: his other books you buy and put on the shelf. This one you can really use.
Remark.
But other people had different opinions. Some use Topological vector spaces.
I used Functions of the real variable and Integr... | https://mathoverflow.net |
319,221 | [
"https://dba.stackexchange.com/questions/319221",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/263506/"
] | I'm log shipping from SERVER_A with backups every 10 minutes.
I restore the logs to SERVER_B every 20 minutes.
I pause the restores while I do a DWH load from SERVER_B into SERVER_C
I report out of SERVER_B, and I want to know the time the backup was taken on SERVER_A so that I can show the users how fresh the data is ... | You don't need to rely on backup history: you can just check the restore history! In addition to having backup history, <code>msdb</code> also saves the restore history.
Here's a sample query you might use to find the data freshness, based on most recent backup to be restored.
<pre><code>SELECT TOP 5
RestoredDbName... | As the other answer states, restore history is probably the best approach, however, to offer an alternative, another approach I have seen used in the past is to query some high traffic transactional table which has a datestamp for its most recent timestamp value. This doesn't require any permissions outside of the data... | https://dba.stackexchange.com |
18,515 | [
"https://cs.stackexchange.com/questions/18515",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11747/"
] | I need to modify the Dijkstra's algorithm to get the shortest path in a directed graph and get the one with the least amount of edges if there are equal paths.
I am thinking to add another data field to count the number of edges from start and compare them in same way as weights. Would that work?
| Yes, it should. You can simply keep a count of edges traveled. If you discover a new shortest path which is of the same distance as the last shortest path, make an if statement asking whether or not the new path has less number of edges. Here is a short pseudo code that you can use in the "relaxation" part of algorithm... | If you want a simpler answer and want to minimize space cost, you can simply add .00000001 (or some other extremely small fraction that is small enough that it will not significantly affect the weights of the paths and thus will not alter the overall result of running Dijkstra's) to every edge. This way, a path of size... | https://cs.stackexchange.com |
1,458,636 | [
"https://math.stackexchange.com/questions/1458636",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/219373/"
] | So I'm aware that I can solve simple summations like:
$\sum_{i=1}^{5} (2)/(i(i+2)$
By just pluging in i = 1 to 5 and summing up the values,
but how would I go about approaching something like this?
$\sum_{i=1}^{100} (2)/(i(i+2))$
Or if the numerator changed to a 3 (as well as a denominator), would it be the same proc... | Actually, partial fractions work just fine:
$$\begin{align*}
\sum_{k=1}^{100}\frac2{k(k+2)}&=\sum_{k=1}^{100}\left(\frac1k-\frac1{k+2}\right)\\
&=\sum_{k=1}^{100}\frac1k-\sum_{k=1}^{100}\frac1{k+2}\\
&=\sum_{k=1}^{100}\frac1k-\sum_{k=3}^{102}\frac1k\\
&=\frac11+\frac12-\frac1{101}-\frac1{102}\;,
\end{a... | <strong>Hint:</strong> $\dfrac{1}{i(i+1)} = \dfrac1i-\dfrac1{i+1}$
| https://math.stackexchange.com |
146,961 | [
"https://softwareengineering.stackexchange.com/questions/146961",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/37580/"
] | Meaning that OOP allows me to have data-trees, of arbitrary depth and breadth, with some leafs being functions (and those leafs would be called methods) ?
Because everything else that people often put near "OOP" mark, just don't seem to have anything to do with it. (Inheritance, subtype polymorphism and encapsulatio... | <blockquote>
Is it fair to reduce OOP to mere hierarchical composition of data structures?
Meaning that OOP allows me to have data-trees, of arbitrary depth and breadth, with some leafs being functions (and those leafs would be called methods) ?
</blockquote>
I guess you can choose to look at it that way, but I do... | You're missing something. Probably several somethings, in fact.
Objects are a powerful means of abstraction. They don't just organize data, they organize code. You could argue that that abstraction isn't necessary, that you could produce equivalent code using purely procedural techniques, but that'd be like arguing th... | https://softwareengineering.stackexchange.com |
6,476 | [
"https://dsp.stackexchange.com/questions/6476",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/473/"
] | I encountered a problem when I tried to generate by a program an sinus audio signal.
My parameters are
Sample Rate: 44100 Hz
Data Bits: 16 bits
Channels: 2
I need to create a WAV file that is generated on the fly in and play in real time directly to a audio out port.
There are two more requirements. I ne... | It seems to me that your phase accumulator gets reset at the beginning of each chunk/buffer. When the waveform exactly goes through an integer number of periods over the duration of a buffer, there is no discontinuity, but if a buffer contains a non-integer number of periods, then a discontinuity will appear at each bu... | As pointed by the other people you most likely have a frame boundary error. Let me suggest a different approach outlined in the code below. This is based on creating a oscillator using complex multiplication. In order to prevent amplitude drift there is a "stabilization" function that needs to be called every once in a... | https://dsp.stackexchange.com |
329,663 | [
"https://softwareengineering.stackexchange.com/questions/329663",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/218080/"
] | New to the field of QA, I've been asked to do SQA for a project that I'm unfamiliar with and that is close to completion. An example of a specific functional task to be tested looks like the following:
<blockquote>
51: Rename Excluded Words at the Topic and Subtopic levels to be Not in Topic and Not in SubTopic
</bl... | If you don't know an application or a feature in an application well enough to basically use it, you need to learn this first, that is an obvious prerequisite of any testing. There are two ways to do this: RTFM, or let someone explain it to you (both ways not mutual exclusive). The person who explains it to you might b... | In my sense, the best way to get an application tested, is to put someone who doesn't know the project at all; especially how it works. Here some points for why:
<ul>
<li>If the project has a user guide/manual, just following that in order to help you to do all of the tasks asked. This will show that the manual is/n't... | https://softwareengineering.stackexchange.com |
352,016 | [
"https://physics.stackexchange.com/questions/352016",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I know that the general equation of motion for a two body problem under gravity is usually an ellipse.
$$r(\theta) = \frac{R}{1-e\cos(\theta-\theta_0)}$$ where $R$ and $e$ depend on initial conditions.
But surely there is some way of changing the initial conditions so that an object spirals into the source of gravity... | Let's think about the total energy of a particle moving in a plane under a $1/r$ potential. Its potential energy is $-GMm/r$; and its kinetic energy is
$$
T = \frac{1}{2} m \left[ \left( \frac{dr}{dt} \right)^2 + r^2 \left( \frac{d \theta}{dt} \right)^2 \right].
$$
Thus, the total energy is
$$
E = \frac{1}{2} m \lef... | An orbit must simultaneously conserve angular momentum and total energy (KE + PE). These two requirement restrict orbits in a $1/r$ potential to be conic sections and there is no way an orbit can spiral towards $r=0$ regardless of the initial conditions.
| https://physics.stackexchange.com |
11,893 | [
"https://cs.stackexchange.com/questions/11893",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/147/"
] | I often hear phrases like 'true concurrency semantics' and 'true concurrency equivalences' without any references. What does those terms mean and why are they important?
What are some examples of true concurrency equivalences and what is the need for them? E.g. in which cases they are more applicable than more standar... | The term "true concurrency" arises in the theoretical study of concurrent and parallel computation. It is in contrast to interleaving concurrency. True concurrency is concurrency that cannot be reduced to interleaving. Concurrency is interleaved if at each step in the computation, only one atomic computing action (e.g.... | To say the truth, I was googling for an answer myself.
What is the semantics here? We assign a meaning "transition system" to the description "process algebra"; i.e. meaning is the transition system that is generated from the initial system description using defined SOS rules. Thus, using interleaving semantics, we los... | https://cs.stackexchange.com |
319,989 | [
"https://stats.stackexchange.com/questions/319989",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/189216/"
] | There is one remark in my lecture notes:
if $X$ (data) is a discrete distribution then one cannot use an improper prior.
Can anyone prove it?
| The reason for not being able to use an improper prior in the case of a finite distribution is that, if the distribution $p_\theta$ of $X$ has support in $\{a_1,\ldots,a_N\}$, then the posterior$$\pi(\theta|x)=\pi(\theta)p_\theta(x)\big/ m(x)$$is not defined as
$$m(x)=\int p_\theta(x)\pi(\theta)\text{d}\theta$$cannot b... | Just a pointer about the $Beta(0,0)$ prior. If $X\sim Binomial(n,p)$, with $n\geq 2$ fixed, then the $Beta(0,0)$ prior for $p$, pointed out by @marmle and which is independent of the sample (opposite to what @Xi'an says), leads to a proper posterior distribution only if $y\neq 0, n$. That is, this is an improper prior ... | https://stats.stackexchange.com |
42,261 | [
"https://electronics.stackexchange.com/questions/42261",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11912/"
] | I have a Verilog gate-level netlist generated by the Synopsys Design Compiler.
DC was directed to flatten all busses and ports when creating the netlist, and the module declaration is given below:
<pre><code>module DES_SBOX1 ( CLK, \ptext[5] , \ptext[4] , \ptext[3] , \ptext[2] ,
\ptext[1] , \ptext[0] , \key[5] , \... | You are running into Verilog's <em>escaped identifiers</em> gotcha. From the IEEE standard reference:
<blockquote>
§2.7.1 Escaped identifiers
Escaped identifiers shall start with the backslash character () and
end with white space (space, tab, newline). They provide a means of
including any of the printable ASCII char... | Wow, I've never seen a netlist with port names escaped like that. I supposed it's because they have <code>[]</code> as part of the port name.
Try dropping the port names from the port connection list. That is, use the positional mapping instead of connecting by name. Normally this would be discouraged because "by na... | https://electronics.stackexchange.com |
21,944 | [
"https://stats.stackexchange.com/questions/21944",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8836/"
] | I would like to compute belief intervals (confidence intervals; CI) for the parameters of an environmental dynamic model within the Bayes' theorem. The measurement model of the data is
$$
d(t)=y(\theta,t)+\epsilon,
$$
where $\epsilon$~Norm(0, $\sigma$) is the assumed measurement error, $y$ is the dynamic system outpu... | Thanks for a long and frank explanation of your worries! Having non-normal errors is not an issue if you incorporate the true distribution of the errors in your Bayesian calculation. If you mis-specify and use another family of distributions than the "true" one, you have to assess the impact of this error either analyt... | I think one needs to distingish between measurement uncertainty and the variability of the process generating the data. For instance convective rainfall can be modelled as having a gamma distribution for the amount that it rains (when it does rain). This uncertainty has nothing to do with the measurements of any quan... | https://stats.stackexchange.com |
43,008 | [
"https://cs.stackexchange.com/questions/43008",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/34064/"
] | I am new to CFG's, Can someone give me tips in creating CFG that generates some language
For example
$L =\{ w v w^R \mid v,w\in \{a,b\}^*\wedge|v| \text{ is even } \}$, where $w^R$ is the reverse of
string $w$.
I'm having trouble understanding the language .. I want to build DFA to convert it
| Mmmm.
Let me note that in fact $L =\{ w v w^R \mid v,w\in \{a,b\}^*\wedge|v| \text{ is even } \}$ equals $\{ v \mid v \in \{a,b\}^*\wedge|v| \text{ is even } \}$.
Al strings in $L$ are of even length, and conversely all strings of even length can be otained by taking $w=\varepsilon$.
That should help.
| Hints:
<ol>
<li>Construct a non-terminal $V$ and appropriate productions so that $V$ generates all strings of even length.</li>
<li>Create productions so that your starting symbol $S$ generates $wVw^R$ for all $w$. To accomplish that, modify a grammar for $ww^R$.</li>
</ol>
| https://cs.stackexchange.com |
204,739 | [
"https://softwareengineering.stackexchange.com/questions/204739",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/96586/"
] | I jumped in to a project and I see that the other developers are adding a lot of logic in the setters of synthesized properties.
I understand how this works, but I think that it makes it hard to understand the flow of the program; while reading the code, whenever I see <code>self.something = whatever</code>, I always c... | <blockquote>
Is it considered a bad practice to add logic in a property setter?
</blockquote>
<strong>No</strong>
Properties were invented to allow class designers to have logic attached to a convenient interface of field access and assignment.
How much is too much? It depends on the responsibilities of the clas... | Setters are typically used to change the state of an object with no significant side effects or heavy calculations;use methods and functions for that. The primary reason for setter implementation is <strong>changing and maintaining a valid state</strong>. So, limiting range, setting flags to request recalculation, or a... | https://softwareengineering.stackexchange.com |
338,900 | [
"https://stats.stackexchange.com/questions/338900",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/181565/"
] | I have the following problem: in year A, we observe that a company sold N_A of its product, in year B, we observe that the company sold N_B of its products. How do I do hypothesis testing that the company sold statistically different number of products in year A and B?
My thought is that
<pre><code> N_A ~ Poisso... | By using the Poisson distribution, we get that the "noise" in the measurements is proportional to the square root of the expected value. This is a pretty major assumption.
The expected value of the difference of two i.i.d. random variables are zero and the variance of the difference is twice the variance of one of the... | Statistical testing is meaningless here as you have no measure of variability. All you have is just two data points, one for company A and for company B.
| https://stats.stackexchange.com |
149,195 | [
"https://cs.stackexchange.com/questions/149195",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/147443/"
] | <blockquote>
In Programming there is different data types (int , cahr , bool ,
float ) and they have different sizes (1,2,4,8 .. Bytes) , and the
size of data type are depends upon hardware or architecture of
computer or any thing else? as a beginner give me answer in simple language plz !
</blockquote>
| C is fastest because there is nothing <em>preventing</em> it from being the fastest.
A CPU always runs machine language. When writing a "fast" program, your goal is to give the CPU the fastest machine language to accomplish the task.
In C, it is usually possible to write something that translates into fast ma... | The OS has virtually nothing to do with the relative performance of languages on benchmarks. You wrote
<blockquote>
“your code —(system calls) —> the OS —(instruction set) —> the hardware”
</blockquote>
suggesting you think that the OS acts as a sort of translation layer between user-mode code and the CPU, but in... | https://cs.stackexchange.com |
7,730 | [
"https://mechanics.stackexchange.com/questions/7730",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4019/"
] | I have a manual 1982 diesel VW Vanagon with a 1996 Passat TDI engine in it.
This morning (low 40s temp), accelerating up a hill, heard a hissing sound in left rear. Check tires, no problems. Able to start back up, change gears, but bad forward lurches past 15mph or so and can't get it going above 20-25mph.
I did ... | I would not think that the brake work is the problem but if you think there is a real possibility that it is, the let the person who done the repair work check it out. The engines performance depends on air, fuel, and mechanical condition all being present and correct. Any unsual or heavy noises from the engine? Check ... | It sounds as if there are bubbles in the fuel. Check for bubbles in the fuel prefilter located between the tank and the pump.
This is a common occurance when the van has been fitted (possibly by a previous owner) with a replacement fuel tank that are built (internally) with a smaller diameter metal "pick-up" tube that... | https://mechanics.stackexchange.com |
133,730 | [
"https://mathoverflow.net/questions/133730",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18256/"
] | This is maybe not really research level, but I have not found anything in the literature, and asking on math.stackexchange wasn't successful either.
Fourier series define an isometry $L^2(\mathbb{Z}) \rightarrow L^2(S^1), (a_k)_{k \in \mathbb{Z}} \mapsto \sum a_k z^k \colon S^1 \rightarrow \mathbb{C}$ (all Hilbert spa... | Maybe you are already aware of the following if-and-only-if condition, though I wouldn't say it counts as "easily checkable": let $(a_k)$ be the coefficient sequence, let $s_N$ denote the partial sums
$$
s_N(z) = \sum_{k=-N}^N a_k z^k
$$
and let $\sigma_N(z)$ denote the Cesaro means
$$
\sigma_N(z)=\frac{1}{N+1}\sum_{... | This is really a glorified comment, but the formatting in answer boxes is easier (and I think the information deserves greater visibility). Apologies to the OP if he already knew this.
From Katznelson's introduction to Harmonic Analysis (the Dover version, 2nd corrected edition). Everything takes place on the circle <s... | https://mathoverflow.net |
2,106,866 | [
"https://math.stackexchange.com/questions/2106866",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/346682/"
] | Surely a $1\times 1$ matrix can only 'produce' vectors with 1 entry, and can take as input also only one entry vectors.
So, is there any use for $1\times 1$ matrices?
Since to me they do the same like scalars, only worse.
| What is the use of the number zero? It doesn't do anything when you add it, and it always does the same thing when you multiply it.
| Maybe the point of $1\times 1$ matrices is to not have to change the definition of matrix to exclude the $1\times 1$ case.
| https://math.stackexchange.com |
496,031 | [
"https://physics.stackexchange.com/questions/496031",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4271/"
] | I'm confused with pressure and condensation of a gas inside a sealed container. Say I boil a liquid to it's gaseous state inside a sealed container and exert more pressure on that container then should the gas not turn back into a liquid?
For instance on Mount Everest the atmospheric pressure is 5psi and water boils ... | Water vapor is not an ideal gas. Due to this, when you compress it instantly, you do work on it, and the temperature of the water vapor rises. Instant compression is adiabatic compression, and without heat transfer to the environment, you will not be able to transfer the heat necessary for condensation to occur.
| Assume that only vapour (and no air) is inside your container and that the temperature is kept fixed. When you use a piston to decrease the volume, and so increase the pressure until it reaches the vapour pressure, then a <em>small</em> amount of the liquid will condense and lower the pressure until it is again at th... | https://physics.stackexchange.com |
97,682 | [
"https://mathoverflow.net/questions/97682",
"https://mathoverflow.net",
"https://mathoverflow.net/users/344/"
] | Let $M$ be a $\pi_*(MU)$-module. The Landweber exact functor theorem gives conditions for the functor that sends a space $X$ to $ MU(X) \otimes_{\pi_*(MU)} M$ to define a homology theory on spaces, which thus comes from a spectrum.
It'd be nice, though, if one could construct the spectrum directly, instead of going t... | Here are three methods that I know:
<ul>
<li>In the case $M_*=(MU_*/I)[S^{-1}]$ (where $I$ is generated by a regular sequence) there is a more direct construction by reducing to the cases $M_*=MU_*/a$ and $M_*=MU_*[a^{-1}]$. My paper 'Products on MU-modules' is probably the sharpest version, but there are many earlie... | I'm not sure that this is exactly what you are looking for, but I looked a bit
at the Landweber exact functor theorem in the context of $MU$-modules
at the end of a very short paper: Idempotents and Landweber exactness in
brave new algebra. Homology, homotopy, and applications 3(2001), 355--359.
Theorem 8 there reads:... | https://mathoverflow.net |
192,930 | [
"https://physics.stackexchange.com/questions/192930",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85279/"
] | In a container the pressure on the walls due to a gas can be calculated using the ideal gas law $\bigl(pV=NRT\bigr)$. However, for a column of water, or the pressure at earth's surface due to a column of air, the pressure can be calculated as $P=F/A=\rho gh$.
When does one use which model or is it two completely diff... | Are you interested in the relative pressure difference between two points or the absolute pressure?
<blockquote>
In a container the pressure on the walls due to a gas can be calculated using the ideal gas law (pV=NRT). However, for a column of water, or the pressure at earth's surface due to a column of air, the pre... | Here it is an incomplete answer, but just to think about some issues.
An ideal gas is assumed to have particles non-interacting and with no extension (point-like particles). In particular for an ideal gas you discard gravity. While the Stevin's law (the relation $\rho g h$) is a direct consequence of the fact that you... | https://physics.stackexchange.com |
82,096 | [
"https://stats.stackexchange.com/questions/82096",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | This is in the context of two random variables. A frequent assumption (e.g. of the error term in ANOVA) is of independent and identically distributed random variables. There is a question on this site asking how the assumption can be checked in a given dataset. Is it an assumption or a fact?
| In practice being independent and identically distributed is an assumption; it may sometimes be a good approximation, but it's next to impossible to demonstrate that it actually holds.
Generally, the best you can do is show that it doesn't fail too badly.
This is what diagnostics, and to some extent hypothesis tests... | Just to add to the discussion, this is mostly an assumption that simplifies the mathematics of inference.
To take a concrete example, I am in the field of image processing and usually most algorithms will assume that the noise in the image is IID. This is hardly ever the case because most of the time we do some pre pr... | https://stats.stackexchange.com |
687,632 | [
"https://physics.stackexchange.com/questions/687632",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266050/"
] | The wavefunction or the abstract ket vector <span class="math-container">$|\psi\rangle$</span> contains <em>all</em> the information about the state of the system.
Before giving more context I word my question as follows, does the information (the most we can have) contained in <span class="math-container">$|\psi\rangl... | <blockquote>
If I were just given <span class="math-container">$|\psi\rangle$</span> I would not know whether the system is (1) or (2). So it seems that <span class="math-container">$|\psi\rangle$</span> does not contain any information that differentiates between (1) and (2).
</blockquote>
The expression
<span class="... | <span class="math-container">$|\psi\rangle$</span> is an element of some Hilbert space and part of defining that Hilbert space is specifying what physical system it describes the states of, so yes the state <span class="math-container">$|\psi\rangle$</span> does contain information about what physical system it describ... | https://physics.stackexchange.com |
147,048 | [
"https://dba.stackexchange.com/questions/147048",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/66032/"
] | We have a table where we are planning to update timestamp fields only.
In the first import these columns will be nulls then we will update them as the computation finished on these rows.
The question is; should we set a fill-factor lower than 100 for this table or PostgreSQL will allocate a fixed size for these colum... | Agree with Scott Hodgin, you essentially want to consider <em>MAX(FormIdNb)</em> instead of just <em>FormIdNb</em>, and count the results based on whether the MAX result is greater than, equal to or less than 3.
Adding a correlated subquery to the joining condition, as Scott is suggesting, would be one way.
Another w... | Perhaps, I'm missing something, but it sounds like to want the max(formidnb) for each NumCavalier in the time slice you're processing. I haven't fully syntax checked this, but I think you could add the following to just above your semicolon
<pre><code>AND d.FormIdNb =
(
select MAX(FormIdNb)
FROM #tmp_DailyMissions
... | https://dba.stackexchange.com |
222,828 | [
"https://electronics.stackexchange.com/questions/222828",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/103694/"
] | I recently took on the job of working on someone's amplifier. There was a burnt smell coming from it. I found the pieces of the puzzle that were fried and replaced the ones I could, two diodes and two resistors. There's a third resistor, however, that was completely blackened. I can't read the color code so I can't tel... | 1) LED lifetime is related to thermal, the higher the temperature the shorter the life. Make your LED's happy by giving them less current and/or cool them off.
2) If your worried about voltage spikes, then find a zener diode and clamp the voltage across C4. Make sure the zener is going to be able to handle the spike a... | R1 is limiting the surge current .R1 sees high peak power at switch on and must be rated for this .Wire wound resistors are better than metal film when it comes to surge rating .Surge currents will blow this thing up .Your caps are not bled .This means that a rapid turn off and switch on will give you up... | https://electronics.stackexchange.com |
79,174 | [
"https://mathoverflow.net/questions/79174",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18805/"
] | The induction schema of Peano Arithmetic is standardly given as the universal closure of $\phi(0)\land \forall x (\phi(x)\rightarrow \phi(x+1)) \rightarrow \forall x\phi(x)$. However, since the language of arithmetic has a name for every standard number, it is not obvious (to a beginner like me) why parameters are nec... | The two theories are equivalent. To see this, let's assume that we have the parameter-free induction, and suppose that $\phi(x,y)$ is a formula with two free variables. Suppose we have a model $M$, satisfying the parameter-free induction, and there is a $b\in M$ such that $\phi(x,b)$ obeys the hypothesis of the inducti... | $\def\fii{\varphi}$While the other answers resolve the question, a simple way of deriving induction for a formula $\fii(x,\vec p)$ with parameters $\vec p$ is to use parameter-free induction on the formula
$$\psi(x)=\forall\vec p\,[\fii(0,\vec p)\land\forall y\,(\fii(y,\vec p)\to\fii(y+1,\vec p))\to\fii(x,\vec p)].$$
... | https://mathoverflow.net |
5,353 | [
"https://physics.stackexchange.com/questions/5353",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/72/"
] | In one dimension -
How can one prove that the Hamiltonian and the parity operator commute in the case where the potential is symmetric (an even function)?
i.e. that $[H, P] = 0$ for $V(x)=V(-x)$
| You prove the equality of operators by applying them to a function, we have
$$
H = - \frac{\hbar^2}{2 m} \frac{d^2}{dx^2} + V(x)
$$
Ergo:
$$
HP f(x) = H f(-x) = (- \frac{\hbar^2}{2 m} \frac{d^2}{dx^2} + V(x)) f(-x) = - \frac{\hbar^2}{2 m} f''(-x) + V(x) f(-x)
$$
and
$$
PH f(x) = P (- \frac{\hbar^2}{2 m} ... | $$[P,H]f(x)=(PH-Hp)f(x)$$
But
$$H=P^2/2m+E(x)$$
$$ =PE(x)-Hf(x)$$
$$ =E(-x)-E(-x)$$
$$ =0 $$
The parity operator therefore commutes with Hamiltonian.
| https://physics.stackexchange.com |
13,849 | [
"https://security.stackexchange.com/questions/13849",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4386/"
] | I hope this question falls within the scope of the faq...I'm curious to see what kind of answers I get.
Suppose the following
<ul>
<li>A user is posting libel and slander on social media (lets say Twitter for example). The posts may be misleading, propaganda or just downright lying</li>
<li>A user has suspicions and ... | I don't see the quoted instruction on that Apple KB article; the closest I see is:
<blockquote>After completing a task as the root user, you should log out of Mac OS X and log back in using a normal or administrator account. You should disable root access if you do not use it often.</blockquote>
Which seems (to me) l... | IMHO there is no practical reason for having the root account enabled
<ul>
<li>At the command line, if you need extra powers you are supposed to work with the <strong><code>sudo</code></strong> command. If you need to do it for many commands, use <code>sudo -s</code> that basically creates another session where you ar... | https://security.stackexchange.com |
572,454 | [
"https://math.stackexchange.com/questions/572454",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/102235/"
] | Prove that $\vec{v}$ is also an eigenvector for $A^{k}$(k = a positive integer). What is the corresponding eigenvalue?
What I have started with is, $A=(CDC^{-1})$ which can be used to prove
$A^{2}=(CDC^{-1})(CDC^{-1})
=C(DC^{-1}C)DC^{-1}
=CD^{2}C^{-1}$
Thus, $A^{k}=CD^{k}C^{-1}$ I think this will help me find my pro... | Try looking at $A^{k-1}(Av)$. Do this process inductively.
| <em>Hint:</em> If $v$ is an eigenvector of $A$ with eigenvalue $\lambda$ then
$$
A v = \lambda v \implies A^2 v = A(Av) = A(\lambda v) = \lambda (Av) = \lambda (\lambda v) = \lambda ^2 v \implies \cdots
$$
| https://math.stackexchange.com |
42,149 | [
"https://electronics.stackexchange.com/questions/42149",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3966/"
] | I'm attempting to measure the voltage developed across a very long piece of cable (upto 500m bundle). The issue is that the cable picks up a lot of noise from nearby radio stations and also has a 50 Hz component which I assume comes from the mains.
I would like to have a filter before my instrumentation amplifier, whi... | First, you don't want to get rid of <i>all</i> AC. If you did, the reading would never change. You need frequencies below some level to get thru, so you have to decide what that level is. You also should look at this in the time domain after deciding how long you are willing to wait for a reading and how accurate it... | I would simply place a capacitor across the InAmp's inputs, or rather a couple of them in parallel, like for instance 10 nF, 100 nF and 10 µF. These should short-circuit any RF signals and 50 Hz noise picked up by the cable. Ignoring the 10 µF for HF (it won't perform that well at high frequencies), 110 nF ... | https://electronics.stackexchange.com |
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