text stringlengths 1 1.11k | source dict |
|---|---|
quantum-state, mathematics, unitarity
If you don't like degeneracy then take any $n$ distinct $\alpha_i$ on the unit circle and then $\mathrm{Diag}(\alpha_1, \dots, \alpha_n)$, the diagonal matrix with $\alpha_1,\dots,\alpha_n$ on the diagonal is a unitary matrix with eigenvalues $\alpha_1, \dots, \alpha_n$.
If you don't like diagonal matrices then take your favorite unitary $V$ and then
$$
V \mathrm{Diag}(\alpha_1, \dots, \alpha_n) V^*
$$
is another unitary matrix with eigenvalues $\alpha_1,\dots, \alpha_n$. | {
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"tags": "quantum-state, mathematics, unitarity",
"url": null
} |
quantum-field-theory, energy-conservation, stress-energy-momentum-tensor, qft-in-curved-spacetime
$$ \frac{\mathrm{d}}{\mathrm{d}t} H_K(\Sigma_t) = 0 \,,$$
which is what is meant by $H_K$ being conserved.
The conservation law $\nabla_\mu T^{\mu \nu} = 0$ is a little different from a conservation law of the form $\nabla_\mu J^\mu = 0$. The presence of an extra free index in the former case means we cannot apply the usual (covariant) divergence theorem to conclude the existence of a conserved charge. | {
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"tags": "quantum-field-theory, energy-conservation, stress-energy-momentum-tensor, qft-in-curved-spacetime",
"url": null
} |
inorganic-chemistry, electronegativity
$$|\chi_{\ce{F}}-\chi_{\ce{Cl}}|=0.102 \sqrt {55.396}=0.7596$$
$$\chi_{\ce{Cl}} \approx 3.2404>3.04=\chi_{\ce{N}}$$
(mileage may vary with these calculations)
Allred-Rochow (AR) electronegativity, on the other hand, is defined directly by the force resisting removal of an atom's valence electron. This force is equivalent to:
$$F=\frac {(Z^*e)(e)}{4\pi r^2\epsilon_o}$$
where $Z^*$ is the effective nuclear charge, either measured experimentally or calculated using Slater's rules. Introducing some more scaling factors, which make things line up with Pauling electronegativity values, the equation for Allred-Rochow electronegativity is:
$$\chi_\text{AR}=0.359\left(\frac{Z^*}{r^2}\right)+0.744$$
where r is the atom's covalent radius, in Angstroms. $\chi_{\text{AR},\mathrm{Cl}}=2.83 < \chi_{\text{AR},\mathrm{Cl}}=3.07$[2] | {
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"tags": "inorganic-chemistry, electronegativity",
"url": null
} |
molecular-structure, electronic-configuration, terminology, intermolecular-forces, steric-effects
Title: Help understanding how "steric effects" are distinct from "electronic effects"? @jakebeal's excellent answer to Why do animal cells “mistake” rubidium ions for potassium ions? includes the following passage:
In the case of potassium versus sodium, which are both very important in biochemistry, a recently discovered mechanism in sodium-potassium pumps uses binding properties to grab both, then atomic size (via steric hindrance) to distinguish sodium versus potassium as described nicely in the answers to this question.
Wikipedia's Steric effects says:
Steric effects are nonbonding interactions that influence the shape (conformation) and reactivity of ions and molecules. Steric effects complement electronic effects, which dictate the shape and reactivity of molecules. Steric repulsive forces between overlapping electron clouds result in structured groupings of molecules stabilized by the way that opposites attract and like charges repel. | {
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"tags": "molecular-structure, electronic-configuration, terminology, intermolecular-forces, steric-effects",
"url": null
} |
fidelity, no-cloning-theorem, cloning
This gives $\lambda=-\frac{1}{2}$ and so:
$$\begin{cases}\frac{1}{2}\vec\pi_i^\dagger\boldsymbol a^\dagger\boldsymbol A\vec\pi_i\vec\pi_i^\dagger\boldsymbol A-\pi_i^\dagger\boldsymbol{\mu a}^\dagger\boldsymbol A^{\circ2}=0&\forall i\\\frac{1}{2}\boldsymbol A\vec\pi_i\vec\pi_i^\dagger\boldsymbol{Aa}\vec\pi_i-\boldsymbol A^{\circ2}\boldsymbol{a\mu}\vec\pi_i=0&\forall i\\\vec\pi_i^\dagger\boldsymbol a^\dagger\boldsymbol A\vec\pi_i\vec\pi_i^\dagger\boldsymbol{A\text{d}a}\vec\pi_i=F&\forall i\\\boldsymbol A=\boldsymbol a^\dagger\boldsymbol A^{\circ 2}\boldsymbol a\end{cases}$$
Then we can easily see that $F=\vec\pi_i^\dagger\boldsymbol{A\mu}\vec\pi_i=\vec\pi_i^\dagger\boldsymbol{\mu A}\vec\pi_i$ for all $i$. However, I do not know how I would proceed further than this.
Another approach would be to use constraint 3 to reduce the degrees of freedom to 6 by showing:
$$de^{i\delta}=-\alpha^*be^{i\beta}+\left|1+\alpha ce^{i\gamma}\right|e^{i\epsilon}$$ | {
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"id": 3032,
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"tags": "fidelity, no-cloning-theorem, cloning",
"url": null
} |
gazebo
<geometry>
<box>
<size>0.07 0.005 0.003</size>
</box>
</geometry>
<material>
<script>Gazebo/Blue</script>
</material>
</visual>
</link> | {
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"id": 3749,
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"lm_name": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "gazebo",
"url": null
} |
graph-theory, graph-algorithms, approximation-algorithms, fixed-parameter-tractable
Title: Is there FPT or XP algorithms known for Shortest Steiner cycle and $(a,b)$-Steiner path problem Shortest Steiner cycle and $(a,b)$-Steiner path problem are generalizations of optimization versions of Hamiltonian cycle and Hamiltonian path problems.
The Shortest Steiner cycle problem is defined as follows:
Input: An undirected and unweighted graph $G=(V,E)$ and $T\subseteq V$ (called terminals).
Find: Shortest cycle (minimum edges) containing all terminals.
The Shortest $(a,b)-$Steiner path problem is defined as follows:
Input: An undirected and unweighted graph $G=(V,E)$, $T\subseteq V$ (called terminals) and two specific terminals $a,b \in T$.
Find: Shortest simple path (minimum edges) containing all terminals, which starts at $a$ and ends at $b$. | {
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"tags": "graph-theory, graph-algorithms, approximation-algorithms, fixed-parameter-tractable",
"url": null
} |
c, arduino, serial-port, device-driver
void autoLand()
{
if (throttle <= 60 && aux1 >= 50) {
throttle = 45;
aux1 = 45;
} else if (throttle >= 45)
if (millis() - lastThrottleUpdate > 400) {
throttle = throttle * .95;
aux1 = 45;
lastThrottleUpdate = millis();
}
writeAllValues();
}
void writeAllValues()
{
Throttle.write(throttle);
Roll.write(roll);
Pitch.write(pitch);
Yaw.write(yaw);
Aux1.write(aux1);
}
void setPowerPinsOn(boolean on)
{
if (on) {
for (byte x = 7; x <= 12; x++)
digitalWrite(x, HIGH);
} else
for (byte x = 7; x <= 12; x++)
digitalWrite(x, LOW);
}
void setGroundPinsOn(boolean on)
{
if (on) {
for (byte x = 14; x <= 17; x++)
digitalWrite(x, LOW);
} else
for (byte x = 14; x <= 17; x++)
digitalWrite(x, HIGH);
}
void circleLed()
{
if (millis() - ledPreviousMillis > 400) {
if (circleIndex == 18)
circleIndex = 14; | {
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"tags": "c, arduino, serial-port, device-driver",
"url": null
} |
fft, power-spectral-density, ofdm, window-functions, symbol-timing
Windowing involves multiplying the time domain data by the window weight sample for sample. After windowing the resulting windowed data is FFT'd. Purpose is to reduce spectral leakage from strong tones, thereby increasing the dynamic range and ability to see weaker signals together with stronger signals. This is at the expense of frequency resolution, or the ability to discern between two closely spaced tones that can be approximately the same power level (with decreased resolution, they would appear as one tone). | {
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"tags": "fft, power-spectral-density, ofdm, window-functions, symbol-timing",
"url": null
} |
which Investopedia receives compensation be used calculate. Annuities: an ordinary annuity which the first payment is not paid immediately, as in an annuity a... Running Out of money in retirement with interest rate somewhere else, the cash flows equal. Issues we Fear the beginning of each month annuity Solves Fear of Running Out of money in retirement part... A monthly deposit of Rs it is simple but extremely important to find present... As the lifetime annuity noted above, which also typically make payments at the of! Of regular payments made at the end of each period years with interest prevailing... Of the Bond now the … Problem 10: future value of an ordinary annuity makes or... Ordinary annuity with present value of a term Warrant the Accuracy or Quality of WallStreetMojo articles â, Copyright 2020. Solves Fear of Running Out of money in retirement regularly paid at the end of each period advance for month! His goal offers that appear in this table are from partnerships from | {
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"lm_q1_score": 0.9744347838494567,
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"lm_q2_score": 0.8459424314825853,
"openwebmath_perplexity": 1631.501933402308,
"openwebmath_score": 0.42821651697158813,
"tags": null,
"url": "https://www.clubecorretora.com.br/common-types-zqlnmqc/fefb12-ordinary-annuity-examples"
} |
statistics, normalization, hypothesis-testing, twitter, pvalue
Title: T-test against normalised or standardised data gives different results I am studying the problem to predict popularity of a tweet, and want to test null hypothesis: there is no relationships between favorite_counts and another set of variables, like number of friends of users.
I am not sure if normalise or standardise the variables, because I am thinking how to model popularity and don't know how the distributions of likes and friends among users are (please advise).
So I tried the two, and tried an independent t_test.
I get very different results:
from sklearn.preprocessing import StandardScaler, MinMaxScaler
do_scaled = pd.DataFrame(StandardScaler().fit_transform(do[columns].values), columns=columns)
ttest_ind(do_scaled.favorite_count, do_scaled.user_favourites_count)
#Ttest_indResult(statistic=-1.682257624164912e-16, pvalue=0.9999999999999999)
#pvalue is about 1 : the association is likely due to pure chance | {
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"tags": "statistics, normalization, hypothesis-testing, twitter, pvalue",
"url": null
} |
The first and last integral evaluate to $$\frac43\left(\frac{\sqrt3-1}2\right)^3=\sqrt3-\frac53$$ and $$\frac\pi4\left(1-2\left(\sqrt2-1\right)\right)^2=\pi\left(\frac{17}4-3\sqrt2\right)$$, respectively. Wolfram|Alpha evaluates the indefinite form of the second integral to
$$-\pi z^2+\pi z+4\sqrt{1-2z-z^2}\left(\frac{z^2}3+\frac z6-\frac56\right)+(6-z)\sqrt{1-2z-z^2}+\frac{15}2\arctan{\frac{1+z}{\sqrt{1-2z-z^2}}}+\frac12\arctan\frac{1-3z}{\sqrt{1-2z-z^2}}-4\arcsin\frac{1+z}{\sqrt2}+4(z-1)z\arccos\frac z{\sqrt{1-2z}}$$
but refuses to evaluate it with limits. Substituting the limits by hand yields
$$-\pi\left(3-2\sqrt2\right)+\pi\left(\sqrt2-1\right)+\frac{15}2\cdot\frac\pi2-\frac12\cdot\frac\pi2-4\cdot\frac\pi2=\left(3\sqrt2-\frac52\right)\pi$$
at the upper limit and | {
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"lm_q1_score": 0.986979508737192,
"lm_q1q2_score": 0.8046177662778635,
"lm_q2_score": 0.8152324938410784,
"openwebmath_perplexity": 382.1676020260141,
"openwebmath_score": 0.9619895815849304,
"tags": null,
"url": "https://math.stackexchange.com/questions/3563395/a-random-sphere-containing-the-center-of-the-unit-cube"
} |
object-oriented, vba
Private Type THotel
PricingRules As New Scripting.Dictionary
Name As String
Rating As Byte
End Type
Private this As THotel
Implements IHotel
Public Property Get Name() As String
Name = this.Name
End Property
Public Property Let Name(ByVal value As String)
this.Name = value
End Property
Public Property Get Rating() As Byte
Rating = this.Rating
End Property
Public Property Let Rating(ByVal value As Byte)
this.Rating = value
End Property
Public Property Get Self() As IHotel
Set Self = Me
End Property
Public Function Create(ByVal hotelName As String, ByVal stars As Byte, Optional ByVal rules As Collection = Nothing) As StandardHotel
Dim rule As IPricingRule
With New StandardHotel
.Name = hotelName
.Rating = stars
If Not rules Is Nothing Then
For Each rule In rules
.AddPricingRule rule
Next
End If
Set Create = .Self
End With
End Function | {
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"tags": "object-oriented, vba",
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algorithm, c, tree, integration-testing
break;
case 2:
printf("Enter the integer you want to delete : ");
scanf("%d", &var);
delete_one_child(search(root, var));
break;
case 3:
printf("Enter search element \n");
scanf("%d", &val);
search(root, val);
break;
case 4:
traversal(root);
break;
case 5: // TODO
test();
break;
case 6:
fl = 1;
break;
default:
printf("\nInvalid Choice\n");
}
if (fl == 1) { break; }
}
return 0;
} | {
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"id": 32605,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithm, c, tree, integration-testing",
"url": null
} |
python, beginner, python-3.x
Title: Number Base Conversion Problem Generator A program that generates questions to train your number base conversion skills. This program is made to ask questions about octet, binary and hexadecimal. No other bases. It first asks a series of questions to the user such as "amount of questions", "question type" and "base". Then, it starts generating questions based on the user's input. The user can give an answer and it will tell them if they're correct. Code is perfectly functional.
I'm asking for a review because I sense a bad smell in my code. It feels overly long, repetitive, and kind of confusing. There surely must be a better way. Maybe an OOP approach? Something to cut down on the complexity and "if-else" repetition. Though, I feel it is this way partly because I have limited it to only 3 bases. I'm a late beginner but I wouldn't say that I am intermediate just yet. | {
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"tags": "python, beginner, python-3.x",
"url": null
} |
# How do you have multiple multiplicities in a polynomial?
I need to make a 3 degree polynomial with the only zeros being 3 with the multiplicity being "1, 4 and multiplicity of 2." I know that the zeros and 3 degree are typed together like so, (x-3)^3. But how can one have multiple multiplicities?
Here is the full question for future users. "Find a formula for a degree three polynomial function whose zeros are 3 with multiplicity 1, and 4 with multiplicity 2" It was worded funny.
-
@Tyler The correct parsing of the sentence is "... whose zeroes are [3 with multiplicity 1], and [4 with multiplicity 2]". So you have two zeroes 3 and 4, and their multiplicities are 1 and 2 respectively. Interpreted this way, the wording is quite normal. – Ted Oct 30 '12 at 6:17
I agree @Ted, the problem is the brackets are not there for me and I'm not the greatest math whiz, yet ;) – Tyler Zika Oct 30 '12 at 6:20 | {
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"lm_q1_score": 0.9891815491146485,
"lm_q1q2_score": 0.8221513758910329,
"lm_q2_score": 0.8311430562234877,
"openwebmath_perplexity": 278.8346824230795,
"openwebmath_score": 0.840469479560852,
"tags": null,
"url": "http://math.stackexchange.com/questions/224991/how-do-you-have-multiple-multiplicities-in-a-polynomial"
} |
general-relativity, differential-geometry, coordinate-systems, tensor-calculus
To be clear, given $f\in C^{\infty}(M)$ for the manifold $M$, I am defining
\begin{align}
\left(\frac{\partial f}{\partial x^{\mu}}\right)_p := &(\partial_{\mu}(f\circ x^{-1}))(x(p));\\
(df)_p:T_pM &\longrightarrow \mathbb{R}\\
X &\longmapsto (df)_p(X) := X(f).
\end{align}
Then we have
\begin{align}
(dx^{\mu})_p\left(\left(\frac{\partial}{\partial x^{\nu}}\right)_p\right) =\left(\frac{\partial x^{\mu}}{\partial x^{\nu}}\right)_p = (\partial_{\nu}(x^{\mu}\circ x^{-1}))(x(p)) = \delta_{\nu}^{\mu}(x(p)) = \delta_{\nu}^{\mu}.
\end{align}
Now let's consider a change of coordinate chart (for an overlapping region of the manifold) in the tangent space. To do this, I will insert an identity operator. I will call my charts $x$ and $y$ for clarity.
\begin{align} | {
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"tags": "general-relativity, differential-geometry, coordinate-systems, tensor-calculus",
"url": null
} |
java, performance, validation
Processor.getInstance().execute(packet);
}
}
} catch (Exception ex) {
System.out.println("error= " + ex);
}
}
}
Below are my corresponding validator classes:
ValidatorA class This class is called by ConsumerA, basically it's isValid method for validation.
public class ValidatorA extends Validator {
private static final Logger logger = Logger.getInstance(ValidatorA.class);
private final String consumerName;
private final GenericRecord genericRecord;
private final Long oldTimestamp;
private final Long newTimestamp;
private final String clientId;
private final String deviceId;
private final Integer payId;
private final Map<String, String> holder; | {
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"openwebmath_score": null,
"tags": "java, performance, validation",
"url": null
} |
organic-chemistry, experimental-chemistry, stereochemistry
Now in the second case I do think we can't prove the two substituents to be same, no matter how much we rotate. So chiral?
CONCLUSION: I am a beginner in this topic and not really confident about my thought process
Can we really use conformers of molecules to support their symmetry because after all conformers are ever changing, not stuck in one orientation?
Also what's the logic behind checking the plane and centre of symmetry of molecules? How does that relate to rotation of PPL light?
->If two substituents of a sp3 hybridized atom are identical, we say not optically active.
But both being identical will rotate PPL light in same direction, so a net rotation will be produced.
->So isn't it optically active? No, it is not an asymmetric centre. To test this, you can draw the two potential stereoisomers: | {
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"openwebmath_score": null,
"tags": "organic-chemistry, experimental-chemistry, stereochemistry",
"url": null
} |
python, performance, python-3.x
I'm running Python in 32 bit, because I'd like to use the nltk module in the future and they discourage users to use 64 bit.
Seeing that the goal of Python was to make everything go smoothly, I was confused. The goal is to beat a similar R script in execution speed. I read Python was fast, so where did I go wrong? A colleague advised me to use Python which might be a faster case. I know you can't simply compare two languages that way, each has its merits. But in this specific case it seemed to me that Python ought to be faster in data crunching. I figured that when both scripts are equally well optimised, Python should be faster in this case. However, my current Python code is badly optimised whereas my R script is decent enough.
Please tell me if I'm completely wrong. If someone could help me use some higher hierarchy functions as proposed on SO (imap, ifilter...) and explaining them that would be great. | {
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"tags": "python, performance, python-3.x",
"url": null
} |
neural-network
Does the validation set just give an indicator of how the neural network performs on unseen data(validation set) then based on that I manually set hyperparameters? or something automatically(the optimizer) tune hyperparameters? The three way - train, validation(dev), test split helps in unbiased evaluation of the model on unseen data , that is the test set. The train and validation sets are used for training weights and hyperparameter tuning respectively. In Keras if you have set the 'validation_split' parameter in 'model.fit' then you can look at the performance of your model on the validation set and tune the hyperparameters manually in order to get a good validation set performance.Once you are satisfied with the performance of your model on the validation set, you finally evaluate your model on the test set.
Hyperparameter tuning is done manually and not automatically by Keras. | {
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"openwebmath_score": null,
"tags": "neural-network",
"url": null
} |
waves, solid-state-physics, acoustics, resonance
Title: We can have resonance with a fluid-gas system. Can we have resonance with a solid fluid system? A gas bubble in a liquid, such as a simple air bubble in water can resonate when it is excited with an acoustic wave at the bubbles natural resonant frequency. So we have resonance effects in fluid-gas systems.
What about the case of fluid-solid system. Say we have some circular rods made of a solid material and we place them in a liquid. Is it possible to have resonance in this case? Imagine that you have some circular rods.
They will have some natural frequencies of oscillation.
If these roods are dirty you might put them into an ultrasonic cleaning bath and the rods will have dirt removed from them by the water transmitting ultrasonic vibrations to the metal rings and causing them to vibrate.
If you could change the frequency of the sound waves you could imagine that there will be frequencies at which the metal rings exhibit maximum amplitude vibrations - resonance. | {
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"tags": "waves, solid-state-physics, acoustics, resonance",
"url": null
} |
clojure, brainfuck
(defn number-box [number text-color box-size]
[:div {:style {:border-color "black"
:border-style "solid"
:border-width "1px"
:min-width (str box-size "px")
:min-height (str box-size "px")
:position "relative"
:color text-color}}
[:div {:style {:position "absolute"
:top "50%"
:left "50%"
:transform "translate(-50%, -50%)"
}} (str number)]])
(def input-buffer (chan 1))
;; Interpreter start ---------------------------------------------
(defn initialize-cells [number] (vec (repeat number 0)))
(defn out-of-upper-sourcecode-bounds? [interpreter-state]
(= (:reader-position interpreter-state) (count (:src interpreter-state)))) ;;TODO currently only checks for upper bounds
(defn retrieve-current-symbol [interpreter-state]
(nth (:src interpreter-state) (:reader-position interpreter-state))) | {
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molecular-biology, transcription
Title: Why does RNA synthesis in E.coli begin with a Purine? From Berg's Biochemistry:
Most newly synthesized RNA chains carry a highly distinctive tag on the 5′ end: the first base at that end is either pppG or pppA.
Is there a reason why the synthesis initiates with a purine?
Purine-rich sequences at the 5' ends of the nascent transcripts of many genes act to stabilize the early ternary(elongation) complex.
P.S.Source: MattDMo's comment. | {
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recurrence-relation, pi-calculus
What should be ruled out is the presence of infinite descending chains involving infinitely many constants $K$. This is however a different requirement from well-foundation. | {
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the-sun, orbit, exoplanet, nemesis
Now the middle part of your question: A star will "wobble" in response to its companion with exactly the same period as the orbit. So, if you are prepared to wait for an appreciable fraction of 26 million years, then yes, the presence of the binary companion might be revealed in a net small oscillation of average proper motions over the whole sky, with a period of 26 million years! Otherwise not. Measuring the "wobble" by doppler methods is currently capable of detecting Jupiter-mass objects in orbital periods of 10-20 years. Measuring the wobble "astrometrically" - that is measuring the position displacement of the star due to an unseen companion is more sensitive to distant companions, but still, one is limited by the fact that the wobble period will be the same as the orbital period of the companion. An assessment of the performance of the Gaia astrometry satellite by Perryman et al. (2014) suggests detection of planets with orbital periods out to 10 years might be possible. | {
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ros, stack
Is there a way to install only the stack I want? "--no-install-recommends" flag for apt-get does not seem to help. (EDIT: "--no-upgrade" also does not work, the same list of extra packages shows)
I also tried to "git clone" the source into /opt/ros/electric/stacks, but I will get an error at "rosbuild_include(qt_build qt-ros)" during rosmake. (Update:As pointed out by joq and snorri, git clone gets the fuerte version, which is irrelevant to the problem here since I'm looking at the electric version)
(EDIT: This does not happen on another machine with same Electric on Lucid ie I get to install only the stack I want. But, it could also be that this machine is regularly updated, while I've freezed the updates for the turtlebot machine)
Originally posted by weiin on ROS Answers with karma: 2268 on 2012-07-01
Post score: 0 | {
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resource-recommendations, many-body, greens-functions
Title: Resources for applications of Keldysh Green's functions I am looking for resources to learn Keldysh formulation of Green's functions. I am especially interested in learning how they are applied to calculate transport characteristics.
Most of the books I could find introduce the definitions of the formalism but never apply it to concrete physical realizations. So I am looking for an applied reference on the topic. Here is a tutorial paper, written by A.P. Jauho, to introduce the Keldysh formalism.
For application in transport here is a nice paper. | {
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ros, frame, camera, ros-fuerte, lsd-slam
Conetnt of bashrc file is below :
source /opt/ros/fuerte/setup.bash
export ROS_WORKSPACE=~/fuerte_workspace/
export ROS_PACKAGE_PATH+=:~/fuerte_workspace/sandbox/
export ROS_PACKAGE_PATH+=:~/fuerte_workspace/gscam/
How can I handle this error? Or, how can I get frame from webcam using ubuntu, ROS, fuerte?
Originally posted by jossy on ROS Answers with karma: 83 on 2015-06-29
Post score: 0
Did you install gscam?
rosdep does NOT install gscam, but dependencies for gscam.
Originally posted by dornhege with karma: 31395 on 2015-06-29
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by jossy on 2015-06-29:
I install gscam using svn. It locates under fuerte_workspace.
Comment by dornhege on 2015-06-29:
Something with your paths seems to be wrong. You list the gscam export, but the error provided by rosdep does not contain that path. Maybe you forgot to source something. | {
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python, beginner, programming-challenge
A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number. A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
My Work:
import math
dict = {} | {
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Here is a graph (not as pretty as above, but I thought I'd give google docs drawing a try):
not included because this is my first math post.
LINK: graph of p(A meets B | A's arrival time)
The shaded portion of the first and third segments are half the area of that segment, the middle is 2/3, so the total area is $$p = {1\over 3} \times ({1\over 2} + {2\over 3} + {1\over 2}) = {1 \over 3} \times {5\over 3} \ = {5\over 9}$$
-
Here is a simple qbasic simulation of the situation:
The answer yielded over 1 million trials was 0.5555 ~ 5/9
CLS
RANDOMIZE TIMER
count = 0
N = 1000000
FOR i = 1 TO N
LET x = (RND * 45 + 1)
LET y = (RND * 45 + 1)
tx = x + 15
ty = y + 15
IF ABS(tx - ty) < 15 THEN
count = count + 1
END IF
NEXT i
PRINT count / N | {
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algorithm-analysis, proof-techniques, correctness-proof
Title: Proof of correctness of algorithm Can someone help me prove the correctness of this algorithm:
MUL(a,b)
x=a
y=b
WHILE x≥b DO
x=x-b
y=y+1
IF x=0 THEN
RETURN(true)
ELSE
RETURN(false)
I had to prove that $x_n + b\cdot y_n = a$ by induction, where $x_n$ and $y_n$ are the values of the variable x and y after the loop has iterated n times.
I have done that, but I am not sure how to prove the correctness of the algorithm. To prove that the algorithm is correct, we assume that the loop invariant $x_n + by_n = a$ is true per induction.
we have the following two cases:
case 1:
If MUL(a,b) returns true, then $x_n = 0$ and $y_n = n$,
so
$x_n + by_n =a \rightarrow bn = a \rightarrow a$ is a multiplum of b
case 2:
if MUL(a,b) returns false, then $x_n \not= 0$, so we have
$x_n + by_n = a \rightarrow bn \not= a \rightarrow a$ is not a divisor of b. | {
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\draw[thick] (2,3) -- (2,2) -- (1,1) -- (1,0) ;
\end{tikzpicture}
to be the same, or different?
HapaxOromenon
New member
1) Yes, I would count this as a valid cut.
2) I would consider them to be different.
Opalg
MHB Oldtimer
Staff member
Each cut must start and finish at points on the boundary of the grid. There are two sorts of boundary points, namely the four corners of the grid, and the eight points on the edges that are not corners (I'll call these edge points).
Trying to find a systematic way to count the number of possible cuts, I split them into three classes:
1. cuts that go from corner to corner;
2. cuts that go from a corner to an edge point;
3. cuts that go between two edge points.
For the first class, there are nine cuts between the northwest and southeast corners of the grid, as in this diagram
. | {
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electric-current, electrical-resistance, voltage, power, batteries
(1) Voltage isn't "a push"; its units are joules per coulomb! But, as I tried to explain above, it is related to the push (that is the force) that charges get in an electric field.
(2) The thermal energy comes from the collisions that the electrons, driven by the electric field and losing electrical potential energy, make with the lattice of ions. This increases the random vibration energy of the ions. [The extra kinetic energy that the electrons acquire due to the voltage applied is pretty negligible. For a current of a few ampère in an ordinary wire, the drift speed is in the order of a millimetre per second.] | {
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python, algorithm
attemptGrid / __init__ and makeGrid
The names attemptGrid and makeGrid are almost exactly backwards for what those functions do. attemptGrid does the actual work of creating the grid and inserting the words, and raises an exception if it can't; makeGrid makes a certain number of attempts at doing that successfully. But with my prior suggesting of making this a class, attemptGrid is now __init__, which means makeGrid should be an alternate constructor (usually a classmethod), and the name attemptGrid is free to use. Except I'll PEP8ify it to attempt_grid and explicitly document why it's even a thing to start with:
@classmethod
def attempt_grid(cls, words, size, n_attempts):
'''
Try `n_attempts` times to make a grid of the
given size with the given words. | {
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homework-and-exercises, newtonian-mechanics, work
edit I followed the given instructions in the green ticked answer to arrive at the correct answer like this
https://drive.google.com/file/d/1U8iNNakUPRrw3mTgl-w89WnR5IRR6mNS/view?usp=sharing
https://drive.google.com/file/d/1UIK0C43TMX-INY1WZJU0t6H5pAjBbXxl/view?usp=sharing To accomplish this maneuver quickly (at the lowest point of swing) the man would need to start with his feet on the seat (in a squat). Then he could lift with his arms and legs. He would need to increase his gravitational energy (mgh) and (in a rotating system) do work against the centrifugal force (m$v^2$/r) (where v is determined by conservation of angular momentum). (That work would require an integral.) | {
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mathematics, measurements
Title: Does one require calculus to work with uncertainities? I'm very young so know no calculus whatsoever.
I want to be able to calculate uncertainties for a Physics course I'm doing online, but I believe you need to have knowledge of differentials to do this in some cases.
Do you need knowledge of calculus to be able to calculate with differentials? You can treat differentials in a first approximation as tiny quanitites whose square you neglect. Thus they satisfy equations df*dg=0, which isn't possible in a field, but is mathematically rigorous (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.3019)
and captures what physicists do.
Later, one learns what differentials are in differential geometry, but this advanced use is of no help for error analysis (where you work with the rule df*dg=0 until only linear terms remain, and then plug in actual errors). | {
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# Probability of an obtuse triangle in a circle.
Suppose we randomly pick 2 points A, B within a circle centered at point O. What is the probability that the triangle formed by ABO is an obtuse one? (Note that A and B are not exclusively on the circumference).
And what is the conclusion extended to A, B within a ball instead?
Thanks!
PS this is from a Quant interview.
The following is what I have derived during the exam: (Edited, thank you for your corrections!) consider the joint probability of x, y coordinate for any point in a unit circle, then $$f_{XY}(x, y) = \frac{1}{\pi}$$, uniformly distributed inside the circular region. The distance between the point and the center, has thus a distribution $$f_Z(z) = 2z$$ for $$z$$ in [0, 1] ($$z^2 = x^2 + y^2$$). Randomly pick an A, rotate the circle so that A is right on top of the center O. Suppose now A has a distance $$z = a$$ $$(a > 0)$$ away from the origin, then B could only be chosen in the region of | {
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biochemistry, energy
About 86% of carbon loss is through exhaling carbon dioxide.
However, this will certainly vary depending upon the amount of indigestible carbon such as fiber, in ones diet.
Also, if mass loss through nitrogen and phosphorous (but not hydrogen and oxygen) were also considered the loss through breathing would come down to about 80%. Inclusion of salts would bring this percentage down further.
The sum of water from feces, urine and respiration is about 1.8 kg per day and the total mass emission of the body is 2.6kg, according to the Carnigie source above. | {
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Second bullet implies first bullet | {
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@MarcvanDongen: Oh, I agree that it can be done with the tools of TikZ, and I probably would do it that way. But it seems to me that it doesn't have to be done with TikZ and others might know of ways to do it without which are more elegant/load fewer packages. Specifically saying TikZ in the question title seems to preclude those solutions, and I wondered if there was a reason why TikZ was preferred as it might be useful background information on the question. – Loop Space Jan 30 '12 at 10:36
In fact, I would like to draw a tessellation of Poincare disk. This algorithm is a part of it! – Farey Jan 30 '12 at 12:08 | {
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# Proof of inequality $\lceil x \rceil \le x+1$
I went through the Master Theorum extension for floors and ceiling section 4.6.2 in the book Introduction to Algorithms
Using the inequality $$\lceil x \rceil \le x+1$$
But I haven't seen the inequality anywhere and could not understand the verifiability of inequality.
Instead the Chapter Floors and ceilings defined floors and ceilings as:
$$x-1 \lt \lfloor x \rfloor \le x \le \lceil x \rceil \lt x+1$$
Please clear my doubt over this.
On how to use this identity and which identity to be considered when because both of them define completely different inequalities.
Thank you.
• The inequality $\lceil x \rceil < x+1$ is stronger than $\lceil x \rceil \leq x+1$, but both are valid. – Yuval Filmus Jul 1 at 16:49
The definition of $$\lceil x \rceil$$ is:
$$\lceil x \rceil$$ is the minimal integer $$n$$ such that $$n \geq x$$.
(The existence of such an integer makes the reals an Archimedean field.) | {
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fluid-dynamics, aerodynamics, stability, turbulence, vortex
Title: What causes the formation of vortices in a separated flow? Consider flow over a cylinder. At a high enough Reynold's Number, the strength of the adverse pressure gradient becomes too large for the boundary layer to be able to remain attached to the cylinder. Hence, the fluid is decelerated to rest, and the flow eventually reverses at some point.
The image below shows the behaviour of flow at different Re: | {
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java, object-oriented, assembly
instructionToConvert should be instruction, unless you have some other instruction in your code block.
if (instructionToConvert.contains(instructionCommentRemover.getCommentRule())) instructionToConvert = instructionCommentRemover.removeCommentFromSingleInstruction(instructionToConvert); is a code smell for several reasons. At worst, it should be if (commentRemover.containsComment (instruction)) instruction = commentRemover.process (instruction). Better would be simply instruction = commentRemover.process (instruction). But the best would be if you let the preprocessor do its work on the entire assembly file before passing it to the assembler.
An Instruction should know how to encode itself (and expose toMachineCode()). That is the aim of OOP, after all. Internally, it can call a class Architecture with a method encode(Instruction).
I would replace InstructionFactory.buildInstruction with Instruction.valueOf, but you can also have an InstructionParser.parse | {
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nuclear-physics, radiation, nuclear-engineering
Title: Is it possible to make an all natural smoke detector from Brazil nuts? After reading about Brazil nuts, I discovered they have very high levels of radiation due to trace amounts of Ra-226 and Ra-228 and their decay products. A kilogram of the nut, for instance, gives a reading between 40 and 2660 becquerels.
Ionizing smoke detectors use a strong alpha-emitter to ionize air molecules between two plates. When smoke particulates in the air obstruct the flow of ions between the plates an alarm is triggered. Radium-226 was the first radioactive source in smoke detectors before it was switched over to Americium-241.
Given that today's smoke detectors operate on 0.05 µCi or 1850 Bq of radiation, is it possible to build a smoke detector apparatus using Brazil nuts as a radiation source?
Citations:
Smoke detectors | {
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electromagnetic-radiation
Title: Do electromagnetic waves occupy varying amounts of space, or do they simply vary in magnitude?
(source: nde-ed.org)
The above diagram shows an electromagnetic wave propogating in the $x$ direction, if the electric field is in the $y$ direction and the magnetic in the $z$ direction.
I was taught however that the strength of an electric field is given by the 'density' of field lines in a region, and in the above graphic it seems that the density is always the same, but that the area the electric field occupies changes. This implies that the strength of the electric field along the x axis never really changes, but it just spreads into the y axis. | {
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type-theory, curry-howard
The idea behind Design by Contract is software designers should define formal, precise and verifiable interface specifications for software components, which extend the ordinary definition of abstract data types with preconditions, postconditions and invariants.
Now many claim that using 'Types' in your programs leads to 'more correct programs' (via the Howard Curry Correspondence). From what I can see - even the most advanced use of Dependent Typing in Idris and Scala is limited to Sum Types and list lengths (correct me if I'm wrong).
By contrast - the power of 'Design By Contract' in establishing the correctness of my program is more general and more powerful. (Albeit not necessarily at compile-time - but at test time). I can for example establish in my banking program that all deposits are positive, and all reported account balances are positive. | {
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general-relativity, spacetime, coordinate-systems, time, observers
However, in the context of general relativity what would a faraway observer entail? Since the definition of coordinate time says it's the time measured by a faraway observer.
For example, consider a case where we are comparing the amount of time measured between two events in a strong gravitational field by two different observers. One observer is traveling through the gravitational field and the other observer is not in the gravitational field. | {
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population-genetics
Title: Average and lowest degrees of kinship/consanguinity among humans? I would appreciate insight into the average, median, RMS or any similar measure of relatedness among the current world population - and perhaps something about how rapidly this may be changing. A similar question is how un-related any two humans can be: i.e., what is the lowest degree of consanguinity between the two most distantly related people. The context is an exploration of how humans have evolved tendencies toward racism and other in/outgroup distinctions, when all humans share such a large fraction of DNA with each other, very nearly as much with non-human primates, and about half even with fruit flies. Might be some helpful lessons in there!
Apologies if the question is ill-formed, or answer readily available someplace - I've browsed the Web for several years on this topic, and found nothing I could understand.. | {
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vba, excel
Dim element As Variant
'Set the default return value
IsArrayAllNumeric = False
If Not IsArray(Arr) Then Exit Function
If Not IsArrayAllocated(Arr) Then Exit Function
'Loop through the array
For Each element In Arr
If IsObject(element) Then Exit Function | {
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below, determine if triangle FGH is congruent to triangle JKL. Their interior angles and sides will be congruent. In which pair of triangles pictured below could you use the Side Angle Side postulate (SAS) to prove the triangles are congruent? Triangle Congruence SSS,SAS,ASA,AAS DRAFT. It's like saying that if two Oompa-Loompas wear clothes with all the same measurements, they're identical. Edit. If any two corresponding sides and their included angle are the same in both triangles, then the triangles … Congruent Triangles by SSS, SAS, ASA, AAS, and HL - practice/ review activity set for triangle congruence with shortcutsThis activity includes three parts that can be done all in one lesson or spread out across a unit on congruent triangles. If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. In this case, measure any two sides and the angle between both sides in each triangle. Side Angle SideSide Side SideAngle Side AngleAngle | {
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graph-theory, approximation-algorithms, optimization, approximation-hardness, approximation
(Informal note: we will not get any better algorithms if we assume that the graph has a high average degree or a relatively low average degree.)
Generalization: The proof can be adapted in a straightforward way to this problem, where instead of looking for a permutation of the nodes, we look for an orientation of the edges (that is a less constrained problem where the edge orientation does not have to induce a DAG).
It can also be adapted in a straightforward way to the case where the objective to minimize is $\sum_{v\in V} ~\min(\left|\text{succ}_{\pi}(v)\right|,
\left|\text{pred}_{\pi}(v)\right|)$ instead of $\sum_{v\in V} ~\left|\text{succ}_{\pi}(v)\right|\times
\left|\text{pred}_{\pi}(v)\right|$. Interestingly, with that new objective we have $U_G = P_G$. | {
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botany, ecology, photosynthesis, marine-biology, energy
Modified from figures 4-5 of George Kling (University of Michigan) course page
Since only autotrophs can convert non-biologic forms of energy into chemical stored energy that heterotrophs such as fish and other water creatures can consume, all non-photosynthesizing organisms throughout the ocean's depths rely on the consumption of these autotrophs (or lower trophic-level heterotrophs) for energy. In fact, according to sigman and Hain (2012), usage of the energy captured but autotrophs and utilized by higher-trophic heterotrophs is so robust that all but <1% of the energy initially captured ever reaches the ocean floor as fallen debris/wastes/decomposing "snow". | {
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c++, beginner, queue
This is a dangerous way to do copy assignment. If any of the copying at the end fails, you’ve lost the original data. A better way is to use the “copy and swap” idiom.
queue<value_type> &operator=(queue<value_type> &&oth) {
if (&oth != this) {
clear();
m_Size = oth.size();
m_CheckOrAlloc(m_Size);
std::uninitialized_move(oth.begin(), oth.end(), m_RawData);
oth.~queue();
}
return *this;
}
It’s usually possible, and much easier, to implement moving in terms of swapping.
But in any case, explicitly calling the destructor of oth is definitely wrong. Except in very rare, special-case situations, you should never manually call destructors.
queue<value_type> &operator=(const queue<value_type> &&oth) = delete; | {
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electromagnetism
Specifically, imagine any loop $L$ encircling the wire. The net amount of bound current passing through this loop is
$$
I_b = \iint_S \vec{J}_b \cdot d \vec{a},
$$
where $S$ is a surface spanning our loop $L$. Since $\vec{J}_b = \vec{\nabla} \times \vec{M}$, we can apply Stokes's theorem to find that
$$
I_b = \iint_S \vec{J}_b \cdot d \vec{a} = \iint_S \left( \vec{\nabla} \times \vec{M} \right) \cdot d \vec{a} = \oint_L \vec{M} \cdot d\vec{l}.
$$
But $\vec{M} = 0$ everywhere on the loop (since it sits outside the wire), and so $I_b = 0$ as well.
This means that when we apply Ampere's Law, we have
$$
\oint \vec{B} \cdot d\vec{l} = \mu_0 I = \mu_0 (I_b + I_f) = \mu_0 I_f,
$$
i.e., only the free current contributes to the integral. If we further assume that the problem has axial symmetry (which is reasonable in this problem, assuming that the copper rod is homogenous), then Griffiths's derivation of the magnetic field follows. | {
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gazebo
Comment by GoRobotGo on 2013-04-18:
Yes, the robot falls down when using the qual 1 world with the unmodified tutorial.
Comment by GoRobotGo on 2013-04-18:
Looking at my LD_LIBRARY_PATH, the only place where the library exists is in /usr/lib/drcsim-2.4/AtlasSimInterface_1.0.8 There is a libAtlasSimInterface.so that is 13037808 bytes in size. To verify that was the library used, I removed it and started the simulator and noted that there was an error about the plugin not found.
Comment by GoRobotGo on 2013-04-18:
To be more specific - it sometimes falls down at the end with qual 1 world and the unmodified tutorial after taking steps as expected, but sometimes it fails to take the steps with the qual 1 world and just wobbles a bit.
Comment by GoRobotGo on 2013-04-20:
Submitted issue about single STEP interface as drcsim issue 211
Comment by GoRobotGo on 2013-04-20:
Submitted issue about WALK as drcsim issue 212
Issue submitted to the issue tracker. See comments. | {
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beginner, c, linked-list
Then for each node, from first to last call f(state, node). If the function returns non-zero, return immediately with that value, else go on to the next node.
Think of how easy then to use this to print the list, search the list, count the list, update nodes of the list, ... Just create a supporting function that handles one node. No need to create yet another iterator. | {
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quantum-state, hilbert-space
Is there some map between $f: \times_N SU(2) \to SU(2^N)$ for $N>1$?
If not, isn't the claim that the Hilbert space of $N$ qubits is $SU(2^N)$ false? Just a small remark for part of the question: Letting two Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$ (this can be generalized to any linear space) the tensor product $\mathcal{H}_1 \otimes \mathcal{H}_2$ is again a space. The dimension is the product $\dim(\mathcal{H}_1 \otimes \mathcal{H}_2) = \dim(\mathcal{H}_1)\dim(\mathcal{H}_2)$ and this becomes general for arbitrary tensor of spaces. So, for instance, we get that $\dim(\mathcal{H}_N) = \dim(\mathcal{H_{qubit}}^{\otimes N}) = \dim(\mathcal{H}_{qubit})^N$.
So, the claim that Hilbert space of $N$ qubits is $\mathcal{H_{qubit}}^{\otimes N}$ is true in the standard formalism. But I think that there is a distinction between Hilbert spaces and Lie Groups to be made as well, and I shall leave someone else that is an expert to do so. | {
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javascript, matrix
function rotatePixels(image) {
var x, y, x1, y1, edge;
const N = image.length;
const N1 = N - 1;
const N2 = N / 2;
x = y = 0;
edge = x1 = y1 = N1;
while (y < N2) {
while (x < edge) {
const a = image[y][x];
image[y][x] = image[x1][N1-y1];
image[x1][N1-y1] = image[y1][x1];
image[y1][x1] = image[x][y1];
image[x][y1] = a;
x += 1;
x1 -= 1;
}
x = y += 1;
y1 = x1 = N1-x;
edge -= 1;
}
return image;
} | {
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homework-and-exercises, waves, refraction, double-slit-experiment, interference
I cannot understand why this would happen. Where is the error in my understanding? It is not refraction which you need to consider it is the change in the length of the optical path.
If you have a ray of light incident on a parallel sided piece of glass all that happens is that the ray suffers a lateral shift but the ray would still be travelling in the same direction as shown in the diagram below.
Since the wavelength of light is less in the glass for a given thickness of glass would have more wavelength in it than the same thickness of air. | {
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general-relativity
Exotic differentiable structures could be counterexamples to what I just wrote - because they're "qualitatively" different and their pathological behavior is the very point of their existence (so in some important sense, the ability of them to mimic the normal functions disappears) - but their role in physics remains very confusing and limited as of today. | {
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string-theory, conformal-field-theory, brst, ghosts
The $P_a$ are lonely, and they need conjugate variables. These are given by so-called longitudinal 1-forms on the constraint surface, where a longitudinal vector field on the constraint surface is one that is tangent to the gauge orbits. Their duals are 1-forms which are only defined on longitudinal vectors. It should be geometrically intuitive (and it is in fact true) that the longitudinal vector fields are precisely the fields generating the gauge transformations (they are again just another incarnation of the gauge Lie algebra). Therefore, there are as many basic longitudinal 1-forms $\eta^a$ as there are constraints, and as there are anti-ghosts $P_a$. Since there is the natural action $\eta^a(P_b) = \delta^a_b$ by definition of the dual, it is also natural to just define the Poisson bracket on an enlarged phase space with coordinates $(x^i,p_i,\eta^a,P_a)$ by
$$ [\eta^a,P_b] = \delta^a_b$$ | {
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homework-and-exercises, velocity, kinematics
and in the limit as $t\to\infty$,
$$x(\infty) = x(0) + \frac{v(0)\tau}{1-C}$$
which, again, you can solve for $C$. It turns out to be the same thing as before, only with $\tau$ instead of $\Delta t$. This is only the case because this is an exceptionally simple equation, and because of the particular way in which I chose to define the time scale $\tau$. In general, these two methods won't give identical results, in part because of the inaccuracies of the particular finite difference approximation I used. | {
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discussed. "vertical asymptotes" (where the function is undefined). Google Classroom Facebook Twitter. 1) 1 6 k2 = 1 3k2 − 1 k 2) 1 n2 + 1 n = 1 2n2 3) 1 6b2 + 1 6b = 1 b2 4) b + 6 4b2 + 3 2b2 = b + 4 2b2 5) 1 x = 6 5x + 1 6) 1 6x2 = 1 2x + 7 6x2 7) 1 v + 3v + 12 v2 − 5v = 7v − 56 v2 − 5v 8) 1 m2 − m + 1 m = 5 m2 − m 9) 1. we try to find interval (s), such as the ones marked "<0" or ">0" These are the steps: find "points of interest": the "=0" points (roots), and. Understand solving an equation or inequality as a process of. distance from 0: 5 units. , using technology to graph the functions, make tables of values, or find successive approximations. Pulling Out Like Terms. Next, find a common denominator, which is x+2: Now, you have two choices for method of solving the inequality. Solve the following: This is already factored for me, so I don't have to bother with that. The following are notes and examples. com is without question the best destination to take a look at!. From cracking | {
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c, library, socket, wrapper, client
You might think, if the server calls send() once, shouldn't the client be able to call recv() once and receive everything that was sent? The issue though is that whatever you send() has to go on the network in packets. If you use a SOCK_STREAM socket with an IPv4 or IPv6 address, the connection will use the TCP protocol. This will treat all data that is being sent as one contiguous stream, and it will chop that stream up in to packets in a way that makes it efficient to traverse the network, but it does not have to correspond to how much you send() at a time. Furthermore, for IPv4 even routers between the sender and receiver can chop up the packets even more, called packet fragmentation. On the receiving side, there is also no guarantee how much you will recv() in one go; maybe it is however much there was in one network packet, but the kernel can buffer more or less than one packet. | {
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hector-quadrotor, transform
Title: Tf has two or more unconnected trees
Hi,
I am new to ROS and I am trying to run the indoor example of the hector_quadrotor packadge. I followed the instructions ,ran the launch file (indoor_slam_gazebo.launch) and rviz and gazebo windows appeared. The problem is that rviz shows errors in the laserscan, map and robot model all of which are related to not having a transform and having two unconnected trees. I made an image of the tf tree and this showed two seperate trees: a world tree and a base_link tree.
How can I fix this?
Originally posted by anonymous16901 on ROS Answers with karma: 16 on 2014-05-06
Post score: 0
Fixed the laser and robot model by setting the fixed frame parameter in rviz to base_link. The map still gives the error "no transform from [map] to [base_link]"
Originally posted by anonymous16901 with karma: 16 on 2014-05-06
This answer was ACCEPTED on the original site
Post score: 0 | {
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excel, vba
Title: Iterating worksheets and cells, copying data to summary sheet I have been working on this particular sub for a while and it was very very slow from the beginning. Compared to my other subs that go through a lot more data the task of this one is almost minuscule. All it has to do is to go through about ~15 sheets and parse through a couple hundred cells. Since this is a fairly complicated task I need to test it a lot which becomes almost unbearable with how long it takes. I am not sure if there is anything I can do or if there even is a solution. I am open to all kinds of suggestions.
Private Sub CommandButton24_Click()
Dim xSheet As Worksheet
Dim DestSh As Worksheet
Dim Last As Long
Dim copyRng As Range
Dim destRng As Range
Dim cRange As Range
Dim c As Range
Dim uniqueVal() As Variant
Dim x As Long
With Application
.ScreenUpdating = False
.EnableEvents = False
End With | {
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newtonian-gravity, mass, gauss-law
While all the reference frames we can construct would be non-inertial, we can at least select non-rotating frames where no Coriolis forces occur. Thus we arrive at a class of preferred, non-rotating reference frames for this problem: their Cartesian coordinate systems $(t,x^a)$ are all related by the transformations:
$$
{x^a}' = R^a{}_bx^b+{d^a}'(t) \tag{t},
$$
where $R^a{}_b$ is a constant rotation matrix, and $d^a(t)$ is a translation vector depending arbitrarily on a time $t$. All physical quantities transform in the obvious ways under such transformation. In particular, even after fixing origin and orientation of a reference frame, gravitational acceleration field at a given moment can only be defined up to an overall additive constant, acceleration of non-inertial reference frame. In other words, there is a “gauge transformation” for gravitational acceleration:
$$
\mathbf{g}'(\mathbf{r})= \mathbf{g}(\mathbf{r})+\mathbf{a}. \tag{g}
$$ | {
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autoencoders, semantic-segmentation, encoder-decoder
Thanks in advance! It's possible to mix and match all sorts of encoders and decoders. If the output of the encoder can be mapped to the input of the decoder, and a loss function can be backpropagated through the model, then it is possible to combine them.
Image segmentation, however, can be done simply with U-NET, as it can be trained as an image segmentation model. You can use an encoder to 'encode' your image, to make it easier to segment with the U-NET. Im assuming that the Image-Segmentation library you linked is actually just doing that, using an encoder and then applying U-NET for image segmentation. | {
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Python startswith() and endswidth() functions; Hash Functions and Hash Tables; Python maketrans() and translate() functions; Date and Time Functions in DBMS; Ceil and floor functions in C++ Functions that have inverse functions are said to be invertible. The very least ) injective have just a few values, but functions usually on. Converse is not true... Today we present... ta ta taaaann.... the bijective functions of output. Output value is connected to the input set, and each output value is connected to only one value. Usually work on sets with infinitely many elements can write such that, like that....., like that and a surjection, to find out more you can injective! Out by M. Winter, the converse is not true a one one! A few values, but is not a function f: a → B is! Few values, but is not true have just a few values but! Just a few values, but functions usually work on sets with infinitely many elements stricter rules, find. Be inverted below represents a one to one and onto or | {
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fluid-dynamics, stress-strain
Title: Are Normal Stress Differences in Newtonian Fluids Equal? I was reading about normal stress differences in the context of Non-Newtonian fluids. There was a remark that the normal stress differences in Non-Newtonian fluids are not equal whereas the normal stress differences in Newtonian fluids are equal. I can't figure out why the normal stress differences in a Newtonian fluid should be equal. Can anyone highlight a proof? In general they are not equal.
A counter example would be a uni-axial straining flow, say $\mathbf u = x\hat{\mathbf x}-y\hat{\mathbf y}$. The stress tensor is
$$
\sigma = -p\mathbb I+\mu \begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}\,.
$$
Clearly, $\sigma_{xx}-\sigma_{yy}\neq \sigma_{yy}-\sigma_{zz}$. Sometimes the normal stresses are interpreted as the stresses along the eigendirections of $\sigma$. Then the differences are differences between the eigenvalues. In this diagonal example it's equivalent. | {
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This entry was posted in Uncategorized. Bookmark the permalink. | {
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"url": "https://wp.mooretree.com/tmp/journal/fxvuzk.php?page=f77c65-memoryless-property-of-exponential-distribution"
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thermodynamics, thermal-radiation, absorption
Title: Absorption vs emission not in thermodynamic equilibrium I have read that good absorbers are good emitters. The argument goes that at thermodynamic equilibrium, the amount of radiation a body emits must be the same as it absorbs, otherwise the body will get hotter and the surroundings will get colder which violates 2nd low of thermodynamics. The question is why the same holds in non-equilibrium? Suppose we heat a body to a high temperature (via conduction) and the surroundings are cold, then it will emit a lot more radiation than it absorbs. If the most energy used for emission comes via conduction and not absorption of radiation, why the ability to absorb would influence emissivity at all in this case? | {
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quantum-mechanics, particle-physics, mathematical-physics, wavefunction, scattering
$$
\frac{\psi({\bf r}) - \psi_0({\bf r})}{\sqrt{n}} = \underbrace{\frac{e^{ikr}}{r}}_{\rm outgoing}f(\theta) \tag{3}
$$
which means that the incoming waves in Eq. (1) and (2) must be equal to each other, that is, each term in the sum associated with an incoming wave must be equal
$$
C_l e^{-i(-l\pi/2 + \delta_l)} = i^l(2l+1)e^{i(l\pi/2)} ~~\Rightarrow~~ \tag{4} C_l e^{-i\delta_l} = i^l(2l + 1)
$$
Now, just remember that $i = e^{i\pi/2}$ so that Eq (4) becomes
$$
C_l=(2l+1)e^{i(l\pi/2 + \delta_l)}
$$ | {
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astrophysics, orbital-resonance
Specific Example (Mercury Spin-Orbit Resonance):
Common wisdom holds that orbiting bodies will eventually achieve a 1:1 orbital/spin resonance with a main body, like the Earth's Moon. Though the Moon was spinning faster in the past, tidal torque caused it's spin to slow until the spin rate was equal to the orbital period. As the Moon spun down, it passed through many other ratios of orbital periods.
The case for Mercury's orbital/spin resonance around the Sun is a lot more complicated. Scientists and astronomers are still working out how and why Mercury was caught in a 3:2 spin/orbit resonance as it spun down, rather than passing through the resonance. From this excellent news article: | {
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python, statistics, pandas
Title: Am I doing a log transformation of data correctly? I'm doing some exploratory data analysis on some data and I get these histograms:
That looks like a candidate for a log transformation on the data, so I run the following Python code to transform the data:
df["abv"].apply(np.log).hist()
df["ibu"].apply(np.log).hist()
plt.show()
And I get this new plot of the transformed histograms:
Am I correct that a log transform was ok to do in this case, and if so, what's the best way to interpret the results? Yes, log transform seems a good solution for better interpretation. Overlap between these two datasets is really small, so, only by looking at the plot, you can say with high certainty, that they are significantly different from each-other. | {
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java, tic-tac-toe
Structure
You already have a vision of where you want to end up, which is good, as it can help you learn to plan ahead when designing your code, and make it easily extendable.
However, right now, your code is not all that extendable. For example, you have a plan to accept input from different sources than the command line (in your case a GUI and an AI).
If you want to add that later on, you would have to change your Game class. But the Game class shouldn't actually care where input comes from. It should manage the game logic, nothing more. Currently, it's responsible to read input, print output, create the players, etc, making it more difficult to apply changes. | {
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algorithms, algorithm-analysis, asymptotics
Title: n log n = c. What are some good approximations of this? I am currently looking into Big O notation and computational complexity.
Problem 1.1 in CLRS asks what seems a basic question, which is to get an intuition about how different algorithmic complexities grow with the size of the input.
The question asks:
For each function $f(n)$ and time $t$ in the following table, determine the largest size $n$ of a problem that can be solved in time $t$, assuming that the algorithm to solve the problem takes $f(n)$ microseconds.
The time periods are 1 second, 1 minute, 1 hour, 1 day, 1 month, 1 year, 1 century.
The functions $f(n)$ are seemingly common time complexities that arise in algorithms frequently, the list being:
$$ \log_2n, \quad \sqrt{n}, \quad n, \quad n \log_2 n, \quad n^2, \quad n^3, \quad 2^n \quad \text{and} \quad n!$$
Most are fairly straightforward algebraic manipulations. I am struggling with two of these, and both for the same reason: | {
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between the rectangualr (x,y) and polar (R,t) coordinates of a points are given byR 2 = x 2 + y 2 y = R sin t x = R cos t. Expand the left side of the given equation.R(-2 sin t + 3 cos t) = 2-2 R sin t + 3 R cos t = 2eval(ez_write_tag([[580,400],'analyzemath_com-box-4','ezslot_7',260,'0','0']));Use y = R sin t and x = R cos t into the given equation to rewrite as follows:-2 y + 3 x = 2 2 2 How to convert between Polar and Rectangular form ( in Physics and Engineering, Exercises de Mathematiques Utilisant les Applets, Trigonometry Tutorials and Problems for Self Tests, Elementary Statistics and Probability Tutorials and Problems, Free Practice for SAT, ACT and Compass Math tests, Convert Equation from Rectangular to Polar Form, Convert Polar to Rectangular Coordinates - Calculator, Free Geometry Tutorials, Problems and Interactive Applets, Convert Rectangular to Polar Coordinates - Calculator. 4 The calculator will convert the polar coordinates to rectangular (Cartesian) and | {
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ros, navigation, mapping, gmapping, depthimage-to-laserscan
Title: How to use depthimage_to_laserscan package to create map?
I am running rosrun depthimage_to_laserscan depthimage_to_laserscan and the scan topic is published and when I rosbag record -o /scan /tf the scan topic is not been recorded and the map is not created. I am new to ros and also read thewiki page bit didn't understand how to do that any suggestion. I want to make a 2D map to implement localization.
Originally posted by Dhagash Desai on ROS Answers with karma: 16 on 2016-10-25
Post score: 0
Original comments
Comment by Dhagash Desai on 2016-10-25:
Plz anyone...
Comment by gvdhoorn on 2016-10-25:
Really? A bump after ~20 minutes? This is not a (slow)chat ..
Download the gmapping package sudo apt-get install ros-[version]-gmapping. Then I would suggest launching both nodes using a launch file like so:
<launch> | {
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and two pairs of angles equal in measure in two equal half form of a are... Of other math skills ( d1 x d2 ) /2 square units, we get shape rhombus... Fact that the sides ( d₁ x d₂ ) Here d₁ and d₂ are diagonals yourself: what the. Will help you solidify the properties of rhombus: there are several formulas properties of rhombus the area rhombus! Differs from square in its interior angles which are not perpendicular a rectangle is a polygon 4! Rhomb or even a diamond or rhombus diamond area is 121 cm2 and length measure of diagonals a... Your math knowledge with free questions in properties of rhombus divided by 2 shape of a involving... There is the value of x, if a quadrilateral whose all four of boundaries! Shape is that all four sides of equal length given the angle below! Are intersecting each other at right angle length measure of longest diagonal is cm! If side BA = 5x-11 and side AD = 6x-18 definition ( Illustrated Dictionary... Have the same length units, we get square units, | {
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Count up the number of factors of $5$ and the number of factors of $2$ in $20!$. Since we get a zero for every pair of factors $5\cdot 2$, then the minimum of these will answer your question. More simply, $5$ happens less often as a factor (since it's bigger than $2$), so we need only count up the number of $5$'s. In particular, there's one each in $5,10,15,20$, so there are $4$ zeroes at the end.
If the problem had asked about $25!$, then there'd be $6$ zeroes--not $5$--because there are two factors of $5$ in $25$. Similar idea for other numbers.
-
It gets harder when you try it with bases other than 10. – marty cohen Oct 18 '12 at 1:44
That's true, Marty, though not relevant to the context. – Cameron Buie Oct 18 '12 at 1:52
General formula (for the interested) about the number of zeroes in n! in any base (b). First consider all prime factors of b, then consider the biggest one (p). Then use this formula. | {
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hope this helps. © copyright 2003-2021 Study.com. In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. Yes, I agree, … 1. two pairs of consecutive sides are congruent … Let's see some important theorems related to isosceles trapezoid to help her out. convex polygon. In order to prove that the diagonals of an isosceles trapezoid are congruent, you could have also used triangle ABD and triangle DCA. Next, we know that ADCE is a parallelogram, so the opposite angles would be equal. Isosceles trapezoids have some additional properties: Angles on the same base are congruent. Find all angles of the trapezoid. The diagonals (not show here) are congruent. By definition, an isosceles trapezoid is a trapezoid with equal base angles, and therefore by the Pythagorean Theorem equal left and right sides. (trapezoid and its theorems) ∠S = ∠R and ∠P = ∠Q But ∠S = 60 0 ∴ ∠R = 60 0 | {
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This leaves us with a set of numbers that have duplicates and I cannot see any direct formula to subtract these duplicates.
My #2 attempt at a solution:
Here I can start with a set of all the possible numbers that could be generated:
$3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6$ and subtract that with the set of numbers that does not contain a zero: $2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6$.
This would give me the answer: $3^6 - 2^6$. Which seems to be wrong.
Thank you!
• Your second attempt is very close, but you will find that the product of threes has to start with a $2$, since the first digit cannot be a $0$ (it wouldn't be a $6$-digit number if it did). So $2\cdot 3^5 - 2^6$ would be my guess. – Arthur Jan 21 '14 at 10:18 | {
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classical-mechanics, energy, lagrangian-formalism, energy-conservation
Title: Potential energy with Taylor series for particle I have been doing the following problem:
Imagine we got a particle in $U(x)$ field and we need to consider the motion of the particle near $x=a$. It says to use Taylor series for $U(x)$
$U(x) = U(a) + U'(a)(x-a) + \frac{1}{2}U''(a)(x-a)^2 + ...$
The problem goes to ask to consider cases: $U'(a) = 0$ and $U'(a) \neq 0$, $U''(a) \neq 0$. Note that it exactly mentions cases like that word by word, so I don't know which cases I need to consider.
When I treat $U'(a) \neq 0$, I arrived at the correct answer but only when I treated $U''(a) = 0$, but when I treat $U'(a) = 0$, I arrive at the correct answer when $U''(a) \neq 0$.
I don't get it. Why should I make $U''(a) = 0$ when doing $U'(a) \neq 0$ case and not neglect when I do $U'(a) = 0$. The book mentions the cases in this exact order: $U'(a) = 0$ and $U'(a) \neq 0$, $U''(a) \neq 0$ | {
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homework-and-exercises, hamiltonian, eigenvalue
Note that these states are simultaneous eigenstates of the Hamiltonian and the angular momentum operator, $L_z$, with eigenvalue $m \hbar$.
To demonstrate that the $\left| n,l,m \right>$ states are eigenstates of the Zeeman Hamiltonian, express the Hamiltonian as
$$H_{zeeman} = H_{hydrogen} - \frac{qB_z}{2mc}L_z$$
where I've used the fact that $\mathbf{B}$ only has a $z$ component. I've already told you how $L_z$ acts on the $\left| n,l,m \right>$ states. I'll leave the rest to you. | {
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quantum-mechanics, heisenberg-uncertainty-principle, vacuum
Then in engineering one would often use vacuum in a specific sense of no atoms or molecules (often only with precision up to some concentration). This is the use we often encounter when we speak of vacuum pumps or vacuum bulb or vacuum tube in old TV monitors. This does exist, because it is by definition is non-ideal.
Finally, in quantum theories one often uses term vacuum as equivalent of a ground state - a state with no excitations in it. In many cases it actually means unperturbed ground state, which changes once we account for the interactions between the particles. It is in this sense that vacuum or empty space is referred to as a boiling soup of virtual particles. | {
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organic-chemistry, reaction-mechanism, thermodynamics, halides, nucleophilic-substitution
Reactions of the blue benzhydrylium salts, $\bf{1}$-$\ce{BF4}$, with $\ce{n-Bu4N+NO2-}$ in anhydrous acetonitrile gives colorless adducts, $\bf{1}$-$\ce{NO2}$ (Ref.5):
The monitoring method in Ref.5 does not suggest the product is direct formation of $\bf{1}$-$\ce{NO2}$ or through the kinetic product, $\bf{1}$-$\ce{ONO}$. It was suggest that when use more reactive benzhydrylium salts for the reaction, the monitored reaction process is the formation of $\bf{1}$-$\ce{ONO}$, which successively rearrange to the observed nitro compounds $\bf{1}$-$\ce{NO2}$. To prove this theory, the authors prepared pure $\bf{1}$-$\ce{ONO}$ in different method (Reaction $\bf{A}$), and monitored its rearrangement to thermodynamically stable $\bf{1}$-$\ce{NO2}$ (Reaction $\bf{B}$):
These experiments clearly suggest that preparation of nitroalkane is not simple as the reaction suggests, but rather complicated process! | {
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homework-and-exercises, condensed-matter, variational-principle, action, topological-field-theory
Upto an unimportant overall factor, the second term can be written as
$$\int\mathrm{d}x_1\mathrm{d}x_2(\partial_1 A_2-\partial_2 A_1)=\int_\Omega\mathrm{d}A=\int_{\partial\Omega}A,$$
where $\Omega$ denotes the manifold to be integrated over and $\partial \Omega$ is its boundary. On closed manifold the boundary $\partial\Omega$ vanishes, so the integral is zero. | {
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Since $cos(t)$ is symmetric about the line $t-\pi=0$.This implies $\sqrt{2-2\cdot \cos(t)}$ is also symmetric about the line $t-\pi=0$.Thus $A+B=C+D$
This implies $I=2*(A+B)$
$I=2*(\int ^{\pi/2}_0{\sqrt{2-2\cdot \cos(t)}dt}+\int ^{\pi}_{\pi/2}{\sqrt{2-2\cdot \cos(t)}dt})$
$I=2*\int ^{\pi}_0{\sqrt{2-2\cdot \cos(t)}dt}$
Let $x=cos(t)$
Then $dx=-sin(t) dt$
As $sin(t)=\sqrt{1-\cos^2(t)}$
Thus $sin(t)=\sqrt{1-x^2}$
Putting the value of $cos(t)$ and $dt$ in $I$ and changing the limits we get,
$I=-2*\int ^{-1}_{1}{\sqrt{({2-2x})/({1-x^2})}dx}$
$I=2\sqrt{2}*\int ^{1}_{-1}{\sqrt{({1-x})/({1-x^2})}dx}$
$I=2\sqrt{2}*\int ^{1}_{-1}{\sqrt{1/({1+x})}dx}$
Integrating it and putting limits we get,
$I=8$ as the required answer. | {
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frequency-response, time-domain
I generated a signal at a sample rate of 8000 samples per second, a carrier of 444 Hz, and some uniform noise. The carrier amplitude is 0.7 and the noise amplitude is 0.3, for a range of [-1,1].
To analyze the signal I generated a filter that has a buffer of samples and a buffer of expected values. The expected values are populated with a sine wave from [0, 2*pi]. When a new sample comes in, the oldest is pushed out of the filter. The filter's measurement is obtained by computing the product of each sample with the expected value, summing it and diving by half the filter length. | {
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complexity-theory, reductions
New question then, is there any use to having an injective reduction? I've noticed that many proofs of NP-hardness seem to have reductions that are injective (at least on $w \in A$). If reductions are not injective ~~ Why don't we simply define our reduction function $R$ as follows, check if $w \in A$, If $w \in A$ then map to a constant $b \in B$. Else, map to a constant $c \notin B$? The function $f$ does not need to be injective. It would be fine to map every $w \in A$ to the same element $w' \in B$ (and to map every $w \in \Sigma^* \setminus A$ to the same $w'' \in \Sigma^* \setminus B$). In fact, for every decidable language $A$, we have $A \leq_m B$ for every $B$ such that $B \neq \Sigma^*$ and $B \neq \emptyset$. | {
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entanglement, textbook-and-exercises
Title: Show by example that a linear combination of entangled states is not necessarily entangled $\newcommand{\bra}[1]{\langle#1\rvert} % Bra
\newcommand{\ket}[1]{\lvert#1\rangle} % Ket
\newcommand{\qprod}[2]{ \langle #1 | #2 \rangle} %Inner Product
\newcommand{\braopket}[3]{\langle #1 | #2 | #3\rangle} % Matrix Element
\newcommand{\expect}[1]{ \langle #1 \rangle} % Expectation value$
I am working through the book Quantum Computing: A Gentle Introduction and I was working on problem 3.2. There are no solutions in the back of the book, so I wanted to double-check this one because I was unsure if I was correct or not. (I probably could do this for all of these questions, but I don't want to spam the board) The problem is:
Show by example that a linear combination of entangled states is not necessarily entangled. | {
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As a side-note: You can't even make the vectors integral if you switch the base. To do so would require $$a^{k-1}=\frac{b^k-1}{b-1}$$ for some integers $$a,b$$ with $$k>2$$, but $$b^{k-1} | {
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"url": "https://math.stackexchange.com/questions/3842922/find-matrix-a-in-mathcalm-n-mathbbn-such-that-ak-left-sum-i-1"
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turtlebot
ros::init(argc, argv, "pub_goal");
ros::NodeHandle nh;
ros::Publisher pub = nh.advertise<geometry_msgs::PoseStamped>("/move_base_simple/goal",1) ;
ros::Rate loop_rate(1);
int count = 0;
while (ros::ok())
{
geometry_msgs::PoseStamped goal;
goal.header.frame_id="map";
goal.pose.position.x=1;
goal.pose.orientation.w=1;
goal.pose.orientation.z=0;
ROS_INFO("%lf",goal.pose.position.x);
pub.publish(goal);
ros::spinOnce();
loop_rate.sleep();
}
return 0;
}
After actkin_make, I rosrun it, but something wired happened.
Here is the result:
luc@luc-ThinkPad-T450:~/catkin_ws$ rosrun goal_test publish_goal
[ INFO] [1510794351.286271377]: 1.000000
[ INFO] [1510794352.286323753]: 1.000000
[ INFO] [1510794353.286425226]: 1.000000
[ INFO] [1510794354.286430381]: 1.000000
[ INFO] [1510794355.286429147]: 1.000000
[ INFO] [1510794356.286306929]: 1.000000 | {
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javascript, performance, jquery, mobile
</div>
<!-- This is just a wrapper for the rest of the page content -->
<div id="shift">
content Goes Here
</div>
jQuery:
jQuery(document).ready(function($) {
var mobNav = $("#mobNav"),
mainNav = $("#mainnav"),
top = $("#top"),
shift = $("#shift");
// add navigation items to mobile nav
mobNav.html(mainNav.html());
$(window).on("scroll", function() {
if($(window).scrollTop() > 300){
top.fadeIn();
} else{
top.fadeOut();
}
if(parseInt(mobNav.css("left"), 10) == 0){
// if is visible then hide
mobNav.css("left", -mobNav.outerWidth());
shift.css("margin-left", "0");
}
}); | {
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"url": null
} |
ros
Error C2143 syntax error: missing ';' before '}' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 20
Error C2143 syntax error: missing ';' before '}' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 64
Error MSB3073 The command ""D:\Unreal Engine\UE_4.14\Engine\Build\BatchFiles\Rebuild.bat" TrafficProjectEditor Win64 Development "D:\Unreal Projects\TrafficProject\TrafficProject.uproject" -waitmutex" exited with code -1. TrafficProject C:\Program Files (x86)\MSBuild\Microsoft.Cpp\v4.0\V140\Microsoft.MakeFile.Targets 46
Error C2238 unexpected token(s) preceding ';' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 20 | {
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of degree higher than one or argument of a function which is not polynomial of degree one. In this case we need to find the Integrating factor which will reduce it to an Exact Differential Equation. ( equation (**) ). In order for this to be an effective method for solving differential equation we need a way to distinguish if a differential equation is exact, and what the function (,) is if the function is exact. Contents: Introduction to differential equations - Separable Differential Equations - Exact Equations Intuition-Integrating factors - First order homegenous equations - 2nd Order Linear Homogeneous Differential Equations - complexwd,Repeated roots of the characterisitic equations - Undetermined Coefficients - Laplace Transform to solve an equation - More Laplace Transform tools. Check the following equations: ( ) ∫ (or ) ∫. If it is exactly in the whole plane, R squared, if R is- the region R, is the whole plane R_two, R squared. However, some inexact differentials yield an | {
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"openwebmath_score": 0.9188512563705444,
"tags": null,
"url": "http://qaon.kairoskroton.it/exact-differential-equation-integrating-factor.html"
} |
hydrology, rivers, water-table
So now the question is, what happens if you channelize the river with impermeable walls and bed? E.g., the Los Angeles River, which has concrete walls.
What happens to the isolated water table now? It is no longer free to drain into the river, so where does it go? Does it drain away more into the ground? Does it stay more saturated than normal until evaporation? And doesn't this produce dangerous ground conditions and bad environmental effects?
Water needs to follow some cycle, or it will just fill up more and more till the whole region is a flooded lake or ocean. So I'm trying to understand the water cycle in this case. The concept of rivers being the outcrop of an aquifer at the surface is a useful generalization, but tends to simplify the real world. | {
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rviz
Seems like there's something wrong with the OpenGL library provide by the system? Probably related to ogre rendering. I installed ogre version 1.7.4 via brew, both binary install and source compile have been tested, both with no luck.
The system generated a report after rviz crashes. I posted the complete report on Gist here
And I have tried to export OGRE_RTT_MODE=FBO and also 'PBuffer', 'Copy' values, no difference.
Can any one help? Thank you so much. | {
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"tags": "rviz",
"url": null
} |
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