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 |
|---|---|---|---|---|---|
3,970,323 | [
"https://math.stackexchange.com/questions/3970323",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/775498/"
] | I'm learning statistics and trying to calculate the parameters of a regression line based on the data:
<span class="math-container">$(x,y)=(0,-1),(1,2),(2,9/2)$</span>
Could you please tell me how would I do so? I'm not sure how to calculate the parameters based just on a table of values.
Thanks
| <h1>Inductive definition of duality operator <span class="math-container">$\_{}˘$</span></h1>
Here is a fragment of the categorial language,
<pre><code>| src f | tgt f |
| Idₐ | f ∘ g |
| p + q | p × q |
</code></pre>
Then, we can define the <strong>dual <span class="math-container">$e ˘$</span></strong> of an exp... | The idea of duality is that, whenever you have a purely categorical statement (or concept), you can look at what that statement means for a category <span class="math-container">$ C $</span> when applied to <span class="math-container">$ C^{\mathrm{op}} $</span>: this gives you the dual statement or concept. Then, if y... | https://math.stackexchange.com |
2,675,358 | [
"https://math.stackexchange.com/questions/2675358",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
We have <strong>$30$ books</strong>. <strong>$15$ of them are Literature Books(LB)</strong> and <strong>the other $15$ are Mathematic Books(MB)</strong>. We randomly distribute those $30$ books to <strong>$3$ libraries</strong>, giving to <strong>each library $10$ books</strong>. What's the <strong>proba... | First the probability that $10$ literature books are distributed to the first libary and no mathematic books to the second libary:
$$\frac{\binom{15}{10}\cdot \binom{15}{0}}{\binom{30}{10}}$$
Now we can distribute 5 literature books to the second libary. That means that 5 of 15 mathematic books are distributed to the... | After you give the first library 10 books, you have $\binom{20}{10}$ ways to choose $10$ books of the remaining $20$ to give to the second library. There no choice for the third library -- it gets whatever's left. So, there are $$\binom{30}{10}\binom{20}{10}$$ ways to distribute the books.
Now apply the same kind of... | https://math.stackexchange.com |
391,892 | [
"https://physics.stackexchange.com/questions/391892",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/94282/"
] | Let me begin by noting that for a surface with charge density $\sigma$, we know the component of the electric field perpendicular to the surface is discontinuous. This relation is given as
$$\mathbf{E_{above}-E_{below}}=\frac{\sigma}{\epsilon_0}\mathbf{\hat{n}},$$ or equivalently in terms of the potential
$$\nabla V_{... | The quantity $\frac{dV}{dn}$ is defined by Griffiths to be equal to $\frac{dV_{above}}{dn}-\frac{dV_{below}}{dn}$. This is equivalent to the following (valid) definition of the derivative of a function:
$$f'(x)=\lim_{h\to 0}\frac{f(x+h/2)-f(x-h/2)}{h}$$
Regarding your specific problem, the trick is that the potential... | Griffiths equation $$\sigma=-\epsilon_0 \frac{\partial V}{\partial n}$$hold for the case of a metal surface charge where the interior electric field is zero. It is equivalent to $$\frac{\partial V_{above}}{\partial n}-\frac{\partial V_{below}}{\partial n}=-\frac{\sigma}{\epsilon_0}$$ where $$\frac{\partial V_{below}}{... | https://physics.stackexchange.com |
5,198 | [
"https://scicomp.stackexchange.com/questions/5198",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1050/"
] | Reading today about the theory of differential forms, I was left impressed how much it reminded me of second order Finite Volume Method (FVM).
I'm struggling to figure out is thinking this way just trivial or is there some deeper connection.
Well, differential forms serve to generalize some concepts deeply rooted in... | Short answer: nothing more than $U_{ii} = 0$, i.e. that your <em>computed</em> $U$ factorization is exactly singular.
<code>xGETRF</code> is not safe as a rank revealing factorization, so I would not draw any conclusion, apart from the fact that $A$ is ill-conditioned and no solution to $Ax=b$ can be safely computed.... | If you compute the LU factorization of an $n$ by $n$ matrix $A$, then you'll end up with
$PA=LU$
where $P$ is a permutation matrix, $L$ is lower triangular and nonsingular, and $U$ is upper triangular. If $A$ happens to singular then the LAPACK routine will produce a $U$ matrix that is singular. The only way that ... | https://scicomp.stackexchange.com |
3,932,366 | [
"https://math.stackexchange.com/questions/3932366",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/823011/"
] | <blockquote>
Suppose <span class="math-container">$f(x)$</span> is continuous on <span class="math-container">$[a, b]$</span>. Prove that <span class="math-container">$\forall x\in (a,b)$</span>, we have
<span class="math-container">$$
\lim_{h\rightarrow 0}\frac{1}{h}\int_a^x[f(t+h)-f(t)]\mathrm{d}t=f(x)-f(a).
$$</span... | Two things:
<ol>
<li>This is only a partial answer (you'll see why at the end), but it might still help.</li>
<li>It seems like the limit should be regarded as a right-hand limit.
Please let me know if I'm wrong.</li>
</ol>
The limit <span class="math-container">$\lim_{h\to 0^{+}}\frac{1}{h}\int_{a}^{x}\left[f(t+h)-f(t... | This is a simple consequence of the Fundamental Theorem of Calculus. Also you need to have <span class="math-container">$h\to 0^{+}$</span> instead of <span class="math-container">$h\to 0$</span> (why? Explain yourself).
Clearly if <span class="math-container">$F$</span> is an anti-derivative of <span class="math-conta... | https://math.stackexchange.com |
168,366 | [
"https://dba.stackexchange.com/questions/168366",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/33074/"
] | I'm on MySQL trying to get the user's daily <code>post</code> count grouped by <code>post category</code>.
So for every day in a given date range, with no gap, I need the post count for each existing post category for a given user. When the user has not posted anything in a category for that day, that category must st... | You need to first <code>CROSS JOIN</code> the two tables, <code>list_of_dates</code> and <code>post_categories</code> and then <code>LEFT JOIN posts</code>:
<pre><code>SELECT
ld.date AS date,
pc.name AS categoryName,
COUNT(p.id) AS postCount
FROM
( SELECT
DATE_ADD('2016-12-28', ... | LEFT JOIN includes all the records on the LEFT. Your join on post_categories is however your last join (i.e. it is on the RIGHT) - try it with RIGHT JOIN and you should get all the categories irrespective of whether they match.
Alternately move post_categories up so it is on the LEFT and you can continue using a LEFT ... | https://dba.stackexchange.com |
89,804 | [
"https://mechanics.stackexchange.com/questions/89804",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/73397/"
] | I've got a 2007 Hyundai Elantra that's got a mostly-functional AC, but consistently blows warm air when at lower speeds (or idle) on warm days.
So far, I've tested the following:
<ol>
<li>I press the A/C button and I see under the hood that the clutch starts/stops spinning</li>
<li>When I drive on the freeway, the A/C ... | I was able to resolve the warm AC by replacing the condenser fan. After replacing it, I noticed the new one (which I pulled out of a 2010 Elantra) was much quieter. I also noticed that the old one had a thermocouple that looked cracked and crusty -- that was probably contributing to incorrect readings, and I assume p... | A couple of things ... is there anything obstructing the air flow through the condenser? Like a plastic bag or something. Rapid clicking of the A/C clutch is usually an indication there is a low refrigerant charge. If you haven't looked at both high/low side readings, while compensating for ambient temperatures, then ... | https://mechanics.stackexchange.com |
19,905 | [
"https://stats.stackexchange.com/questions/19905",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7535/"
] | Does RSS + ESS = TSS all the time?
I am thinking - does it hold if there is no intercept?
Does this apply for all regressions, or are there certain conditions that need to be met?
| If the values of X1 and X2 are positive and positively correlated with Y, then <strong>of course</strong> X1*X2 will be significant when used alone in a model: it is positively correlated with both X1 and X2 and therefore should be correlated with Y. But that tells us nothing.
Let's look at a small example using the ... | The problem which arises is an issue of interpretation. Consider a simple linear regression model with a continuous main effect and continuous outcome. Suppose further you have a binary factor and you're interested in the model with interaction. When you adjust for the lower level terms, the interaction parameter has a... | https://stats.stackexchange.com |
4,001,372 | [
"https://math.stackexchange.com/questions/4001372",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/878444/"
] | We define an equivalence relation <span class="math-container">$≡$</span> in the set <span class="math-container">$\mathcal{P}(\mathbb{Z})$</span> as:
<span class="math-container">$$A \equiv B \iff \exists_{r \in \mathbb{Z}} ( \forall_{x \in A} (x + r \in B) ∧ \forall_{y \in B} (y - r \in A))$$</span>
Determine <span c... | HINT: It is not necessarily true that <span class="math-container">$A$</span> and <span class="math-container">$A+1$</span> are one unit wide and lie next to each other: <span class="math-container">$A$</span> could be all of <span class="math-container">$\Bbb Z$</span>, in which case <span class="math-container">$A+1=... | Since the quotient map <span class="math-container">$\mathcal{P}(\mathbb{Z}) \to \mathcal{P}(\mathbb{Z})/\equiv$</span> given by <span class="math-container">$A \mapsto [A]_\equiv$</span> is surjective, <span class="math-container">$$\left|\mathcal{P}(\mathbb{Z})/\equiv\right| \leq |\mathcal{P}(\mathbb{Z})| = |\mathbb... | https://math.stackexchange.com |
3,197 | [
"https://mechanics.stackexchange.com/questions/3197",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1671/"
] | I have a (South African) Opel (Chev? Vauxhall?) Corsa bakkie (ute?). But I think this is more a general question than specific to this type of car. However, this model I own does not have many onboard computers etc - it is a really basic car - so I'm hoping the fix to this question is quite basic too.
When the ignitio... | Just to report back - I hate leaving questions unanswered on the Stack... forums.
I don't understand it, but when my mechanic swapped the 2 wires that connect the horn-push-button to the steering wheel, the horn started working properly.
Perhaps this had something to do with grounding or something...
Anyway, there ... | This is far fetched, but maybe when the car is running its pulling too much power (through spark) for the horn to have any "left over" juice to use? I know I've seen headlights go dim in this case.
Maybe your alternator isn't working efficiently.
| https://mechanics.stackexchange.com |
198,671 | [
"https://softwareengineering.stackexchange.com/questions/198671",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/91264/"
] | I program in C mostly. However, it is pretty obvious that many more commercial applications are done in C++.
As far as I can tell, C++ is a very complex language, with seemingly convoluted syntax and too many constructs. C++ also encourages the abuse of Objects where structs and functions will do. In fact, the only si... | <blockquote>
Basically, my question is, did I miss something?
</blockquote>
I believe you did, but it has less to do with programming languages and more to do with the human tendency to denigrate the unfamiliar. We do that. It's natural. Rising above it takes a willingness to endure the cognitive dissonance that ... | People want to use OOP. Also programmers want to learn as few new things as possible. Thus, when C++ first came out. It gained massive popularity thanks to backwards compatibility with C and because it implemented OOP, which was gaining massive popularity at the time. This popularity created so much momentum, that it m... | https://softwareengineering.stackexchange.com |
1,115,783 | [
"https://math.stackexchange.com/questions/1115783",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/197705/"
] | Is saying each point of a topological manifold has a neighborhood homeomorphic to $\Bbb{R}^{n}$ the same thing as saying there is a local coordinate system at each point?
I'm not really sure what I mean by coordinate system. It's just a term I have heard used. If someone could define that at the same time that woul... | Yes. This is true by definition:
A topological space $M$ is said to be locally Euclidean of dimension $n$ if each point $x \in M$ has a neighbourhood $U$ homeomorphic to an open subset $V$ of $\mathbb{R}^n$. A homeomorphism of this sort is by definition a coordinate chart.
| I believe you mean that each point has a neighborhood homeomorphic to $\mathbb{R}^n$. A local coordinate system about a point is basically a choice of homeomorphism from a neighborhood of that point to $\mathbb{R}^n$.
| https://math.stackexchange.com |
142,167 | [
"https://security.stackexchange.com/questions/142167",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/129805/"
] | If I manage to enter javascript in a website search bar that will then run the javascript on the results page, it only runs on my local session in my browser right? So unless the website stores my javascript-filled query and displays it elsewhere to other users, it won't do anything to other uses will it?
| When you enter something in a search bar and it gets executed, it is called reflected XSS because the payload is reflected from the URL (e.g. <code>https://example.com?search=[javascript code]</code>). If it would be stored and displayed to others later it would be what is called, well, stored XSS.
I read your questio... | It depends. You are talking about 'stored' XSS attacks - that is, you put in some Javascript, the website stores it and shows it to someone else. There are also reflected XSS attacks - that's when a query parameter is exposed and vulnerable to XSS - that is, you can create a URL that contains the attack. You can the... | https://security.stackexchange.com |
1,053,801 | [
"https://math.stackexchange.com/questions/1053801",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/88965/"
] | <blockquote>
Find the derivative of the following function using the Fundamental Theorem of Calculus:<br>
$$F(x)=\int_{x^3}^{x^6}(2t-1)^3dt$$
</blockquote>
I don't know how to do this problem using FTOC because this is not a bounded function...
The answer that I got (which is wrong) was: $$6(2x^3-1)^2(3x^2)+6(2... | <blockquote>
Ah, You're not at all supposed to differentiate terms inside the integral
</blockquote>
See, Using FTC
$$F(x)=\int_{x^3}^{x^6}(2t-1)^3dt=\int_{0}^{x^6}(2t-1)^3dt-\int_0^{x^3}(2t-1)^3dt$$
$$\begin{align}
F'(x)&=\frac{d}{dx}\left[\int_{0}^{x^6}(2t-1)^3dt-\int_0^{x^3}(2t-1)^3dt\right]\\
&=(2x^6-1... | By fundamental theorem of calculus and chain rule
$$F(x)=\int_{x^3}^{x^6}(2t-1)^3dt\\
F'(x)=\left[\int_{x^3}^{x^6}g(t)dt\right]',g(t)=(2t-1)^3\\
=\left[G(x^6)-G(x^3)\right]'
=(x^6)'g(x^6)-(x^3)'g(x^3)\\
=6x^5(2x^6-1)^3-3x^2(2x^3-1)^3
$$
| https://math.stackexchange.com |
1,758 | [
"https://mechanics.stackexchange.com/questions/1758",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/912/"
] | So does forced induction negate the effect of engine braking on compression motors?
For example, going down an incline, drop into 3rd (automatic) to get some engine braking going. With my new Chevy Cruze which has a turbo, it seems like it doesn't matter what I do in what gear, there just isn't any engine braking abil... | The turbo shouldn't have any effect here after the first fraction of a second - a turbo runs off exhaust gases so with your foot off the accelerator it will spin down, and thus giving no forced induction. I don't know if there would be an effect with a supercharger, but I'm guessing not much.
The difference in size wi... | This may also have to do with your new vehicle more than anything else.
You didn't mention what your previous one is but did mention your new one is a Cruze. Especially if you purchased the ECO model than this may be the case.
Chevy is trying to squeeze every MPG they can out of this car, such as on the ECO manual h... | https://mechanics.stackexchange.com |
4,171,206 | [
"https://math.stackexchange.com/questions/4171206",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/347678/"
] | Determine the minimal polynomial of <span class="math-container">$\sqrt[10]{5}$</span> over <span class="math-container">$\mathbb{Q}(e^{2\pi i/10})$</span>.
Progress so far: 1) Its degree must divide <span class="math-container">$10$</span> (since the extension <span class="math-container">$\mathbb{Q}(\sqrt[10]{5},e^{2... | The easiest way to see the answer to this is to use the well-known result that for any field <span class="math-container">$ F $</span> and for a prime <span class="math-container">$ p $</span>, the polynomial <span class="math-container">$ X^p - a $</span> is irreducible in <span class="math-container">$ F[X] $</span> ... | Let <span class="math-container">$$a=5^{1/10},b=e^{2\pi i/10},c=a^5=\sqrt{5}$$</span> You have already shown that <span class="math-container">$b$</span> is a root of <span class="math-container">$x^4-x^3+x^2-x+1\in\mathbb {Q} [x] $</span> and <span class="math-container">$$b+b^{-1}=2\cos(\pi/5)=\frac{1+c}{2}$$</span> ... | https://math.stackexchange.com |
32,426 | [
"https://quant.stackexchange.com/questions/32426",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/26571/"
] | Is there a more cost-effective alternative to Bloomberg Excel Add-In? 90% of the time I only use Bloomberg to download security (hundreds of U.S. and international stocks) historical price data. The formula I use is <code>=BDH(security, field,start date [mm/dd/yyyy], end date [mm/dd/yyyy], optional arguments)</code>.
... | Quandl - you can use Excel, R python addin/code to pull data
| I also heavily rely on Bloomberg for price data at work. For single stock price history I leveraged <strong>Yahoo Finance</strong> in the past. The quantmod() R package has some functions that can pull Yahoo Finance equity quotes. I'm sure there are others, too. I would try that route first.
| https://quant.stackexchange.com |
1,460,484 | [
"https://math.stackexchange.com/questions/1460484",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/273575/"
] | $$\lim_{x\to \infty} \frac{6x^4+4}{(x^2-2)(6x^2-1)}$$
Based on the way the function behaves I can say it will reach 1, but I can't seem to be able to calculate the limit. Thanks for the help!
| <strong>Hint.</strong> Expand the denominator and use dominant terms.
| Multiply the numerator and denominator by $1/x^4$, then take the limit.
| https://math.stackexchange.com |
2,753,326 | [
"https://math.stackexchange.com/questions/2753326",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/385702/"
] | When introducing curvature (p.183), Huybrechts uses a notation which I don't really understand: For example in the formulas
$$F_{\nabla}=d(A)+A\wedge A, $$
$$dF_\nabla = F_\nabla \wedge A - A\wedge F_\nabla.$$
What does "$\wedge$" stand for? It doesn't seem to be the usual exterior product, because from the way the for... | In addition to @Andrew's explanation, $\wedge$'s therein are not only exterior products, but also respective algebraic arithmetic. Here are two examples.
Suppose $A$ is a usual $1$-form, e.g., $A=\omega$. Then $A\wedge A=\omega\wedge\omega=0$ follows the usual exterior product.
Suppose $A$ is a matrix $1$-form, e.g.,... | The wedge here indicates the combination of wedge product on forms and composition of the endomorphisms. So, if we have $A= \sum_i \phi_i\otimes a_i$ and $B=\sum_j \psi_j \otimes b_j$, where $\phi_i,\psi_j$ are forms and $a_i,b_j$ are endomorphisms, then
$$
A\wedge B = \sum_{i,j} (\psi_i\wedge \phi_j) \otimes (a_i\cir... | https://math.stackexchange.com |
160,540 | [
"https://mathoverflow.net/questions/160540",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10059/"
] | Is there a finite set $P$ of non-elementary functions $f_n$ such that the derivative of any function $f$ from that set is not elementary, but expressible with functions from the same set $P$ plus elementary functions?
| Let $g$ be an elementary function whose indefinite integral $f$ is nonelementary, and set $P = \{\cos(t)f(t), \sin(t)f(t)\}$.
| <ul>
<li>The Bessel functions, $\{J_\nu(x), K_\nu(x) | \nu\in\mathbb{Z}\}$</li>
<li>Airy functions, $\{Ai(x), Ai^\prime(x)\}$, $\{Bi(x), Bi^\prime(x)\}$</li>
<li>Complete elliptic integrals, $\{E(x), K(x)\}$</li>
</ul>
And also many other solution sets to classes of differential equations. You can also replace $x$ by ... | https://mathoverflow.net |
4,171 | [
"https://chemistry.stackexchange.com/questions/4171",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1225/"
] | Please correct me if I’m wrong, but I’ve read that the reason why we use significant figures is to avoid making the result of a calculation more accurate than the starting values prior to the calculation. For example, if we were seeking the ratio of two weights, lets call them A and B, using a cheap scale and an expens... | This is part of the reason I really don't like the way we teach significant figures. What's really important isn't the number of digits you have, but rather the uncertainty in your measurements. I think significant figures are taught as an approximation to the proper uncertainty analysis, but it really seems to be not ... | In your example 0.000023 oz does indeed have two significant figures. It is indeed probably something only a very fine tuned scale could measure.
Now consider that you add that mass to another sample that you measured with the much less accurate scale, let's say the other scale measured that other weight as 23 oz. Bot... | https://chemistry.stackexchange.com |
59,921 | [
"https://mechanics.stackexchange.com/questions/59921",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/26792/"
] | I notice when checking the dipstick sometimes it is black or brown at bottom and gets lighter at top.
Why is this?
| There can be a number of factors causing this:
<ul>
<li>If you've just topped the oil up but not driven the car yet then the fresh oil is sat at the top</li>
<li>The darkening/blackening you see is caused by dirt (for want of a better word) in the oil, if these particulates are heavier than the surrounding oil then th... | It could be dirt accumulation on the dipstick from before the oil change. It reaches to where the old oil level was. You can try to clean the dipstick with some solvent. Petrol could work.
| https://mechanics.stackexchange.com |
4,234,059 | [
"https://math.stackexchange.com/questions/4234059",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/799923/"
] | <span class="math-container">$$A=\begin{pmatrix}
4 &-1& 1\\
8&-2&2\\
-6&1&-2\\
\end{pmatrix}$$</span>
I have to show <span class="math-container">$p=\begin{pmatrix}
1 \\
2\\
-2 \\
\end{pmatrix} \in \mathrm{Im}A=\left\{Ax \mid x\in \mathbb{R^3} \right\}$</span>
If I let <span class="math-containe... | Your mistake is that <span class="math-container">$\mathrm{C\left(A\right) ≠ span}\left(\begin{bmatrix}1\\0\\0\end{bmatrix},\ \begin{bmatrix}0\\1\\0\end{bmatrix}\right)$</span>.
Elimination actually changes the column space of <span class="math-container">$\mathrm A$</span>, so <span class="math-container">$\mathrm{C\l... | The image is the span of linearly independent vectors in the column of the matrix. It suffices to show that <span class="math-container">$p$</span> is redundant and can be written as a linear combination of the other columns. After your row reduction, notice that only the first two columns have free variables whereas t... | https://math.stackexchange.com |
32,063 | [
"https://electronics.stackexchange.com/questions/32063",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9816/"
] | I have been given the followign circuit diagram:
<img src="https://i.stack.imgur.com/N1bqm.png" alt="enter link description here">
and have been asked to compute \$R_2\$ and \$R_C\$ such that, at the Q-point, the circuit will behave as follows:
\$V_{CE}=5\:\mathrm{V}\$<br>
\$V_{BE}=0.7\:\mathrm{V}\$<br>
\$I_C=2\:\ma... | There are many places we can begin looking at this.
We know that the collector current is 2 mA, and that \$V_{CE}\$ is 5V. Since the emitter is at ground, the collector must be at 5V, and so the voltage across \$R_C\$ is therefore 10V: the difference between 5V and 15V. So \$R_C\$ must be \$10V/.002A = 5K\Omega\$.
Ne... | \$ I_1 = \dfrac{V_{BE} - V_{EE}}{R1} = \dfrac{0.7V - (-15V)}{100k\Omega} = 157\mu A \$
\$ I_2 = I_1 + I_B = I_1 + \dfrac{I_C}{\beta} = 157\mu A + \dfrac{2mA}{100} = 177\mu A \$
\$ R_2 = \dfrac{V_{CE} - V_{BE}}{I_2} = \dfrac{5V - 0.7V}{177\mu A} = 24294\Omega \$
\$ R_C = \dfrac{V_{CC} - V_{CE}}{I_2 + I_C} = \dfrac{... | https://electronics.stackexchange.com |
96,010 | [
"https://softwareengineering.stackexchange.com/questions/96010",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32004/"
] | We're implementing an CMS based on ASP.NET MVC. Now, any designer should be able to provide themes for this CMS. But to write a theme, they need to be able to modify the generated HTML, thus the concept of View. In other words, they should be capable to either modify current views, or create new views from scratch, to ... | Yes, A web designer (a good one) knows about templating engines and can learn new ones.
You cannot expect him to understand your bloated "smart" templates. As long as your templates are dumb and driven by simple data you can expect him to learn your particular templating engine.
Of course he'll bill you an extra day... | If you implement your views so that the design is handled through css then it is not needed. In this manner they do not need to modify any server side code to tweak the layout. Most designers I have worked with give me the specs and I implement them. Few ever really understood css beyond simple formatting. They kno... | https://softwareengineering.stackexchange.com |
59,781 | [
"https://dba.stackexchange.com/questions/59781",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/26576/"
] | I have two machines A & B. I shared a folder from machine B and mapped it as a drive on machine A. Now I want to configure my Oracle Database in Archive Log mode and want to set the Archive location to that mapped drive. I have also set full (Read/Write) permissions to that folder. But for testing purpose I tried t... | A logical schema won't exist in your database. A logical schema is a design-centric database structure built to meet your business requirements. It is a model that exists on a white board or in a diagraming tool. It is like the architect's drawings of your database.
A physical model is what is <em>actually implemen... | <strong><em>How Logical schema and physical schema are related?</em></strong><br>
I will explain this concepts with the help of this picture bellow:<br>
We will take as an example an Oracle database(but this apply's to most of RDBMS).
<strong>Logical Schema</strong> <br>
- is made out of actually what you plan(your i... | https://dba.stackexchange.com |
144,792 | [
"https://softwareengineering.stackexchange.com/questions/144792",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/47546/"
] | When I learned the C++ language for the first time I learned that besides int, float etc, smaller or bigger versions of these data types existed within the language. For example I could call a variable x
<pre><code>int x;
or
short int x;
</code></pre>
The main difference being that short int takes 2 bytes of memory ... | Most of the time the space cost is negligible and you shouldn't worry about it, however you should worry about the extra information you are giving by declaring a type. For example, if you:
<pre><code>unsigned int salary;
</code></pre>
You are giving a useful piece of information to another developer: salary cannot b... | The OP said nothing about the type of system they are writing programs for, but I assume the OP was thinking of a typical PC with GB's of memory since C++ is mentioned. As one of the comments says, even with that kind of memory, if you have several million items of one type -- such as an array -- then the size of the ... | https://softwareengineering.stackexchange.com |
411,893 | [
"https://electronics.stackexchange.com/questions/411893",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/147013/"
] | General question for those who have worked in the consumer electronics industry:
Are small rechargeable devices (like bluetooth audio devices specifically) designed to fail after a set time to force customer replacement? Is there for instance a mechanism that disables charging once the battery has totally failed or aft... | I've worked on countless consumer products, and I've never seen a "kill" circuit that intentionally causes the product to fail after some specified period or event.
However, consumer products are designed for a certain lifetime, with a certain number of failures in that lifetime being acceptable. That's just a realit... | You cannot just replace the battery, you also have to reset the charge counter chip.
If you want to reach maximum charge over cycles, you should never charge a LiPo battery to more than 90% and never discharge it to less than 10% of the capacity. This measurement accuracy cannot be reached by checking the unloaded vol... | https://electronics.stackexchange.com |
546,685 | [
"https://physics.stackexchange.com/questions/546685",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/203557/"
] | Landau-Ginsburg theory efficiently describe physics in vicinity of critical point and predict approximate critical exponents in 3d through <span class="math-container">$4-\varepsilon$</span> expansion.
But as I understand, in continuous limit LG theory in principle also describe physics not only in vicinity of critica... | First of all, it seems there are some disagreements in both the comments and other answers about what actually constitutes Landau-Ginsburg theory. But based on what you have said in the comments, it seems that you are asking about using statistical or quantum field theory to describe the scaling limit of a system near ... | I am not sure that I understand your question correctly.
You can check Chapter 2 (paragraphs 2.2 & 2.3, where authors uses GL theory for Ising model) of "Introduction to the Functional Renormalization Group" by Kopietz. In my opinion, GL theory is nothing more than introducing an auxiliary field to simplify descri... | https://physics.stackexchange.com |
8,171 | [
"https://robotics.stackexchange.com/questions/8171",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/10374/"
] | Given a set of robot joint angles (i.e. 7DoF) $\textbf{q} = [q_1, ... , q_n]$ one can calculate the resulting end-effector pose (denoted as $\textbf{x}_\text{EEF}$), using the foward kinematic map.
Let's consider the vice-versa problem now, calculating the possible joint configurations $\textbf{q}_i$ for a desired en... | Nowadays we no longer employ exact solutions for the IK problem, simply because the number of degrees of freedom so as the number of constraints the final configuration needs to comply with make the so called geometric approach intractable.
By contrast, iterative methods are used to converge to the most plausible sol... | It depends on how theroetical/practical solution you are looking for.
If you are considering a theoretical workspace, with no angular limits of your joints (e.g. due to mechanical constraints) then the calculating the inverse kinematics for a Cartesian pose which is out of the workspace would result in complex joint ... | https://robotics.stackexchange.com |
124,789 | [
"https://dba.stackexchange.com/questions/124789",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/75651/"
] | I've had trouble finding a straight definition of normal forms online.
I don't want any examples or metaphors, just what each form is defined by in a nice format ! I believe there is more than 4 normal forms so it would be greatly appreciated if you could provide the extra information.
Please complete any missing inf... | Typically indexes will be used by SQL Server if it deems it more expedient to use the index than to directly use the underlying table.
It would seem likely the cost-based optimizer thinks it would be more expensive to actually use the index in question. You may see it use the index if instead of doing <code>SELECT *<... | For using the index, because you're doing <code>select *</code>, then SQL Server must first read each of the rows from the index that match the value you have in the where clause. Based on this, it will get the clustered index values for each of the row, and then it has to seek each of them separately from the clustere... | https://dba.stackexchange.com |
3,062,291 | [
"https://math.stackexchange.com/questions/3062291",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/492727/"
] | I needed some help with computing a limit of a function. I can compute it directly but I'm asked to use L'Hopital's and can't see where to start or how to use it for my function.
My limit expression is:
<span class="math-container">$$\lim_{x \to 0^+} (\sin x)^{\sin x}.$$</span>
Any help would be appreciated. Thanks... | Let's say the limit is <span class="math-container">$y$</span>:
<span class="math-container">$$y=\lim_{x\to 0^+} (\sin x)^{\sin x}$$</span>
Let's take the natural log of both sides in order to get rid of the exponentiation:
<span class="math-container">$$\ln y=\lim_{x\to 0^+} (\sin x)\ln(\sin x)$$</span>
Now, this ... | Using <em>T.Bongers</em> hint we are first of all left with the following
<blockquote>
<span class="math-container">$$\log(L)=\lim_{x\to 0^+}\sin(x)\log(\sin x)$$</span>
</blockquote>
Approaching zero from the RHS we can conclude that the sine term tends to <span class="math-container">$0$</span> whereas the logar... | https://math.stackexchange.com |
117,151 | [
"https://physics.stackexchange.com/questions/117151",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28468/"
] | When I tried to calculate the moment of inertia ($I_C$) of a cylinder (mass M, height H, radius R) around the rotating axis going symmetrically through its middle, I came up with a different result than expected ($\frac{1}{2}MR^2$), but I do not spot my mistake, since my calculation makes perfect sense to me:
$$
I_C :=... | You made two mistakes:
<ol>
<li>$dV = dr d\phi dh$ is wrong.
<ul>
<li>$dV = r dr d\phi dh$.</li>
</ul></li>
<li>$V = 2πR H$ is wrong.
<ul>
<li>$V = πR^2 H$. </li>
</ul></li>
</ol>
$$
I_C := \int_V{ρr^2dV} = \int_0^H{\int_0^{2π}{\int_0^R{ρr^3 dr dφ dh}}} = ρ \int_0^H{\int_0^{2π}{\frac{R^4}{4} dφ dh}} = ρ \cdot 2πH ... | Lets start from the general definition for the moment of inertia
$$I=\int_{0}^{M}r^{2}dm$$
The mass element is $dm=\rho dV$ with $dV=L2\pi rdr$ ($L$ being the length of the cylinder). Substituting you'll get
$$I=2\pi\rho L\int_{0}^{R}r^{3}dr$$
.Taking into account that $\rho=\frac{M}{\pi R^{2}L}$ can you spot you'... | https://physics.stackexchange.com |
60,202 | [
"https://physics.stackexchange.com/questions/60202",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22150/"
] | <img src="https://i.stack.imgur.com/muwVu.png" alt="enter image description here">
How to solve these kind of questions , where $|F| \propto x^2$?
How to find time period and velocity type related things to the oscillatory motion?
$$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$
But after this $$m\dfrac{d^2x}{dt^... | These kinds of proportionality questions are often best answered with dimensional analysis. You want to know a form a quantity with the units of time in terms of what you have.
You have a quantity $k$ with units $\frac{\text{Energy}}{\text{Distance}^3} = \frac{\text{Mass}}{\text{Distance} \times \text{Time}^2}$. You a... | The dimensional analysis in zkf's answer completely solves the exercise.
Nevertheless, it is possible to give a closed formula for the period
$$ T~=~ 4 ~\sqrt{\frac{m}{2k}} \int_0^a\! \frac{dx}{\sqrt{a^3-x^3}}
~\stackrel{x=au}{=}~ 4 ~\sqrt{\frac{m}{2ka}} \int_0^1\! \frac{du}{\sqrt{1-u^3}}. $$
Can you see why? Unsurp... | https://physics.stackexchange.com |
47,679 | [
"https://physics.stackexchange.com/questions/47679",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17213/"
] | Distant galaxies are said to be moving away from the Milky Way (and us) at speeds approaching the speed of light. Since Special Relativity tells us that any object moving away from us at a velocity of near the speed of light will increase in mass in our observations, i.e. it will appear to be much more massive than its... | I thought that since I brought this up and I didn't get any good explanations, I'd answer it myself. Plugging in some numbers helps. I used this for light speed = 299,792.458 km/sec. Hubble constant = 72 km/sec/megaparsec. The Hubble constant is necessarily an approximation because nobody knows exactly what it is and t... | Let us not forget that in addition to far-away galaxies at high redshift we can observe nearby galaxies (and many at every distance in between). Those observations of nearby galaxies can resolve individual stars which are clearly the same as stars in our own galaxy and obey physics consistent with the physics that powe... | https://physics.stackexchange.com |
415,538 | [
"https://softwareengineering.stackexchange.com/questions/415538",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/104636/"
] | YAGNI might tell us, that in the below implementation the generic version is not needed, as long as the function is only used once.
But to me personally, it seems, the generic version is more readable because I'm not distracted by all the possibilities the special class has, but are not used. The generic version is exp... | There are definitely cases where solving a more general problem than required makes code easier to read, to reason about and to maintain. The most simple example I can think of is when code deals with input data consisting of four or five similar attributes, and the processing code gets duplicated up to 5 times because... | There's has been some back and forth in the comments, and my feedback generally boils down to the same argument every time:
Your problem, as you describe it, always starts from the really unusual assumption that you don't know what it is you should be doing and would just interact with random available things <em>just ... | https://softwareengineering.stackexchange.com |
16,170 | [
"https://stats.stackexchange.com/questions/16170",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5405/"
] | I have a doubt regarding the variance, I try to explain It with an example.
I have two vectors, like:
<pre><code>a <- c(1:10)
1 2 3 4 5 6 7 8 9 10
b <- c(10:1)
10 9 8 7 6 5 4 3 2 1
</code></pre>
the variance is obviouly the same:
<pre><code>> var(a)
9.166667
> var(b)
9.166667
</code></... | I would suggest covariance because it will tell you direction with variance. e.g.,
cov(a,b)= -9.16667
you can also do correlation test in R. e.g., cor.test(a,b)
| Variance Change Detection is part of diagnostic checking to ensure that the Gaussian Assumptions are met regarding the error series. Make sure that there are no violations of the mean of the errors being zero everywhere or at least not-significantly different from zero as this oftentimes is the cause of perceived varia... | https://stats.stackexchange.com |
337,177 | [
"https://softwareengineering.stackexchange.com/questions/337177",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/220480/"
] | <strong>Context</strong>: I'm creating some applications to help me on my daily tasks, it does not connect anywhere and the only "data" it has to deal with is the parameters that I enter on the input fields.
This is how I structured my solution:<br>
|- Helpers (Folder + Class Library)<br>
|- Core (Folder + Class Libr... | <blockquote>
Should I create a new project to hold all these UserControls and reference it from App1, App2 and App3?
</blockquote>
That's the general idea, yes. Anytime you have functionality that is common to several projects, the way you prevent code duplication is by putting the common functionality into its own ... | Yes you should, if you know you will use something on multiple projects you want to make it easily portable. From my previous experiences, you really want to give you easy access to things you have already done in order to avoid duplication.
| https://softwareengineering.stackexchange.com |
15,942 | [
"https://physics.stackexchange.com/questions/15942",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/753/"
] | General relativity tells us that there is no absolute frame of reference (actually, it tells us that all frames are relative, which is close but not the same as there is no absolute frame).
Special relativity demonstrates that there <em>is</em> an absolute: the speed of light.
Notwithstanding the impracticality of th... | Technically, doppler shift for light happens due to relativistic time dilation, so it is subtly different than acoustic doppler shift. It cannot therefore be used to determine an absolute reference frame.
That doesn't mean there isn't one. Spacetime as we know it is formed by the big bang, so that might be an absolu... | By compression of light you mean the Doppler shift?<br>
Then yes you can measure your speed relative to the light source by comparing the Doppler shift in different directions.
It's been used for a number of different radio positioning systems - but it only gives you a motion <strong>relative</strong> to the light sou... | https://physics.stackexchange.com |
132,053 | [
"https://physics.stackexchange.com/questions/132053",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57730/"
] | When the pressure on the liquid surface is less than the vapor pressure of the liquid at a given temperature, the liquid will start to evaporate. This is common sense.
The problem is more difficult when the liquid and its vapor are heated inside a rigid container, with the specific volume of the mixture less than the... | With a constant volume for the container, the sum of the volume of the liquid and vapor is constant.
Let's start in an equilibrium position, temperature $T_1$. Volume of liquid is $V_l$ and vapor is $V_v$. Vapor pressure = $P_v$. Now we increase the temperature to $T_2$.
The first thing that happens is that the pre... | If you add heat to the system, it will be absorbed by liquid molecules changing to the gas phase. That reduces the number of liquid molecules (which reduces the liquid volume) and increases the number of gas molecules (which increases the pressure). The higher pressure will compress the liquid (probably a small amoun... | https://physics.stackexchange.com |
53,008 | [
"https://physics.stackexchange.com/questions/53008",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12250/"
] | what does it mean that a beta particle has a 1.6 MeV of energy , does it mean that it can ionize 120000 hydrogen particle with ionization energy of 13.6 MeV ?
| It is a measure of either the electron's kinetic energy or it's total energy (including mass). Because the electron's mass is $511\text{ keV} = 0.511\text{ MeV}$, it matters which in this case. By default particle physicists mostly talk about <em>total</em> energy, but nuclear physicist often talk about kinetic energy.... | An electron volt (eV) is just a unit of energy like a Joule. In fact 1eV = 1.602 $\times$ 10$^{-19}$J. Historically the eV originated as the work you have to put in to move 1 electron through a potential difference of 1 volt, hence the name. It's used in Physics because it's a very convenient unit. If we used joules we... | https://physics.stackexchange.com |
4,033,875 | [
"https://math.stackexchange.com/questions/4033875",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/311798/"
] | This is totally a homework problem, but it's due in 27 minutes so I know I won't get anything in time for that. I don't want the answer, I just want to learn the technique. I've started a MS program but it's been over 30 years since my calculus classes.
I'm trying to solve the following recurrence:
<span class="math-co... | <span class="math-container">$$T(2^k) = 3T(2^{k-1}) + 8 \cdot2^k \tag{1}$$</span>
<span class="math-container">$$T(2^{k-1}) = 3T(2^{k-2}) + 8 \cdot2^{k-1}\tag{2}$$</span>
<span class="math-container">$$T(2^{k-2}) = 3T(2^{k-3}) + 8 \cdot2^{k-2}\tag{3}$$</span>
<span class="math-container">$(3)$</span> in <span class="ma... | As
<span class="math-container">$$
T\left(2^{\log_2 n}\right)=3T\left(2^{\log_2\left(\frac n2\right)}\right)+8n
$$</span>
calling now <span class="math-container">$\mathcal{T}\left(\cdot\right) = T\left(2^{(\cdot)}\right)$</span> and <span class="math-container">$z = \log_2 n$</span> we have the linear recurrence
<span... | https://math.stackexchange.com |
76,709 | [
"https://softwareengineering.stackexchange.com/questions/76709",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15455/"
] | I've been reading over some proposals for software projects recently and I'm a little concerned by what I've seen. Often I feel that proposals have been rushed and/or poorly thought out.
It's very possible that proposals don't need to look like a basket of fruit, but if your pitching for work or seeking approval for f... | Having written and been part of numerous project proposals, the key thing is: <strong>know your audience</strong>. Presumably, the people you are writing to have the power to accept/decline funding (financially, people power, etc.). Ensure that you <em>show</em> them in their language why this little project of yours w... | Kind of goes without saying but focus on what value the project has to the organization and why/how its going to save money. That savings could be direct bottom line dollars or in efficiencies.
| https://softwareengineering.stackexchange.com |
690,285 | [
"https://math.stackexchange.com/questions/690285",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/10394/"
] | So i have some series, it is $\sum a_n$ and i know it converges absolutely.
Is it true that for given: $$b_n = \frac{n^2+1}{n^2}$$
$\sum a_n \cdot b_n$ converges absolutely too?
What about $\sum a_n$ semi-converges, $b_n$ is the same. Does $\sum a_n \cdot b_n$ semi-converges too?
In general, i have given some, any ... | Notice that
$$b_n\sim_\infty1$$
then
$$|a_nb_n|\sim_\infty |a_n|$$
hence the series
$$\sum_n a_nb_n$$
is absolutely convergent by asymptotic comparison. We have the same result for the semi-convergent series.
| $\sum a_n*b_n$ converges absolutely if $\sum |a_n(1+\frac{1}{n^2})|$ converges.
We know, $\sum\limits_{n=1}^N |a_n(1+\frac{1}{n^2})|\le \sum\limits_{n=1}^N |a_n|+|\frac{a_n}{n^2}|\le \sum\limits_{n=1}^N |a_n|+ \sum\limits_{n=1}^N \frac{|a_n|}{n^2}$.
Since, $\sum\limits_{n=1}^N |a_n|$ converges, $|a_n|\rightarrow 0$, ... | https://math.stackexchange.com |
89,306 | [
"https://mathoverflow.net/questions/89306",
"https://mathoverflow.net",
"https://mathoverflow.net/users/703/"
] | I am searching for a constructive proof of the following fact: If $X$ is an infinite set, there exists an uncountable family $(X_\alpha)_{\alpha \in A}$ of infinite subsets of $X$ such that $X_\alpha \cap X_\beta$ is finite whenever $\alpha \neq \beta$. The way I know how to prove this statement is as follows.
First,... | This all hinges on what you mean by constructive. An easy way to get such a family is to proceed as follows:
Put your countable set $X$ in bijective correspondence with the collection of finite sequences of 0s and 1s.
For every every subset $A$ of the natural numbers, let $\chi_A:\mathbb{N}\rightarrow\{0,1\}$ be the... | I think that you feel your construction <em>non constructive</em> because you have no way to establish a priori if a given real number is rational or irrational. The following construction avoids the problem: I suppose directly that $X=\mathbb N$. For <strong>any</strong> $\frac{1}{10}\leq t< 1$, for instance $t=0,3... | https://mathoverflow.net |
213,526 | [
"https://stats.stackexchange.com/questions/213526",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/111402/"
] | Suppose we have $X_n$ a random variable, that can take two values:
$X_n =
\begin{cases}
0, & \text{with probability 1 - $\frac{1}{2n}$,} \\
n, & \text{with probability $\frac{1}{2n}$} \end{cases}$
Does $X_n$ converge almost sure to $0$? I don't need a rigorous proof, but I would like to have an intuition for... | Just use the contrapositive Borel Cantelli Lemma, which says that if your events $A_i$ are independent and $\sum_i P(A_i)=\infty$ then $A_i$ occur infinitely often. In this case, pick $A_i=\{X_i>1\}$. Can you finish it from here?
For "intuition," $X_n$ grows too fast with high probability. If you want, modify $P(X... | You can't prove it because $X_n$ could either converge to zero almost surely or not. You haven't provided enough information.
As has already been pointed out if the $X_n$ are independent then the fact that $X_n = n$ infinitely often with probability one follows from the second Borel-Cantelli lemma. However, we could... | https://stats.stackexchange.com |
83,767 | [
"https://stats.stackexchange.com/questions/83767",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/38009/"
] | I am doing multiple regression on a subset of the NLYS79 dataset, namely a subset containing 540 respondents. And am interested in the significance of race upon earnings. My variables here are: years in school, ASVABC(a measure of intelligence), ethnicity is black, ethnicity is white, female, tenure, hours per week wor... | Let the data be $X_1, X_2, \ldots, X_n$ and, noting that all the $X_i$ are interchangeable, we may without loss of generality extremize $f(X_1, \ldots, X_n) = (X_1 - \bar{X})/\text{sd}(X)$ assuming $\text{sd}(X)\ne 0$ (which implies $n\gt 1$). Because $f$ is unchanged under translations and rescalings of the $X_i$, we... | I think I understand now. You want to know what the maximum and minimum possible values of $(X-m)/s$ can be.
My feeling (I haven't worked this out analytically) is that this will be maximized when all of the observed values are the same except for one. Suppose without loss of generality that have $N-1$ observed v... | https://stats.stackexchange.com |
53,638 | [
"https://chemistry.stackexchange.com/questions/53638",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/31026/"
] | I am confused regarding significant figures. Consider "Calculate the volume of 2.8 kg of liquid with density of 1.11 g/cm^3"
Then,
Volume = 2.8 kg * (cm^3 / 1.11 g) = 2522.522 (where 522 is recurring).
Since the original figure (2.8 kg) has only two significant figures, I thought the answer should be 2.5 kg.
The tex... | Unless greater precision is indicated by adding terminal zeroes to the mass measurement (2.8<strong>00</strong> kg) you should assume only two significant digits. Note also that even if the mass is reported to high accuracy the density is given with only three significant digits. The book is wrong to ask for four sig... | Your answer of $2500$ and the book's answer of $2523$ both have four significant figures.
If you want to keep your answer to the same degree of accuracy as the given data with the least number of significant figures, i.e. $2.8$ kg, it is best to express your answer as $2.5\times10^{3}$.
| https://chemistry.stackexchange.com |
566,122 | [
"https://physics.stackexchange.com/questions/566122",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208825/"
] | Today I was reading about mass-energy equivalence and their respective conservations laws. I have come up with two definitions about mass:
<ol>
<li>Amount of matter an object consists of.</li>
<li>A measure of an object's inertia.</li>
</ol>
I was always satisfied with the first definition. That is, mass is about how ... | What Einstein proved with his famous formula, is that your first definition is just wrong. Mass isn't a measure of the amount of matter an object consists of. Instead, it is a measure of how much energy that is contained in the object or system. I like your analogy with currencies. Just like you can convert from dollar... | Actually, in a thought experiment with a box with perfectly reflective interior walls, the box will have an observable additional mass if there is electromagnetic radiation inside the box.
Conceptually, you can understand this as the photons getting a redshift (from general relativity) when they travel upwards and a bl... | https://physics.stackexchange.com |
157,125 | [
"https://cs.stackexchange.com/questions/157125",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/157168/"
] | I am currently learning about how the compilation and linking works in C++. I think I kinda get how the compiler works, and that for a file to fully compile you don't need to have function implementations, but only declarations. It is the linker's job to link the function declaration to its implementation.
But now I ha... | The compiler compiles from a .cpp file to an object file (.o) with the binary code.
The linker combines all of the object files together into a single binary.
So, the linker doesn't need to know which cpp to look at, because the linker doesn't look at cpp files. Instead, the linker looks at all of the .o files, figure... | The linker is given explicitly the list of files to use, in the command line of the linker. They can be object files (.obj / .o) - compiled code - or libraries (.lib / .a) - object files structured in a single one.
Part of the job of the linker is to establish a list of the available functions and assign them an addres... | https://cs.stackexchange.com |
78,620 | [
"https://chemistry.stackexchange.com/questions/78620",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/48489/"
] | If we use a strong base such as LDA or NaH, will the rate-determining step change from enolate ion formation to nucleophillic acyl substitution step?
| Let me get one thing out of the way: the hydride ion is <strong>not</strong> a strong base. However, once a hydride is protonated to form hydrogen the acid-base equilibrium breaks down which makes it seem like a much stronger base than it is.
<hr>
Your actual question — whether the rate determining step shifts from e... | If a strong base is used, it will result in complete formation of the enolate ion, while in weaker bases, the RDS is enolate ion formation as it is a very weak acid.
| https://chemistry.stackexchange.com |
144,128 | [
"https://softwareengineering.stackexchange.com/questions/144128",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51741/"
] | I need to design a database that will contains information about personal disease of users.
What can be the approach in order to implement the columns of the DB's tables: encrypt the information, separate data within two differents DB, one for sensitive data and another for not sensitive data, or both or another appro... | You could encrypt the data with a key stored in your web application so that the data is written/read from db in its encrypted form. However anyone with access to the code would have access to the key and with the key the unencrypted data. This solves the requirement
<blockquote>
the dba should not be able to view t... | Ominus' answer addresses your first question. The answer to the second question may require more details about your application.
Another approach with even greater security if the patients must access the database could be to have a separate database for each user. In this approach you might use a framework that prov... | https://softwareengineering.stackexchange.com |
281,234 | [
"https://physics.stackexchange.com/questions/281234",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57983/"
] | If the state function Enthalpy $H$ is defined by
$$H=U+PV\tag{1}$$
where $U$ is the internal energy of the system, $P$ is the systems pressure and $V$ is its volume.
It follows that $$dH=TdS + VdP\tag{2}$$ by use of the product rule and the first law of thermodynamics: $$dU=TdS - PdV\tag{3}$$ where $T$ is the thermod... | Since Enthalpy $(H)$ is a state function, it can be expressed as a function of either of the two variables of $P,\,V,\,T\,.$
So, consider enthalpy as a function of $T$ and $P\,.$
So, its differential can be written as
$$\mathrm dH = \left(\frac{\partial H}{\partial T}\right)_P ~\mathrm dT + \left(\frac{\partial H}{\... | In freshman physics, we learned that, when heat is added to a constant volume system, we can write Q = CΔT, where C is called the heat capacity. However, when we got more deeply into the basics and learned thermodynamics, we found that this elementary approach is no longer adequate (or precise). We found that Q depen... | https://physics.stackexchange.com |
38,009 | [
"https://engineering.stackexchange.com/questions/38009",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/27643/"
] | In particular drone propeller blades. I read that the noise we hear is the propeller compressing the air at the edge of it to produce a sonic boom. Is that true and is there a way to negate that?
| Operating the unmanned aerial system in a vacuum will remove almost all of the noise.
Unfortunately, the unmanned aerial system will not fly in a vacuum, because air is required. The compression of air is part of the mechanics of flight, along with the rarefaction of air.
In the world of aerodynamics, a high speed prop... | in a subsonic air propeller blade, there are two sources of noise: first, the "hiss" of air moving past the blades and then <em>blade passage noise</em> which is a sound wave that sweeps around with the blade as it revolves, producing a sound pulse with each blade passage. It has a characteristic frequency of... | https://engineering.stackexchange.com |
148,072 | [
"https://electronics.stackexchange.com/questions/148072",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/56797/"
] | I want to make a power supply that outputs 90v DC, and I was looking for a 0...100v voltage regulators, but I don't find any...? How can I achieve this if I can't find them? The input voltage of the circuit would be 220V 50Hz.
EDIT: I have 220v to 110v 5A transformer although is really big.
| If you don't need regulation at all, what you probably want is a transformer with about a 63VAC output. Full wave bridge module (easily available up to 35A or more) and a filter cap (value depends on ripple you can live with, but usually 100V or better) and you're done.
As an added advantage, the galvanic isolation ... | You can't use a linear regulator for this application. You would burn over 250W in the regulator! A switching power supply is needed for this application.
<strong>Safety Notice</strong>
Please do not take this the wrong way, but the fact that you are talking about a linear regulator at this power level concerns me.... | https://electronics.stackexchange.com |
81,946 | [
"https://physics.stackexchange.com/questions/81946",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26063/"
] | Somewhere I read that spin quantum number is a particularly interesting theory of quantum mechanics as what it really implies is that particles like electrons do not come back to the initial state of observation after one rotation, but if they rotate 2 times then the same state is obtained. Is it really so?
Even if i... | Generally taking note of these relationships is a precursor to either (a) applying an approximation or (b) using a purturbative or series solution.
In case (a) what qualifies is completely a matter of your sensitivity to error. If you are going to throw out terms $\mathcal{O}(C^{\pm 2})$ and require a 1% approximatio... | This is a complement to dmckee's answer by way of an example.
Suppose that I want to determine the acceleration due to gravity of an object near the surface of the earth. Let $h$ be the height of the object above the surface, then according to Newton's Law of Gravitation, I get
\begin{align}
a = \frac{GM}{(R+h)^2} ... | https://physics.stackexchange.com |
328,806 | [
"https://electronics.stackexchange.com/questions/328806",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/145752/"
] | I’m a bit confused about capacitors. I understand they store energy in a field by accumulating opposite charges on the different plates. So a 1 farad capacitor will store 1 coulomb of charge if subjected to 1 volt if I understand the math right.
1 coulomb is also 1 amp-second, so this capacitor can supply 1 amp of cur... | Answering the second comment to the question.
Yes, that is exactly correct. They would both be storing 1C of charge. Think of a capacitor like a (perfect) balloon where the larger the capacitance, the larger the balloon volume and the more you expand the balloon, the higher the pressure inside the balloon.
Imagine o... | It is not clear what your problem is. The main relationship of concern here is that Q=CV (clearly Q = charge, C = capacitance, and V = voltage). So any combination of C and V that results in 1 yields a capacitor with 1 coulomb of stored charge. Taken together, the capacitance and the amount of charge to store determin... | https://electronics.stackexchange.com |
95,972 | [
"https://dba.stackexchange.com/questions/95972",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/18606/"
] | I have a MySQL single server setup with all tables using the InnoDB engine (because I need support for foreign keys). As response times are getting longer, I now believe I need to create a cluster of servers to be able to cope with an ever-growing database load.
Is it possible to create a cluster of MySQL servers usin... | Yes and no.
No, there is no way to apply multiple cores or servers to a single InnoDB transaction.
Yes, you can build a cluster with InnoDB. But it is a Galera (PXC or MariaDB) Cluster, which means multiple servers replicating to each other. Overall throughput increases, but response time for individual queries won... | Moving to Galera would be an option. Then your application has to be aware of 'deadlock detected try restarting transaction' errors.
Another possibility is to set up a read slave and configure your application to use this slave for read_only queries. If one slave isn't enough you can add more and use them with a loadb... | https://dba.stackexchange.com |
24,568 | [
"https://stats.stackexchange.com/questions/24568",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9649/"
] | I have a 2D-histogram for two vectors, <em>s1</em> and <em>s2</em>, generated using the <em>hist3</em> function in Matlab:
<pre><code>[hist2D, binC] = hist3([s1' s2']);
</code></pre>
I am normalizing it by making its total volume equal to unity, in the following manner:
<pre><code>L = binC{1}(2) - binC{1}(1);
B = bi... | Densities can be hard to work with. Whenever you can, <strong>calculate with the total probabilities instead.</strong>
Usually, histograms begin with point data, such as these 10,000 points:
<img src="https://i.stack.imgur.com/tlrPK.png" alt="Scatterplot">
A general 2D histogram tessellates the domain of the two va... | If you normalize a histogram, you don't need to take the bin-width into account. You can look at it like this: When estimating a histogram from continuous data, you basically discretize it first (by setting each value to the bin center which is closest to it) and then generate a discrete histogram for the discretized d... | https://stats.stackexchange.com |
207,660 | [
"https://physics.stackexchange.com/questions/207660",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/93107/"
] | How is the differential form of Gauss's Law $\mathbf{\nabla}\cdot{\bf E} = \dfrac{ρ}{ɛ}$ used? What I mean is, where am I measuring $E$ and what is $ρ$ in this context?
| Let me clarify you what divergence actually is.
Consider an arbitrary finite volume $V$, whose surface is $S$, in a vector-field $\bf h$. Then total flux emerging from $S$ is given by $$\text{Net flux from the surface} = \int_S \mathbf{h}\cdot ~\mathrm d{\bf a}.$$
Divide $V$ into two parts: $$V = v_1 +v _2\,.$$ Now ... | You are measuring $\vec E$ due to the continuous volume charge distribution enclosed by the Gaussian surface. $\rho$ refers to the volume density of charge of the continuous charge distribution.
| https://physics.stackexchange.com |
44,874 | [
"https://chemistry.stackexchange.com/questions/44874",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/25550/"
] | How can you calculate the total bond energy of CO2? I've searched for the bond energy of C=O and found it was 745, but sometimes 799. Which one is the right one to use? And do those numbers mean the bond energy of CO2?
| You're asking a pretty complex question. The short answer is that to calculate such an energy you have to utilize quantum mechanical calculations, or otherwise perform macroscopic experiments on bulk $\ce{CO2}$.
A quick ab-initio calculation of a O=C=O molecule with bond-length 1.164 Angstroems (quite close to experim... | I wouldn't worry too much about the slight differences in the bond enthalpy for the C$=$O. I will discuss why after the next paragraph.
The bond enthalpy is the amount of energy (in kJ) that is required to break 1 mol of that bond. Therefore, it is also a measurement of how much energy is released as 1 mol of that sa... | https://chemistry.stackexchange.com |
210,681 | [
"https://math.stackexchange.com/questions/210681",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/23350/"
] | I need some help to finish this proof:
<strong>THEOREM</strong>
Let $\{a_n\}$ be such that $\lim a_n=\ell$ and set
$$\hat a_n=\frac 1 n \sum_{k=1}^na_k$$
Then $\lim\hat a_n=\ell$
<strong>PROOF</strong>
Let $\epsilon >0 $ be given. Since $\lim a_n=\ell$ , there exists an $N$ for which $$\left| {{a_n} - \ell } ... | For the tail sum
$$\frac1n\sum_{N+1}^n|a_k-\ell|\leq \frac{(n-N)}{n}\varepsilon<\varepsilon$$
for all large $n$, hence
$$\limsup_n \frac1n\sum_{1}^n|a_k-\ell|\leq 0+\varepsilon=\varepsilon...$$
| Just rewriting your argument:
The sequence $\{|a_n-\ell|\}$ converges to $0$ therefore it's bounded, so there exist some $M\gt 0$ such that
$$|a_n-\ell|\leq M\quad\forall n\in \Bbb N.$$
This $M$ plays the role of the $\zeta$ in your proof, but notice it does not depends on $n$.
Let $\epsilon\gt 0$. There exist $n_1\... | https://math.stackexchange.com |
458,552 | [
"https://physics.stackexchange.com/questions/458552",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208825/"
] | According to quantum mechanics it should be possible. But can it happens when it has so small probability to occur? also if it can happens that means that energy must be provided in order to the electron escape the attractive force of the nucleus (ionization energy)?
| Here is the setting. You have a system that is described by some generalized coordinates <span class="math-container">$q_i$</span> and some generalized momenta <span class="math-container">$p_i$</span> (in the Lagrangian formalism, you'd use <span class="math-container">$\dot{q_i}$</span> instead). Hamilton's equations... | If a function (of time) is invariant under time translation then it is constant. In other words the Hamiltonian does not depends explicitly on time.
The (admittedly a bit sibylline) paragraph that you cite wants to stress the fact that, from the get go, the Hamiltonian is assumed to be <em>time local</em> i.e., to be ... | https://physics.stackexchange.com |
317,020 | [
"https://dba.stackexchange.com/questions/317020",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/260746/"
] | Im trying to create a function that accepts a list of uuids as a parameter.
My code:
<pre><code>create or replace function get_child_groups(input_parents_id uuid[])
returns table(id uuid, name text, parent_id uuid)
as
$$
WITH RECURSIVE c AS (
SELECT da.*
from device_group_v2 d
JOIN device_group... | The IN operator only works with "lists" or "sets", not with arrays. You need to use the <code>ANY</code> operator:
<pre><code>where id = ANY (input_parents_id)
</code></pre>
| While calling function, you should either typecast proper variable to <code>uuid[]</code>, or use <code>uuid[]</code> type variable.
Check below;
Passing uuid[] type variable
<pre><code>DO $$
DECLARE
param uuid[];
rec record;
BEGIN
SELECT array_agg( uuidcolumn ) INTO param FROM anothe... | https://dba.stackexchange.com |
34,120 | [
"https://mathoverflow.net/questions/34120",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1483/"
] | I was just going through the 3rd Proof of Sylow's theorem given in the "Topics In Algebra" Book by I.N. Herstein. It looked very interesting and i really liked its Philosophy. My question what is its significance, and how can it be applied to problems, or something else.
| This is the proof that uses the lemma that if a finite group $G$ has
a Sylow $p$-subgroup then so does each subgroup of $G$. To complete
the proof of existence of Sylow $p$-subgroups, it suffices to show
one can embed each group in a group with a Sylow $p$-subgroup.
By Cayley's theorem each finite $G$ embeds in $S_n$ w... | As Robin Chapman has given an elegant and compact proof, I content myself with answering your query about applications. Sylow's three theorems are a very interesting tool to classify groups of low cardinality. Some exercises are on this given in Herstein's book itself. Upto groups of order 60, you can use just the thre... | https://mathoverflow.net |
11,076 | [
"https://astronomy.stackexchange.com/questions/11076",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/7528/"
] | If photon is mass-less and gravity can interact only with matter, then how does gravity alter the trajectory of light?
| It is simply not true that gravity can only interact with mass. Rather, any long-range spin-2 force interacts with all energy-momentum equally, and it source is the stress-energy-momentum tensor. That is one way to state the equivalence principle.
Note that a massive object in its own rest frame has an associated ener... | <blockquote>
If photon is mass-less and gravity can interact only with matter, then how gravity can alter the trajectory of light?
</blockquote>
The second part of your "if" clause is incorrect. It's mass-energy, not just mass, that gravitates.
| https://astronomy.stackexchange.com |
173,190 | [
"https://dba.stackexchange.com/questions/173190",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/124534/"
] | I have a query which selects rows from a source database (DatabaseA), and inserts them into a target database (Database B). The collation type differs between the databases and they cannot be changed. I need to address the collation difference in my query by explicitly specifying the collation for varchar fields.
Curr... | You can once create a view using column definitions like this:
<pre><code>FirstName COLLATE SQL_Latin1_General_CI_AS, ...
</code></pre>
Then anytime you'd like to use User tables, you can use this view instead.
| Collations are per each string column / expression (XML datatype excluded). So in this sense, no, Collations cannot be set per Table or query.
<blockquote>
I need to address the collation difference in my query by explicitly specifying the collation for varchar fields.
</blockquote>
Um, why? You shouldn't need to d... | https://dba.stackexchange.com |
258,664 | [
"https://physics.stackexchange.com/questions/258664",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/114366/"
] | I was under the impression that gluons had no mass. Then Wikipedia throws this curveball:
<blockquote>
Mass:
0 (theoretical value)
< 0.0002 eV/c2 (experimental limit)
</blockquote>
Which one should a poor soul go by? If the theoretical value just the one that people "thought" was right, until they found ou... | The Standard Model was explicitly constructed to match experiments. As of today, we have no reason to believe gluons should be massive - and as you can see, the experimental upper bound is very tiny - and so we write no mass term in the Standard Model Lagrangian. Or put it another way: we strongly believe gluons are m... | So far gluons appear massless, and if they have mass this would mean there is some sort of symmetry breaking or Higgs mechanism involved with QCD. So far there is no evidence of this, and theory does not make predictions of gluon masses.
The coupling parameter of QCD decreases with transverse momentum or $\sqrt{s}$. T... | https://physics.stackexchange.com |
285,971 | [
"https://stats.stackexchange.com/questions/285971",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/143316/"
] | To derive moment generating function(mgf) of $f(x) = 1/2 e^x $ when $x<0$ and $= e^{-2x}$ when $x > 0$,
Since mgf $M(t) = E(e^{tx})$, we get
$E(e^{tx}) = \int_{-\infty}^\infty e^{tx}\cdot f(e^{tx})dx = \int_0^\infty e^{tx}\cdot e^{-2e^{tx}} + \int_{-\infty}^0e^{tx}\cdot {1\over 2}e^{e^{tx}}$
But is there any w... | Your formula for the moment generating function is wrong.
$$E(e^{tX})=\int_{-\infty}^{\infty}e^{tx}f(x)dx=\int_0^{\infty}e^{tx}e^{-2x}dx+\int_{-\infty}^0e^{tx}\frac{1}{2}e^{x}dx$$
Then you can start from here to calculate the $M(t)$. It should not be very difficult.
| An alternative viewpoint is that $X$ has a <em>mixture</em> density that consists of an equally-weighted sum of the density of an <em>exponential</em> random variable with parameter $2$ (the
$e^{-2x}\mathbf 1_{\{x>0\}} = \frac 12\cdot 2e^{-2x} \mathbf 1_{\{x>0\}}$ part) and the density of the <em>negative</em> o... | https://stats.stackexchange.com |
384,427 | [
"https://softwareengineering.stackexchange.com/questions/384427",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/324076/"
] | I have a mathematical model with two main "stages" 1. data loading (only a few KB of data) and 2. running a model on the data. I want to implement some tests and checks to ensure the data being fed into the model are valid (correct types, correct values etc.) to ensure the model output is correct.
<strong>At what stag... | <blockquote>
At what stage in the whole process is the best time to implement these tests - when loading the data or when running the model on the data?
</blockquote>
<strong>Neither</strong>.
Instead, separate the process in 3 stages:
<ol>
<li>Data loading</li>
<li>Validation</li>
<li>Running the model on the d... | The validation belongs in the model. Whether the data is bad or not depends on the model it is ultimately fed to and at the loading stage this is not known yet. OK, you currently have only one model but from a software engineering perspective that could change. So just like you test for null before using an object you ... | https://softwareengineering.stackexchange.com |
233,057 | [
"https://electronics.stackexchange.com/questions/233057",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/105619/"
] | When you plug in your computer, shouldn't all the NAND gates activate (because the output turns on when the both inputs are off) at the same time, causing chaos?
For example: RAM is made of memory circuits, which are made entirely of NAND gates, so wouldn't it go insane, storing random values at startup?
Edit: I did... | <blockquote>
When you plug in your computer, shouldn't all the NAND gates activate (because the output turns on when the both inputs are off) at the same time, causing chaos?
</blockquote>
Well what if they did? The CPU won't do anything until the power-up reset (usually a resistor-capacitor time delay) lets go of ... | Well, first of all, a NAND gate "turns on" (drives its output low) whenever both inputs are active (high).
And since some of the gates are driven by other gates, it is possible to keep them from all activating at once.
But yes, RAM generally has "random" values in it at power-up. That's why computers go through a car... | https://electronics.stackexchange.com |
371,835 | [
"https://physics.stackexchange.com/questions/371835",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/177103/"
] | If someone was to, put 2 magnets, spaced out. then put one in the middle, while both are attracting. would it float? I'm just starting to do stuff related to this. then if it was spun, would it spin for a bit?
| In terms of a thought experiment, yes it's possible. If you consider a free-body diagram, and you put the magnets in a pure vacuum free of perturbing air currents, and remove other vibrations, then the force of gravity could exactly cancel out the magnetic attraction force, and if F_net=0, there is no movement.
Howeve... | No, that floating arrangement is not stable, even if all the magnets are identical. It's not practically possible to make the distances exactly equal, so the middle magnet will be slightly closer to one of the outer magnets and move towards it.
So it won't work even with a horizontal arrangement. A vertical arrangeme... | https://physics.stackexchange.com |
4,765 | [
"https://mathoverflow.net/questions/4765",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1648/"
] | What is the exact relationship between Lie groups and Lie algebras? I know it's not bijective because all commutative Lie groups have isomorphic Lie algebras.
| Up to isomorphism, there is one <em>simply connected</em> Lie group for every Lie algebra. Indeed, there is also a homomorphism of simply connected Lie groups for every homomorphism of the corresponding Lie algebras so one gets an equivalence of categories this way.
This pans out nicely in yr commutative example: the... | I'd suggest taking a look at "Lecture 23" of Fulton-Harris. In particular, given a complex Lie algebra, there's a unique connected, simply connected complex Lie group G with that Lie algebra. The other connected Lie groups with the same Lie algebra are quotients of G by discrete subgroups of its centre Z(G) (so G is th... | https://mathoverflow.net |
16,400 | [
"https://electronics.stackexchange.com/questions/16400",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4172/"
] | I've narrowed down an issue in my code which creates an extra 260 bytes of static RAM usage:
<pre><code>BYTE Height = 150;
BYTE sampleLevel(BYTE ADCchan,BYTE averages)
{
float samp;
//int samp;
BYTE level;
samp = avgSampleADC(ADCchan,averages);
level = 100-(samp*100/Height);
return level;
}
... | For many mathematical functions there's a trade-off between RAM usage and speed. I guess the AVR floating-point library will be optimized for speed.<br>
Bitrex is right: try to avoid floating-point in microcontrollers unless absolutely necessary. Do you really need floating-point, or will fixed-point do? You can emulat... | Are you using floats anywhere else ? If not, the float here may be pulling in the whole floating-point library, which may be allocating memory for itself.
There's very rarely any need to use floating point in embedded apps as you don't need the large range of PF to process the limited range of values from real-world i... | https://electronics.stackexchange.com |
114,702 | [
"https://softwareengineering.stackexchange.com/questions/114702",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35790/"
] | In my work the language used to write applications is Visual Basic .NET.
I read on internet and almost all the examples and questions are about C#.
Is there any comercial application written in Visual Basic .NET? Is there any field for a VB Net developer?
| I think your question is related to whether you can get a job as a VB.NET developer.
You can get VB.NET jobs, they do exist - but don't restrict yourself by something as unimportant as a language. Learn C# and then you can choose from a much bigger range of jobs. All of your understanding of the .NET framework is imme... | There are plenty actually. I don't know why, but some companies chose VB.net over C#, probably because they used to be VB shops, possibly because they feel VB.net is a better language (!)
I know of a very large design suite that is used for oil platform and ship building that has a large part written in vb.net.
I know... | https://softwareengineering.stackexchange.com |
3,769,795 | [
"https://math.stackexchange.com/questions/3769795",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/713597/"
] | I'm considering the different cases for <span class="math-container">$a$</span> and <span class="math-container">$b$</span>
<strong>Case 1)</strong> <span class="math-container">$ a\geq 0$</span> and <span class="math-container">$ b\geq 0$</span>
Given both terms are positive, <span class="math-container">$ a + b \geq ... | Dealing with absolute values, the general strategy is: if you can avoid the cases method, do it.
Here , we have a typical example of this strategy: as both expressions are non-negative numbers, we compare them by comparing their squares, using that <span class="math-container">$|x|^2=x^2\,$</span>:
<span class="math-co... | <em>Something similar to yours:</em>
The first part was, indeed, easy.
<blockquote>
For the second part:
</blockquote>
Without loss of generality, take <span class="math-container">$|a|>|b|~~~~~~~~~(*)$</span>
<ul>
<li><span class="math-container">$a>0, b<0 \overset{(*)}\implies a+b>0$</span>. Then, indeed,... | https://math.stackexchange.com |
691,721 | [
"https://physics.stackexchange.com/questions/691721",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/326803/"
] | In all quantum field theory books, you read something like
<blockquote>
QED is a QFT from Abelian <span class="math-container">$U(1)_Q$</span> that describes the electromagnetic interaction ...
</blockquote>
But I fail to understand what is really meant by that. How is a QFT linked to group theory? How do you come up w... | The basic reasoning is presented in Weinberg's "The Quantum Theory of Fields" Volume 1. It goes along the following lines: we want to consider the possible quantum mechanical theories of relativistic particles. These are, by definition, constrained by Poincaré symmetry. Moreover, we want to focus on theories ... | The answer by <code>@Gold</code> is perfect, I would just add the following supplementary point:
Notice that the <span class="math-container">$U(1)$</span> gauge redundancy is already present in classical electrodynamics when you formulate it using electromagnetic potentials. However, in classical mechanics, you can co... | https://physics.stackexchange.com |
1,315,865 | [
"https://math.stackexchange.com/questions/1315865",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/195688/"
] | Define the Laplacian matrix as $L = D - A$. Here $A$ is the adjacency matrix of the directed graph so that the entries $A_{ij}$ of $A$ are equal to $1$ if there is an arrow form the vertex $j$ to $i$ and $0$ otherwise, and $D = \operatorname{diag}(\sum_{j=1}^n A_{1j},\cdots,\sum_{j=1}^n A_{nj})$.
My question is: $L$ i... | The two vertex graph with one directed edge provides a counterexample. In that case the Laplacian is given by
$$\left( \begin{array}{cc}
1 & -1 \\
0 & 0 \\ \end{array} \right)$$
For the vector $x = (x_1, x_2)$ we have that
$$x^TLx = x_1(x_1 - x_2)$$
We can make this negative by choosing $x_2 > x_1 > 0$.
| Note that with your definition, the Laplacian corresponds to the quadratic form
$$\sum_{ij \, \mbox{arc in D}} x_i^2-x_ix_j$$
It is easy to construct examples of such forms which are not positive semi-definite.
Now, if for $D$ you use the sum of in and out degree, the "new" Laplacian is corresponding to
$$\sum_{ij ... | https://math.stackexchange.com |
390,709 | [
"https://softwareengineering.stackexchange.com/questions/390709",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/326412/"
] | Right now we have a set of micro services with a client-facing gateway responsible for authentication and routing. MySQL database and RabbitMQ for the message queue. Internal services may queue up requests as necessary but the gateway never does. What I’m finding is that the time for the gateway to respond is too long.... | The main purpose of encapsulation is to hide complexity from the user of a class to make his life easier. This implies that there is such internal information that is irrelevant to the user.
While this is probably not always the case in practice, I do believe that there are such things as good abstractions where the u... | <blockquote>
Interface of the library should be defined by a user not by the creator. And user defines it by pattern of usage.
</blockquote>
Exactly the opposite is true. The library provider has the job of understanding the domain of the library to the maximum extent possible, with every minute detail possible, and... | https://softwareengineering.stackexchange.com |
687,168 | [
"https://physics.stackexchange.com/questions/687168",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | There is an operator that takes a state for example of the type
<span class="math-container">$$|\psi \rangle=\frac{1}{\sqrt2}( |0\rangle | 1\rangle+|1\rangle | 0\rangle)$$</span>
Into a not entangled type,and i guess that for unitary operators it's not possible, because the von Neumann entropy are invariant under unita... | von Neumann entropy is defined for a subsystem. It is invariant under unitary operators acting just on that system. But you can still apply unitary operators that act on the whole system to entangle/disentangle. In this case, one unitary that disentangles your state <span class="math-container">$|{\psi}\rangle$</span> ... | For <em>any</em> given initial state <span class="math-container">$\lvert\psi\rangle$</span> and <em>any</em> final state <span class="math-container">$\lvert\phi\rangle$</span>, there is a unitary which maps <span class="math-container">$\lvert\psi\rangle$</span> to <span class="math-container">$\lvert\phi\rangle$</sp... | https://physics.stackexchange.com |
618,295 | [
"https://electronics.stackexchange.com/questions/618295",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | The question pretty much sums up everything.
| No, you cannot swap emitter with a collector mainly due to the different doping (and size) between the collector and the emitter. The reverse beta <span class="math-container">\$\beta_R\$</span> will be much lower than the "normal" forward beta <span class="math-container">\$\beta_F\$</span>. Also, <span clas... | A BJT is not symmetric. The emitter is much more heavily doped than the collector. Although a transistor <em>can</em> be operated in what is called the "reverse active" region, where the roles of emitter and collector are swapped, this is usually avoided because the current gain (beta) in such a configuration... | https://electronics.stackexchange.com |
50,176 | [
"https://quant.stackexchange.com/questions/50176",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/43606/"
] | Can someone help me solve this following Itô Calculus problem?
Let <span class="math-container">$Z(t):= [B(t)*X(t)]/S(t)$</span>
We have the following dynamics of B(t), X(t) and S(t):
<span class="math-container">$dS(t)=\alpha S(t)dt+\sigma S(t)dW(t)$</span>
<span class="math-container">$dB(t)=rB(t)dt$</span>
<spa... | You have <span class="math-container">$$dZ_t = df\left(S_t, B_t, X_t\right) = \frac{\partial f}{\partial s}dS_t + \frac{\partial f}{\partial b}dB_t + \frac{\partial f}{\partial x}dX_t + \frac{1}{2}\left[\frac{\partial^2 f}{\partial s^2} d\langle S\rangle_t + 2\frac{\partial^2 f}{\partial s\partial x} d\langle S, X\rang... | If you are happy to try the brute force approach, then here are the relevant formulae:
In ordinary calculus, you have the product rule for the differential of two variables:
<span class="math-container">$$d \left( x_1 x_2\right)=x_1 dx_2+x_2 dx_1$$</span>
The general version of this for differential of products of n... | https://quant.stackexchange.com |
153,107 | [
"https://softwareengineering.stackexchange.com/questions/153107",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/50056/"
] | My team shares a "work" branch and a "stable" branch. Whenever a particular work branch is approved for further testing/release/etc, we merge it into stable. No code is ever checked directly into the stable branch.
Because of this, merge conflicts simply won't happen, and it seems silly to pull down the work branch an... | It's kinda in the nature of a DVCS that the action happens on a local machine, and gets pushed back to the main repo.
If it's that onerous, script it.
<pre><code>#!/bin/bash
if [ ! -f ".git" ]
then
echo "Not in a git repo!" >&2
exit 1
else
git checkout stable && \
git pull origin stable &... | Yes - by using SSH. Just SSH into the server containing the repo. If you have permissions to write to the repository and execute git, then just cd into the repository's directory and run the git merge command.
| https://softwareengineering.stackexchange.com |
290,984 | [
"https://softwareengineering.stackexchange.com/questions/290984",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/188823/"
] | It's a pretty naive question to ask but I got this doubt while programming for Android. I use to initialize my new strings like <code>String a=null</code>, so in my code there remains a probability to get <code>NullPointerException</code> if I forget to initialize the variable before accessing it but what about the oth... | First let's clarify something: You mention that after assigning null to the variable you could forget to initialize it, but by assigning null to it you are in effect initializing it.
<pre><code>public static void main (String args[]){
String s;
System.out.println(s); // compiler error variable may not b... | In general you want to keep declaration and initialisation as close as possible to minimise exactly the type of problem you're talking about.
There is also the issue of redundant initialisation where the value null you're assigning is never used which is extra code that harms readability even if the redundant assignme... | https://softwareengineering.stackexchange.com |
577,186 | [
"https://physics.stackexchange.com/questions/577186",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262635/"
] | I have a question that is bothering me, Lets assume that I have a parallel plates capacitor with distance <span class="math-container">$d$</span> between them. Now connect it to DC voltage source <span class="math-container">$V$</span>.
according to equation <span class="math-container">$$V=\frac{Q}{C}$$</span> <span ... | When the separation distance <span class="math-container">$d$</span> increases, all other things being equal, the capacitance is less, as you already know. But the charge doesn't "go anywhere". You don't "lose charge".
With no voltage applied to the capacitor, the charge on the metal plates consists... | The electric field on one plate is "felt" by the other.
A simple way to think about why the distance between the plates matters, is that the closer the plates are, the more strongly will the field of one plate help pull charges towards the other plate. Thus, more charge can be accumulated on the plates when t... | https://physics.stackexchange.com |
12,916 | [
"https://quant.stackexchange.com/questions/12916",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5052/"
] | I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates.
$$ \frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)} $$
I can understand the logic behind it but i am failling at proving/disproving it.
I've tried to rewrite it in term of Zero Coupon Bond Price, in ... | Note that $\frac{F(0,s,T)}{F(0,t,T)} = \frac{T-t}{T-s}\frac{B(0,s)-B(0,T)}{B(0,t)-B(0,T)}$ and $\frac{F(s,s,T)}{F(s,t,T)} = \frac{T-t}{T-s}\frac{B(s,s)-B(s,T)}{B(s,t)-B(s,T)}$. Multiplying the numerator and denominator of the last expression with $B(0,s)$ and noting that $B(0,s)B(s,u)=B(0,u)$ (investing one Dollar for ... | Here is a simple (trivial) non-finance answer for the case of flat interest rates. Multiply both the denominator $F(s,t, T)$ and the numerator $F(s,s,T)$ with $e^{rs}$.
| https://quant.stackexchange.com |
14,702 | [
"https://scicomp.stackexchange.com/questions/14702",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/3290/"
] | I'm looking for a method to solve a large overdetermined system of linear equations in a least squares sense. The matrix is dense.
I'd like to use a method that works even with limited memory (we can't load the full matrix in RAM).
The matrix dimensions are something like 10,000,000 by 10,000, where I have a very lar... | One option here would be to form the normal equations $A^{T}Ax=A^{T}b$ and solve them by Cholesky factorization of the resulting $n$ by $n$ matrix. This squares the condition number of the problem which could potentially be a significant problem.
Forming $B=A^{T}A$ doesn't require more than $O(n^2)$ memory, assumin... | I think the answer to your problem is called Recursive Least Squares. Basically you treat each row one after the other, and the algorithm is based on the Woodbury matrix identity to update the inverse matrix.
Enjoy ;)
| https://scicomp.stackexchange.com |
110,273 | [
"https://mathoverflow.net/questions/110273",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2191/"
] | The Fontaine-Mazur conjecture predicts that an $l$-adic Galois representation of a number field is 'geometric' if it is unramified outside a finite set of primes and is De Rham for primes lying over $l$. Now, what happens if one forgets about the latter restriction; are there any counterexamples, and is there any (gene... | There is a nice lemma that relates ideals and subalgebras in graded rings that can be applied to the problem:
<blockquote>
<strong>Lemma:</strong> Let $A=\bigoplus_{n \ge 0}A_n$ be a graded ring that is commutative (or graded commutative). Then for homogeneous elements $p_i \in A\; (i \in I)$ of positive degree ar... | Consider the map from $\mathbb P^r$ with coordinates $(x_0:x_1:\dots:x_r)$ to a weighted $\mathbb P^t$ with coordinates $(y_0:y_1:....:y_r)$ with weights $w_0=1$ and $w_i$ is the degree of $p_i$ given by $y_0=x_0$, $y_i=p_i$. This map is well-defined, since if all $p_i$ vanish then all $x_i$ vanish. This map is proper,... | https://mathoverflow.net |
4,540 | [
"https://mechanics.stackexchange.com/questions/4540",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2326/"
] | I got my 2002 Camry when it had 86K and now it has 97K on it. In the morning when I start the engine, I see blue-ish smoke coming out of the exhaust for a while. I don't know if I had it before, but it's more noticeable recently. The smoke does go away after driving for a while.
I assume the original owner used regula... | Whether you stick with synthetic or switch back to traditional oil, if it is your valve seals (which does seem likely) you will still need to get them replaced.
Quite often that is all you will need to replace - but worth getting your garage to have a look at head gasket at the same time as they will be in there anywa... | Certain Toyota engines are notorious for valve stem seal leaks starting at right around 60k miles. It's exacerbated by using synthetic oil. I put 180k miles on a 5S-FE engine that had that problem all the way from 55k miles. Just had to top off the oil periodically. The Toyota mechs I know all say it's not worth th... | https://mechanics.stackexchange.com |
670,927 | [
"https://physics.stackexchange.com/questions/670927",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/314943/"
] | So basically my question is when a force acts on a rigid body I know that the part of the force perpendicular to the rotation axis of the object causes a torque and therefore a rotation (If it is the only force on the object), but does the whole magnitude of the force then also contribute to the objects liner motion or... | <blockquote>
but does the whole magnitude of the force then also contribute to the
objects liner motion or only the magnitude left over by the torque?
</blockquote>
The force does not "divide itself" up between linear motion and rotation. Linear motion and rotation are the results of the same magnitude of for... | Newton's second law states that for a set of forces acting on a system, there is a corresponding acceleration of the centre of mass that is proportional to the net force. The law does not state that the force is "spent" to produce the acceleration; a force is not a fuel (and in particular a force is not a &qu... | https://physics.stackexchange.com |
679,629 | [
"https://physics.stackexchange.com/questions/679629",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167872/"
] | Suppose I have a positively charged object A (+100C) and two other charged objects B (+10C) & C (+5C) in the vicinity of A i.e. in A's electric field. They are both equidistant from A. So, we can understand that B has a higher electric potential energy than C with respect to A due to the higher magnitude of charge ... | The short answer to your question is potential energy. Absolutely everything is always trying to get to the lowest potential energy state possible.
Let's start with the fundamental difference between electric potential and electric potential energy: electric potential energy is always in reference to a specific charge ... | 1.We usually calculate the potential to infinity and not to a near charge,
so You can always compare C and B.
there is only the factor q between potential and potential energy, so it makes no sense to differentiate between them. a charge q gains or looses its kinetic energy if it moves in a potential difference.
| https://physics.stackexchange.com |
506,311 | [
"https://electronics.stackexchange.com/questions/506311",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/193501/"
] | I'm using an ESP32 with a 12V battery and solar panel. I've created a voltage divider for 0-15v (3.3v input to MCU at 15v at battery side).
For that I used a 100kOhm , and 300kOhm to get a 0.3 ratio.
For measuring purposes, result measured is close enough (0.1v error), but Battery-wise, selecting those resistors were ... | 0.25 ratio? That's 3v into the ESP at 12V. They are fine, impedance wise, but esp32 has a pretty poor ADC, it samples very fast so gets a lot of noise, and is poor linearity best the extremes of range.
Should divide it more, 12v batteries often go up to 14V or more when charging, and you want to avoid the high end of t... | As commented above, are you trying to power your ESP32 with a 12v battery via a voltage divider?
If so, then a better solution is to use a voltage regulator to regulate your 12v to 3.3v. Even better, you could use a DC-to-DC buck converter for high efficiency.
The voltage difference between 12v and 3.3v is quite high, ... | https://electronics.stackexchange.com |
48,893 | [
"https://engineering.stackexchange.com/questions/48893",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/36289/"
] | Recently, I dipped my spoon into my tea. I saw that as I dipped my spoon into my tea, two vortices formed at both edges of the spoon. I guess this is similar to vortices forming at the end of aeroplane wings. Here I assume both vortices have equal strength and according to Kelvin's circulation theorem, the sum of circu... | To my understanding the circulation of the tea when you stirred it was not zero. So the vortex that formed from the two smaller one must have had the same direction of the initial stir.
I would consider that they <em>if</em> there is any difference in vorticity "strength" is probably due to viscous phenomena... | Trying to "see" your experience without pictures.
First, when you inserted your spoon, you could have lowered it at an angle causing it to displace the liquid like a row causing two trailing vortices at the edges.
Later when you dipped it into circulating tea, the current interacted with the two vortices. The... | https://engineering.stackexchange.com |
160,692 | [
"https://mathoverflow.net/questions/160692",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25516/"
] | I am recently concerned with the following problem: Given a parametrized curve in $\mathbb{R}^6$, what is the condition that it belongs to a hyper-sphere of dimension 5?
The more general question would be what are the conditions for a given parametrized curve in $\mathbb{R}^n$ to belong to a given hyper-surface of $\m... | Working this out in full generality is likely to be rather messy and unenlightening, but there are a few remarks about the nature of the problem (and special cases) that can be made, so I'll put them here.
First, for any $n$-manifold $M$, let $\mathcal{C}_k(M)$ denote the space of $k$-jets of unparametrized, oriented,... | I would reformulate the problem in the following manner:
Given is a manifold with codimension 1 (→ 1 equation), the hypersurface $H$ and a manifold with dimension 1 ($n-1$ equations), the curve $C$.
Now a <em>necessary</em> condition for $C\in H$ is
$$\rm d h \wedge \rm d c_1 \wedge \ldots \wedge \rm d c_{n-1} = 0,$$... | https://mathoverflow.net |
156,290 | [
"https://mathoverflow.net/questions/156290",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5181/"
] | I have the following somewhat vague question. I am not sure if it is appropriate for this forum, please feel free to close (or migrate to stackexchange).
I have been "brought up" as an algebraic geometer. Spectral sequences are obviously ubiqutous and useful in this subject. The conclusion I have drawn from my exposur... | It seems to me that everything written so far is addressing the title, not the body of the question, in particular focusing on the unstable. Part of that is people asking their own questions. But I think it is best to start with the easiest questions. Indeed, Tom, you have singled out the right place to start: Yes, the... | I am very surprised that nobody has yet mentioned Massey's beautiful
general theory of exact couples. This to my mind answers the
alternative version of the question, and does so without restriction
to algebraic topology. Filtrations give rise to exact couples, but they
can perfectly well come from data that has not... | https://mathoverflow.net |
109,269 | [
"https://biology.stackexchange.com/questions/109269",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/66906/"
] | Would it be possible for short DNA molecules to replicate, for example, if it's heated to the point where the strands separate (as far as I know, that's what happens in PCR?) and freely floating bases could "connect" to their correspondent bases (A/T, C/G)?
I'm assuming that A/T and C/G bases strongly 'attrac... | No, replication cannot happen in the absence of polymerase (on the timescales relevant to humans).
You are correct that in PCR, the first step is to separate DNA strands at 98 C. This heating dissociates the strands semi-permanently. So when you cool down the reaction, the strands do not re-associate very quickly.
When... | Nope. Not happening.
The high temperature (90 °C) needed to separate a DNA strand also makes an association of free floating bases to a template strand much too unstable.
Even if the bases associated with the template strand, they wouldn't spontaneously connect (phosphodiester bond formation) with each other. It needs ... | https://biology.stackexchange.com |
103,797 | [
"https://softwareengineering.stackexchange.com/questions/103797",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6435/"
] | Is there any solid evidence behind the reasons for decline in search volume for popular programming languages?
Could this possibly be due to improvements in finding necessary information (no need to search 10 times to find something) and quality of information?
<img src="https://i.stack.imgur.com/Wfc7T.jpg" alt="ente... | I can think of at least four factors that might be underway here:
<ol>
<li>As you say - resources are improving all the time, and less searching is required to find useful information</li>
<li>People search at specific sites more (such as stackoverflow) rather than a broader search through Google</li>
<li>People are s... | I think your point about the search engine queries being more precise might be the possible explanation.
Another one would be that people perhaps use this site or their favourite forum/site/blog to ask the "big questions".
One more reason, people are using paper books or ebooks with the information.
Interesting ques... | https://softwareengineering.stackexchange.com |
2,262 | [
"https://biology.stackexchange.com/questions/2262",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/86/"
] | My russian friend says that the USSR agents used/use the trick that they offered the victim first vodka and then last wine.
I have noted that this puts you faster to hangover: decreasing the alcohol proof.
Some people lose their motor function immediately and some their memory only.
<strong>Why does a decrease in th... | I would argue that your central point is intrinsically flawed. Your claim is that starting at a high alcohol percentage, then gradually decreasing alcohol content, gets you intoxicated faster. @nico is correct that you will get drunk faster this way (more alcohol sooner rather than later, so this is trivial). If we all... | This has more to do with the person's tolerance to alcohol than the trick itself. People will be affected by different amount of alcohol differently. From personal experience in college, I have seen many people take several shots of vodka and still carry on a conversation. In the same night, I have seen others take a g... | https://biology.stackexchange.com |
604 | [
"https://stats.stackexchange.com/questions/604",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/165/"
] | I am puzzled by something I found using Linear Discriminant Analysis. Here is the problem - I first ran the Discriminant analysis using 20 or so independent variables to predict 5 segments. Among the outputs, I asked for the Predicted Segments, which are the same as the original segments for around 80% of the cases. Th... | For optimisation, you don't need to perform a grid search; a Nelder-Mead simplex(fminsearch in MATLAB) approach is just as effective and generally much faster, especially if you have a lot of hyper-parameters to tune. Alternatively you can use gradient descent optimisation - if your implementation doesn't provide grad... | There are no general heuristics, you should make a grid search, especially since the value of nu must be between 0-1.
| https://stats.stackexchange.com |
1,547,593 | [
"https://math.stackexchange.com/questions/1547593",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Find the limit:
$$\lim_\limits{x\to 0^+}{\left( e^{\frac{1}{\sin x}}-e^{\frac{1}{x}}\right)}$$
</blockquote>
Using graph inspection, I have found the limit to be $+\infty$, but I cannot prove this in any way (I tried factorizing, using DLH)... Can anyone give a hint about that? The limit should be don... | First, you can show that $$\lim_{x\to 0^+}\left(\frac{1}{\sin x}-\frac{1}{x}\right)=0.$$ This shows that $$\lim_{x\to 0^+}\frac{e^{\frac{1}{\sin x}-\frac{1}{x}}-1}{\frac{1}{\sin x}-\frac{1}{x}}=1.$$
Now, write $$e^{1/\sin x}-e^{1/x}=e^{1/x}\left(\frac{1}{\sin x}-\frac{1}{x}\right)\frac{e^{\frac{1}{\sin x}-\frac{1}{x}}-... | By the Mean Value Theorem applied to $f(x)=e^{1/x}$ with $f'(x)=-x^{-2}e^{1/x}$, we have
$$e^{1/\sin x}-e^{1/x}=f(\sin x)-f(x)=(x-\sin x)f'(\xi)=\frac{x-\sin x}{\xi^2}\cdot e^{1/\xi} $$
with $\xi$ between $x$ and $\sin x$.
We can find $a>0$ such that for all small enough positive $x$ we have
$$\tag1 \sin x < x ... | https://math.stackexchange.com |
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