text stringlengths 1 1.11k | source dict |
|---|---|
special-relativity, quantum-entanglement, faster-than-light
Title: Gear Theory -- Entanglement -- Spooky action at a distance explained? Nothing can travel faster than the speed of light. Not even an electrical signal. Entanglement seems to violate this. But, does it?
Imagine 100 gears lined up in sequence all the way across a basketball court. As you turn the gear under one hoop, all 100 gears simultaneously spin. Even the gear across the court would simultaneously spin.
Could you in theory connect gears a longer distance? Even Miles?
Imagine 100 basketballs in a straight line from one hoop to the other hoop with gears around the circumference parallel to the floor. You spin one ball, and they all spin. Spinning the ball under one hoop, simultaneously spins the other ball. Imagine, the in-between balls were not visible. Would this be a similar pattern to what we are seeing with entanglement?
Is it possible that it is not empty space between the two particles, yet some gear like matter that is connecting entangled particles?
Gear Theory | {
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"tags": "special-relativity, quantum-entanglement, faster-than-light",
"url": null
} |
find. The rule can be an effective way to cut through the anxiety of decision-making. The net present value (NPV) is the sum of present values of money in different future points in time. Get Finance homework help today. When doing DCF (Discounted Cash Flows) exercises, it is necessary to take effect of the taxes and for this, it is necessary to understand which cash flows get affected with the tax factor. Mostly NPV function is used in financial analysis work where we need to calculate the investment done in any project or assignment by any company. Calculate the Net Present Value. Net present value uses initial purchase price and the time value of money to calculate how much an asset is worth. Summary and Calculation of NPV. As explained by financial authors, the Net Present Value or Net Present Worth is defined as the present values of the individual cash flows, both incoming and outgoing, of a business entity. Let's find out how to calculate NPV in Excel. - Net present value method | {
"domain": "agenzialenarduzzi.it",
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.98228770337066,
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"openwebmath_score": 0.24044151604175568,
"tags": null,
"url": "http://agenzialenarduzzi.it/owwr/npv-calculator.html"
} |
javascript, fibonacci-sequence
My idea is to return an array holding fibonacci sequence up to n in index 0 and fibonnaci's n-th value in index 1. Can someone help me with a prettier way of constructing this function. I'd like to avoid holding the array in temp arr variable if possible, but still use a single expression for return statement. Quick review
Try to avoid very long names "generateFibonnaciSequence" can be "fibonnaciSequence".
The new array arr is undeclared and thus will be in the global scope. Chrome has recently improved how it handles optional parameters so there is no penalty to declare the array as an argument scoped to the function.
It seems to me that the reducer can return the last Fibonnaci number rather than a array which will make the code a little cleaner.
You can also reduce the iteration by one because you are starting the sequence at 1 rather than 0.
Filling the array is a lot of extra work as you only need the first value set. | {
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"tags": "javascript, fibonacci-sequence",
"url": null
} |
vba, excel, statistics
Exit Function
ErrHandler:
RMSE = "Error"
End Function
Root Mean Square Deviation (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed.
Wikipedia
Formula:
Questions
How is the performance? Can it improve?
Are the results ok? Are the functions working properly?
How to make a proper ErrHandler?
Should i use WorksheetFunction or created my own UDFs? If the quantity of data gets really large.
I was thinking... Should I use a Global Array for each Sheet? So it doesn't have to calculate an array of data for each function again?
Further tips/help are welcome. Or another improvements.
Just for reference: | {
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The prior Bezout equation $$\Rightarrow 141^{-1}\equiv \color{c00}{-7}\pmod{\!19},\,$$ & $$\,\color{#0a0}{19^{-1}\!\equiv 52}\pmod{\!141}\,$$ by reducing the Bezout equation $$\bmod19\,$$ and $$\bmod 141\,$$ resp., as explained here. Thus we see that using the extended Euclidean algorithm to compute the gcd Bezout equation yields one method of computing modular inverses (and fractions). See here and here for many more examples of this and various other methods. | {
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"openwebmath_perplexity": 1107.8914830890442,
"openwebmath_score": 0.9637992978096008,
"tags": null,
"url": "https://math.stackexchange.com/questions/616881/extended-euclidean-algorithm-backward-vs-forward/616893"
} |
feynman-diagrams, perturbation-theory, linear-algebra, eigenvalue
The Feynman diagrams are essentially simply a convenient way to write a particular term of the perturbation expansion when your objects are (quantum) field theories. For example, it turns out that, because of the form of the interaction term (your $B$) you can already say that some terms in the perturbation expansion are going to be zero. In general you have a diagrammatic way to write such terms which is useful because it provides an easy way to write down these terms. At the same time it also provides a physical intuition for what these terms do and this is probably even more important.
In a simple matrix setting Feynman diagrams are of no use as they cannot even be defined. | {
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"tags": "feynman-diagrams, perturbation-theory, linear-algebra, eigenvalue",
"url": null
} |
Upper bound, specified as a number, symbolic number, variable, expression, or function (including expressions and functions with infinities).
Name-Value Pair Arguments
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Example: 'IgnoreAnalyticConstraints',true specifies that int applies purely algebraic simplifications to the integrand.
Indicator for applying purely algebraic simplifications to the integrand, specified as true or false. If the value is true, apply purely algebraic simplifications to the integrand. This option can provide simpler results for expressions, for which the direct use of the integrator returns complicated results. In some cases, it also enables int to compute integrals that cannot be computed otherwise. | {
"domain": "mathworks.com",
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"lm_q2_score": 0.8633916011860785,
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"openwebmath_score": 0.8929407000541687,
"tags": null,
"url": "https://la.mathworks.com/help/symbolic/sym.int.html"
} |
javascript, object-oriented, reinventing-the-wheel, api, music
return this;
}
translate(n) {
let d = 0;
if (n instanceof Coil) {
d = n.Value;
} else {
d = n;
}
this.Value += d;
return this;
}
invert() {
this.Class = this.Size - this.Class;
return this;
}
reflect(pivot, pivot2) {
if (typeof pivot2 === "undefined") {
pivot2 = pivot;
}
this.Value = pivot + pivot2 - this.Value;
return this;
}
negate() {
this.Value *= -1;
return this;
}
add(other) {
return this.translate(other.Value);
}
addScalar(n) {
return this.translate(n);
}
subtract(other) {
return this.translate(-other.Value);
}
subtractScalar(n) {
return this.translate(-n);
}
modulo(n) {
return ((n % this.Size) + this.Size) % this.Size;
}
} | {
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"tags": "javascript, object-oriented, reinventing-the-wheel, api, music",
"url": null
} |
slam, navigation, odometry, realsense, robot-localization
<remap from="rgb/image" to="/camera/color/image_raw"/>
<remap from="depth/image" to="/camera/depth/image_raw"/>
<remap from="rgb/camera_info" to="/camera/color/camera_info"/>
<param name="rgb/image_transport" type="string" value="compressed"/>
<param name="depth/image_transport" type="string" value="compressedDepth"/>
<param name="Reg/Strategy" type="string" value="1"/> <!-- 0=Visual, 1=ICP, 2=Visual+ICP -->
<param name="Optimizer/Slam2D" type="string" value="true"/>
<param name="Reg/Force3DoF" type="string" value="true"/>
</node>
</group>
<!-- Visualisation RVIZ -->
<node pkg="rviz" type="rviz" name="rviz" args="-d $(find rtabmap_ros)/launch/config/demo_robot_mapping.rviz" output="screen"/>
</launch>
Using it and resulting map:
$ roslaunch test.launch
$ rosbag play --clock light-tf-ok.bag | {
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"tags": "slam, navigation, odometry, realsense, robot-localization",
"url": null
} |
machine-learning, nlp, prediction, word2vec, gensim
fastText provides two models for computing word representations: skipgram and cbow ('continuous-bag-of-words'). The skipgram model
learns to predict a target word thanks to a nearby word. On the other
hand, the cbow model predicts the target word according to its
context. The context is represented as a bag of the words contained in
a fixed size window around the target word.
The explanation is not clear for me since the "nearby word" has a similar meaning as "context". I googled a bit and ended up with this alternative definition:
In the CBOW model, the distributed representations of context (or surrounding words) are combined to predict the word in the middle.
While in the Skip-gram model, the distributed representation of the
input word is used to predict the context. | {
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"tags": "machine-learning, nlp, prediction, word2vec, gensim",
"url": null
} |
newtonian-mechanics, fluid-dynamics, buoyancy, viscosity, inertia
However, once an object is fully submerged, its buoyant force remains constant because the difference in pressure above and below it is the same. So what is it that's causing the object's velocity to slow to 0?
I have a feeling my understanding of inertia here is wrong so if anyone can clarify how inertia affects objects in a fluid or provide an explanation as to how this: | {
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$\int (ln(x))^{2}dx$
any hints ?
P.S must use parts on this one
May be that the substitution $u = 1 + 3x$ that leads to the indefinite integral...
$\displaystyle 3\ \int \ln u\ du\ (1)$
... is better. The (1) and the indefinite integral...
$\displaystyle \int \ln^{2} x\ dx\ (2)$
... can be found with the general formula described in...
http://www.mathhelpboards.com/f49/integrals-natural-logarithm-5286/#post24093
Kind regards
$\chi$ $\sigma$
#### Prove It
##### Well-known member
MHB Math Helper
$$\displaystyle \(\displaystyle \int\frac{1}{x}dx=\text{log}x+c$$\)
\displaystyle No, \displaystyle \begin{align*} {\frac{1}{x}\,dx} = \log{|x|} + C \end{align*}. | {
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"tags": null,
"url": "https://mathhelpboards.com/threads/integration-by-parts.5680/"
} |
quantum-mechanics, condensed-matter, greens-functions, non-equilibrium, quantum-transport
$$
G^t_{n,k\alpha} = \sum_m G^t_{nm}V^*_{k\alpha,m}\ g^t_{k\alpha}.\quad (II)
$$
The operator $g^t_{k\alpha}$ is the inverse of the operator $g^{-1}_{k\alpha}$, this operator corresponds to the function $g^t_{k\alpha}(t-t')$. Equation (**), written in terms of functions, coincides with equation (52). From the operator equality $G^t_{n,k\alpha}\ g^{-1}_{k\alpha}\ g^t_{k\alpha} = G^t_{n,k\alpha}$ follows the equation for the function $g^t_{k\alpha}(t-t')$
$$
\int dt_1\ \left(\left(-i\frac{\partial}{\partial t_1} - \varepsilon_k\right) G^t_{n,k\alpha}(t-t_1)\right) g^t_{k\alpha}(t_1-t') = G^t_{n,k\alpha}(t-t').
$$
From the last equation we arrive at the following equation for the function $g^t_{k\alpha}(t-t')$
$$
\left(i\frac{\partial}{\partial t} - \varepsilon_k\right)g^t_{k\alpha}(t-t') = \delta(t-t').
$$
Thus, the function $g^t_{k\alpha}(t-t')$ is itself a (contact?) Green's function and depends on $\varepsilon_k$. | {
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"url": null
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special-relativity
This technique actually works to break down every geometrical object into the parts different observers see. For instance if you see an electric and magnetic field you have six numbers, $E_x,E_y,E_z,B_x,B_y,$ and $B_z$ which actually are the components of one six component object (the electromagnetic field $F$) built out of the basis object $WX, WY, WZ, YZ, XZ,$ and $XY$. So to see what electric and magnetic parts someone else sees you can take their unit motion vector $U=M/\sqrt{M^2}$ compute $FU$ and $UF$ and add them $FU+UF$ get the three components for the magnetic field $B=(UF+UF)/2$ and subtract them to get the three components of the electric field $E=(UF-FU)/2$. So there is one electromagnetic field and it's a simple multiplication to find out how people see the parts. Everyone can make the same geometrical objects and break them down the same way. | {
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"tags": "special-relativity",
"url": null
} |
everyday-life, batteries, electrochemistry
ETA: I found a paper that addresses exactly this question.
within the electrolyte solution, the electric field always points from the positive to the negative electrode - but when the circuit is closed, the positive ions, and hence the net current, flow from the negative to the positive electrode | {
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"tags": "everyday-life, batteries, electrochemistry",
"url": null
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gravity, newtonian-gravity
Because the person rotates with earth at $\omega_{\rm E}=\frac{2\pi}{T_{\rm E}}$ ($T_{\rm E}=24\:\rm Hours$), he accelerate with acceleration $a=m\omega_{\rm E}^{2}R_{\rm E}$ (this is true only at the equatorial) towards the center of earth. Newton tells us that
$$\Sigma F=ma$$
$$\frac{GM_{\rm E}m}{R_{\rm E}^{2}}-N=m\omega_{\rm E}^{2}R_{\rm E}$$
$$N=mg-m\omega_{\rm E}^{2}R_{\rm E}=m\left(g-\omega_{\rm E}^{2}R_{\rm E}\right)$$
with $g\equiv\frac{GM_{\rm E}}{R_{\rm E}^{2}}\approx9.8\:\rm m/sec^{2}$. The normal force $N$ is what you perceive as weight, not the gravitational force. This is what your scale will read when you stand on them. You can clearly see that as you spin faster - you weigh less. This is the centrifugal effect you mentioned, but you see that when calculating things it is taken as an additional effect other than gravity. But if you'll plug the numbers you'll see that
$$\omega_{\rm E}^{2}R_{\rm E}\approx0.03\:\rm m/sec^{2}\ll g$$ | {
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"tags": "gravity, newtonian-gravity",
"url": null
} |
ros, turtlebot, web, server
[INFO] [WallTime: 1437468129.914613] Notebook's battery is now: 69%
Traceback (most recent call last):
File "coffee_bot.py", line 298, in <module>
while(coffebot.deliver_coffee() and not rospy.is_shutdown()):
File "coffee_bot.py", line 102, in deliver_coffee
data = json.load(urllib2.urlopen(self.server_public_dns + "/var/www/html/turtlebot-server/coffee_queue.php?pop"))
File "/usr/lib/python2.7/urllib2.py", line 127, in urlopen
return _opener.open(url, data, timeout)
File "/usr/lib/python2.7/urllib2.py", line 404, in open
response = self._open(req, data)
File "/usr/lib/python2.7/urllib2.py", line 422, in _open
'_open', req)
File "/usr/lib/python2.7/urllib2.py", line 382, in _call_chain
result = func(*args)
File "/usr/lib/python2.7/urllib2.py", line 1214, in http_open
return self.do_open(httplib.HTTPConnection, req)
File "/usr/lib/python2.7/urllib2.py", line 1184, in do_open
raise URLError(err)
urllib2.URLError: <urlopen error timed out> | {
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"tags": "ros, turtlebot, web, server",
"url": null
} |
c++, programming-challenge, time-limit-exceeded, binary-search, vectors
int arraysize;
int numberofsubarrays;
long long usernumber;
vector<long long> userArray; //Used in main()
vector<vector<long long>> subarrays; //Used in isPossible()
int vectorsum(vector<long long> userVector) {
int ans = accumulate(userVector.begin(), userVector.end(), 0);
return ans;
}
bool isPossible(long long n) {
subarrays = {};
subarrays.push_back({});
for (auto u : userArray) {
subarrays.back().push_back(u);
if (vectorsum(subarrays.back()) <= n) {
continue;
}
else {
subarrays.back().pop_back();
subarrays.push_back({ u });
}
}
if ((long long)subarrays.size() > numberofsubarrays) {
return false;
}
else {
return true;
}
}
int main()
{
cin >> arraysize >> numberofsubarrays; //Input handling
for (int u = 0; u < arraysize; u++) {
cin >> usernumber;
userArray.push_back(usernumber);
} | {
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"tags": "c++, programming-challenge, time-limit-exceeded, binary-search, vectors",
"url": null
} |
c++, object-oriented, rational-numbers
public:
fraction();
fraction(int, int);
fraction(unsigned int);
fraction(int);
fraction(float);
fraction(double);
fraction reduce();
int unsigned get_numerator();
int unsigned get_denominator();
void set_numerator(int);
void set_denominator(int);
void set_neg();
bool check_neg();
friend std::istream& operator >> (std::istream & is, fraction & p);
friend std::ostream& operator << (std::ostream & os, fraction & p);
friend fraction operator+ (fraction, fraction);
friend fraction operator- (fraction, fraction);
friend fraction operator* (fraction, fraction);
friend fraction operator/ (fraction, fraction);
friend bool operator== (fraction, fraction);
friend bool operator!= (fraction, fraction);
friend bool operator<= (fraction, fraction);
friend bool operator>= (fraction, fraction); | {
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"tags": "c++, object-oriented, rational-numbers",
"url": null
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beginner, c, compiler
if (chr == '\n') {
tokenizer->lineNumber++;
continue;
}
// remove comments if they are present
if (chr == '/') {
int chrSecond = getc(tokenizer->inStream);
if (chrSecond == '/') {
while (getc(tokenizer->inStream) != '\n');
tokenizer->lineNumber++;
continue;
} else if (chrSecond == '*') {
int tmp1 = getc(tokenizer->inStream);
if (tmp1 == '\n') tokenizer->lineNumber++;
while (true) {
int tmp2 = getc(tokenizer->inStream);
if (tmp2 == '\n') tokenizer->lineNumber++;
if (tmp1 == '*' && tmp2 == '/') break;
tmp1 = tmp2;
};
continue;
} else {
ungetc(chrSecond, tokenizer->inStream);
}
}
if (chr == '"') {
StringBuilder *tmpSb = new_sb();
int tmp;
while ((tmp = getc(tokenizer->inStream)) != '"') {
sb_add(tmpSb, tmp);
}; | {
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"openwebmath_score": null,
"tags": "beginner, c, compiler",
"url": null
} |
c, linked-list, reinventing-the-wheel
struct dlist_elem_##alias *cur = list->first; \
while (cur != NULL) { \
struct dlist_elem_##alias *next = cur->next; \
if (destroyer != NULL) \
destroyer(cur->value); \
free(cur); \
cur = next; \
} \
free(list); \
} \
/* Insertion. */ \
int \
push_dlist_##alias(struct dlist_##alias *list, type value) \
{ \
struct dlist_elem_##alias *new_first = create_dlist_elem_##alias(value); \
if (new_first == NULL) return 0; \
if (list->first == NULL) { \
list->first = list->last = new_first; \
} else { \
struct dlist_elem_##alias *old_first = list->first; \
old_first->prev = new_first; \
list->first = new_first; \
new_first->next = old_first; \
} \
return 1; \
} \
int \ | {
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"tags": "c, linked-list, reinventing-the-wheel",
"url": null
} |
quantum-mechanics, angular-momentum, symmetry, schroedinger-equation, coordinate-systems
$$P(\varphi)=c_{1}\cos m\varphi$$
with $m=0,1,2,3...$.
$c_{1}$ is a normalisation constant that works out as:
$$c_1=\frac{1}{\sqrt{\pi}},$$
except for $m=0$, then:
$$c_1=\frac{1}{\sqrt{2\pi}}$$
For $Z$ and $R$ I get, respectively, a sine function and a Bessel of the first kind $J$.
So this is quite uneventful, really. | {
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terminology, sea-ice, cryosphere
$$\begin{align}
h_1 &= 0.5 \times 0 \text{m} + 0.25 \times 0.5 \text{m} + 0.25 \times 0.3 \text{m} = 0.2 \text{m} \\
h_2 &= 0.5 \times 0.5 \text{m} + 0.5 \times 0.3 \text{m} = 0.4 \text{m}
\end{align}$$
Both variables can be useful. As I have seen conflicting names, I am a bit puzzled with the naming for $h_1$ and $h_2$. What are the standard names for $h_1$ and $h_2$ used in the sea ice community? It would appear that you are spot on with the commonly used terms in your question. A well-referenced post on the Arctic forums (not by me) entitled 'Average sea ice thickness vs effective sea ice thickness', provide information about this very question. Specifically:
Average Sea Ice Thickness = Volume of Sea Ice/Ice Covered Area
Effective Sea Ice Thickness = Volume of Sea Ice/Grid Cell Area | {
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machine-learning
I have a set of variables $V=\{v_1,v_2,...,v_n\}$ where each variable has a set of possible values (its domain). $V$ defines an outcome space $\mathcal{O}$ (the set of all possible assignments over $V$ from their domain values). For example, if $A=\{1,2\}$ and $B=\{3,4\}$ we have $\mathcal{O}=\{(1,3),(1,4),(2,3),(2,4)\}$. The input space $X$ is the set of all pairs of outcomes from $\mathcal{O}$. Each example $x$ consist of pairs of outcomes $a$,$b\in \mathcal{O}$ (denoted as $x[a]$,$x[b]$ respectively). The target function is a strict order relation $\succ$ over $\mathcal{O}$. I am adopting the active learning paradigm. I first choose $\mathcal{U}$ unlabelled examples, then ask the oracle to label an example $x\in \mathcal{U}$. $h(x)=+$ if $x[a]$ is better than $x[b]$ otherwise $-$. The hypothesis class $\mathcal{H}$ is the set of all possible strict (partial/total) orders consistent with the examples seen so far. My main concern is how to select representative hypotheses from | {
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algorithm-analysis, asymptotics, runtime-analysis
We choose $n_0 = max(n_1, n_2)$
Then, $\\$
$\frac{c_1 n^2}{d_1 n^3} \leq \frac{T_1(n)}{T_2(n)} \leq
\frac{c_2 n^2}{d_2 n^3} \text{ for all } n \geq n_0$
$\lim_{n \rightarrow \infty} \frac{c_1 n^2}{d_1 n^3} = 0$ and $\lim_{n \rightarrow \infty} \frac{c_2 n^2}{d_2 n^3} = 0$
Hence, by Squeeze Theorem, $\lim_{n \rightarrow \infty} \frac{T_1(n)}{T_2(n)} = 0$.
Therefore, Algo1 runs faster than Algo2 for $n >= n_0$
This is my solution, and I am wondering if this is right way to solve this question.
Any help is appreciated, thank you, If $T_1(n) = \Theta(n^2)$ and $T_2 = \Theta(n^3)$, then since $n^2 = o(n^3)$, it follows that $T_1(n) = o(T_2(n))$. In particular, $T_1(n) < T_2(n)$ for large enough $n$. In fact, for every $C>1$, $T_1(n) < CT_2(n)$ for large enough $n$ (how large depends on $C$). | {
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discrete-signals, fourier-transform, frequency-spectrum, filter-design, time-series
Title: What is the proper way to compute a real-valued time series given a continuous $1/\sqrt{\omega}$ spectrum? I have never fully been able to wrap my head around Fourier transforms, so I apologize if what I am trying to do is trivial or violates basic theory in some way.
What I have is a "made up" frequency spectrum (well, it comes from somewhere but not relevant for my problem). The spectrum has the form:
$$|G(\omega)| = \frac{a}{\sqrt{b\omega }}$$
where $a$ and $b$ are arbitrary (real) constants for my particular application. Note that I only show the spectrum but the real complex-valued Fourier spectrum would be:
$$G(\omega) = \frac{a}{\sqrt{b\omega }}e^{i\phi(\omega )}$$
For my purposes, $\phi(\omega)$ can be anything and is not physically constrained. As a starting point I've just set $\phi(\omega)=0$ so that the spectrum is real-valued. Sampling rate (or frequency spacing) can be arbitrary as can the length of signal. | {
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python, neural-network, audio-recognition
If you can store pronunciations of all the phonemes in all the possible contexts and can smooth the transition between adjacent phonemes then you can copy-paste sounds.
With a generative model we try model the human vocal tract system and depending on input context, speaking rate audio data is generated. Go through the first and third resource for detailed explanations.
All these problem arise because we want to make it sound more human. Phoneme transition and diffusion are the major hurdles.
todo: Pick any word and record it in different context, different speaking rate, different speakers and plot waveforms. You'll see each time it has a different waveform. Even if you don't change any condition each time there will be a slight variation in pronunciation of same word. Save pronunciations of few phoneme and copy paste them to generate a word and listen to it. | {
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$$\int_{-\infty}^{+\infty} \frac{dx}{\cosh^{n} x}=\frac{\sqrt{\pi}}{2}\frac{\Gamma \left(\frac{n}{2}\right)}{\Gamma \left(\frac{n+1}{2}\right)}$$
"n" can be complex,even.
Daniel.
EDIT:The correct result is multiplied by 2.See posts #4 & #7.
#### Attached Files:
• ###### Integrate.gif
File size:
1.6 KB
Views:
93
Last edited: May 19, 2005
4. May 19, 2005
### Zurtex
O.K, in Mathematica I go that if $\Re (n) > 0$ then:
$$\int_{-\infty}^{+\infty} \cosh^{-n} (x) dx = \frac{ \sqrt{\pi} \, \Gamma\left( \frac{n}{2} \right)}{ \Gamma\left( \frac{n + 1}{2} \right)}$$
5. May 19, 2005
### dextercioby
How do you explain the "1/2" factor discrepancy...?
Daniel.
EDIT:See post #7 for details.
Last edited: May 19, 2005
6. May 19, 2005
### Zurtex
Well if I left n=1 and integrate in mathematica I get $\pi$ and:
$$\Gamma \left( \frac{1}{2} \right) = \sqrt{\pi}$$
Are you sure you did not integrate between 0 and Infinity?
Last edited: May 19, 2005
7. May 19, 2005
### dextercioby | {
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"url": "https://www.physicsforums.com/threads/integral-evaluation-analytical-vs-numerical.76232/"
} |
python, python-3.x, file
I'm currently not automatically iterating over all suppliers because for some different standards apply.
This also increases customization, as you can easily define multiple classes with the different validation checks. Utilizing either inheritance or mixins to simplify the code.
Since the Classifier class will have lots of functions that will be called in the same way, I would opt to make a BaseClassifier class that magically handles everything.
Since I would pass values in at instantiation I would define the __init__ and simply assign the value to the instance.
Since we'll have lots of functions, to reduce the amount of WET I would automagically find the functions to run using dir and getattr.
Since the functions will all be called in the same way, defining a simple validate function can reduce the amount of code to write on each classifier. | {
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inorganic-chemistry
Title: Which coordination complex does not absorb visible light? A question was asked in one competitive exam (AIPMT 2010). It said:
Which of the following complex ions is not expected to absorb visible light?
$\ce{[Ni(CN)4]^2-}$
$\ce{[Cr(NH3)6]^3+}$
$\ce{[Fe(H2O)6]^2+}$
$\ce{[Ni(H2O)6]^2+}$ | {
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//[Defining posterior lowrankGp given the landmark transformations from reference to a target mesh]
// finding points (nodes) corresponding/associated to/with landmarks of the refMesh
// The nodes on the mesh closest to the landmarks are the nodes associated with the landmarks
val refLMs = LMs(0)
val refLMNodeIds = refLMs.map(eachLM => refMesh.pointSet.findClosestPoint(eachLM.point).id)
Generating the regression data, i.e. known deformation vectors (from the reference mesh to each target mesh). | {
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"openwebmath_score": 0.7260680198669434,
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"url": "https://empty-set.me/?author=1&paged=3"
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local-features, harris, corners, detection
where $I_{x}$ and $I_{y}$ are the smoothed images (with $\sigma_{D})$ on the respective location.
How do I apply the integration scale $\sigma_{I}$ now?
Do I have to store separate images $I_{x}^{2}$, $I_{y}^{2}$ and $I_{x}I_{y}$ and smooth these with $\sigma_{I}$ before computing the matrix and Harris corner response from it? I think the first smoothing, by $\sigma_D$, is only done to get more stable derivatives whereas in the second step the convolution by a Gaussian with $\sigma_I$ is done to establish the 'scale-space' in which the operator is applied.
Ignoring $\sigma_D$, this looks like this in Matlab:
dx = [-1 0 1; -1 0 1; -1 0 1]; % Simple mask for derivative
Ix = conv2(im, dx, 'same'); % Convolve against image
Iy = conv2(im, dx', 'same'); % Again for y-direction with transposed mask | {
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homework-and-exercises, electromagnetism, general-relativity, coordinate-systems
Title: Maxwell tensor in spherical and static spacetime I am approaching Problem 6.3 of Wald’s General Relativity.
I have some issues in understanding why the most general form of the Maxwell tensor in a static and spherically symmetric spacetime is
$F_{ab}= 2A(r)(e_{0})_{[a}(e_{1})_{b]}+2B(r)(e_2)_{[a}(e_3)_{b]}$
where the tetrad $e_\mu$ is defined as
$(e_0)_a = f^{1/2}(r) (dt)_a$
$(e_1)_a = h^{1/2}(r) (dr)_a$
$(e_2)_a = r (d\theta)_a$
$(e_3)_a = r \sin(\theta) (d\phi)_a$
I know I am missing something very stupid here...
The general form should be something like
$F_{ab}= 2A(r)(e_{0})_{[a}(e_{1})_{b]}+2B(r)(e_2)_{[a}(e_3)_{b]} + C(r)(e_{0})_{[a}(e_{2})_{b]} + D(r) (e_{0})_{[a}(e_{3})_{b]} + E(r) (e_{1})_{[a}(e_{2})_{b]} + G(r) (e_{1})_{[a}(e_{3})_{b]}$
since the coefficients cannot depend on $\theta$ or $\phi$ for spherical symmetry, and $F_{ab}$ is antisymmetrical.
If I apply a transformation $\theta^{'} = -\theta$ to the tetrad, I get | {
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electromagnetism, classical-electrodynamics
$$\nabla\cdot\mathbf{B}=0$$
$$\nabla\times\mathbf{B}=0$$
There is a very important theorem in vector calculus (commonly called the Helmholtz theorem) that, in a particular formulation, states: | {
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quantum-mechanics, homework-and-exercises, angular-momentum, hamiltonian, commutator
$$H = -\dfrac{\hbar^2}{2m}\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}r + \dfrac{1}{2mr^2}L^2+ V(r), $$
where $V(r)$ is the potential energy you are considering. This is easy to see, you just substitute the laplacian in spherical coordinates and you'll see that the $L^2$ term appears naturally. In that case it's obvious the operators commute. Recall that $L^2$ just affects angular coordinates, for the purpose of $L^2$ anything $r$-related is a constant. In that case we have that
$$[L^2,V(r)]f = L^2V(r)f - V(r)L^2f = V(r)L^2f-V(r)L^2f = 0.$$
The same happens to the other term involving just $r$ in the $H$ operator. The other piece is obvious also because $[L^2,L^2]=0$. In that case $[L^2,H]=0$.
EDIT: The first term commutes with $L^2$ because it just involves operations over $r$. I think you can see it better applying the commutator to a function | {
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complexity-theory, terminology, algorithm-analysis, time-complexity, runtime-analysis
it depends on the algorithm?
What means and when to use each input length "version"
Is there are some rule I can use to decide which one to use? In the most formal sense, the size of the input is measured in reference to a Turing Machine implementation of the algorithm, and it is the number of alphabet symbols needed to encode the input.
This is of course rather abstract, and is very difficult to work with in practice, or at least very annoying - we would need to consider how we're going specify delimeters etc. etc. What happens normally in practice then is that we look for a proxy measurement of the size of the input - something more convenient and accessible, but that does not cause any mathematical problems in our analysis. | {
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"tags": "complexity-theory, terminology, algorithm-analysis, time-complexity, runtime-analysis",
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Financial Markets. SOA EXAM FM STUDY NOTES. Exam IFM is a three-hour multiple-choice examination designed to build your knowledge of the theoretical elements of corporate finance and financial models. Intuitively, the return in time $$\Delta t$$ is $$\mu \Delta t$$ and the standard deviation is $$\sigma \sqrt{\Delta t}$$. Your Actuarial Exam IFM prep can be a resource that offers test-taking strategies specific to this exam. SOA Exams. It is offered via computer–based testing (CBT). Welcome to ACTEX Learning and Mad River Books. Approved Calculators. Our study notes have been made by academics and actuaries actually working in the field of investment. Exam 5 Basic Techniques for Ratemaking and Estimating Claim Liabilities Exam 6 Regulation and Financial Reporting Exam 7 Estimation of Policy Liabilities, Insurance Company Valuation, and Enterprise Risk Management These will teach you all the math concepts you need for the exam. SOA Exam P / CAS Exam 1 SOA Exam FM SOA IFM CAS MAS-I CAS | {
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objective-c, ios
[super setAlpha:alpha];
} First of all, using the tag to distinguish between views is almost everytime (there are exceptions) a bad idea. It's much cleaner to use your own variable (pointers to view, BOOL flags).
10 is a magic number. What does it mean? Use a constant.
Use methods. Four levels of if are terrible. Extract the code into methods.
if ([self isVerticalScrollingDisabled] || [self isHorizontalScrollingDisabled]) {
return;
}
[super setAlpha:alpha];
By the way, changing the behavior of a method in a subclass (the method sets alpha only if some conditions are valid) is smelly from architecture point of view. Declaring a special method, e.g. setAlphaIfScrollingEnabled: would be better. | {
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c++, image, template, classes, c++20
friend std::ostream& operator<<(std::ostream& os, const Image<ElementT>& rhs)
{
const std::string separator = "\t";
rhs.print(separator, os);
return os;
}
Image<ElementT>& operator+=(const Image<ElementT>& rhs)
{
assert(rhs.width == this->width);
assert(rhs.height == this->height);
std::transform(std::ranges::cbegin(image_data), std::ranges::cend(image_data), std::ranges::cbegin(rhs.image_data),
std::ranges::begin(image_data), std::plus<>{});
return *this;
} | {
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I decided to go about it another way---by using equivalent fractions in the original equation instead of decimals, i.e., (93/100 - 90/100) / (90/100); this time I did indeed come up with $$\displaystyle \frac{1} {30}$$!
But I'm still not getting why it is that way. $$\displaystyle \frac{1} {30}$$is exactly equal to 0.0333.... But when you try to then turn that 0.0333 back into a fraction, the resulting fraction is $$\displaystyle \frac{333} {10000}$$, which is NOT equal to $$\displaystyle \frac{1} {30}$$. And yet... it is equal to the decimal form of $$\displaystyle \frac{1} {30}$$.
How can both of those fractions equal 0.0333, and yet... they don't equal each other? | {
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"url": "https://mathhelpforum.com/threads/converting-decimals-to-fractions-help.260259/"
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# TrigonometryTrigonometric equation: 2cos(θ) + 2sin(θ) = √(6)
#### karush
##### Well-known member
$2\cos{\theta}+2\sin{\theta}=\sqrt{6}$
$\displaystyle\cos{\theta}+\sin{\theta}=\frac{ \sqrt{6} }{2}$
$\displaystyle(\cos{\theta}+\sin{\theta})^2=\frac{3}{2}$
$\displaystyle\cos^2{\theta}+2cos\theta\sin\theta+\sin{\theta}^2=\frac{3}{2}$
$\displaystyle\sin{2\theta}=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{12}=15^o$
the other answer is $75^o$ but don't know how you get it.
#### soroban
##### Well-known member
Re: 2costheta+2sintheta=sqrt6
Hello, karush!
You have: .$$\sin{2\theta}\:=\:\tfrac{1}{2}$$
Then: .$$2\theta \:=\:\begin{Bmatrix}\tfrac{\pi}{6} \\ \tfrac{5\pi}{6} \end{Bmatrix}$$
Therefore: .$$\theta \:=\:\begin{Bmatrix}\tfrac{\pi}{12} \\ \tfrac{5\pi}{12}\end{Bmatrix}$$
#### Prove It
##### Well-known member
MHB Math Helper
Re: 2costheta+2sintheta=sqrt6 | {
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sql, vba, excel, db2
'SEARCHES BY LOWER AGE RANGE
If wsCity.Value = vbNullString And wsState.Value = vbNullString And wsGender.Value = vbNullString And _
wsAgeL <> vbNullString And wsAgeU = vbNullString Then a = 24
'SEARCHES BY UPPER AGE RANGE
If wsCity.Value = vbNullString And wsState.Value = vbNullString And wsGender.Value = vbNullString And _
wsAgeL = vbNullString And wsAgeU <> vbNullString Then a = 25
'SEARCHES BY FULL AGE RANGE
If wsCity.Value = vbNullString And wsState.Value = vbNullString And wsGender.Value = vbNullString And _
wsAgeL = vbNullString And wsAgeU = vbNullString Then a = 26
'SEARCHES BY CITY, STATE, FULL AGE RANGE
If wsCity.Value <> vbNullString And wsState.Value <> vbNullString And wsGender.Value = vbNullString And _
wsAgeL <> vbNullString And wsAgeU <> vbNullString Then a = 27 | {
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"openwebmath_score": null,
"tags": "sql, vba, excel, db2",
"url": null
} |
newtonian-mechanics, forces, acceleration, differentiation, mathematics
$$\lim_{\epsilon \to 0^+} \frac{v(t_2+\epsilon)-v(t_2)}{\epsilon}=\lim_{\epsilon \to 0^-} \frac{v(t_2+\epsilon)-v(t_2)}{\epsilon}=a(t_2)$$
Well, let’s consider the two reasons why the above condition could not be met. Let’s first imagine that at this specific time $t_2$, this limit takes an infinite value. That means I can pick an arbitrarily small $\epsilon>0$ such that $a(t_2-\epsilon)$ is arbitrarily large. That would require through newton’s law (which is still defined at $t_2-\epsilon$), an arbitrarily large force. I’m sure you can see how that would be unphysical to have an infinitely large force. | {
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general-relativity, black-holes, metric-tensor, singularities, reissner-nordstrom-metric
However, there is also no guarantee that you are in the original universe. There might be many insides and outsides and you might have travelled from an earlier outside to a later outside. In a sense more than an infinite amount of time passed on your original outside while you were inside, all of the outside had it's chance to enter the first horizon by the time you crossed the second horizon the second time. That door is closed. So in the causal sense that even arbitrarily late events outside the black hole can't (might not) be affected by you means it is later. We don't know if you'd come out to a different universe. Everyone seems to assume it is a different universe. The theory is pretty crazy having a singularity you can see, so maybe you shouldn't read too much into it. | {
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"url": null
} |
html, css
blockquote {
background-color: rgb(255, 255, 255);
border-radius: 6px;
font-family: Georgia, serif;
font-size: 22px;
line-height: 1.4;
margin: 0;
padding: 17px;
}
p.author {
background-color: transparent;
font-weight: 500;
font-size: 22px;
line-height:22px;
margin: 24px 0 0 18px;
}
strong {
color: rgb(68, 68, 68);
}
a {
color: rgb(64, 131, 169);
text-decoration: none;
}
I would say that for it to be semantically accurate, the author should be a part of the blockquote, perhaps using a footer.
You should include a cite attribute if the quote has a source.
The quote content should be inside a paragraph element.
I guess now you don't need the wrapper any more.
<blockquote cite="http://knowyourmeme.com/memes/doge">
<p>“Such cool. Much awesome. WOW”</p>
<footer class="author">
–
<strong>Doge</strong>,
<a href="#">The Moon</a>
</footer>
</blockquote> | {
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c#, console, error-handling
Console.WriteLine("[{0}]Base Exception: {1}\n\nStacktrace: {2}",
DateTime.Now.ToShortTimeString(),
e.GetBaseException(), e.StackTrace);
}
else
{
Logger.Info(String.Format("\n[{0}] Error: {1}\n\nBase Exception: {2}\n\nStacktrace: {3}",
DateTime.Now.ToShortTimeString(), verboseMessage,
e.GetBaseException(), e.StackTrace));
Console.WriteLine("[{0}] Error: {1}\n\nBase Exception: {2}\n\nStacktrace: {3}",
DateTime.Now.ToShortTimeString(), verboseMessage,
e.GetBaseException(), e.StackTrace);
}
}
break; | {
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} |
org-mode source
## Nonlinear curve fitting by direct least squares minimization
| categories: data analysis | tags: | View Comments
Here is an example of fitting a nonlinear function to data by direct minimization of the summed squared error.
from scipy.optimize import fmin
import numpy as np
volumes = np.array([13.71, 14.82, 16.0, 17.23, 18.52])
energies = np.array([-56.29, -56.41, -56.46, -56.463,-56.41])
def Murnaghan(parameters,vol):
'From PRB 28,5480 (1983'
E0 = parameters[0]
B0 = parameters[1]
BP = parameters[2]
V0 = parameters[3]
E = E0 + B0*vol/BP*(((V0/vol)**BP)/(BP-1)+1) - V0*B0/(BP-1.)
return E
def objective(pars,vol):
#we will minimize this function
err = energies - Murnaghan(pars,vol)
return np.sum(err**2) #we return the summed squared error directly
x0 = [ -56., 0.54, 2., 16.5] #initial guess of parameters
plsq = fmin(objective,x0,args=(volumes,)) #note args is a tuple
print 'parameters = {0}'.format(plsq) | {
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} |
python, python-3.x, comparative-review
Generally I think your second approach using zip is preferable, but it isn't enough. You should write well-typed functions. Iterator functions are a convenient way to capture your logic.
Suggested
This (intentionally) isn't exactly equivalent in terms of logic, but since all of your timestamps already meet the interval minimum, the output is the same.
from datetime import datetime, timedelta
from typing import Iterable, Iterator, Literal, Sequence | {
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c++, matrix, c++14, template, vectors
Title: Simple Matrix Template Class I wanted to make a matrix template class to see if I can learn how to use templates, work on figuring out the indexing in loops, and making an interface so the user can know if an operation will work. Eventually I would like to add more cache optimization, calculating the inverse, and other ways to get data into the matrix such as raw pointers.
For now everything is one header and I will separate out the implementation
#pragma once
#include <cstdint>
#include <vector>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <type_traits>
template<typename T>
class LiteMatrix
{
public:
LiteMatrix(const size_t &rows, const size_t &cols);
LiteMatrix(const size_t &rows, const size_t &cols, const std::vector<T>&data);
~LiteMatrix() = default;
LiteMatrix(const LiteMatrix &rhs) = default; // copy constructor
LiteMatrix(LiteMatrix && rhs) = default; // move constructor | {
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} |
ros, ros2, transforms, eigen, tf2
6.91763e-310 7.29112e-304 0 1
cam -> tag:
0.939404 0.342707 -0.00846977 0.407591
0.326405 -0.886622 0.327659 -0.352925
0.104781 -0.310569 -0.944758 0.968488
6.91763e-310 7.29112e-304 0 1
cam -> tag:
0.951675 0.266108 -0.153299 0.369307
0.29877 -0.917761 0.261632 -0.40231
-0.071069 -0.29479 -0.952916 0.809793
6.91763e-310 7.29112e-304 0 1
cam -> tag:
0.934415 0.263749 -0.239384 0.379393
0.323434 -0.909803 0.260095 -0.429692
-0.149192 -0.320462 -0.935439 0.778602
6.91763e-310 7.29112e-304 0 1
cam -> tag:
0.91128 0.234292 -0.338638 0.323273
0.300529 -0.940601 0.15796 -0.414841
-0.281515 -0.245716 -0.927563 0.869551
6.91763e-310 7.29112e-304 0 1
cam -> tag:
0.916233 0.259035 -0.305643 0.234101 | {
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"tags": "ros, ros2, transforms, eigen, tf2",
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} |
beginner, shell, ant
<echo message="usage –> Display this target listing"/>
<echo message="init –> Create project directory structure"/>
<echo message=""/>
<echo message="compile –> Compile application sources"/>
<echo message='execute -Dmain="package.subpackage.ClassName"'/>
<echo message=" –> Execute program at a provided main"/>
<echo message=""/>
<echo id="compile-tests"
message="compile-tests –> Compile unit test sources"/>
<echo id="test"
message="test –> Execute unit tests"/>
<echo id="blank" message=""/>
<echo message="clean –> Clean output directories"/>
<echo message="generate-javadoc –> Generate javadocs"/>
</target>
<target name="init">
<!-- Create project directory structure -->
<mkdir dir="${main.src.dir}"/>
<mkdir dir="${test.src.dir}"/>
</target> | {
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"tags": "beginner, shell, ant",
"url": null
} |
buoyancy, fluid-statics
Title: Why buoyancy is applied on centroid? My book says: "The point of application of the buoyancy force is the geometric center(centroid) of the submerged part of the body, whereas the specific gravity of the fluid is constant."
But why buoyancy is applied on centroid? The statement in that book is not fully correct. It's only correct if the composition of the fluid surrounding the body is of the same material, thus having the same density at every point around the body. In this specific case only does the center of buoyancy coincide with the geometric centroid of the body. A more correct statement for the book would have been "The point of application of the buoyancy force is the center of gravity of the submerged part of the body...." | {
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"tags": "buoyancy, fluid-statics",
"url": null
} |
java, mvc, javafx
@FXML
private void updateDraftListWithFinalDrafts(ActionEvent actionEvent) {
setDraftSelectionOptions(model.getFinalDrafts(getSelectedYear()));
actionEvent.consume();
}
@FXML
private void updateDraftList(ActionEvent event) {
ObservableList<DraftPK> drafts = getDrafts();
setDraftSelectionOptions(drafts);
event.consume();
}
private void setDraftSelectionOptions(ObservableList<DraftPK> drafts) {
ObservableList<DraftPK> items = documentChooser.getItems();
items.clear();
items.setAll(drafts);
}
@FXML
private void setDrafterChooser() {
drafterChooser.setItems(model.getDrafters());
}
@FXML
private void toggleChangeDraft(ActionEvent event) {
changeDraft.setSelected(!notChangeDraft.isSelected());
event.consume();
} | {
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"tags": "java, mvc, javafx",
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ros, navigation, ekf, navsat-transform, robot-localization
0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1e-9, 0, 0, 0, 0, | {
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"tags": "ros, navigation, ekf, navsat-transform, robot-localization",
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electromagnetism, black-holes
Title: Could a magnetar retrieve information from Beyond The Event Horizon? I'm not exactly sure how the mathematics would work here but if an electron or any charged particle were in the magnetic grasp of a magnetar and it's electromagnetic field somehow crossed the boundary of its binary Partners Event Horizon would the magnetar's electromagnetic field, electromagnetism being significantly stronger than gravity, be able to retrieve information from Beyond an event horizon? Now, I get the feeling the event horizon would dissolve the electromagnetic bonds; however, is there anywhere in the math that could allow for a black hole with x properties to have information siphoned by a magnetar with y properties? Statements such as "electromagnetism is much stronger than gravity" have an extremely specialized meaning. In this case the statement refers to the typical magnitude of forces between elementary particles with a charge of a few units of elementary charge and masses comparable to | {
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metallurgy, metals, consumer-electronics
Piezoelectric speaker | {
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You can rearrange as follows:
$$\begin{eqnarray} Var(X) &=& E[X^2] - (E[X])^2\\ E[X^2] &=& (E[X])^2 + Var(X) \end{eqnarray}$$
Then, interpret as follows: the expected square of a random variable is equal to the square of its mean plus the expected squared deviation from its mean.
• Oh. Huh. Simple. But the squares still seem kinda uninterpreted. I mean it makes sense (sort of, extremely loosely) without the squares. – Mitch Jan 3 '17 at 19:39
• I am not sold on this. – Michael R. Chernick Jan 3 '17 at 19:57
• If the Pythagorean theorem applies, what is the triangle with what sides and how are the two legs perpendicular? – Mitch Jan 4 '17 at 15:31
Sorry for not having the skill to elaborate and provide a proper answer, but I think the answer lies in the physical classical mechanics concept of moments, especially the conversion between 0 centred "raw" moments and mean centred central moments. Bear in mind that variance is the second order central moment of a random variable. | {
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} |
inverse, and it will necessarily have more than one left inverse. We have just seen that some functions only have inverses if we restrict the domain of the original function. So if a function has two inverses g and h, then those two inverses are actually one and the same. 19,124 results, page 72 Calculus 1. However, if a function is restricted to a certain domain so that it passes the horizontal line test, then in that restricted domain, it can have an inverse. Yes, a function can possibly have more than one input value, but only one output value. Can a (non-surjective) function have more than one left inverse? A quick test for a one-to-one function is the horizontal line test. If the function is one-to-one, write the range of the original function as the domain of the inverse, and write the domain of the original function as the range of the inverse. A few coordinate pairs from the graph of the function $y=\frac{1}{4}x$ are (−8, −2), (0, 0), and (8, 2). can a function have more than | {
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"openwebmath_score": 0.6838260293006897,
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"url": "https://pamrealthai49.com/unusual-things-yosbzjh/can-a-function-have-more-than-one-inverse-ab8a14"
} |
In other words, passivity is a particular sector bound on the system defined by:
`$H=\left(\begin{array}{c}G\\ I\end{array}\right).$`
### Frequency-Domain Condition
Because the time-domain condition must hold for all $T>0$, deriving an equivalent frequency-domain bound takes a little care and is not always possible. Let the following:
`$Q={W}_{1}^{T}{W}_{1}-{W}_{2}^{T}{W}_{2}$`
be (any) decomposition of the indefinite matrix $Q$ into its positive and negative parts. When ${W}_{2}^{T}H\left(s\right)$ is square and minimum phase (has no unstable zeros), the time-domain condition:
`${\int }_{0}^{T}\left(Hu\right)\left(t{\right)}^{T}\phantom{\rule{0.2777777777777778em}{0ex}}Q\phantom{\rule{0.2777777777777778em}{0ex}}\left(Hu\right)\left(t\right)dt<0,\phantom{\rule{1em}{0ex}}\forall T>0$`
is equivalent to the frequency-domain condition:
`$H\left(j\omega {\right)}^{H}QH\left(j\omega \right)<0\phantom{\rule{1em}{0ex}}\forall \omega \in R.$` | {
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php, beginner, html, random, image
<?php
$gcode1=generateCode(5);
$url3="http://i.imgur.com/".$gcode1.".jpg";
?>
<div id="bg">
<img src="<?=$url3?>" alt="">
</div>
<?php
$pagepath=$_SERVER["PHP_SELF"];
if ($_GET['numimg']=='') {
$numimg=20;
} else {
$numimg=$_GET['numimg'];
}
?>
<h1 style='font-family: verdana;'><?=$numimg?> random imgur images</h1>
<table border=0><tr>
<?php
function generateCode($length=6) {
$source='abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890';
$code='';
for ($i=0; $i<$length; $i++) {
$code .= $source[(rand() % strlen($source))];
}
return $code;
}
$ii=1;
while ($ii<=$numimg):
$gcode=generateCode(5);
$url="http://i.imgur.com/".$gcode.".jpg";
$url2="http://www.imgur.com/".$gcode;
$headerfile=get_headers($url2, 1);
$http_code=$headerfile[1];
$imgheader=get_headers($url, 1);
$imgcode=$imgheader["Content-Type"];
#echo $imgcode; | {
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"url": null
} |
• I cross-confirmed that the above works. However, 1 + 1 = 2. \begin{bmatrix} x^2+y^2 & x & y & 1 \\ \mathbf 2 & 1 & 1 & 1 \\ 20 & 2 & 4 & 1 \\ 34 & 5 & 3 & 1 \\ \end{bmatrix} So $x_0$ = 3, $y_0$ = 2, and $r^2$ = 5. Aug 9, 2016 at 17:41
• Since the link in the post seems to be dead, here is a link to a version in the Wayback Machine. Dec 10, 2018 at 18:55
I'm surprised this one hasn't been mentioned; you can find the equation by using the determinant of a matrix:
$$\left|\begin{array}{cccc} x^2+y^2&x&y&1\\ 1^2+1^2&1&1&1\\ 2^2+4^2&2&4&1\\ 5^2+3^2&5&3&1\\ \end{array}\right|=0$$ This gives the equation of the circle through those three points. This sort of thing can be used in a lot of situations: matrix-determinant solutions are available for any shape I can think of where you're given points that land on the shape. | {
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ros, navigation, stack
Originally posted by Gav with karma: 478 on 2013-04-20
This answer was ACCEPTED on the original site
Post score: 3
Original comments
Comment by acp on 2013-05-24:
Thank you a lot for your long answer, The robot is working properly with the navigation_stack. I now want to move further. I want to use actionlib to pass 2D Pose estimate and 2D Nav goal. Do you know how to do that?
Comment by ctguell on 2013-10-15:
@acp do you know how to make the robot move slower? and also where you able to use actionlib? thanks
Comment by ZdenekM on 2013-10-15:
@ctguell See this for setting parameters of robot movement: http://wiki.ros.org/base_local_planner#Parameters. Btw, it would be better to ask new question. | {
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} |
newtonian-mechanics, everyday-life, centripetal-force, centrifugal-force
A similar system you can think of that you are probably familiar with is projectile motion. At the top of the trajectory the force points down, the velocity is horizontal, and the projectile continues on its parabolic path with both horizontal and vertical velocity. The difference between the projectile and the bucket is that the net force is constant for the projectile. The horizontal component of the velocity never changes. For the bucket the net force is always changing so that the motion is circular. The vertical and horizontal components of the velocity are always changing around the circle. The projectile is falling, but the water isn't purely falling. It's also being pushed by the normal force provided by the bucket. | {
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optics, electromagnetic-radiation
Title: Is it possible to control phase of a light radiation? Is it possible to control phase of a light radiation?
Assume I have two point sources A and B. They emit spherical waves of a green light (or any other color).
Is it possible to make such physical system where the phase of B is shifted by some $\theta$ in comparison to A. The challenge is to make two sources that are highly coherent but spatially separated. The easy ways to do that generally involve starting with a single source and splitting its output (for example with beam splitters, partially reflective mirrors, or fiber optic couplers) and routing the beams to different locations. | {
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python, pygame
def mouse_in_botton(self,pos):
if GAME_WIDTH // 2 - 50 <= pos[0] <= GAME_WIDTH // 2 + 50 and GAME_HIGHT - 50 <= pos[1] <= GAME_HIGHT - 20:
return True
return False
def render_button(self):
color = GREEN if not self._playing else RED
info = "Start" if not self._playing else "Surrender"
pygame.draw.rect(self._display_surf, color,
(GAME_WIDTH // 2 - 50, GAME_HIGHT - 50, 100, 30))
info_font = pygame.font.SysFont('Helvetica', 18)
text = info_font.render(info, True, WHITE)
textRect = text.get_rect()
textRect.centerx = GAME_WIDTH // 2
textRect.centery = GAME_HIGHT - 35
self._display_surf.blit(text, textRect)
def render_game_info(self):
#current player color
color = BLACK if not PLAYER else WHITE
center = (GAME_WIDTH // 2 - 60, BOARD + 60)
radius = 12
pygame.draw.circle(self._display_surf, color, center, radius, 0) | {
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quantum-gravity, spacetime, universe, discrete
http://arxiv.org/abs/1102.2784
one may improve the bounds by 14 orders of magnitude! This safely kills any imaginable theory that violates the Lorentz symmetry - or even continuity of the spacetime - at the Planck scale. In some sense, the birefringence method applied to gamma ray bursts allows one to "see" the continuity of spacetime at distances that are 14 orders of magnitude shorter than the Planck length.
It doesn't mean that all physics at those "distances" works just like in large flat space. It doesn't. But it surely does mean that some physics - such as the existence of photons with arbitrarily short wavelengths - has to work just like it does at long distances. And it safely rules out all hypotheses that the spacetime may be built out of discrete, LEGO-like or any qualitatively similar building blocks. | {
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A set is countably infinite if its elements can be paired up with natural numbers so that (a) no elements are paired up with the same number, (b) no element is paired with two numbers, (c) there are no numbers or elements left unpaired. In other words, a set is countably infinite if there is a one-to-one correspondence between the elements of the set and the elements of the natural numbers. In this case, we consider the size (cardinality) of the set to be the same as the size $$|\mathbb{N}|$$ of the natural numbers.
Consider the set of ordered pairs of natural numbers $$(n,m)$$. Your intuition that the number of elements in this set is $$|\mathbb{N}|\times|\mathbb{N}|$$ is correct, but the intuition that this quantity is greater than $$|\mathbb{N}|$$ is incorrect: we can pair the elements of the set of pairs of natural numbers with the natural numbers according to a one-to-one correspondence. | {
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error-correction
Title: If a quantum error correcting code corrects both $X$ and $Z$ errors, will it be able to also correct $Y$ error? Does the ability to correct $Y$ error follow from the ability to correct $X$ and $Z$ errors? I suspect, that in general the answer is no. Are there examples, then? If there are no examples, is there a proof? I've understood from the comments that the OP is willing to consider a more general error set, rather than focussing specifically on the more standard case of distance being a measure of the number of single-qubit errors that can be tolerated. In that context, the following construction may be of assistance: | {
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observational-astronomy, gravity, asteroids, natural-satellites, size
None of these claims has ever been substantiated after more than forty years of observation. It has been surmised that some of these objects—and other alleged intra-Mercurial objects—may exist, being nothing more than previously unknown comets or small asteroids. No vulcanoid asteroids have been found, and searches have ruled out any such asteroids larger than about 6 km (3.7 mi).[4] Neither SOHO nor STEREO has detected a planet inside the orbit of Mercury.[4][23] | {
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quantum-gate, quantum-state, quantum-operation
For the operations $\phi_{3,b}$ to $\phi_{6,b}$ they have $\beta M_{A_1,\beta}$. How is this operations actually implemented? My understanding is that I have a measurement operations in the circuit that after running multiple shots records that probability of getting either a +1 or -1. I then calculate 2 expectation values from this circuit for when the state was projected to $|0>$ and $|1>$.These expectation values have to then be multiplied by the probability and then summed together along with the rest of the terms in the equation to match the expectation of the non-decomposed circuit.
Is my reasoning correct? | {
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javascript, functional-programming, coffeescript, primes
Now, when I hear "functional paradigm," I hear "loopless way" and "immutability." Functional programming is about more things, of course.
EDIT: oh man, I had limit = 100 in the code. Stupid mistake :) Fixed now.
sieve_sundaram = (limit) ->
start = 4
half = limit/2
numbers = (n for n in [3...limit+1] by 2)
steps = numbers[..] # copy of numbers | {
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Signals and Systems − Periodic, aperiodic and impulse signals. The step response is the convolution between the input step function and the impulse response: s(t) = u(t) h(t). Network response to unit step function and unit impulse. The impulse response for each voltage is the inverse Laplace transform of the corresponding transfer function. The transient response is not necessarily tied to abrupt events but to any event that affects the equilibrium of the system. Impulse response 17 Solving for Impulse Response We cannot solve for the impulse response directly so we solve for the step response and then differentiate it to get the impulse response. 11 Technology brief: Neural simulation and recording 6. Homework Statement Let us consider a simple physical system consisting of a resistor (with resistance R) and an inductor (with inductance L) in series. RLC Low-Pass Filter Design Tool. CAD tool test 10%. It affects the shape of the filter’s frequency response. RLC Resonance. Amplifiers: | {
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ros2, ros-humble, colcon, rospackage, launch
setup(
name=package_name,
version='0.1.9',
# Packages to export
packages=[package_name],
# Files we want to install, specifically launch files
data_files=[
# Install marker file in the package index
('share/ament_index/resource_index/packages', ['resource/' + package_name]),
# Include our package.xml file
(os.path.join('share', package_name), ['package.xml']),
# Include all launch files.
('share/' + package_name, ['launch/brobot.launch.py']),
],
# This is important as well
install_requires=['setuptools'],
zip_safe=True,
author='kopiousKaro',
author_email='foobar@email.biz',
maintainer='KopiousKarp',
maintainer_email='foobar@email.biz',
keywords=['brace', 'root'],
classifiers=[
'Intended Audience :: Developers',
'License :: Apache 2.0',
'Programming Language :: Python',
'Topic :: Agricultural Robotics',
], | {
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"tags": "ros2, ros-humble, colcon, rospackage, launch",
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newtonian-mechanics, forces, rotational-dynamics
Forces and torques are separate things, but still related. A torque is produced by a force
$$\mathbf\tau=\mathbf r\times\mathbf F$$
So fundamentally you are just applying a force. That affects the linear motion of the object. If your force also happens to have a torque about the COM of the object, then the object will start spinning as well.
In other words, your force is not a torque. Your force has a torque about the COM. Torque is a manifestation of where and in what direction the force is being applied to the object.
Another way to look at this is to compare units. Forces have units of $\rm N$ where as torques have units of $\rm N\cdot\rm m$, so they cannot be the same thing. | {
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matlab, fft, frequency-spectrum
\,=\, \frac{1}{T_0} \int_{T_0} x(t) \, e^{-j \frac{2\pi}{T_0} kt} \operatorname{dt}
\,=\, \frac{1}{NT_s} \sum_{n=0}^{N-1} x(nT_s) \, e^{-j \frac{2\pi}{NT_s} k nT_s}
\,=\, \frac{1}{NT_s} \underbrace{\sum_{n=0}^{N-1} x(nT_s) \, e^{-j \frac{2\pi}{N} k n}}_{\text{DFT}}
$$
Take bin #31 as an example, the analog amplitude that corresponds to $ 20\operatorname{Hz} $ is $3$ (or two spectral lines each with height $1.5$ at $ \pm 20 \operatorname{Hz} $ because $ \cos(\theta) = 0.5e^{j\theta}+0.5^{-j\theta} $). If I scale the unscaled magnitude of $x[31]$ I get $ 2250 \times \frac{1}{NT_s} = 2250 \times \frac{1}{1500\times 1000} = 0.0015 $, which is obviously wrong. If I want to get to the value of $ 1.5 $, I have to divide the digital magnitude by $ 1500 $, which is exactly my sampling rate .... why? | {
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dynamic-programming, python
lcs('amin', 'kahmjiknln')
# Returns 'amin'
lcs('amin', 'aaaakahmjiknln')
# Returns 'aaaaamin' Lets deal with the issues one at a time, since there are a few of them.
Problem 1
Take a look at those lines of code:
trow = [0] * (m+1)
table = [trow] * (n+1)
srow = [""] * (m+1)
solution = [srow] * (n+1)
The problem with this code, is that the same list is being placed a few times. This means, that every list in $table$ must be all identical to $trow$ at all times. By changing one of the values in there, it will change all of them. For example, if $m=n=1$, then table == [[0,0],[0,0]]. Now, assume we somehow did this update: table[0][1] = 9. Then, we will have table == [[0, 9], [0, 9]] since $table$ contains the same list twice. This is essentially caused because lists are just pointers, and thus if you just copy the value in them it will just copy the pointer. A similar behavior can be seen in this code:
a = 5 # a == 5
b = a # a == 5, b == 5
b = 10 # a == 5, b == 10 | {
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php, html, wordpress
</div><!-- col -->
</div><!-- row -->
<div class="row">
<div class="col-sm-8">
<?php if( $image_4_video == "Yes" ): ?>
<a data-toggle="modal" data-target="#myModal2" href="#">
<img src="<?php echo $grid_image_4['url']; ?>" alt="<?php echo $grid_image_4['alt']; ?>">
</a>
<?php else: ?>
<img src="<?php echo $grid_image_4['url']; ?>" alt="<?php echo $grid_image_4['alt']; ?>">
<?php endif; ?>
</div><!-- col -->
<div class="col-sm-4"> | {
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rotational-dynamics, angular-momentum, rigid-body-dynamics, angular-velocity
Title: Does an irregular rigid body can only rotate in three directions? Suppose that at a certain instant the angular momentum with respect to the center of mass is not parallel to the angular velocity. Does this necessarily imply that the angular momentum is rotating around the axis of rotation? If so, then an isolated body must necessarily have angular momentum with respect to the center of mass parallel angular velocity (otherwise the angular momentum varies and the system is not isolated). However, this gives me a perplexity: an irregular rigid body has only 3 axes such that $ \vec{L}_{cm} $ and $ \vec{\omega} $ are parallel. Does this mean that the irregular rigid body can only rotate in three directions? It seems completely absurd to me, but where is the mistake? A general rigid body has 3 principal axis. Suppose $I_1<I_2<I_3$. If it rotates around $I_1$ or $I_3$ without external torques, the angular velocity doesn't change and is parallel to the angular momentum. Theoretically | {
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c#, sql, null
Is entirely sufficient.
Avoid cluttering your code with comments that don't bring anything to the table:
// as long as we found a result, we're happy
Good comments should say why the code does what it does - don't bother commenting just to state the obvious, or to rephrase what the code is already saying.
If this needs a comment every time it's used:
// log and email error
ErrorContinue(recordID, strMessage);
...then perhaps the ErrorContinue method needs a better, more descriptive name?
You're catching a System.Exception here:
try
{
// Query our existing list of StateConfig objects for a match, then return the value of RoundMinutes.
result = (from x in listStateConfig
where x.State == stateAbbrev
select x.RoundMinutes).First();
}
catch (Exception e)
{
//...
} | {
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electromagnetism, photons, collision
Title: Collision of light waves & matter When light or electromagnetic wave hits an obstacle, what happens? Are the reactions times always negligible?
By reaction I mean all that happens after the hit like reflection for example. There are several things that can happen, depending on the nature of the obstacle.
The simplest case is if, classically, we think that the obstacle is not too much smaller than the wavelength of the light. Then, the light wave can be reflected, absorbed, or diffracted.
Most people are familiar with reflection, the light more or less bounces off the obstacle. The reflected light wave will still travel at the speed of light.
Absorption happens when the material absorbs the energy of the light, and changes its form, usually to heat. This happens as the light travels just below the surface (exactly how far depends on how absorbing the material is.). | {
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kinect, openni, ros-kinetic
<transparency>0</transparency>
</visual>
<collision name='collision'>
<laser_retro>0</laser_retro>
<max_contacts>10</max_contacts>
<pose frame=''>0 0 0 0 -0 0</pose>
<geometry>
<box>
<size>0.073 0.276 0.072</size>
</box>
</geometry>
<surface>
<friction>
<ode>
<mu>1</mu>
<mu2>1</mu2>
<fdir1>0 0 0</fdir1>
<slip1>0</slip1>
<slip2>0</slip2>
</ode>
<torsional>
<coefficient>1</coefficient>
<patch_radius>0</patch_radius>
<surface_radius>0</surface_radius>
<use_patch_radius>1</use_patch_radius>
<ode>
<slip>0</slip>
</ode>
</torsional>
</friction>
<bounce>
<restitution_coefficient>0</restitution_coefficient> | {
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quantum-mechanics, wavefunction, symmetry, group-theory, hamiltonian
then yes, it's possible - but it is absolutely crucial to have non-degenerate eigenvalues. (This is of course also true in the parity case, and if you have even and odd eigenstates at the same eigenvalue then it's trivial to construct mixed-parity eigenstates that do not have any definite symmetry.)
If you do manage to find a translationally invariant hamiltonian $H$ such that $[H,T_a]=0$ and some eigenvalue $p$ is non-degenerate (like e.g. $p=0$ for a free particle as the unique physically relevant case), then yes, the eigenstate $|\psi_p\rangle$ must be translationally invariant, since $T_a|\psi_p\rangle$ must be an eigenstate of the same eigenvalue, and by non-degeneracy it must be proportional to $|\psi_p\rangle$ , i.e. $T_a|\psi_p\rangle = e^{i f(a)}|\psi_p\rangle$, so $|\psi_p\rangle$ is translationally invariant. | {
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isosceles: Angles on the same base are congruent ABCD is an isosceles trapezoid with AB … b. So, the sum of interior angles on the same side, angle DAE and angle CEA is 180 degrees. The angles across from the legs are called the base angles. It is a special case of a trapezoid.Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of the same measure. Basic-mathematics.com. In isosceles trapezoid, base angles are equal. polygons. Both L K ¯ and M N ¯ are congruent due to the definition of an isosceles trapezoid. of Congruent Triangles are Congruent) If base angles of triangle are congruent, then triangle is isosceles Statements BD = CE BD and CE are altitudes ABD and AEC are fight angles Reasons 1) Given 2) Given 3) Definition of Altitude 4) All fight angles are congruent 5) Reflexive property 6) A-AS (5, 4, 1) (Angle-Angle-Side) 7) CPCTC If we can place the two things that we want to prove are the same in corresponding places of two triangles, and | {
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nC(n-2) , nC(n-1) , nCn. You can compute them using the fact that: - J. M. Bergot, Oct 01 2012 You can specify conditions of storing and accessing cookies in your browser. A different way to describe the triangle is to view the first li ne is an infinite sequence of zeros except for a single 1. That means in row 40, there are 41 terms. Blaise Pascal was born at Clermont-Ferrand, in the Auvergne region of France on June 19, 1623. In this example, you will learn to print half pyramids, inverted pyramids, full pyramids, inverted full pyramids, Pascal's triangle, and Floyd's triangle in C Programming. relationship. If you will look at each row down to row 15, you will see that this is true. The coefficients of the terms come from row of the triangle. Magic 11's. In 1653 he wrote the Treatise on the Arithmetical Triangle which today is known as the Pascal Triangle. {(0, 0), (1, 5), (2, 8), (3, 9), (4, 8), (5, 5), (6, 0)} Using this we can find nth row of Pascal’s triangle. Define a finite | {
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"url": "https://miro.acadiasi.ro/ev9ccu/0398e0-90th-row-of-pascal%27s-triangle"
} |
c#, xml
public void iStart()
{
if (!File.Exists(this.SettingsFile))
{
this.createDefaultsFile();
}
this.iLoad();
}
public void iEnd()
{
this.alterNodeValue(this.SettingsFile, "Settings", "fObj1", this.form.fObj1.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj2", this.form.fObj2.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj3", this.form.fObj3.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj4", this.form.fObj4.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj5", this.form.fObj5.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj6", this.form.fObj6.ToString());
this.alterNodeValue(this.SettingsFile, "Settings", "fObj7", this.form.fObj7.ToString());
} | {
"domain": "codereview.stackexchange",
"id": 242,
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"lm_name": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, xml",
"url": null
} |
c#, jquery, linq, entity-framework, asp.net-mvc-4
<script>
$(function () {
$("#userPreferences").click(function () {
$("#dialog").html('<img src="../Styles/images/CircularProgressAnimation.gif" alt="Please wait..." />');
$("#dialog").css("display", "");//show the dialog div
$('#dialog').dialog({
dragable: true,
resizable: false,
title: this.title,
modal: true,
width: Math.min(450, $(window).width() * .8),
position: {
my: "center top",
at: ("center top+" + ($(window).height() * .1)),
collision: "none"
},
open: function (event, ui) {
//Load the UserPreferences action which will return the partial view UserPreferences
$(this).load('/Common/UserPreferences' + "?t=" + new Date().getTime()); | {
"domain": "codereview.stackexchange",
"id": 19249,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, jquery, linq, entity-framework, asp.net-mvc-4",
"url": null
} |
2. Let $$r\in R$$, then $$n \cdot r = \underbrace{r + \cdots + r}_{n}= r \cdot \underbrace{(1_R + \cdots + 1_R)}_{n}=r \cdot0_R=0_R.$$ Hence $$n \cdot r \cdot 1_R = 0$$.
But I don't know if my proof is correct. What do you think? (I'd like to make sure my task is correct before I handle it)
• Is the ring R commutative? If so then $n⋅r⋅1_{R}=0$ follows when you show that $n⋅1_{R}=0$ – user758469 Apr 1 at 15:47
There are some small errors in your proof, and the proof can be made much more direct:
1. In the expression $$\phi(k)=\phi(n\cdot z)=\underbrace{1_R+\cdots+1_R}_{n\cdot k}\; \forall k \in \mathbb{Z},$$ you should have $$n\cdot z$$ below the brace, not $$n\cdot k$$. Also the last part ($$\forall k\in\Bbb{Z}$$) makes no sense here; you have already specified $$k$$ to be an element of $$\ker\phi$$.
2. There is no need to consider a general element in the kernel. Instead you can argue as follows: | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9653811611608242,
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"lm_q2_score": 0.8418256432832333,
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"openwebmath_score": 0.9460005760192871,
"tags": null,
"url": "https://math.stackexchange.com/questions/3605068/some-properties-about-the-characteristic-of-a-ring"
} |
aluminum
$d_{max}$ is the max deflection. Usually, its defined as a fraction of the beam span length to avoid visible sagging (e.g. 1/250 L =0.1505'' ).
$E$ is the elasticity modulus of aluminium = 10000 ksi
So again (after some algebra):
$$t = \sqrt[3]{\frac{12 P L^3}{48 E\cdot d_{max}\cdot w}}$$
If you apply the values, then the minimum thickness results in 0.3564 inches. As you can see its double the minimum thickness when you calculate based on stresses.
So, if you use 0.17 inches the shelf will not break, but it will have a noticeable by eye sag, which will not be pleasant. | {
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"tags": "aluminum",
"url": null
} |
javascript, calculator, ecmascript-6, math-expression-eval
With different behavior between operations, is it possible to remove this redundant line or is it neccesary?
Yes you can iterate over the operations using Object.keys(calculatorOperations), since the functions are listed in order of highest precedence first:
Object.keys(calculatorOperations).forEach(function(functionName) {
while(userEntry.includes(functionName)) {
indexOfOperand = userEntry.indexOf(functionName);
userEntry = calculatorOperations
.calculationSequence(functionName, indexOfOperand, userEntry);
}
});
Though be aware that all keys will be iterated over, including returnIndexOfEntry, returnSpliced and calculationSequence. If you didn't want those to be iterated over, the functions for the four mathematical operations could be moved into a sub-property and those could be iterated over instead, or else move the other helper functions out of the object.
With this approach, there is no need for the variable operationsMD.
Other feedback | {
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"openwebmath_score": null,
"tags": "javascript, calculator, ecmascript-6, math-expression-eval",
"url": null
} |
c++, interview-questions, c++20
void test() {
constexpr const char *cases[] = {"small", "medium", "large"};
for (const char *const case_name: cases) {
std::stringstream out_act;
{
std::ostringstream fnin;
fnin << "sample_input_" << case_name << ".txt";
std::ifstream in;
in.open(fnin.str());
process_streams(in, out_act);
}
std::ostringstream fnout;
fnout << "sample_output_" << case_name << ".txt";
std::ifstream out_exp;
out_exp.exceptions(std::ios::badbit);
out_exp.open(fnout.str());
out_act.seekp(0);
compare(out_exp, out_act);
}
}
void main() {
process_streams(std::cin, std::cout);
}
} | {
"domain": "codereview.stackexchange",
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"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, interview-questions, c++20",
"url": null
} |
quantum-mechanics, energy, discrete, blackbody
I am under the impression here that quantization ~ discreteness.
I'll give an example where discreteness pops up in a classical system. Consider a simple stretched string with boundary conditions such that the string has a vanishing amplitude at both ends for all times relevant. Excitation of this string will result in standing waves on the string, which also is the only type of wave such a string will entertain. The thing here is that the frequency specra of allowed oscillations (the standing waves) is of a discrete, or rather quantized, nature.
Is everything quantized? Perhaps. One can argue that any quantum mechanical wave function (modelling some system) experiences some all enclosing boundary conditions to some surrounding such that the only modes of oscillation for the wave function are discrete, in the same sense as the above example with the string. The very basic example would be the 'particle in a box'. | {
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"openwebmath_score": null,
"tags": "quantum-mechanics, energy, discrete, blackbody",
"url": null
} |
quantum-field-theory, dirac-equation
Empty space is a lot like a metal, or maybe a semiconductor, because like those materials its chock full of negatively charged electrons occupying different velocity states, only...
Unlike metals or semiconductors, the density of electrons in any one region of space is infinite, because there is no limit to how fast the electrons can move. That is because these are negative energy states in which an electron can always move faster simply by emitting a photon, so there's not "bottom" to how far they can drop and how dense they can become, and...
Unlike metals or semiconductors, there is no exactly balancing sea of positive atomic charges, well, unless maybe there are infinite numbers positively charged atoms too, and...
The resulting infinite negative charge density of real electrons not only doesn't matter but is in fact completely and totally invisible for some reason, and... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-field-theory, dirac-equation",
"url": null
} |
special-relativity, speed-of-light, coordinate-systems, dimensional-analysis, physical-constants
In more detail, let $c_{0}$ be the usual speed of light constant and let $c(t)$ be the speed of light function from above. Then let $f$ be any solution of the first-order ODE
$$ f'(t)t + f(t) = \frac{c(t)}{c_{0}}. $$
Then take the change of coordinates by
$$ T = f(t)t, \qquad X = x, \qquad Y = y, \qquad Z = z. $$
Then
$$ \frac{dT}{dt} = f'(t)t + f(t) \implies dT = (f'(t)t + f(t))dt \implies c_{0}dT = c(t) dt. $$
In the new coordinates, we find
$$ ds^{2} = -c_{0}^{2} dT^{2} + dX^{2} + dY^{2} + dZ^{2} $$
and in these new coordinates it seems as though the speed of light is constant. | {
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"tags": "special-relativity, speed-of-light, coordinate-systems, dimensional-analysis, physical-constants",
"url": null
} |
measurements, error-analysis
Classification
There are multiple ways to classify uncertainty. You likely only need to know about statistical/systematic for now, but it may be worth being aware of the existence of a few other schemes, especially Type A/B.
Statistical/Systematic
Classifies uncertainties by how they scale with how much data is collected: | {
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"openwebmath_score": null,
"tags": "measurements, error-analysis",
"url": null
} |
homework-and-exercises, special-relativity
As the correct answer notes, according to X event 1 is simultaneous with event 2. But what your handwritten answer is calculating is the simultaneity according to B. For B, event 2 is simultaneous with event 3: B will argue, after doing some observations, that X's clock was at 10.7 at the moment when Y arrived at B.
Since question 7b is asking for the result according to X, 9.2 yr is the right answer. | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "homework-and-exercises, special-relativity",
"url": null
} |
beginner, parsing, serialization, lua
local function parse_block(str)
-- parses a string, inserts the content into tbl and returns processed length
local function parse_add_string(tbl, toparse)
local data = parse_string(toparse)
table.insert(tbl, data[1])
return data[3]
end | {
"domain": "codereview.stackexchange",
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"lm_q1_score": null,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "beginner, parsing, serialization, lua",
"url": null
} |
• cons can contain equations, inequalities or logical combinations of these.
• The following options can be given:
• Assumptions \$Assumptions assumptions on parameters GenerateConditions True whether to generate conditions on parameters PerformanceGoal \$PerformanceGoal whether to prioritize speed or quality StrictInequalities False whether to require strict sign
• Possible settings for GenerateConditions include:
• Automatic non-generic conditions only True all conditions False no conditions None return unevaluated if conditions are needed
• Possible settings for PerformanceGoal are "Speed" and "Quality". | {
"domain": "wolfram.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9863631643177029,
"lm_q1q2_score": 0.8064253539801949,
"lm_q2_score": 0.8175744828610095,
"openwebmath_perplexity": 6197.223755699079,
"openwebmath_score": 0.8255516290664673,
"tags": null,
"url": "https://reference.wolfram.com/language/ref/FunctionSign.html"
} |
You are given $$\vec w \cdot \vec u =0$$.
Note $$\vec w \cdot \vec u = (\vec u + \vec v) \cdot \vec u$$
$$= \vec u \cdot \vec u + \vec v \cdot \vec u$$
(distributivity of the dot product)
$$=\vec u \cdot \vec u + \vec u \cdot \vec v$$
(commutativity of the dot product)
$$= | \vec u|^2+\vec u \cdot \vec v$$
So, $$| \vec u|^2+\vec u \cdot \vec v=0$$
$$3^2+\vec u \cdot \vec v =0$$
$$\therefore \vec u \cdot \vec v = -9$$ | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.971129090546975,
"lm_q1q2_score": 0.8215193060266897,
"lm_q2_score": 0.8459424334245618,
"openwebmath_perplexity": 361.3724192665278,
"openwebmath_score": 0.765846848487854,
"tags": null,
"url": "https://math.stackexchange.com/questions/3417077/problem-with-calculation-of-dot-product-of-two-vectors"
} |
javascript, node.js, asynchronous
return function (err, docs) {
if (err) {
next("Database error fetching field: " + field);
return;
}
if (docs) {
var error = [{
'field' : field,
'message' : errorMessage
}];
serverResponse(res, error);
return;
}
callback();
};
};
var getUserSaveFunc = function (req, res, next, user) {
return function (err) {
if (err) {
next("Database error saving user");
return;
}
var w = new Workspace();
w.name = req.body.workspace;
w.activeFlag = true;
w.ownerUserId = user._id;
w.countryId = null;
w.save(function (err) {
if (err) {
next("Database error saving workspace. WATCH OUT: user " + user.login + " doesn't have a workspace!");
return;
}
serverResponse(res, []);
});
};
}; | {
"domain": "codereview.stackexchange",
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"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, node.js, asynchronous",
"url": null
} |
lisp, scheme, sicp, symbolic-math
Book:
(else
(error "unknown expression type -- DERIV" exp))))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (make-sum a1 a2)
(cond ((=number? a1 0) a2)
((=number? a2 0) a1)
((and (number? a1) (number? a2)) (+ a1 a2))
(else (list '+ a1 a2))))
(define (=number? exp num)
(and (number? exp) (= exp num)))
(define (make-product m1 m2)
(cond ((or (=number? m1 0) (=number? m2 0)) 0)
((=number? m1 1) m2)
((=number? m2 1) m1)
((and (number? m1) (number? m2)) (* m1 m2))
(else (list '* m1 m2))))
(define (sum? x)
(and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
(define (augend s) (caddr s))
(define (product? x)
(and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p)) | {
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"id": 279,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "lisp, scheme, sicp, symbolic-math",
"url": null
} |
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