text stringlengths 49 10.4k | source dict |
|---|---|
oceanography, sea-level, seasons, enso
Title: What do interannual, annual and intrannual and interseasonal, seasonal and intraseasonal mean in the context of Oceanography? Currently I am studying the period of oceanographic phenomena such as El Niño, and I have seen the next concepts: interannual, annual and intrannua... | {
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"openwebmath_score": null,
"tags": "oceanography, sea-level, seasons, enso",
"url": null
} |
greedy-algorithms
Title: An independent d-division I would love to have a direction for the following exercise (the material for this exercise is greedy algorithms):
Let $G = (V,E)$ an undirected graph whose vertices $V = \{v_1,\dots,v_n\}$ appear in this order on the real line (meaning forall $1 \leq i < j \leq n$, $... | {
"domain": "cs.stackexchange",
"id": 16438,
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"openwebmath_score": null,
"tags": "greedy-algorithms",
"url": null
} |
matlab, autocorrelation
Title: Confusion about ensembles and averages in autocorrelation matrices I just noticed that until now I often don't cared about the scaling of the autocorrelation Matrix in Matlab. I then checked with the book Statistical Digital Signal Processing from M. H. Hayes. There it is defined like th... | {
"domain": "dsp.stackexchange",
"id": 12193,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "matlab, autocorrelation",
"url": null
} |
organic-chemistry, reaction-mechanism, stereoselectivity
With the coordination of diamine ligands to the osmium tetroxide understood, several groups began to think about why this allowed for hydrogen bond based direction of the dihydroxylation. The most comprehensive reference I've found is a chapter in Organic Reacti... | {
"domain": "chemistry.stackexchange",
"id": 6254,
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"openwebmath_score": null,
"tags": "organic-chemistry, reaction-mechanism, stereoselectivity",
"url": null
} |
textbook-and-exercises, mathematics, density-matrix, bloch-sphere, matrix-representation
So I ask, is this a typo? (There have been others)
Or is there something I have not thought of to manipulate this to get the correct result? It must be a typo. Remember that a density matrix must have trace 1, which yours does, a... | {
"domain": "quantumcomputing.stackexchange",
"id": 4127,
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"openwebmath_score": null,
"tags": "textbook-and-exercises, mathematics, density-matrix, bloch-sphere, matrix-... |
general-relativity, metric-tensor, spacetime-dimensions, topology, topological-field-theory
While $2+1$ gravity doesn't have local degrees of freedom, the topology is still a geometric property of the spacetime manifold $\mathcal{M}$, and is thus still important and nontrivial.
Global nontrivialities can play an impor... | {
"domain": "physics.stackexchange",
"id": 41130,
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"tags": "general-relativity, metric-tensor, spacetime-dimensions, topology, topological-fie... |
Use the other initial condition:
$$f(x)+\int_0^x \int_0^y f(z) dz dy = x^3.$$
This looks different from the original thing, but it is actually the same. One way to make it look the same is to use integration by parts together with the initial conditions on the outer integral of the second term. Another way is to inte... | {
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"id": null,
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"lm_q1_score": 0.9719924777713886,
"lm_q1q2_score": 0.8392101519737594,
"lm_q2_score": 0.863391611731321,
"openwebmath_perplexity": 115.07234517369088,
"openwebmath_score": 0.9304203987121582,
"tag... |
gravity, universe, big-bang, dark-matter, dark-energy
Title: Could Dark Matter/Energy be explained by a second universe? Is it possible that prior to our current universe's Big Bang, there was a universe made up of Dark Matter/Energy created from a prior Big Bang? Its physics/matter could have been different than wha... | {
"domain": "physics.stackexchange",
"id": 45588,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "gravity, universe, big-bang, dark-matter, dark-energy",
"url": null
} |
quantum-mechanics, wavefunction
Title: What is the physical meaning of a two-particle wave function? A single-particle wave function is specified in three-dimensional configuration space, but a two-particle wave function is specified in six-dimensional space. What is its physical meaning? The square of the modulus of ... | {
"domain": "physics.stackexchange",
"id": 80750,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "quantum-mechanics, wavefunction",
"url": null
} |
# How many ways are there to count binary trees with "superleaves"
From what I read, the number of binary trees can be counted with respect to their internal nodes using the Catalan numbers:
$$T(z) = \frac{1-\sqrt{1-4z}}{2z}$$
Taking the Taylor series of $$T(z)$$ at $$z=0$$, we get the series:
$$1 + z + 2z^2 + 5z^3... | {
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"lm_q1_score": 0.9888419684230911,
"lm_q1q2_score": 0.8218691336892595,
"lm_q2_score": 0.831143054132195,
"openwebmath_perplexity": 760.2721781890042,
"openwebmath_score": 0.7334949970245361,
"tags... |
quantum-mechanics, energy, hilbert-space
Title: Discrete energies allowed for a particle in a box For a cubic box the energy of a particle is given by:
$$ E = \frac{\pi^2 \hbar^2}{2mL^2} [n_1^2+n_2^2+n_3^2]$$
It is possible that $E$ has the same value for different combinations of $n_1, n_2$ and $n_3$.
I have read tha... | {
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"id": 40081,
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"lm_q2_score": null,
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"tags": "quantum-mechanics, energy, hilbert-space",
"url": null
} |
xv=δ() (C. Dear all, I would like to give you the physics context in which this question emerged, but that would be a very long explanation (sorry!). function, Heaviside unit step function, displaced Heaviside unit step function, dirac-delta function (impulse function ) ,inverse laplace transform. The Heat Equation – G... | {
"domain": "comproorosoldisubito.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683476832692,
"lm_q1q2_score": 0.8272069631755768,
"lm_q2_score": 0.8376199633332891,
"openwebmath_perplexity": 708.7659774314237,
"openwebmath_score": 0.91251099109649... |
algorithm, c, library, pathfinding
p_cost_map = unordered_map_t_alloc(INITIAL_CAPACITY,
LOAD_FACTOR,
hash_function,
equals_function);
if (!p_cost_map)
{
heap_t_free(p_open_set);
... | {
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"id": 15553,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithm, c, library, pathfinding",
"url": null
} |
javascript, performance, jquery
Title: Multiple similar event handlers for input validation I want to reduce my repetitive code used to validate inputs values. For that I'm using:
a class associated to the input
a condition to validate the input value
an event handler
First I declare the classes I'm using:
var input... | {
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"openwebmath_score": null,
"tags": "javascript, performance, jquery",
"url": null
} |
## Limit approaching infinity with an unknown in the exponent
Limits, differentiation, related rates, integration, trig integrals, etc.
jimmy_boots
Posts: 4
Joined: Thu Dec 18, 2008 3:14 pm
Contact:
### Limit approaching infinity with an unknown in the exponent
Find the limit, as x approaches infinity, of (1+(2/x))x... | {
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"id": null,
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"lm_q1_score": 0.975946445706356,
"lm_q1q2_score": 0.8174722300238069,
"lm_q2_score": 0.8376199673867852,
"openwebmath_perplexity": 839.812024342229,
"openwebmath_score": 0.929065465927124,
"tags": nu... |
ds.algorithms, advice-request, formal-modeling, ni.networking-internet
Title: PageRank for a Non-Random Searcher I'm looking to adapt the PageRank algorithm as a centrality measure in a network. This network however, unlike the "random surfer" of the original paper on PageRank, or the random library browser for Eigenf... | {
"domain": "cstheory.stackexchange",
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"tags": "ds.algorithms, advice-request, formal-modeling, ni.networking-internet",
"url": ... |
quantum-mechanics, density-operator, open-quantum-systems
$$ \dot{\rho}' = \frac{\partial}{\partial t}\left( U\rho U^\dagger\right) = U \dot{\rho} U^\dagger,$$
where we used the fact that $\dot{U} = 0$ by assumption. Plugging away and making liberal use of $U U^\dagger = 1$, one obtains
$$ \dot{\rho}' = -i[H',\rho']... | {
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"openwebmath_score": null,
"tags": "quantum-mechanics, density-operator, open-quantum-systems",
"url": null
} |
pharmacology, structural-biology, medicinal-chemistry
Title: Do drugs' levo isomers have a better interaction with the receptors in our body than dextro isomers? Examples of levo drugs include levothyroxine, levocitrizine, and levodopa. Is there any specific reason why the receptors in our body exhibit this stereoisom... | {
"domain": "biology.stackexchange",
"id": 4555,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "pharmacology, structural-biology, medicinal-chemistry",
"url": null
} |
computability, closure-properties
Title: Closure property of recursively enumerable language I read that recursively enumerable languages are closed under intersection but not under set difference.
We know that, $A \cap B = A - ( A - B)$.
Now for LHS (left-hand side) to be closed under intersection, RHS(right-hand sid... | {
"domain": "cs.stackexchange",
"id": 10003,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "computability, closure-properties",
"url": null
} |
quantum-mechanics, electrons
Title: Is electron energy spectrum quantized in the presence of an electric field? Maybe this is a stupid question, but is free electron's energy spectrum continuous in the presence of an external field? For example, if a free electron flies between two plates in a capacitor. Boundary cond... | {
"domain": "physics.stackexchange",
"id": 66810,
"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": "quantum-mechanics, electrons",
"url": null
} |
python, python-3.x
def get(self):
"""Call the ``next`` function on self """
return next(self)
def load(self):
"""Load the transaction ref data from the local file
:raises errors.UniqueTransactionRefError: Cannot find file
"""
try:
with open(self.file) a... | {
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"id": 29576,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x",
"url": null
} |
bcftools, liftover, merge
write_delim(file = str_glue("{some_path}some_file_v1.vcf"),
k col_names = F, quote = 'none', escape = 'none') | {
"domain": "bioinformatics.stackexchange",
"id": 2299,
"lm_label": null,
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"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "bcftools, liftover, merge",
"url": null
} |
c#, dependency-injection, factory-method, static, autofac
Title: Using Autofac to do DI in a static factory method I'm using Autofac to create one of my classes inside of a static factory method Create. This code is working and I haven't noticed any side effects yet. Admittedly, I've only used it in unit-tests so far ... | {
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"id": 28060,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "c#, dependency-injection, factory-method, static, autofac",
"url": null
} |
A well-known shuffling algorithm that produces an exchangeable sequence of values is the Fisher-Yates shuffle. In this algorithm (forward version) you go through the units in the original population sequentially and swap each one with a uniformly randomised unit that is no earlier in the sequence than the one under con... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668701095653,
"lm_q1q2_score": 0.8259714315981813,
"lm_q2_score": 0.8418256432832332,
"openwebmath_perplexity": 688.8466625418768,
"openwebmath_score": 0.6753267049789429,
"tag... |
php, object-oriented, mysql, json, mysqli
Title: OOP - Contact Form PHP Backend - Procedural to OOP - Dynamic MySQL Prepared Statement PHP I just converted procedural code to OOP code. Is there any performance or security issue with this code or what should I consider further?
interface
interface IContactform {
... | {
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"id": 41697,
"lm_label": null,
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"lm_q2_score": null,
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"tags": "php, object-oriented, mysql, json, mysqli",
"url": null
} |
c, c99
return idx;
}
I changed several things:
EOF is handled correctly. On EOF, the string is returned, properly null-terminated. (This was not the case in your code.)
Leading whitespace does not count towards the buffer, it is simply ignored, like you said in your description. Your code counted it.
Each call to an... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c, c99",
"url": null
} |
thermodynamics, thermal-radiation
Title: Why is power emission between one body and its surroundings equal to the difference of $T^4$? According to the Stefan-Boltzmann Law:
$P=e\sigma AT^{4}$
For any body
However, the power it releases when its surroundings has a temperature $T_s$ is $P=e\sigma A(T^{4}-T_{s}^{4})$ (a... | {
"domain": "physics.stackexchange",
"id": 77822,
"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": "thermodynamics, thermal-radiation",
"url": null
} |
astronomy, terminology, definition, galaxies
Title: Definition of a Supercluster A group of astronomers in September 2014 redefined what classifies a supercluster. Before this, the supercluster where the Milky Way resides was the Virgo Supercluster. Now, the Virgo Supercluster & three other previously defined superclu... | {
"domain": "physics.stackexchange",
"id": 24071,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "astronomy, terminology, definition, galaxies",
"url": null
} |
cells for ADH?! You to find the solution to a quadratic function means it is of the form +... $is a constant then the function is called a parabola as you watch, think about you... A smile or a frown a video on estimating the zeros are the. X=\Frac { -b\pm\sqrt { b^2-4ac } } { 2a }$ a smooth, approximately u-shaped or ... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660949832345,
"lm_q1q2_score": 0.8108436851030907,
"lm_q2_score": 0.8499711775577736,
"openwebmath_perplexity": 687.9319890469096,
"openwebmath_score": 0.5007145404815674,
... |
# An inequality on trace of product of two matrices
Suppose we have two $n \times n$ positive semidefinite matrices, $A$ and $B$, such that $\mbox{tr}(A), \mbox{tr}(B) \le 1$.
Can we say anything about $\mbox{tr}(AB)$? Is $\mbox{tr}(AB) \le 1$ too?
In the space of positive semi-definite matrices, trace is a proper i... | {
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"lm_q1_score": 0.9865717436787542,
"lm_q1q2_score": 0.8424461899612972,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 177.58823142251953,
"openwebmath_score": 0.9980753064155579,
"ta... |
cosmic-microwave-background, dust
Title: What is the physics of the "spinning dust" contribution to Cosmic Microwave Background measurements? The lengthy paper Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results mentions "spinning dust" about 51 times. It is a potential contribut... | {
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"id": 2520,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cosmic-microwave-background, dust",
"url": null
} |
inorganic-chemistry, orbitals, hybridization
mono-, di- and tri-coordination: use 1, 2 or 3 $\mathrm{p}$ orbitals to form bonds; keep one lone pair in an $\mathrm{s}$ type orbital. (Predicted bond angle: $90^\circ$.)
tetracoordination (no additional lone pairs): since the former is not possible, hybridise $\mathrm{s}... | {
"domain": "chemistry.stackexchange",
"id": 15775,
"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": "inorganic-chemistry, orbitals, hybridization",
"url": null
} |
ros, pcl, pcl-conversions, velodyne, pointcloud
Title: converting velodyne packets to pointcloud
Hii,
I have velodyne packets and its config file . I want to convert it to point cloud in a C++ program. Can anyone provide me API to do this .
Originally posted by shashank on ROS Answers with karma: 70 on 2017-05-04
Po... | {
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"openwebmath_score": null,
"tags": "ros, pcl, pcl-conversions, velodyne, pointcloud",
"url": null
} |
Another approach:
Rewrite \begin{align} 4\sin\theta +3\cos\theta &= 5\\ 4\sin\theta&=5-3\cos\theta.\tag1 \end{align} Square $(1)$, yields $$16\sin^2\theta=25-30\cos\theta+9\cos^2\theta.\tag2$$ Use identity $\sin^2\theta=1-\cos^2\theta$ and substitute to $(2)$. \begin{align} 16(1-\cos^2\theta)&=25-30\cos\theta+9\cos^2\... | {
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"lm_q1_score": 0.9811668679067631,
"lm_q1q2_score": 0.815490027205347,
"lm_q2_score": 0.831143054132195,
"openwebmath_perplexity": 512.3702789921335,
"openwebmath_score": 0.9648978114128113,
"tags"... |
c#, object-oriented, xml, database, inheritance
Title: Loading items from XML document I'm making a game in Unity and I need to have a inventory/item system, I decided to store my items in simple XML document which I later read from. I'm planning to have different varieties of items and they will all have distinct cla... | {
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"tags": "c#, object-oriented, xml, database, inheritance",
"url": null
} |
We consider the simple poset ${\displaystyle P=[n]}$, where ${\displaystyle \leq }$ is the total order. It follows directly from the recursive definition of Möbius function that
${\displaystyle \mu (i,j)={\begin{cases}1&{\text{if }}i=j,\\-1&{\text{if }}i+1=j,\\0&{\text{otherwise.}}\end{cases}}}$
Usually for general p... | {
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"lm_q2_score": 0.8128673246376009,
"openwebmath_perplexity": 757.1168362379117,
"openwebmath_score": 0.9848743081092834,
"tags": null,
... |
quantum-mechanics, resource-recommendations, path-integral
Title: Path integral formulation understanding I have done basic quantum mechanics and now I want to do the path integral formulation. I find Feynman's book Path Integrals in Quantum Mechanics difficult. Is there an easier alternative? Maybe you should start w... | {
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"tags": "quantum-mechanics, resource-recommendations, path-integral",
"url": null
} |
ros, openni, subscribe
Title: Subscribe to multiple topics simultaneously
Hi,
I implement a stair detection algorithmus for ROS. Therefore the node analyzes input data from an Asus Xtion camera via openni_launch. Can the node subscribe to both topics, /camera/depth/image and /camera/rgb/image, and receive both image ... | {
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"tags": "ros, openni, subscribe",
"url": null
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newtonian-gravity, astrophysics, density, fusion, jupiter
Many would not see falling below some mass threshold as a good definition for a "planet". Indeed whilst many astronomers would refer to objects between the deuterium- and hydrogen-burning thresholds as "brown dwarfs", rather than planets, others argue that the ... | {
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} |
$d=1$
$a_{n}=1.(2^n)-1$
$T(n)=O(2^n)$
1 vote
Hope this helps :)
## Related questions
1
6.5k views
The recurrence equation $T(1) = 1$ $T(n) = 2T(n-1) + n, n \geq 2$ evaluates to $2^{n+1} - n - 2$ $2^n - n$ $2^{n+1} - 2n - 2$ $2^n + n$
Let $A[1,\ldots,n]$ be an array storing a bit ($1$ or $0$) at each location, and... | {
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quantum-mechanics, angular-momentum, symmetry, atomic-physics
However, since it is in general not a product of single-electron wavefunctions the angular momenta of the two individual electrons are not defined (which makes it difficult for me to exploit symmetries for the integration of the two coordinates).
In princi... | {
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"tags": "quantum-mechanics, angular-momentum, symmetry, atomic-physics",
"url": null
} |
boundary-conditions, crystals, lattice-model, tight-binding
The bottom line is: it doesn't matter how many sites you have, to establish whether or not a Brillouin zone exists, you have to look at the boundary conditions.
In a 2d square lattice with $L_x \times L_y$ sites, with PBC on the y direction and OBC on the x d... | {
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"tags": "boundary-conditions, crystals, lattice-model, tight-binding",
"url": null
} |
error-correction, pauli-gates, stabilizer-code
Find a non-zero entry in the state vector, then apply Pauli X gates to permute the vector so that the found non-zero amplitude ends up as the amplitude of the $|000..0\rangle$.
Find a second non-zero entry in the state vector. If there is none, goto 6. Otherwise let $k_2$... | {
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"tags": "error-correction, pauli-gates, stabilizer-code",
"url": null
} |
quantum-mechanics, quantum-field-theory, hamiltonian, fermions, perturbation-theory
Title: Expectation value of time-evolved number operator for ground state Coulomb system I'm going through "Advanced Quantum Mechanics" by Franz Schwabl, and he calculates the electron energy levels from the Coulomb interaction in a pe... | {
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"tags": "quantum-mechanics, quantum-field-theory, hamiltonian, fermions, perturbation-theor... |
c++, performance, c++11, inheritance, casting
void accept(ConstVisitorBase &visitor)const override{
try_to_accept<T, Bases...>(visitor);
}
};
A Benchmark shows approximately 77 times slower execution time using dynamic_cast and 25 times slower execution time using the dictionary compared to the standard approa... | {
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"tags": "c++, performance, c++11, inheritance, casting",
"url": null
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python, performance, primes
def calculate_perfects():
yield 6
primes = prime_sieve()
pool = Pool(processes=8)
while True:
next_primes = [next(primes) for _ in range(8)]
is_mersenne = pool.map(is_mersenne_prime, next_primes)
for prime in compress(next_primes, is_mersenne):
... | {
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"tags": "python, performance, primes",
"url": null
} |
javascript, html, form, dom
Title: Simplifying Counter of Checked Checkboxes Is the following code a proper solution to my problem? I have a feeling it can be simplified quite a bit.
If one of the first four checkboxes is checked the sum is 1; if two 1.5; if three 2; if four 2.5. If the bar5 is checked then it's 1 + ... | {
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"tags": "javascript, html, form, dom",
"url": null
} |
optics, reflection, geometric-optics
Title: How specular are diffuse reflectors? I understand the primary difference between the two being that in the former, the light rays at a point is regularly reflected while in the latter, each point throws of light in all directions.
But since the principle of least time must ... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "optics, reflection, geometric-optics",
"url": null
} |
proteins, vaccination, mrna
Title: mRNA vaccines: Can a spike protein by itself have different side-effects than the virus itself? I was wondering, is it possible for the isolated spike protein, as resulting from an mRNA vaccine, to cause harmful side effects in an individual, that would not have developed in that ind... | {
"domain": "biology.stackexchange",
"id": 11765,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "proteins, vaccination, mrna",
"url": null
} |
energy, photons, momentum, reflection
Title: Does a reflection still transfer momentum to an mirror? I have been recently wondering, if I take a powerful enough energy source (photon) and I have an perfect mirror exactly in front of it and assume an "emitter" shot the light towards the mirror.
As perfect mirrors abso... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "energy, photons, momentum, reflection",
"url": null
} |
regular-languages, context-free, proof-techniques
Title: Is there a *simple* proof that the intersection of a CFL and a regular language is a CFL? I am following a course on complexity theory where languages are a part of the course. There is a proof that no matter how hard I try to understand, it is till so complex t... | {
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"tags": "regular-languages, context-free, proof-techniques",
"url": null
} |
# Least-squares fitting of circles
## Hypotheses
This page explains how to fit a 2D circle to a cloud of point by minimizing least squares errors.
The point cloud is given by $$n$$ points with coordinates $${x_i,y_i}$$. The aim is to estimate $$x_c$$ , $$y_c$$ and $$r$$, the parameters of the circle that fit the bes... | {
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"tags": nu... |
and hence $\mu$ is a probability measure that satisfies the condition.
Is this correct? As a follow up question, is a probability measure $\mu$ satisfying the condition I wrote down unique?
• Yes, you are correct. This is true for arbitrary $\sigma$-algebras on the real line. The measure you defined is unique; if the... | {
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"openwebmath_score": 0.9757503867149353,
"tags... |
homework-and-exercises, fluid-dynamics, flow, bernoulli-equation
Seems reasonable to me, at least to zeroth order.
You are basically using:
$$
v_1 A_1 = v_2 A_2\; \qquad(1)
$$
and
$$
v_2 = v_1 + gt\;. \qquad (2)
$$
If you want to get rid of the Eq. (2) and the time dependence in favor of, say, distance ($d$) below th... | {
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"tags": "homework-and-exercises, fluid-dynamics, flow, bernoulli-equation",
"url": null
} |
electrostatics, gauss-law, dielectric
Title: Electric displacement at the boundary of a dielectric and vaccum At the boundary of an infinite linear dielectric with constant $\kappa$ and a vacuum, a charge q is placed. In order to calculate the electric displacement$(\mathbf{D})$ we can use Gauss's law for dielectrics ... | {
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"tags": "electrostatics, gauss-law, dielectric",
"url": null
} |
algorithms, algorithm-analysis
Title: Finishing Time in DFS, is that necessary? According to DFS algorithm for graph traversing:
DFS(G)
for each v ∈ V (G)
v.mark = false
time = 0
for each v ∈ G.V
if not v.mark
DFS-Visit(v)
DFS-Visit(v)
v.mark = true
time = time + 1
v.d = time
fo... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, algorithm-analysis",
"url": null
} |
bacteriology, plant-physiology, light, fruit, vitamins
Can it be true? How can dead (picked, transported and refrigerated) fruit produce more vitamins? How does blue light affect this?
Furthermore I thought that only UV light kills bacteria.
Therefore my question is: how much truth was on that sticker? Maybe a littl... | {
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"id": 8106,
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"tags": "bacteriology, plant-physiology, light, fruit, vitamins",
"url": null
} |
-
+1 for actually using the fact the ring has no zero divisors... – Goos Apr 27 at 19:30
@Goos: Well, the claim is false without something extra, and that was the only piece available :-) All: Sorry about spoiling the problem. I really should have come up with an appropriate hint. – Jyrki Lahtonen Apr 27 at 19:45
yes... | {
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"lm_q2_score": 0.8791467675095294,
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"openwebmath_score": 0.9344157576560974,
"ta... |
being x. Consequently, the definition of the derivative for a function of one variable applies: The above procedure can be performed for any choice of a. 4 years ago. x z 1 You da real mvps! with coordinates Lets start with the function f(x,y)=2x2y3f(x,y)=2x2y3 and lets determine the rate at which the function is chang... | {
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"lm_q1_score": 0.9863631635159683,
"lm_q1q2_score": 0.8176346970004308,
"lm_q2_score": 0.8289387998695209,
"openwebmath_perplexity": 560.6435858355239,
"openwebmath_score": 0.9494776129722595,
... |
# Combination of Simple Harmonic Motions
Will the combination of 2 Simple Harmonic motions will be an SHM in itself? For example for simple functions such as
$$\ f(t)=\sin\omega t-\cos\omega t$$ I can use trigonometry to show that it can be expressed as $$\ f(t)=\sqrt 2\sin(\omega t-\pi/4)$$.
But what about function... | {
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"lm_q2_score": 0.8152324848629215,
"openwebmath_perplexity": 353.57816962675605,
"openwebmath_score": 0.9927248358726501,
"tag... |
arduino, i2c
Which is basically the same, except all the 10s are changed for 5. That is, in the expanded form, each digit is multiplied by b^p where b is the base and p is its position in the number.
Now you know that in base 10, you have digits from 0 to 9. Similarly, in base 5, you have digits from 0 to 4. In base 2... | {
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"tags": "arduino, i2c",
"url": null
} |
r, software-recommendation, sequence-annotation
Title: Software recommendation: find DNA sequence distribution over entire transcript I would like to create a density/histogram of the distribution of a particular DNA sequence over the entire transcript using R and/or command line tools. From here, I would like to use ... | {
"domain": "bioinformatics.stackexchange",
"id": 252,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "r, software-recommendation, sequence-annotation",
"url": null
} |
algorithms, algorithm-analysis, recursion
Title: Recursive factorial algorithm I'm struggling to understand this factorial algorithm.
Falling(n, m):
if m = 0
return 1
if m = 1
return n
return Falling(n, floor(m/2))*
Falling(n - floor(m/2), ceil(m/2))
The algorithm should compute... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, algorithm-analysis, recursion",
"url": null
} |
java, android, bluetooth
Title: Android Bluetooth device application I am writing my first Android application and have mainly been using code examples online. However, I have been going hard at it for a while now and realize that I have some overlapping methods and such in my code.
I have three classes:
AndroidBluet... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, android, bluetooth",
"url": null
} |
ros, drone, ros-kinetic
Title: Ardupilot + ROS
Hi !
I have made a hexacopter with APM 2.8 and would love to deploy ROS on it using a Raspi. I aim to use opencv with ros to detect landing marker and make it land autonomously. But I don't know what camera to use! Any suggestions on this would be great.
Have looked into... | {
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"tags": "ros, drone, ros-kinetic",
"url": null
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-
Why isn't $f_{n+2}=3f_n-f_{n-2}$ suitable? – Guess who it is. Dec 27 '11 at 4:31
@J.M., sorry I do not understand. If I were to expand $f_{n+2}$ the way I do it, I would end up with $2f_n + f_{n - 2} + f_{n - 3}$. Again, I can make this work if I know what I am trying to get. I wonder if you have read the question c... | {
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"openwebmath_score": 0.973792552947998,
"tags... |
rviz, camera, plugin, ros-fuerte, tracking
Title: Set RViz camera/view on fuerte
Hi,
I'm writing a RViz plugin which allows the user to play rosbags and record them.
During playing the rosbags I would like to make it possible to do a tracking shot in the scene. Therefore I have to set the current view in RViz.
Is the... | {
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"id": 13059,
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"tags": "rviz, camera, plugin, ros-fuerte, tracking",
"url": null
} |
atomic-physics, quantum-chemistry
So the negatively charged electron will be in a specific location (x,y,z) at a specific time .This allows the positive charge of the nucleus range to affect other charges, and the orbitals of different molecules can fit , like lego blocks, positive attracting negative. i.e. a new pote... | {
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"tags": "atomic-physics, quantum-chemistry",
"url": null
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The Mrowka space (also called Psi space) was discussed previously in this blog (see this post). For the sake of completeness, the example is defined here.
First, we define some basic notions. Let $\omega$ be the first infinite ordinal (or more conveniently the set of all nonnegative integers). Let $\mathcal{A}$ be a f... | {
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"openwebmath_score": 0.9476520419120789,
"tags": ... |
javascript, jquery, functional-programming, observer-pattern, frp
// **********************************
// *** start: Sources constructor ***
// **********************************
function Sources() {
this.sources = {};
}
Sources.prototype.subscribe = function(subscriptionID, subscriberID) {
if(!this.sources[s... | {
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"tags": "javascript, jquery, functional-programming, observer-pattern, frp",
"url": nu... |
solar-system, galaxy, ecliptic
Title: Oscillation in tilt of the solar system I know that the solar system is tilted 62.6° to the plane of the galaxy. I'm curious whether this angle changes over time, and what are the extents and time frame of any such oscillations if they exist?
Upon reflection, I'm assuming that si... | {
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"tags": "solar-system, galaxy, ecliptic",
"url": null
} |
# Why do we divide Permutations to get to Combinations?
I'm having a hard time reasoning through the formula for combinations $$\frac{n!}{k!\left(n-k\right)!}$$. I understand the reason for the permutations formula and I know that for the combinations we divide by $$k!$$ to adjust for the repeated cases, since order d... | {
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"lm_q1_score": 0.9820137900379085,
"lm_q1q2_score": 0.8266843944086281,
"lm_q2_score": 0.8418256472515684,
"openwebmath_perplexity": 167.3886790718227,
"openwebmath_score": 0.7704142332077026,
"tag... |
c++, algorithm
I'll make the trivial observation that the inputArray parameter should be const. Just call it input; the "Array" adds nothing of value, and in any case, it's a std::vector, not an array.
Wherever you say (n + 1) % 2 to map 0 to 1 and vice versa, you can just say !n.
That said, I can make absolutely no ... | {
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"tags": "c++, algorithm",
"url": null
} |
special-relativity, time-dilation
$$0= \gamma c\Delta t -\gamma\beta\Delta x$$
or $$ \gamma c\Delta t =\gamma\beta\Delta x$$
With that we get the length in $S'$ to be
$$\Delta x' = \gamma \left(1 -\beta^2\right) \Delta x = \frac{\Delta x}{\gamma}$$
Admonition
Whenever you are considering any equation, you need to cons... | {
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"tags": "special-relativity, time-dilation",
"url": null
} |
c#, parsing, template, iterator, email
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; max-width: 600px;" width="100%">
<tr>
<td align="center" bgcolor="f7f8f6">
<img src="#" alt="alttext... | {
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"id": 35042,
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"tags": "c#, parsing, template, iterator, email",
"url": null
} |
If you continue with multiplying the factor for P with 2, you get the next round of iteration, where "odd" indicates the upper half of the interval and "even" indicates the lower half.
• we know that P < N, if 2P is odd, then 2P > N => P > N/2, if 4P is odd, then 4P > N => P > N/4. Where does that 3/4 comes from? – Da... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9808759604539051,
"lm_q1q2_score": 0.8297646025885446,
"lm_q2_score": 0.845942439250491,
"openwebmath_perplexity": 864.9243373529753,
"openwebmath_score": 0.7786990404129028,
"tags... |
java, unit-testing, mocks
CompleteRoutingResponseShort currentResponse = routingResponsesInMemoryFactory.getOneAlternative();
CompleteRoutingResponseShort baselineResponse = routingResponsesInMemoryFactory.getOneAlternative();
alternativeShortTotalChecker.checkAllAlternativesShort(currentResponse, baselineRes... | {
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"id": 12836,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, unit-testing, mocks",
"url": null
} |
matlab, python, noise-cancellation, lms
output = y_main_path - input_value
# LMS update
filt.adapt(y_main_path,input_value)
output = np.clip(output, -MAXVALUE, MAXVALUE)
output = output.astype(int)
binary_date = struct.pack('h', output)
stream.write(binary_data)
output_wf.writeframes(binary_data... | {
"domain": "dsp.stackexchange",
"id": 9965,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "matlab, python, noise-cancellation, lms",
"url": null
} |
ros
Title: Get sensor_msgs/LaserScan message from simulation(v-rep)
Hello all,
is it possible to use LMS1xx package, but get the messages from simulation(eg. in vrep) instead of the real laser scanner?
Thanks in advance.
Originally posted by Yami on ROS Answers with karma: 1 on 2013-09-25
Post score: 0
It should wo... | {
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"id": 15648,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "ros",
"url": null
} |
black-holes, astronomy, telescopes
Title: Picture of Sgr A* As a lot of you may know, on April 10th we'll get to see the so said "first picture of a black hole" from the EHT. I'm no expert in observational astrophysics, so my questions are: how are they taking this radio image? Is it the same as the "old" radio telesc... | {
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"id": 57104,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "black-holes, astronomy, telescopes",
"url": null
} |
mysql, bash, configuration
Title: Create Apache2 virtualhost, Mysql db & user. CLI tool and GUI on top of it Review for optimization, code standards, missed validation.
What's in this version:
Rewritten, instead of large complex script - few tools with each own
task.
Solid CLI tool and GUI script on top of it.
Apply ... | {
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"id": 34133,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "mysql, bash, configuration",
"url": null
} |
cosmology, universe, education, estimation, software
So 4.8 billion light years. Still off by a factor of 10.
EDIT: So sad that I made typos that led to serious errors. Number of Hydrogen per volume
The critical density of the universe is a handful of hydrogen per cubic meter.
The actual number of hydrogen per cubic m... | {
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"openwebmath_score": null,
"tags": "cosmology, universe, education, estimation, software",
"url": null
} |
reaction-mechanism, experimental-chemistry
So, to answer the question: "which reagents in the experiment are responsible for changing the time before the colour change in the clock", the answer is H2O2 and Vitamin C. Now, while the rate-controlling step, associated with the slowest reaction is H2O2 (creating the colou... | {
"domain": "chemistry.stackexchange",
"id": 13966,
"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": "reaction-mechanism, experimental-chemistry",
"url": null
} |
java, performance, programming-challenge, memory-optimization, bigint
11111000000111111100000000 / 2^8
111110000001111111 +1
111110000010000000 / 2^7
11111000001 ... | {
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"tags": "java, performance, programming-challenge, memory-optimization, bigint",
"url"... |
# Sort a list of derivatives
I have a list of variables, both constant and functions of an independent variable, including derivatives. I'd like to sort these by the variable name, rather than the derivative order. For example, the default Sort gives:
Sort[{x[t], x'[t], x''[t], y[t], y'[t], y''[t],a}]
{a, x[t], y[t],... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9728307716151472,
"lm_q1q2_score": 0.8209671218706914,
"lm_q2_score": 0.8438951005915208,
"openwebmath_perplexity": 3871.964038769169,
"openwebmath_score": 0.45026081800460815,
"ta... |
ros, ros-melodic, boost
Title: ROS cannot find Boost header files
I am running Ubunti 18.04 with ROS Melodic. I was installing ROSPlan and while doing that I get errors related to Boost Headers. The output of catkin build is as follows,
catkin build --cmake-args \
-DCMAKE_BUILD_TYPE=Release \
... | {
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"tags": "ros, ros-melodic, boost",
"url": null
} |
c#, .net, wpf, mvvm, xaml
<Label Grid.Row="1" Grid.Column="0" Margin="8,8,0,0">Name:</Label>
<TextBox Name="TextBoxName" Grid.Row="1" Grid.Column="1" Text="{Binding Name}" Margin="8,8,8,0" GotFocus="TextBox_GotFocus"/>
<StackPanel Grid.Row="2" Grid.ColumnSpan="2" Grid.Column="0" Orientation="Horizontal... | {
"domain": "codereview.stackexchange",
"id": 19272,
"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#, .net, wpf, mvvm, xaml",
"url": null
} |
gazebo
</link>
<joint name='joint5' type='revolute'>
<child>link5</child>
<parent>link4</parent>
<axis>
<xyz>0 1 0</xyz>
<limit>
<lower>-3.14159</lower>
<upper>3.14159</upper>
<effort>1000</effort>
<velocity>10</velocity>
</limit>
... | {
"domain": "robotics.stackexchange",
"id": 3678,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "gazebo",
"url": null
} |
Starting with $$Y = \text{Bottom} +\frac{\text{Top}-\text{Bottom}}{1+10^{\log_{10} EC50 -X}}$$
then using $10^{\log_{10} EC50 -X} = EC50 /10^X$ (if that is what you meant) you get $$Y -\text{Bottom} =\frac{\text{Top}-\text{Bottom}}{1+EC50 /10^X}$$ or $$1+EC50 /10^X =\frac{\text{Top}-\text{Bottom}}{Y -\text{Bottom}}$$ ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9511422158380861,
"lm_q1q2_score": 0.804611562445996,
"lm_q2_score": 0.8459424353665381,
"openwebmath_perplexity": 295.9377982411776,
"openwebmath_score": 0.8553591370582581,
"... |
So this sets up a heuristic search which finds (a=24, (a+1)=5^2=25, b=7) and the other side $$(a+1)-b = 25-7 = 18$$ Since we knew a >= 2b
We only needed to consider the candidates a = 12,24,40,60,... and b= prime legs p = 3,5,7,11... where p doesn't also divide a, and also a >= 2b.
You could turn that into one or two... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9748211619568681,
"lm_q1q2_score": 0.8102158398201629,
"lm_q2_score": 0.8311430562234877,
"openwebmath_perplexity": 920.2466979267646,
"openwebmath_score": 0.7919704914093018,
"tag... |
cc.complexity-theory, sat, exp-time-algorithms
Title: Computational Model in SETH Impagliazzo, Paturi and Calabro, Impagliazzo, Paturi introduced Exponential-Time Hypothesis (ETH) and Strongly Exponential-Time Hypothesis (SETH). Roughly, SETH says that there is no algorithm which solves SAT in time $1.99^n$.
I was w... | {
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "cc.complexity-theory, sat, exp-time-algorithms",
"url": null
} |
python, yaml
# example of a child class:
@dataclass(kw_only=True)
class StudyYamlData(MappedYaml):
study_id: str = ''
year: int = None
abstract: str = ''
reference: str = ''
keywords: str = ''
domain_general: str = ''
domain_specific: str = '' nouns and verbs
We use nouns for class names an... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, yaml",
"url": null
} |
general-relativity, black-holes, hawking-radiation, qft-in-curved-spacetime, black-hole-thermodynamics
"Adding charge" always seems to decrease $C$. Is there a clear reason for this?
Physically, should one expect a diverging heat capacity at a certain charge (for fixed mass) at all? Why is it located at $q=\pm\frac{\s... | {
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"tags": "general-relativity, black-holes, hawking-radiation, qft-in-curved-spacetime, black... |
machine-learning, data-mining, statistics, algorithms, recommender-system
Title: Mahout Similarity algorithm comparison Which of the following is best (or widely used) for calculating item-item similarity measure in mahout and why ?
Pearson Correlation
Spearman Correlation
Euclidean Distance
Tanimoto Coefficient
LogLi... | {
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"id": 156,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "machine-learning, data-mining, statistics, algorithms, recommender-system",
"u... |
motor, servomotor, torque, movement
Title: What is the type of electric motor that can lift 1.6 kg just like micro servos, but without the reduction gear? Micro servo motors, normally the 9g type can lift 1,6kg with a reduction box made of nylon.
However, I'm interested on lifting this amount of weight (1,6 kg) in a f... | {
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"id": 2590,
"lm_label": null,
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"openwebmath_score": null,
"tags": "motor, servomotor, torque, movement",
"url": null
} |
You have the right answer; you just have a different constant. Using $$C_1$$ instead of $$C$$, set your answer $$\frac{x^2-3}{2}+x+\ln|x-1|+C_1$$ equal to option (C) and simplify. You'll get $$C-C_1=-\frac32$$, which is fine since the difference is constant.
Now, as an alternative approach to the problem, consider tha... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9802808753491773,
"lm_q1q2_score": 0.8014526297221414,
"lm_q2_score": 0.8175744828610095,
"openwebmath_perplexity": 677.6880254129212,
"openwebmath_score": 0.9201125502586365,
"tag... |
c#, mysql, database
return readerSql;
}
protected int ExecuteSQLReturnId(string sSql)
{
MySqlCommand cmd = new MySqlCommand(sSql, conn);
cmd.ExecuteNonQuery();
return Convert.ToInt32(cmd.LastInsertedId);
}
In others part of my project i then use
db = new dbConnection();
db.op... | {
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"openwebmath_score": null,
"tags": "c#, mysql, database",
"url": null
} |
ds.algorithms, reference-request
Then in order to be able to add $v_{clean}$ that has a $-q$ in column $b$; we must add exactly $q$ vectors $v_{C_i}$ that contains $[....,1_{b}]$; we cannot add more than $q$ otherwisee the column $z$ becomes negative.
Furthermore we cannot add two $C_i$ that has the same element in th... | {
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"openwebmath_score": null,
"tags": "ds.algorithms, reference-request",
"url": null
} |
standard-model, gauge-theory, yang-mills, non-linear-systems
Now, the Lagrangian for gauge theories is usually (note that one may consider GR a gauge theory, and this is certainly not true for GR - it is true for Yang-Mills type theories basically) given by $$ \mathcal L\sim F^2 $$ where $$ F^a_{\mu\nu}=\partial_\mu A... | {
"domain": "physics.stackexchange",
"id": 49266,
"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": "standard-model, gauge-theory, yang-mills, non-linear-systems",
"url": null
} |
special-relativity, energy-conservation
\begin{equation}
\mathbf{f}=-\boldsymbol{\nabla} U_{pot}
\tag{A-05}
\end{equation}
then
\begin{equation}
\dfrac{dW}{dt}=\mathbf{f}\circ \mathbf{v}=\left(-\boldsymbol{\nabla} U_{pot}\right)\circ \dfrac{d\mathbf{r}}{dt}=-\dfrac{\boldsymbol{\nabla} U_{pot}\circ d\mathbf{r}}{dt}==... | {
"domain": "physics.stackexchange",
"id": 23155,
"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": "special-relativity, energy-conservation",
"url": null
} |
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