url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
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https://www.physicsforums.com/threads/silly-root-question.53955/ | # Silly root question
1. Nov 24, 2004
### dogma
Here's a silly roots question that has my congested mind temporarily stumped:
Let $$z = 1 + \sqrt{2}$$. Find the five distinct fifth roots of z.
Thanks in advance for helping me relieve the pressure.
2. Nov 24, 2004
### loandbehold
Some of the roots are going to be complex, so the way I would tackle the problem is to rewrite your number in the form:
$$z=(1+\sqrt{2}){\rm e}^{2\pi ni}$$,
where n=0,1,2,.... Then taking the fifth root gives:
$$z^{1/5}=(1+\sqrt{2})^{1/5} {\rm e}^{2\pi ni/5}$$,
which you can write in the form:
$$z^{1/5}=(1+\sqrt{2})^{1/5} \left \{ \cos \left ( \frac{2\pi n}{5} \right) +i \sin \left( \frac{2\pi n}{5} \right) \right \}$$.
Evaluating this for different n, should give 5 distinct roots.
3. Nov 24, 2004
### dogma
thank you very much for the insight...I now proceed to kick myself for not seeing it on my own {sound of kicking}
Thanks! | 2017-01-21 11:12:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5999375581741333, "perplexity": 2125.8858550378063}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281069.89/warc/CC-MAIN-20170116095121-00319-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.baryonbib.org/bib/2e8f7fff-b64c-4020-91ed-3f1b84dd8787 | PREPRINT
2E8F7FFF-B64C-4020-91ED-3F1B84DD8787
# Mass flows and their behaviors in the SS433--W50 system
Hajime Inoue
arXiv:2206.14353
Submitted on 28 June 2022
## Abstract
We propose the scenario to interpret the overall observational features of the SS433--W50 system. The most unique features of SS433 are the presence of the precessing, mildly relativistic jets and the obscuration of the central engine, which are considered to be due to a supercritical accretion on to the central compact object. The jets are likely to be ejected from the innermost region of the accretion flow. The concept of the accretion ring (Inoue 2021, PASJ, 73,795) is applied to the outer boundary of the accretion flow and the ring is supposed to have a precession. The accretion ring is expected to extend a two-layer outflow of a thin excretion disk and a thick excretion flow, as well as the accretion flow. The thin excretion disk is discussed to eventually form the optically thick excretion belt along the Roche lobe around the compact object, contributing to the obscuration of the central engine. The thick excretion flow is likely to turn to the supersonic wind (disk wind) with the terminal velocity of $\sim {10}^{8}$ cm s${}^{-1}$ and to collide with the SNR matter at the distance of $\sim {10}^{18}$ cm. The interactions of the jets with the disk wind are considered to cause the features of the jets observed at the distances of 10${}^{14}\sim {10}^{15}$ cm and $\sim {10}^{17}$ cm. Finally, it is discussed that the jets are braked by the SNR matter at the distance of $\sim$10 pc and the momentum carried by the jet is transferred to the SNR matter shoved by the jet. The SNR matter pushed to the inside of the precession cone is expected to gather along the cone axis and to form the elongated structures in the east and west directions from the main W50 structure.
## Preprint
Comment: Accepted to PASJ
Subject: Astrophysics - High Energy Astrophysical Phenomena | 2022-08-15 19:10:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6883338689804077, "perplexity": 1171.984839893107}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00044.warc.gz"} |
http://www.zanshin.com/pipermail/latte/2001-March/000085.html | # [Latte] words and variables
Daniel Mahler mahler@cyc.com
Mon, 19 Mar 2001 17:10:57 -0600
What I have in mind is something like
{\defmacro {\template \name}
\{\def {{\make-var ,\name} \n}
{... \name ... \n ...}}}
{\template T}
{\T 1}
or, alternatively,
{\defmacro {\template \ref}
\{\def {\,\ref \n}
{... \,{\ref-name \ref} ... \n ...}}}
{\template \T}
{\T 1}
I realize that an almost equivalent soltion is to simply parametrize
{\def {\template \name \n}
{... \name ... \n ...}}
{\template T 1}
but one of the above solutions would be more convenient.
I have people typing in manually a large amount of marked up text.
I am therefore trying to design minimal markup for them to type.
They invent new tags on the fly, but the desired expansions are
systematic, and they keep a list of the tags introduced.
I wanted to write a function that enerates the definitions
from the list of tags,
and allow them to use the tags the invent as function names,
which minimizes typing.
I know there are other ways to achieve this,
but the above idea seemed cleanest
and most in the spirit of scheme/lisp.
regards
Daniel
Bart Schaefer writes:
> On Mon, 19 Mar 2001, Daniel Mahler wrote:
>
> > I would like to write macros that define functions on the
> > fly based on a simple naming convention.
>
> Why? How exactly would you call such a function once you'd defined it?
> | 2018-10-19 21:38:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6446635127067566, "perplexity": 9511.054465039802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512460.41/warc/CC-MAIN-20181019212313-20181019233813-00264.warc.gz"} |
https://massivefile.com/NoneLinearRegression/ | 0%
Non Linear Regression Full Implementation with the dataset EDA and Other Techniques.
You will use use the most basic and the Non Linear model to predict results.
# Non Linear Regression Analysis
If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression because, as the name implies, linear regression presumes that the data is linear. Let's learn about non linear regressions and apply an example on python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014.
## Importing required libraries
In [2]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
Though Linear regression is very good to solve many problems, it cannot be used for all datasets. First recall how linear regression, could model a dataset. It models a linear relation between a dependent variable y and independent variable x. It had a simple equation, of degree 1, for example y = $2x$ + 3.
In [3]:
x = np.arange(-5.0, 5.0, 0.1)
##You can adjust the slope and intercept to verify the changes in the graph
y = 2*(x) + 3
y_noise = 2 * np.random.normal(size=x.size)
ydata = y + y_noise
#plt.figure(figsize=(8,6))
plt.plot(x, ydata, 'bo')
plt.plot(x,y, 'r')
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
Non-linear regressions are a relationship between independent variables $x$ and a dependent variable $y$ which result in a non-linear function modeled data. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$).
$$\ y = a x^3 + b x^2 + c x + d \$$
Non-linear functions can have elements like exponentials, logarithms, fractions, and others. For example: $$y = \log(x)$$
Or even, more complicated such as : $$y = \log(a x^3 + b x^2 + c x + d)$$
Let's take a look at a cubic function's graph.
In [4]:
x = np.arange(-5.0, 5.0, 0.1)
##You can adjust the slope and intercept to verify the changes in the graph
y = 1*(x**3) + 1*(x**2) + 1*x + 3
y_noise = 20 * np.random.normal(size=x.size)
ydata = y + y_noise
plt.plot(x, ydata, 'bo')
plt.plot(x,y, 'r')
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.
Some other types of non-linear functions are:
$$Y = X^2$$
In [5]:
x = np.arange(-5.0, 5.0, 0.1)
##You can adjust the slope and intercept to verify the changes in the graph
y = np.power(x,2)
y_noise = 2 * np.random.normal(size=x.size)
ydata = y + y_noise
plt.plot(x, ydata, 'bo')
plt.plot(x,y, 'r')
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
### Exponential¶
An exponential function with base c is defined by $$Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable.
In [6]:
X = np.arange(-5.0, 5.0, 0.1)
##You can adjust the slope and intercept to verify the changes in the graph
Y= np.exp(X)
plt.plot(X,Y)
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
### Logarithmic¶
The response $y$ is a results of applying logarithmic map from input $x$'s to output variable $y$. It is one of the simplest form of log(): i.e. $$y = \log(x)$$
Please consider that instead of $x$, we can use $X$, which can be polynomial representation of the $x$'s. In general form it would be written as
$$y = \log(X)$$
In [7]:
X = np.arange(-5.0, 5.0, 0.1)
Y = np.log(X)
plt.plot(X,Y)
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log
This is separate from the ipykernel package so we can avoid doing imports until
### Sigmoidal/Logistic¶
$$Y = a + \frac{b}{1+ c^{(X-d)}}$$
In [8]:
X = np.arange(-5.0, 5.0, 0.1)
Y = 5-1/(1+np.power(3, X-2))
plt.plot(X,Y)
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
# Non-Linear Regression example¶
For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year.
In [9]:
import numpy as np
import pandas as pd
!wget -nv -O china_gdp.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv
2020-01-14 14:56:32 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv [1218/1218] -> "china_gdp.csv" [1]
Out[9]:
Year Value
0 1960 5.918412e+10
1 1961 4.955705e+10
2 1962 4.668518e+10
3 1963 5.009730e+10
4 1964 5.906225e+10
5 1965 6.970915e+10
6 1966 7.587943e+10
7 1967 7.205703e+10
8 1968 6.999350e+10
9 1969 7.871882e+10
Did you know? When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: Sign up now for free
### Plotting the Dataset¶
This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerate slightly in the 2010s.
In [10]:
plt.figure(figsize=(8,5))
x_data, y_data = (df["Year"].values, df["Value"].values)
plt.plot(x_data, y_data, 'ro')
plt.ylabel('GDP')
plt.xlabel('Year')
plt.show()
### Choosing a model¶
From an initial look at the plot, we determine that the logistic function could be a good approximation, since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:
In [11]:
X = np.arange(-5.0, 5.0, 0.1)
Y = 1.0 / (1.0 + np.exp(-X))
plt.plot(X,Y)
plt.ylabel('Dependent Variable')
plt.xlabel('Indepdendent Variable')
plt.show()
The formula for the logistic function is the following:
$$\hat{Y} = \frac1{1+e^{\beta_1(X-\beta_2)}}$$
$\beta_1$: Controls the curve's steepness,
$\beta_2$: Slides the curve on the x-axis.
### Building The Model¶
Now, let's build our regression model and initialize its parameters.
In [12]:
def sigmoid(x, Beta_1, Beta_2):
y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))
return y
Lets look at a sample sigmoid line that might fit with the data:
In [13]:
beta_1 = 0.10
beta_2 = 1990.0
#logistic function
Y_pred = sigmoid(x_data, beta_1 , beta_2)
#plot initial prediction against datapoints
plt.plot(x_data, Y_pred*15000000000000.)
plt.plot(x_data, y_data, 'ro')
Out[13]:
[<matplotlib.lines.Line2D at 0x7f51a17930b8>]
Our task here is to find the best parameters for our model. Lets first normalize our x and y:
In [ ]:
# Lets normalize our data
xdata =x_data/max(x_data)
ydata =y_data/max(y_data)
#### How we find the best parameters for our fit line?¶
we can use curve_fit which uses non-linear least squares to fit our sigmoid function, to data. Optimal values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.
popt are our optimized parameters.
In [ ]:
from scipy.optimize import curve_fit
popt, pcov = curve_fit(sigmoid, xdata, ydata)
#print the final parameters
print(" beta_1 = %f, beta_2 = %f" % (popt[0], popt[1]))
Now we plot our resulting regression model.
In [ ]:
x = np.linspace(1960, 2015, 55)
x = x/max(x)
plt.figure(figsize=(8,5))
y = sigmoid(x, *popt)
plt.plot(xdata, ydata, 'ro', label='data')
plt.plot(x,y, linewidth=3.0, label='fit')
plt.legend(loc='best')
plt.ylabel('GDP')
plt.xlabel('Year')
plt.show()
## Practice¶
Can you calculate what is the accuracy of our model?
In [ ]:
# write your code here | 2022-05-21 22:32:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.6312685608863831, "perplexity": 2401.479817401078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00101.warc.gz"} |
http://sites.psu.edu/johnroe/tag/incompetence/ | Tag Archives: incompetence
Let $$X$$ be a bounded geometry uniformly discrete metric space. (Something like bounded geometry seems to be necessary, for a reason that I’ll explain below.) We know how to form the translation algebra $${\mathbb C}[X]$$ (the *-algebra of finite-propagation matrices on $$X$$ ), and this has an obvious representation (the regular representation) on $$\ell^2(X)$$. Then the usual version of the (uniform) Roe algebra is just the C*-algebra obtained by completing $${\mathbb C}[X]$$ in this representation. Because it involves only the regular representation we may call this the reduced Roe algebra (in analogy to the group case). Continue reading | 2014-07-23 14:12:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.916994571685791, "perplexity": 684.2773585716056}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997878518.58/warc/CC-MAIN-20140722025758-00230-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-section-1-3-algebraic-expressions-1-3-exercises-page-34/65 | ## Precalculus: Mathematics for Calculus, 7th Edition
$(y-6)(y+9)$
The common factor is $(y-6)$. Couple the remaining terms together. | 2018-05-25 03:38:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9127896428108215, "perplexity": 6499.583430338094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866938.68/warc/CC-MAIN-20180525024404-20180525044404-00073.warc.gz"} |
https://physics.stackexchange.com/questions/504398/poissons-equation-and-electric-field-interpretation | # Poisson's equation and electric field interpretation
My question is this: Are all solutions to Poisson's equation for a certain charge density such that the negative gradient of them will give me the electric field?
In deriving the equation, we say that every potential (function whose negative gradient is E due to charge density) satisfies Poisson's equation (using one of Maxwell's equations), but does every solution to Poisson's equation correspond to a function whose negative gradient is the electric field due to that charge density?
If we have a function $$V$$ that solves Poisson's equation, then it must be true that $$\nabla^2V=\nabla\cdot(\nabla V)=-\frac{\rho}{\epsilon_0}$$
By definition of potential, we have $$\nabla V=-\mathbf E$$, so then $$\nabla\cdot\mathbf E=\frac{\rho}{\epsilon_0}$$
is yes. Just take the gradient of the solution $$V$$. By definition, that is the field caused by the charge distribution. The result is called Gauss's law. | 2019-11-17 17:02:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9806584715843201, "perplexity": 97.49911879272568}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669225.56/warc/CC-MAIN-20191117165616-20191117193616-00107.warc.gz"} |
http://tex.stackexchange.com/questions/5008/when-to-use-bold-italics-small-caps-typewriter-etc/5014 | # When to use bold, italics, small caps, typewriter etc.?
I'm a little confused on the purposes of each kind of text in LaTeX. I know the function of some of them, but sometimes people use each for different reasons. For example:
• \texttt is for code (no discussion right?).
• \emph is to make emphasis.
• \textsc is used for names, right?
• \textbf when should I use it?
• \textmd When should I use it?
And something more: If I write for example "HI-TECH C PIC Compiler" in between a paragraph, the capital words doesn't look very good. Is it convenient to use \textsf?
Can normal text be mixed with different types? Under which circumstances?
P.S: I'm using the article class with the normal font.
-
IS there a right answer to this question. maybe it should be CW? – Seamus Nov 7 '10 at 0:54
Not a bad idea to make this CW. What do the others thing? – Tomas Nov 7 '10 at 6:36
For code there is the listings package, which provides syntax highlighting, line numbers. – 0x6d64 Sep 27 '11 at 8:44
I think you are confusing visual markup with semantic markup.
\emph is semantic markup: it indicates that you want to emphasize some text, without specifying how that will affect the appearance of the text. The default is to make it italic, or for nested emph-within-emph to make it roman again. However, the default can be overridden if you later decide to use bold for emphasis: \renewcommand\emph{\textbf}.
The visual \textXX commands will change 3 axes of the text: shape, family and weight.
• The shape axis covers: \textup, \textit, \textsc and \textsl
• The family axis covers: \textrm, \textsf, \texttt
• The weight axis covers: \textbf, \textmd
• Some fonts provide other options along these axes, or even as with MinionPro, completely new axes. (This functionality is now available independent of MinionPro in the fontaxes package, so that it can be used with other fonts.)
You can combine options from the different axes (some combinations, such as \textbf{\textt{...}} are not available by default, discussed here). For example:
• \newcommand\keyword[1]{\textsf{\textbf{#1}}}
• \newcommand\important[1]{\textbf{\textit{#1}}}
Regarding "HI-TECH C PIC Compiler": Some fonts (especially ones aimed at newspaper and magazine publishing) have a size of capitals that is intermediate between small-caps (\textsc) and full capitals, for exactly this purpose. The default tex computer modern fonts do not have this possibility, but the computer modern \textsc is not a true small-caps, being a little taller than the x-height of the font, so can be used this way: \newcommand\hitechcomp{\textsc{hi-tech c pic} compiler}
-
Excelent answer. The use of \textsc woud have been good if I didn't have to write numbers! For example, in \textsc{pic18f4520} the numbers are capital sized, while pic and f is lower. – Tomas Nov 6 '10 at 16:37
+1 for the difference in semantic vs. visual markup. Even if I want to use a plain \texttt{} for a certain word (e.g. a variable name), I wrap a own command around it (via \newcommand). This way, I can change the appearance of all variables in my text with a single edit. – 0x6d64 Sep 27 '11 at 8:47
(I have no "right" answer, only some typographical hints.)
Most fonts can be categorized as either serif, sans serif or monospaced:
• Serif fonts (\textrm) are regularly used for the main text body. (Serifs are the small bars at the end of letter strokes that establish a visual base for text lines.)
• Sans serif fonts (\textsf) are often used for headings, tables and table/figure captions. (Typesetting the text body in sans serif is often frowned upon because of reasons of legibility.)
• Monospaced ("typewriter") fonts (\texttt) are mostly limited to code listings and URL's.
For every font category or "family", the following attributes (and combinations of attributes) are possible, although often not available in practice:
• Medium is the "normal" (upright, non-bold) font. (The commands \textup resp. \textmd are used to cancel the effects of other attribute commands and switch back to a medium font - see Lev Bishop's answer for details.)
• Italic (\textit) can be used to emphasize parts of the text without making those parts "stick out" at first glance. (\emph defaults to \textit.) Italic fonts are also suited for low-hierarchy headings. Italics are a separate font design - not only are the letters slanted, but many of them (e.g. "a", "g") have distinct forms.
• Slanted (\textsl) is a surrogate font in case no "real" italic font is around.
• Bold (\textbf) is suited for (top) headings. In the text body, a bold font should be used only if you really want some words to "stick out" - e.g. keywords in a dictionary.
• Small caps (\textsc) are another possibility for emphasis. They are sometimes used for names, but are especially suited for acronyms (UNESCO, PIC Compiler) where capital letters would disrupt the text image. "Real" small caps are a separate font design - don't use "faked" small caps (downscaled capital letters).
-
I like the part of \textsf in tables. The problem is: how can I set that font in the hole tabular enviroment? – Tomas Nov 6 '10 at 16:40
If your tabular environments are inside table environments, try \usepackage[font=sf]{floatrow}. – lockstep Nov 6 '10 at 16:53
@lockstep, I'm no typography expert, but I see sans serif fonts are being increasingly used for the main text and serif fonts for the title lines, quite opposite what good old books recommend. Interestingly, that's the style in tex.sx as well. Is there a reason? – Ali Mehrizi May 1 '12 at 20:28
This is a matter of typographic style. There are no definitive rules.
You should consult a style guide to see what is conventionally done. The Elements of Typographic Style and The Chicago Manual of Style are both worth the read.
- | 2014-08-30 18:39:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.806577205657959, "perplexity": 3989.6561208459048}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500835670.21/warc/CC-MAIN-20140820021355-00023-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://openstudy.com/updates/5088ac09e4b004fc96eb86b7 | ## Hero There are bugs all over Open Study. They keep "bugging" me One bug posts responses to questions out of order Another bug makes latex messy An other bug tells me people are just looking around, when they are actually looking at a question. Yet another bug often lags while I am trying to post a response at the same time as someone else. Still, other bugs wait around seeking more opportunities to sabotage OS. None of these bugs are welcome here imo. one year ago one year ago
1. satellite73
i second that i don't even know if the person is responding to a post i wrote, or an earlier one and this constant smartscore over my posts are quite annoying. what happened?
2. farmdawgnation
So, we're addressing some inefficiencies in the code that serves as a "Grand Central Station" of sorts for all of the things going on in Mathematics soon. Some of these are a side effect of that slowness. Fortunately and unfortunately, we've been breaking our website traffic records. This means that things are being put under more stress than ever. It's part of the reason that Mathematics appears to drop off the planet. In regard to LaTeX, that doesn't seem to be a bug in our code, but in MathJAX's from the best I can tell. We just import their code onto the page directly from their server. When they get it fixed, it will appear fixed on OpenStudy.
3. farmdawgnation
In regard to the "looking around" issue, we'll need to look at that. That's troubling. Also, @satellite73 - not quite sure what you mean.
4. FirstFrostByte
If I might add when I bump a question sometimes it does well not bump... And I have experienced all the problems Hero has except the LaTeX thing...
5. lgbasallote
maybe the latex bug is that bug that makes radicals not straight $\huge \sqrt{example}$
6. Hero
It's not just radicals that are affected though
7. lgbasallote
fractions too.. $\Huge \frac{for}{example}$...well..sometimes
8. Hero
And the anamoly with the fractions makes it difficult for users to interpret them because sometimes they run together with other expressions.
9. UnkleRhaukus
zoom out a little bit in your browser
10. karatechopper
I think we need insecticide...
11. Hero
Yeah, then the insecticide will be poisoned and the bugs will live on. | 2014-03-10 19:20:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6281672120094299, "perplexity": 2186.9780232799626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010962725/warc/CC-MAIN-20140305091602-00008-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://eprint.iacr.org/2019/173 | ### Shorter Quadratic QA-NIZK Proofs
Vanesa Daza, Alonso González, Zaira Pindado, Carla Ràfols, and Javier Silva
##### Abstract
Despite recent advances in the area of pairing-friendly Non-Interactive Zero-Knowledge proofs, there have not been many efficiency improvements in constructing arguments of satisfiability of quadratic (and larger degree) equations since the publication of the Groth-Sahai proof system (JoC'12). In this work, we address the problem of aggregating such proofs using techniques derived from the interactive setting and recent constructions of SNARKs. For certain types of quadratic equations, this problem was investigated before by González et al. (ASIACRYPT'15). Compared to their result, we reduce the proof size by approximately 50% and the common reference string from quadratic to linear, at the price of using less standard computational assumptions. A theoretical motivation for our work is to investigate how efficient NIZK proofs based on falsifiable assumptions can be. On the practical side, quadratic equations appear naturally in several cryptographic schemes like shuffle and range arguments.
Available format(s)
Category
Cryptographic protocols
Publication info
Preprint. MINOR revision.
Keywords
zero knowledgeelliptic curve cryptosystem
Contact author(s)
carla rafols @ upf edu
zaira pindado @ upf edu
History
2019-03-29: revised
See all versions
Short URL
https://ia.cr/2019/173
CC BY
BibTeX
@misc{cryptoeprint:2019/173,
author = {Vanesa Daza and Alonso González and Zaira Pindado and Carla Ràfols and Javier Silva},
title = {Shorter Quadratic QA-NIZK Proofs},
howpublished = {Cryptology ePrint Archive, Paper 2019/173},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/173}},
url = {https://eprint.iacr.org/2019/173}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. | 2022-06-26 23:21:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3329491913318634, "perplexity": 7331.824889645649}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103322581.16/warc/CC-MAIN-20220626222503-20220627012503-00384.warc.gz"} |
https://search.r-project.org/CRAN/refmans/apache.sedona/html/sedona_render_scatter_plot.html | sedona_render_scatter_plot {apache.sedona} R Documentation
## Visualize a Sedona spatial RDD using a scatter plot.
### Description
Generate a scatter plot of geometrical object(s) within a Sedona spatial RDD.
### Usage
sedona_render_scatter_plot(
rdd,
resolution_x,
resolution_y,
output_location,
output_format = c("png", "gif", "svg"),
boundary = NULL,
color_of_variation = c("red", "green", "blue"),
base_color = c(0, 0, 0),
shade = TRUE,
reverse_coords = FALSE,
overlay = NULL,
browse = interactive()
)
### Arguments
rdd A Sedona spatial RDD. resolution_x Resolution on the x-axis. resolution_y Resolution on the y-axis. output_location Location of the output image. This should be the desired path of the image file excluding extension in its file name. output_format File format of the output image. Currently "png", "gif", and "svg" formats are supported (default: "png"). boundary Only render data within the given rectangular boundary. The 'boundary' parameter can be set to either a numeric vector of c(min_x, max_y, min_y, max_y) values, or with a bounding box object e.g., new_bounding_box(sc, min_x, max_y, min_y, max_y), or NULL (the default). If 'boundary' is NULL, then the minimum bounding box of the input spatial RDD will be computed and used as boundary for rendering. color_of_variation Which color channel will vary depending on values of data points. Must be one of "red", "green", or "blue". Default: red. base_color Color of any data point with value 0. Must be a numeric vector of length 3 specifying values for red, green, and blue channels. Default: c(0, 0, 0). shade Whether data point with larger magnitude will be displayed with darker color. Default: TRUE. reverse_coords Whether to reverse spatial coordinates in the plot (default: FALSE). overlay A viz_op object containing a raster image to be displayed on top of the resulting image. browse Whether to open the rendered image in a browser (default: interactive()).
No return value.
### See Also
Other Sedona visualization routines: sedona_render_choropleth_map(), sedona_render_heatmap()
### Examples
library(sparklyr)
library(apache.sedona)
sc <- spark_connect(master = "spark://HOST:PORT")
if (!inherits(sc, "test_connection")) {
input_location <- "/dev/null" # replace it with the path to your input file
rdd <- sedona_read_dsv_to_typed_rdd(
sc,
location = input_location,
type = "point"
)
sedona_render_scatter_plot(
rdd,
resolution_x = 800,
resolution_y = 600,
output_location = tempfile("points-"),
output_format = "png",
boundary = c(-91, -84, 30, 35)
)
}
[Package apache.sedona version 1.2.1 Index] | 2022-12-01 04:26:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23150865733623505, "perplexity": 13397.504013739475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710789.95/warc/CC-MAIN-20221201021257-20221201051257-00701.warc.gz"} |
https://rhettallain.com/category/macgyver/ | # MacGyver Season 4 Episode 7 Science Notes: Mac + Desi + Riley + Aubrey
Honest commentary. I figured this would just be a “filler” episode with just a little side action. NO. This episode was great. Now for some science.
Bra Wire—Nickel Titanium
MacGyver uses Desi’s bra underwire to short out a fuse box. That’s cool and everything, but what’s really great is the nickel titanium wire—also known as memory wire. Here, check this out.
Yes, some bra’s have this kind of wire (also called nitinol) for the underwire.
DIY Periscope
MacGyver needs to find out what’s going on in another room by looking through an air vent. He uses a bathroom rail to mount two mirrors (oh, with gum as glue) to build a periscope.
Here’s how to build one yourself.
Lithium Battery Fire Bomb
OK, it’s not really a bomb it just starts a fire. MacGyver needs a distraction. So, he punctures a lithium-ion battery and then covers it with chocolate. When the chocolate melts, the battery is exposed to air. This is where the bad stuff happens. Don’t puncture your phone battery. Check this out.
Ping Pong Ball Flash Bang
It’s a ping pong ball with butane (from a lighter)—it would probably go boom. Don’t do this.
Cooking Spray Fire
Yup. Many cooking sprays are inflammable (which means it can catch on fire). Oh, you think it should be flammable if it can catch on fire? Surprise, those two words mean the same thing.
On top of that, when you get really small particles of stuff the surface area to volume ratio is huge. That means that there is a lot of the material that can interact with oxygen in the air—this makes it burn.
In fact, you can even make flour “explode”.
# MacGyver Season 4 Episode 6 Science Notes: Right + Wrong + Both + Neither
Lifting a glass with fire and suction.
I love this one. MacGyver needs to lift a glass window out of the frame. He uses some glass jars with soap to make a nice air-tight seal. After that, he gets a fire inside of the jar (after it’s up against the window). This fire produces a suction so that he can lift the window.
This is indeed possible (at least plausible). Here, check it out.
• Burning stuff is complicated. Yes, it uses oxygen (O<sub>2</sub>) and creates carbon dioxide (CO<sub>2</sub>). You might think that you don’t lose any gas—but you do. The amount of carbon dioxide is less than the initial oxygen.
• Since there is less gas after the fire, the pressure inside of the jar is LESS than atmospheric pressure.
• This lower inside pressure means the atmosphere pushes the jar onto the glass. This is what causes “suction”.
• The jar would work really well if you lifted a glass straight up. With the jar on the side of the glass it would be more difficult. You would need a large frictional force between the jar and the glass—but it’s at least plausible.
DIY Electric Arc Lighter
The basic idea is to create a homemade arc lighter and use that to destroy the electronic computers in some cars and disable them. I’ve always wanted to build an arc lighter, here’s a nice video.
The basic idea is to create a very high voltage between the two terminals. If the voltage gets high enough, you can create a large spark between them. This spark is hot enough to light a fire or destroy a computer.
Resonance Wall Destroyer
How do you get through a wall with a speaker? Well, if you could have that speaker oscillate at a very particular frequency, it’s possible (but not very likely) that you could set up a resonance.
Here’s an example. Go out to the park and push someone on a swing. The person on the swing will go back and forth with some frequency. Let’s make it easy and say that they complete one oscillation per second (frequency of 1 Hz). Now, how do you make this swing go higher and higher? The answer is to also push with a frequency of 1 Hz. If you pushed every half second, sometimes your pushes would make the swing go higher but sometimes it would be pushing at the wrong time and decrease the amplitude. This is resonance.
Of course, the most famous example of resonance is when someone breaks a wine glass with only a voice—or at least just with sound. If you tap a wine glass (a nice one with thin walls), it will produce a tone at some frequency. Now play an external sound with this same frequency and you can break the glass. It’s awesome (I need to make one of these videos).
Here’s a nice resonance demo.
OK, back to the wall. Could this work? The biggest problem is the frequency. A wall doesn’t have just ONE frequency that it oscillates with—because it’s made of many different parts. If you thump a wall, it doesn’t make a nice tone.
Still, you could claim that this is plausible. Maybe some part of the interior of the wall DOES resonate. That could be enough. Oh, also you could make this a bit better. If you put a microphone on the wall to measure the resonance frequency, then you would know what tone to play.
This one’s tough—but again based on something real. Let’s just focus on the water part. When you increase the temperature of water, it does produce water vapor (water as a gas). If inside a closed container, this water vapor would increase the pressure. For a plastic water bottle, this increased pressure could put it at a tipping point. Just a little nudge in pressure and BOOM. It explodes. Don’t try that at home though.
This is basically the same thing as an automatic baseball pitcher—except for the homemade water bottle grenades instead of balls.
It consists of two wheels—at least one of them is powered. In this case, you could use the starter motor from the car to turn one of the wheels. When you put a bottle in between the rotating tires, the frictional force from the tire increase its speed until it goes flying.
# MacGyver Season 4 Episode 5 Science Notes: Soccer + Desi + Merchant + Titan
It’s not a science comment, but I have to say this: a show is only as good as the villain. In this episode we see James Callis playing The Merchant. Bam. That was pretty good. I like it. I’ll be honest, I didn’t know who was playing the role of The Merchant before the episode. Of course, you might know James Callis from his excellent role as Dr. Gaius Baltar the show Battlestar Galactica.
Now for some science.
Sports Statistics
MacGyver is looking for a way to figure out who is losing soccer games on purpose. You can see the clip right here.
The key to any sports analytics is data. The more data you have, the easier it is to see trends and patterns. Of course, you are still dealing with humans—so they don’t always do exactly what you expect. But really, this is true for most forms of real world data.
If sports stats is your thing, you absolutely need to check out FiveThirtyEight.
Directional microphone
How do you hear people that are far away? What about a directional microphone? MacGyver quickly builds one from a trashcan lid—this is plausible.
Sound is a wave (in the air) and waves reflect when they encounter a boundary (like a trashcan). If the trashcan lid is parabolic, these sound waves from a distant source will reflect in a way that they all meet at the same point. Like this.
Actually, this is a diagram of a parabolic mirror (from a blog post about mirrors) —but the idea works for sound also. You would just replace the red dot above with a microphone.
These things are real. They use something similar in NFL games so that you can hear the collisions between football players on TV. Oh, there’s also this great sculpture on the campus of NC State University. It’s basically two parabolic dishes made of concrete some distance away. You get a person to sit in front of each of the dishes and they can hear each other talk. It’s really cool.
Anyway, this is one of those hacks that I want to try out for real. Maybe soon.
Here’s the one that MacGyver made.
He probably should have had the microphone facing the other way (pointing into the trashcan lid)—but maybe he was in a hurry. He WAS in a hurry.
Card counting
Nice. I could explain the basic idea behind card counting, but this video is better.
Magnet and a Roulette Wheel
How do you opposite cheat at the roulette wheel? What is “opposite cheat”? That’s when you do something to the motion of the wheel to make it so you lose. I guess this is still cheating though.
In this case, MacGyver uses a magnet to effect the outcome of the wheel. He grabs a magnet from a purse latch (fortunately, these are pretty common) and holds it over the wheel. Although magnets only attract ferromagnetic materials (iron and most steel and some other stuff), you can get a magnet to interact with any material that is an electrical conductor.
If you have a CHANGING magnetic field, this will create an electric field—this is just the way electric and magnetic fields work. Then, an electric field in an electric conductor creates an electric current. Here, you can see what happens when a magnet is moved into a coil of wire.
Finally, an electric current creates another magnetic field. So, this changing magnetic field makes another magnetic field to interact with the magnet. I know that seems crazy, but it’s true. All of it. Oh, we call these induced electric currents—eddy currents.
For MacGyver, this small magnet creates an eddy current in the wheel such that there is a tiny interaction to slow it down—and cause Desi to lose.
Seeing through skin with infrared
Yup. Again, this one is real. Apparently human skin is partially transparent to near infrared light. This is the wavelength of light just longer than red light (that’s why it’s near infrared). It’s the same stuff that’s used on IR remotes (compared to far infrared that’s used in thermal cameras).
So, if you shine an infrared light on the skin and look at it with an infrared detector, you can see through the skin. At least that’s the idea. Your puny human eyes can’t detect near infrared light, but most digital cameras CAN detect this. In fact, most cameras include an infrared filter so that you WON’T see the infrared light (many cheaper cameras don’t even have this).
If you have a camera without the IR filter, you can even see if your TV remote is working.
You can build a cell phone (or radio jammer)—it’s not too hard. However, it’s also questionably legal. I’ll just tell you the basic idea.
Suppose you wanted to make a sound jammer. You could do this by playing a REALLY loud sound. Then no one could hear anyone else talking. That’s essentially how the jammer works—but it’s with electromagnetic radiation instead of sound.
DIY Glider
Don’t try this—it’s a bad idea. MacGyver grabs some type of light weight sign and uses it as a glider to get down on the field. Oh, sure—it might make you crash, but it’s at least plausible.
It’s not flying—it’s falling with style. But seriously, pretty much anything could work here. This would really work especially if there was any type of updraft.
# MacGyver Season 4 Episode 4 Science Notes: Windmill + Acetone + Celluloid + Firing Pin
Egg Drop
It’s not really a normal “MacGyver-hack”, but the egg drop does have a bunch of physics in it. Oh, you’ve never heard of this? Well, it’s a fairly common activity in science classes. Basically students build “something” around an egg so that they can drop it from some particular height and the egg won’t break.
There are a whole bunch of extra rules—like “no parachutes” and “no rockets” and stuff like that. It’s all good fun (mostly). But what about the physics?
Most stuff that breaks on impact are the result of high accelerations from differential forces. If the egg (or any object) is being pushed on one side more than the other with some force (like from the floor), this differential force breaks the material.
Now for some real physics—the Momentum Principle. This says that the net force on an object is equal to the time rate of change of momentum where the momentum is the product of an object’s mass and velocity.
$\vec{F}_\text{net} = \frac{\Delta \vec{p}}{\Delta t}$
$\vec{p} = m\vec{v}$
If an egg is going to hit the ground, you know the change in momentum. It’s going to have some initial value and then it will stop. You can’t change this. But you CAN change the time. Let’s write the Momentum Principle in a different way:
$\Delta \vec{p} =\vec{F}_\text{net}\Delta t$
So, how do we get a particular change in momentum? You can think of two extreme cases:
• You can have a VERY LARGE FORCE with a very small time interval.
• You can have a very small force with a VERY LARGE TIME INTERVAL.
Of course you could go somewhere between these two—but you get my point. This is how the egg drop works. You want to build something that INCREASES the impact time so that you get a smaller force.
Why study science?
MacGyver is right. Scientific thinking is problem solving and critical thinking. These are good in any field—not just physics or working at a “think tank”. So, yes science is good for you. But that’s not why you should study it.
Science is one of the things that makes us human. Some of the other human things that we do: art, music, literature, sports, writing and video games (maybe). So, humans should study things that makes us human. That’s why you should take physics (and art).
One last science comment. The Physics Honor Society has this great page on hidden physicists. These are people with degrees in physics that have jobs that might not be labeled as “physicist”. It’s great.
Compound Lever
The keys to all simple machines are force and the distance a force moves. If you apply a force over a greater distance, you can produce a larger amount of energy (to lift stuff or something). This is how a basic lever works. You put a stick on a pivot.
The compound lever is just a way to get the push down force to move over a greater distance. Basically, it’s a lever connected to a lever. It’s lever-inception.
Hoist Lift
Here’s another way to lift something heavy—like a WWII bomb. You can use a hoist. It’s essentially the same idea as a lever except that stuff is hanging from it.
Tri-wheel Stair Climber
This is real.
Of course you can make it more MacGyver-ed by adding a power source. Mac uses some cordless drills to assist with the climb. Oh, you don’t think that would work? Well, if you have a big enough battery you can move anything up the stairs—it just might not be very fast.
Bomb Egg Drop
Putting a bomb in a box with bungees might work. As the bomb-box hits the ground, the bungees will stretch and INCREASE the time that it takes the bomb to stop—thus DECREASING the impact force. It doesn’t matter if it’s a bomb or an egg, it’s the same physics.
OK, you want to win at the egg drop competition at school? Here’s a great video from Mark Rober looking at some of the best egg drop options.
# MacGyver Season 4 Episode 3 Science Notes: Kid + Plane + Cable + Truck
Can you hear a radio transmission through a fan?
So, here’s the deal. MacGyver needs to communicate with this kid on a nearby plane—but he doesn’t have the radio speaker turned on. How do you tell someone to turn on the speaker if they don’t turn on the speaker?
There are two parts to this answer. First, you need to build an AM radio transmitter. This isn’t too difficult—especially for MacGyver and all the stuff he has in the Phoenix jet. Here is a build similar to the one in the show.
Fine. But what about hearing it in a fan? The short answer is that the fan can act like a foxhole radio. Yes, that’s a real thing. It’s a type of radio that soldiers could build using some basic items. But the key to all of this is the diode. A diode is basically a one-way valve for electric current (I said “basically”—so, don’t freak out about that definition). Why do you need a diode? It’s because you can’t “hear” radio frequencies.
Let’s look at AM radios (because FM is a bit more complicated). AM radio stations broadcast at different frequencies for different channels. These frequencies range from 500 kHz to about 1500 kHz. But if you just convert these electromagnetic waves into sound, you wouldn’t hear anything. Humans can only detect frequencies up to about 20 kHz. So, how do you fix this?
The answer is amplitude modulation (the A and M of AM radio). Here is an example of how this would work. Suppose I have a radio frequency of 3333 Hz (I just mostly randomly picked that value to make a pretty graph). Imagine this radio signal is just a cosine function that oscillates with that frequency. Now suppose that I constantly change the amplitude of this radio signal. The amplitude ALSO changes with some frequency—let’s say this amplitude frequency is 150 Hz (typical human voice frequency). Here’s what that would look like (here is the code if you want it).
But this won’t work. You can’t “hear” the 150 Hz signal—the problem is that the average of the AM signal is zero. It goes up as much as it goes down. It won’t work. That’s where you need a diode. This diode only allows the receiving signal to go “one way”. Here’s what that same AM signal looks like when you put a diode in.
Now for that diode. You could use a diode—or an LED light (which is a diode). Old crystal radios use a crystal mineral. If you don’t have that, you could use a pencil with a razor blade. Apparently, this kind of connection acts like a diode. Oh, you could also do this with the metal connection in the brushes of an electric motor—like in a fan.
Here is a story about a guy that thinks he’s crazy because he hears voices in his fan. I guess it’s true. Also, there is the famous (but maybe not true) story of Lucille Ball hearing Japanese spy radios through the fillings in her teeth. Here is the Snopes link for that.
One last comment. If you think “oh, this is awesome—I’m going to go listen to a radio station with my fan.” Nope. It’s probably not going to happen. You need a fairly strong AM radio signal that is tuned to your untunable fan. On top of that—the brushes in the motor of the fan have to be JUST RIGHT for it to work. It’s still plausible.
Defibrillator
A defibrillator uses electrical currents to do something with the electrical nerve signals to the heart. I guess they can trick the heart into restarting if it has stopped. Fine—but how do you build one (note: don’t build one)?
Of course as with most things (especially dealing with living humans) this can get tricky. You want to run electrical current through the heart area, but not too high. Also, it’s probably best to have an alternating current—it’s complicated.
The simplest (and oldest) designs use a DC battery along with an inductor and a capacitor to make an oscillating electric current. MacGyver should be able to use the DC power from the plane as the “battery”. If you want to start with a higher voltage, you could charge up some capacitors and then reconnect them in series to pretty much get whatever voltage you want. The inductor shouldn’t be too hard to find either.
Landing electromagnet
Electromagnets are real. I guess you already knew that. The basic idea is that an electric current creates a magnetic field. If you make the wire into a coil, the magnetic field due to each loop will add together to make an even stronger overall field. Oh, more current is better.
But would this work in real life? Of course it depends on many things. The most important thing is the current. How much electrical current could you get out of an airplane?
I’ll be honest—calculating the current needed for an electromagnet is really tough. The magnetic force depends on the type of material being attracted (probably steel), the distance, the size of the coil, and the current. But still, I think you could get at least something like 1000 Newtons (a little bit more than the weight of a person). This might be enough to help a small airplane stick to the top of a truck. It’s plausible.
But let me just leave you with the BEST use of an electromagnet. Allen Pan made this AWESOME version of Thor’s hammer. It uses an electromagnet and a thumb sensor so that only Allen (who is obviously worthy) can pick it up.
# MacGyver Season 4 Episode 2 Science Notes: Red Cell + Quantum + Cold + Committed
Let’s do this.
Metamaterials and Invisible Cloaks
Of course, this is not a MacGyver hack—but it is some science stuff. So, what is a metamaterial? It sounds cool—and it is, but it’s a very broad term. Usually when we say “metamaterial”, we mean some type of engineered structure that’s made of more than one thing.
What about invisible cloaks? The idea here is to use some type of metamaterial to interact with light using a negative index of refraction. Normally, when light interacts with materials there will be an apparent bend in the light ray as it makes a transition between materials. This bend in light is called refraction.
You see refraction all the time. Here’s an example of a pencil in a glass of water.
When light goes into the water, it bends a bit towards a line that’s perpendicular to the surface of the interface. That’s normal. If you had a negative index of refraction then the light would bend PAST this normal line. You don’t normally see that except with special materials—in fact we can really only get this to work with light in the microwave wavelengths (not for visible light).
But what does this have to do with invisibility cloaks? There’s a bunch of stuff to explain here—so, I’m just going to go with a very basic idea. First, in order to see something light has to reflect off that object and then enter your eye. That’s why you can see anything in a room with no light—there’s no reflection.
So, one way to make an object invisible is to bend the light around it. Suppose I have an apple with an invisible cloak around it. If I could trace a light ray around it, it might look like this.
But how do you make light do that? That’s the tough part—the idea is that you can do this with some type of special material (a metamaterial). You might not have that stuff, but you can make something similar with some mirrors. Check this out.
Quantum Computing
Here is my super short description of quantum computing. Current computers use binary numbers. Essentially, these are voltage signals. It’s either some positive voltage (1) or zero voltage (0). From this you can make logic gates and store data and play cat videos on the internet.
A quantum computer uses qubits that can be 1, 0 or a combination of 1 and 0 (that’s the quantum part). OK, now here’s a much better explanation.
Cold Containment Unit
How do you keep cold stuff cold? Really, you just need some type of thermal insulator. Yes, your jacket would work—so would a cooler for your drinks. But for super cold stuff, you need something a little more. One of the most common methods is to use a vacuum. If you have two containers with a space in between them (with no air), then it makes a great insulator.
What about making some cold stuff? It turns out that you can get really cold liquid from a can of compressed air (the kind you use to clean your keyboard).
Check this out.
Picture of an eye for a retinal scan
Can you take a picture of someone’s eye and then use that to fool a retina scan? Probably not, but it might be plausible. https://www.telesign.com/blog/post/can-biometrics-be-fooled/
Lojack Emulator
In order to throw some baddies off their track, MacGyver makes a lojack emulator and puts it in a teddy bear. It’s plausible. But what is Lojack? Here—this is good. https://www.lifewire.com/what-is-lojack-534878
Drilling tool
MacGyver needs to drill through some rock. They don’t show the build, but there are plenty of parts around. Really, he would just need some type of electric motor—after that, pretty much any thing could work as a drill bit.
Rebreather
In order to get through a super old tunnel, Mac needs to breath (there’s not really any fresh air there). The answer is a rebreather. The basic idea is to use a chemical carbon dioxide scrubber that pulls the CO2 out of his exhaled air. You just need some tubes and stuff as well as the scrubber. I bet he could find the scrubber stuff near by.
# MacGyver Season 4 Episode 1 Science Notes: Fire + Ashes + Legacy = Phoenix
Wow. It’s back. Finally, season 4 has started. I’m actually more pumped up than I thought I would be. Also, I’m ready to get back to my science notes.
Oh, one non-science comment. I think the Russ Taylor (played by Henry Ian Cusik) character turned out really nice. It was difficult for me to picture this guy just from the script. Henry did a great job.
Now for some science.
Professor MacGyver
At the beginning of the episode, we see MacGyver teaching a university class. At least once, they say that he is “professor” MacGyver. Is this possible? Could he be a professor? Could he even teach a university class?
OK, some background. Remember that Angus was a student at MIT before he dropped out to do bomb stuff in the Army. So, he probably doesn’t have a college degree—but it’s not clear. It’s also possible that he picked up some extra courses here and there to finish and graduate. It’s also very plausible that someone in the Phoenix Foundation just said “poof”—now you have an engineering degree. You know, they seem like the type that would do that stuff.
But what about the “professor” part. Oh, I guess I should add (in case you didn’t know) that I have a PhD in physics from North Carolina State University (Go Wolfpack). I’m also an Associate Professor of Physics at Southeastern Louisiana University. So, I kind of know some stuff about this.
There are actually multiple uses of “professor”. It can be used fairly generically to just mean some type of educator—this is common at the university level. But in terms of academic rank, you have the following titles (there are variations in these from place to place).
• Instructor. This is a primarily teaching position. Most instructors have either a Master’s degree or a PhD.
• Visiting Assistant Professor. This is almost always a PhD position for a faculty to come in and work on some research project temporarily. It can sometimes lead to a permanent position.
• Assistant Professor. This is the first step in “tenure track”. When a person gets this rank, they will work for 5-6 years and then apply for tenure (and usually promotion to the next rank).
• Associate Professor. This is the rank obtained after tenure. Oh, just to be clear—tenure is a method to give faculty the job security so that they can take chances on research and teaching that might not work out so well. Yes, sometimes that means the faculty just does nothing. No, they are not fire-proof. You can fire someone with tenure, it’s just not very easy.
• Full Professor. This is just a rank higher than the two Ass-profs (I like to say that).
So, in this episode—it’s probably the generic sense of “professor” that is being used. It’s not very likely that MacGyver has the rank of Full Professor.
But what about teaching a class? Can anyone do that? Probably—yes. Most universities have a minimum requirement of 15 hours of graduate course credit in the field of the class. So, if you want to teach introductory physics you would need probably 5 graduate level courses that you had passed. This is about the same number of courses required to get a Master’s degree in physics (some variations apply).
Some universities also make exceptions for temporary faculty to teach courses. Either in an emergency situation (need some one the day before classes start) or to bring in an expert. Non-qualified experts are often used in fields like journalism (by non-qualified I mean they don’t have the degree requirements).
Now back to MacGyver. I’m going to say that at the end of Season 3, Phoenix Foundation just fixed his transcript. Boom. Easy.
Equations on the boards
Again, not really a MacGyver-hack, but I want to at least mention these equations. The first board is in the lecture hall. There’s a bunch of stuff on there—and it’s not all related.
The one part that I like the most is the stuff on the lower right. These are the tree physics representations of a ball moving vertically with a gravitational force. These three methods are:
• Newtonian Mechanics
• Lagrangian Mechanics
• Hamiltonian Mechanics
Here’s an older post describing these three methods.
What about the other board? There are a bunch of equations on a white board in MacGyver’s place. Russ quickly just erases them—because that’s what he does. But what are these equations? If you look carefully, you can see the Greek symbol $\psi$ (pronounced psi). This is used to represent the wave function in quantum mechanics.
Potassium in Water
Wow. We are still in the first few minutes of the episode. I think I was just excited to write about MacGyver and science such that I got a little out of control. I’m sorry about that.
For this “hack”, Professor MacGyver is trying to get the attention of his students. Simple solution—put some potassium in water. Seriously, don’t ever do this. The stuff on the left side of the periodic table does bad stuff in water. That means Lithium, Sodium, Potassium…they all make fire and then explode. Check it out.
It would be a lot louder and quicker than you saw in the show. Something would break.
Low tech photocopier
How do you copy someone’s hand written notes without a phone camera or an actual photocopier? How about using something hot? If you put a blank piece of paper next to the paper with ink on it, you could be able to partially make an impression on the blank paper. It would be something like this.
Let’s assume that the heat thing doesn’t fully work (it didn’t work perfectly in the video above). Maybe MacGyver needs to add a little something extra to make the copy readable. It’s plausible that he would need some acid to interact with the tiny bits of ink on the paper to make it readable. That’s what the lemon was for.
Hack a car to make it drive
Oh, this is sadly real. You know—we like to assume that we can add cool features to our cars and they will be safe. Apparently, this is not the case. Here’s a video showing a remote car hack.
I guess that 1985 Honda Civic looks like a pretty good choice now. Right?
Rocket fuel
Yes, you can get rocket fuel from liquid oxygen and kerosene – it’s called RP-1.
DIY Nitrous Oxide
Seriously—don’t do this. Here’s how to make it.
https://www.thoughtco.com/make-nitrous-oxide-or-laughing-gas-608280
Stopping a torpedo
I know it’s a stretch—but’s also fun. There’s a torpedo traveling through the water system. MacGyver finds a “diaper factory”—I love that line and then he gets a bunch of sodium polyacrylate. It’s that stuff they put in diapers. When liquids get into this stuff, it gels up. So, putting it in the water will gel it up. The torpedo will hit the gel and slow down and stop. Save the day.
Actually, in a previous episode MacGyver used this stuff to make fake snow.
OK—one more thing. Why can’t MacGyver get out of the gel? Why is he in the gel? You will have to watch the episode to find out.
But here’s the deal. He’s stuck because of the atmosphere. Yes, there is a bunch of air above him pushing down. The air pressure is 10^5 Newtons per square meter. If you try to lift him up, air can’t get in below him so there’s just the atmosphere pushing down. You are going to either have to pull up REAL hard or get some air down into the gel.
Don’t worry, Mac survives. SPOILER ALERT.
# Top 10 Blog Posts from 2019
It’s always difficult to pick the BEST of stuff. This is especially true when it’s all your own stuff.
So, let’s just say these are 10 nice posts from 2019.
How Does the Mandalorian See Through Walls?
You know I love to write about stuff that gets me excited—and I’m super pumped up about The Mandalorian (just finished season 1). In one of the episodes, Mando sees through a wall with his sniper rifle. How would that work?
No, it probably wouldn’t be with infrared.
Modeling the Water from a Spinning Sprinkler
You don’t really understand something unless you can model it. In this post, I use python to model the motion of water shooting from an inward pointing and spinning sprinkler (based on the Steve Mould and Destin video).
This gif pretty much sums it up.
Orbital Physics and the Death Star II at Endor
This is my favorite thing to do (which I also did in the Mandalorian post above)—take some scene from a movie and and then use that as an excuse to talk about physics. In this case, it’s all about geostationary orbits from Star Wars: Return of the Jedi.
Bonus: more python code in this post. Double bonus, I use data from ROTJ to estimate the length of a day on the planet moon of Endor.
All Measurements Are Really Just Distance—or Voltage
I was in lab when I realized that pretty much all of our measurements were actually measuring distance. Well, originally that was true. Now we can make measurements by measuring a voltage.
Here are some measurement devices—this wasn’t in the original post.
You Can’t Calculate the Work Done by Friction
This was a post I wrote after a discussion I had with Bruce Sherwood. He told me this story about how it’s easy to use the momentum principle with a sliding block (with friction), but you can’t use the work-energy principle.
We like to think friction is this simple thing—but it’s not. The above image is an illustration to show that the distance a friction force is applied is not the same as the distance the object moves.
Video Analysis of Captain America vs. Thanos
There is the perfect scene in Avengers: Endgame. It’s not only perfect because of what Captain America does—but it’s perfect for video analysis. So, in case you haven’t seen it, Cap takes Thor’s hammer and smacks Thanos hard.
Here is the frame corrected version after using Tracker Video Analysis.
No, momentum is not conserved. But that’s OK.
What are Maxwell’s Equations?
Yes, Maxwell’s Equations can be tough.
Here is my attempt to explain these equations in a simple way to describe the electric and magnetic fields.
Every Jedi Jump in Star Wars
OK, not every Star Wars movie. I didn’t have Episode IX to include at this time (I will have to wait for the digital version of the video). But the idea is to analyze ALL the jumps. Here they are.
There are too many jumps for me to do a complete video analysis. Instead, I just estimated the jump height and the jump time. From these two values, I can make a graph—if the vertical acceleration is constant then there should be a linear fit.
The best part is that most Jedi have a vertical acceleration LOWER than g (free fall acceleration on Earth). Yoda has a vertical acceleration HIGHER than g because he takes so many short jumps. I need to write a future post just looking at Yoda.
All the Hacks and Science from MacGyver Season 3
Maybe this is cheating since it’s really not just one post. This is a list of all my science explanations for MacGyver Season 3. Oh, just to be clear—I’m the Technical Consultant for the CBS show MacGyver (season 4 starts in February).
It’s a lot of work to help the writers come up with new science tricks for MacGyver, but it’s also super fun. I also really enjoy making these MacGyver at home videos.
I’m really looking forward to sharing more science for season 4.
Projectile Motion in Polar Coordinates
I’ve had this secondary blog for over a year now—and I really like it. It’s like the old days of blogging. I can write whatever the heck I want (example—the top five lightsaber fights in Star Wars). Also, I can go into super complicated physics stuff.
Here is an example from my upper-level classical mechanics course. Can you use polar coordinates for projectile motion? Yes you can—but it’s obviously not the best choice.
There’s python here too.
# MacGyver Season 3 Episode 18 Science Notes: Murdoc + Helman + Hit
I honestly don’t know how I skipped over this episode with my MacGyver science notes. Oh well, let’s finish this up. There aren’t too many hacks in this episode, so this won’t be too long.
One Way Mirror
Murdoc makes a great point. Is it a one way mirror or a two way mirror? The main idea is that Murdoc can’t see through the glass, but the other people can see through to view what Murdoc is doing.
These things aren’t magic. At the most basic level, a “one way mirror” is just a plane of glass. When light hits glass, some of it is reflected and some of it is transmitted. If you are on one side of the glass and there is WAY more reflected light coming back at you than the light transmitted from the other side, then you can’t see that transmitted light. The glass would look like a mirror.
This is exactly what happens when you are inside a house at night with the lights on. The lights reflect too much and there isn’t much light from outside coming in, so you just see a reflection. It would look like this.
If you are outside on a dark night, the opposite is true. You can see INTO the house.
So, for the one way mirror, you need a glass separating two rooms. The dark room is the room with the observers and the light room is where the prisoner sits.
Here is an older post with more details about seeing through windows.
Pulley Skateboard Battering Ram
This is a classic simple machine. The key to all simple machines is that you can make a system that pulls over a greater distance and produces a greater force (or you can do it the opposite of this).
In this case, MacGyver makes a compound pulley. You need two pulleys. If you run the string through these two pulleys, you can make two different distances. The distance one side is pulled is twice the distance of the other side. Here is a diagram.
Yes, that’s a rather crude sketch—I did it fairly quickly. Here is a video that walks through the setup. I mention that there are two ways to set up this skateboard battering ram, this only covers one method.
Here is a much more detailed post on pulleys.
Stopping a Truck with a Truck
MacGyver uses a winch cable to connect their truck to Murdoc’s truck. They then slam on the breaks. So, would this work? Yeah, probably.
Assuming the two vehicles have the same material for the tires, then they would have the same coefficient of friction. A basic model for friction says that the frictional force is proportional to the force the ground pushes up on the object (we call this the normal force).
$F_f = \mu N$
Since both cars are on flat ground, the normal force is equal to the car’s weight. That means the heavier car would have a greater frictional force. Yes, I’m making some other assumptions about the tires “locking up”—but still, this is plausible.
Even if the frictional force wasn’t enough to stop the truck, the cable is attached to the side of Murdoc’s truck. This side force would rotate the truck and also prevent it from driving straight. | 2020-04-06 11:14:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4261668920516968, "perplexity": 859.9369881482176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371624083.66/warc/CC-MAIN-20200406102322-20200406132822-00436.warc.gz"} |
https://www.physicsforums.com/threads/differential-equations-finding-general-solution-problem.279557/ | # Differential Equations: Finding general solution problem
1. Dec 14, 2008
### kdawghomie
1. The problem statement, all variables and given/known data
Find the general solution of (D^4 - I)^2(D^2 - 4D + 13I)^2(y) = 0
2. The attempt at a solution
My issue with this problem is that I have no clue as to what the I's mean. I have become familiar with D being used notationally with differential equations, but the introduction of the I's is totally foreign to me, and my professor has never even addressed them. Am I supposed to assume the I's are simply a constant, or am I totally missing something here?
I can break the problem down to the following, though:
[(D^2 + sqrt(I))(D + sqrt(I))(D - sqrt(I))]^2 * [D^2 - 4D +13I]^2 * y = 0
From here, am I supposed to proceed "as usual" with solving the equation... or do the I's have some significance? It seems very possible to solve w/ I's being a constant, but absolutely brutal to actually find the gen. solution for :/
Thank you for any help!
2. Dec 14, 2008
### CompuChip
I is usually used for the identity operator: I f = f.
So for example, solving
(D^2 - 3 I) = 0
would mean: find all functions such that
$$\frac{d^2}{dx^2} f(x) - 3 f(x) = 0$$.
Also used is "id", a 1 with a hat, or a double struck 1.
Physicists tend to leave out the I altogether, and write
(D^2 - 3) = 0
for the above equation.
3. Dec 14, 2008
### kdawghomie
OK, thank you. So... to clarify, I can essentially ignore the I and just work with the I's coefficient as a constant, correct?
4. Dec 15, 2008
### CompuChip
Essentially, yes.
Note however, that I is an operator, just like D is, so you cannot really write sqrt(I) any more than you can sqrt(D). You can use that I^n = I though, for any (integer) n. | 2018-03-22 14:28:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7812725901603699, "perplexity": 1140.1004102494746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647885.78/warc/CC-MAIN-20180322131741-20180322151741-00570.warc.gz"} |
https://stats.stackexchange.com/questions/523933/simple-mean-or-kernel-estimator | Simple mean or kernel estimator?
Let $$X$$ be a continuous random variable with support $$\mathcal{X}$$ and density $$f(x)$$. Suppose I'm interested in constructing a consistent estimator of $$E(X)$$ using $$n$$ i.i.d. observations $$(X_1,..., X_i, ...,X_n)$$ with $$X_i\sim X$$.
As a first simple thought, I would consider $$\hat{\mu}_n=\frac{1}{n} \sum_{i=1}^n X_i$$ which is a consistent estimator of $$E(X)$$ as $$n$$ goes to infinity, under some conditions.
Suppose I want to complicate my life and take the definition of $$E(X)$$ which is $$E(X)=\int_{x\in \mathcal{X}} x f(x)dx$$ At this point, I could consider a kernel estimator for $$f(x)$$ (let me denote it by $$\hat{f}_n(x)$$) which is consistent for $$f(x)$$ under certain assumptions. In turn, I could compute $$\tilde{\mu}_n=\int_{x\in \mathcal{X}} x \hat{f}_n(x)dx$$ which is a consistent estimator of $$E(X)$$ as $$n$$ goes to infinity, under some conditions.
If the above is correct, it seems to me that $$\hat{\mu}_n$$ and $$\tilde{\mu}_n$$ achieve the same objective, although under different (more or less stringent) set of conditions. Is this true?
They do achieve the same objective, and we can make the comparison even clearer. Let $$\hat F_n$$ give the empirical CDF and let $$\hat f_n$$ be the corresponding pmf that puts a mass of $$1/n$$ on each observed value (which are almost surely unique here). Then the first moment of $$\hat F_n$$ is $$\int x \,\text d \hat F_n = \sum_{x \in \{x_1,\dots,x_n\}} x \hat f_n(x) = \bar x_n \to_p \int x \,\text d F = \text E[X]$$ so even $$\hat \mu_n$$ can be viewed this way.
I think this is a consequence of how we can think of moments as being functionals of probability measures via $$\nu \mapsto \int x \,\text d\nu$$ so it is less surprising that we can approximate a moment of $$P$$ (the probability measure with CDF $$F$$) by using moments of estimators of $$P$$. | 2022-08-15 04:08:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9406909942626953, "perplexity": 107.10388333301648}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572127.33/warc/CC-MAIN-20220815024523-20220815054523-00051.warc.gz"} |
https://www.mechamath.com/geometry/area-of-a-scalene-triangle-formulas-and-examples/ | # Area of a Scalene Triangle – Formulas and Examples
A scalene triangle has three sides that have different lengths from each other and three angles that also have different measurements. There are three main methods that we can use to calculate the area of a scalene triangle depending on the information we have. We can calculate the area using the length of the base and the height. In addition, we can calculate the area using the lengths of the three sides. Also, we can calculate the area if we know the length of its two sides and the angle between those sides.
In this article, we will learn about the formulas that we can use to calculate the area of a scalene triangle using the three mentioned methods. Also, we will look at some solved examples in which we will apply these formulas to find the area with the given information.
##### GEOMETRY
Relevant for
Learning about the area of a scalene triangle with examples.
See examples
##### GEOMETRY
Relevant for
Learning about the area of a scalene triangle with examples.
See examples
## How to find the area of a scalene triangle?
To find the area of a scalene triangle, we need one of the following sets of measurements:
a) The length of one side and the perpendicular distance from that side to the opposite angle (the height).
b) The lengths of the three sides.
### Area of the scalene triangle with base and height
To find the area of a scalene triangle if we know the length of its base and the corresponding height, we can use the following formula:
where b is the length of the base and h is the length of the height.
### Area of the scalene triangle without using the height
To find the area of the scalene triangle if we know the length of two sides and the measure of the angle between them, we can use the following formula:
where a and b are the lengths of two sides and C is the measurement of the angle between those sides.
### Area of the scalene triangle with the length of the three sides
To find the length of a scalene triangle if we know the length of its three sides, we can use Heron’s formula:
where, $latex a, ~b, ~c$ represent the lengths of the sides and S represents the semi perimeter that can be found with the following formula:
$latex S=\frac{a+b+c}{2}$
## Area of a scalene triangle – Examples with answers
In the following examples, we use the formulas detailed above to find the area of the scalene triangles. Each example has its solution, but it is recommended that you try to solve the exercises yourself before looking at the answer.
### EXAMPLE 1
A scalene triangle has a base of 10 m and a height of 8 m. What is its area?
We can recognize the following values:
• Base, $latex b=10$ m
• Height, $latex h=8$ m
We use the first formula with these values:
$latex A=\frac{1}{2}\times b\times h$
$latex A=\frac{1}{2}\times 10\times 8$
$latex A=40$
The area is 40 m².
### EXAMPLE 2
What is the area of a scalene triangle that has a base of 16 cm and a height of 18 cm?
We have the following information:
• Base, $latex b=16$ cm
• Height, $latex h=18$ cm
We substitute these values in the first formula:
$latex A=\frac{1}{2}\times b\times h$
$latex A=\frac{1}{2}\times 16\times 18$
$latex A=144$
The area is 144 cm².
### EXAMPLE 3
The area of a scalene triangle is 84 m². If its base is 14 m, what is the length of its height?
We observe the following information:
• Area, $latex A=84$ m²
• Base, $latex b=14$ m
In this case, we want to find the height. Therefore, we use the first formula with these values and solve for h:
$latex A=\frac{1}{2}\times b\times h$
$latex 200=\frac{1}{2}\times (14)\times h$
$latex 84=7 h$
$latex h=12$
The length of the height is 12 m.
### EXAMPLE 4
A scalene triangle has sides of length 10 m, 12 m, and 14 m. Find the area.
In this case, we have the lengths of the three sides of the triangle:
• Side 1, $latex a=10$ m
• Side 2, $latex b=12$ m
• Side 3, $latex c=14$ m
We use Heron’s formula to find the area. For this, we start by finding the semi perimeter:
$latex S=\frac{a+b+c}{2}$
$latex S=\frac{10+12+14}{2}$
$latex S=\frac{36}{2}$
$latex S=18$
Therefore, we have:
$latex A=\sqrt{S(S-a)(S-b)(S-c)}$
$$A=\sqrt{18(18-10)(18-12)(18-14)}$$
$latex A=\sqrt{18(8)(6)(4)}$
$latex A=\sqrt{18(8)(6)(4)}$
$latex A=\sqrt{3456}$
$latex A=58.8$
The area is 58.8 m².
## Area of a scalene triangle – Practice problems
Put what you have learned into practice and use the formulas for the area of a scalene triangle to solve the following problems. If you need help, you can look at the examples outlined above. | 2022-10-04 13:49:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.868665337562561, "perplexity": 229.71393597186358}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00385.warc.gz"} |
http://www.mathematicalfoodforthought.com/2007/05/ | ## Monday, May 28, 2007
### One By One, We're Making It Fun. Topic: Calculus/S&S.
Theorem: (Stolz-Cesaro) Let $\{a_n\}$ and $\{b_n\}$ be sequences of real numbers such that $\{b_n\}$ is positive, strictly increasing, and unbounded. If the limit
$\displaystyle \lim_{n \rightarrow \infty} \frac{a_{n+1}-a_n}{b_{n+1}-b_n} = L$
exists, then the following limit also exists and we have
$\displaystyle \lim_{n \rightarrow \infty} \frac{a_n}{b_n} = L$.
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Theorem: (Summation by Parts) If $\{f_k\}$ and $\{g_k\}$ are two sequences, then
$\displaystyle \sum_{k=m}^n f_k(g_{k+1}-g_k) = [f_{n+1}g_{n+1}-f_mg_m]-\sum_{k=m}^n g_{k+1}(f_{k+1}-f_k)$.
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Problem: Let $\{a_n\}$ be a sequence of real numbers such that $\displaystyle \sum_{k=0}^{\infty} a_k$ converges. Show that $\displaystyle \lim_{n \rightarrow \infty} \frac{1}{n+1} \sum_{k=0}^n k \cdot a_k = 0$.
Solution: Define the sequence $\{b_n\}$ by $\displaystyle b_n = \sum_{k=0}^n a_k$ and let $\displaystyle \lim_{n \rightarrow \infty} b_n = L$. Then, by summation by parts with $\{f_n\} = \{n\}$ and $\{g_n\} = \{b_n\}$, we have
$\displaystyle \sum_{k=0}^n k \cdot a_k = \sum_{k=0}^n k \cdot (b_{k+1}-b_k) = (n+1)b_{n+1}-\sum_{k=0}^n b_{k+1}$.
The summation we wish to take the limit of is then
$\displaystyle \frac{1}{n+1} \sum_{k=0}^n k \cdot a_k = b_{n+1}-\frac{1}{n+1} \sum_{k=0}^n b_{k+1}$.
But since, by Stolz-Cesaro,
$\displaystyle \lim_{n \rightarrow \infty} \frac{1}{n+1} \sum_{k=0}^n b_{k+1} = \lim_{n \rightarrow \infty} b_{n+1} = L$,
we obtain
$\displaystyle \lim_{n \rightarrow \infty} \frac{1}{n+1} \sum_{k=0}^n k \cdot a_k = \lim_{n \rightarrow \infty} \left(b_n-\frac{1}{n+1} \sum_{k=0}^n b_{k+1}\right) = L-L = 0$.
QED.
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Comment: Summation by parts is a very useful technique to change sums around so that they are easier to evaluate. If you hadn't noticed, it is the discrete analogue of integration by parts and is in fact very similar. Stolz-Cesaro is powerful as well and seems like a discrete analogue to L'Hopital (but I'm not sure about this one). Applying well-known calculus ideas to discrete things can often turn into neat results.
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Practice Problem: If $\{a_n\}$ is a decreasing sequence such that $\displaystyle \lim_{n \rightarrow \infty} a_n = 0$, show that
$\displaystyle \sum_{k=1}^{\infty} a_k \cdot \sin{(kx)}$
converges for all $x$.
## Saturday, May 12, 2007
### Bigger Means Better. Topic: Algebra/Inequalities/Sets. Level: Olympiad.
Definition: A set $S$ is said to be convex if, for any $X, Y \in S$ and $\lambda \in [0,1]$, we have $\lambda X+(1-\lambda)Y \in S$.
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Definition: Let $f: D \rightarrow \mathbb{R}$ be a real-valued function defined on a convex set $D$. We say that $f$ is convex if, for all $X, Y \in D$ and $\lambda \in [0, 1]$, we have
$\lambda f(X) + (1-\lambda) f(Y) \ge f(\lambda X+(1-\lambda)Y)$.
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Theorem: (Jensen's Inequality) Let $f$ be a real-valued, convex function defined on a convex set $D$. Given $x_1, x_2, \ldots, x_n \in D$ and nonnegative reals $w_1, w_2, \ldots, w_n$ such that $w_1+w_2+\cdots+w_n = 1$, we have
$w_1f(x_1)+w_2f(x_2)+\cdots+w_nf(x_n) \ge f(w_1x_1+w_2x_2+\cdots+w_nx_n)$
or, more concisely,
$\displaystyle \sum_{i=1}^n w_if(x_i) \ge f\left(\sum_{i=1}^n w_ix_i\right)$.
Proof: We proceed by induction on $n$.
Base Case - $n = 1$, we have $f(x_1) \ge f(x_1)$ which is trivially true. $n = 2$, we have $\lambda_1 f(x_1)+\lambda_2 f(x_2) \ge f(\lambda_1 x_1+\lambda_2 x_2)$ with $\lambda_1+\lambda_2 = 1$ which is true by the definition of convexity.
Induction Step - Suppose $\displaystyle \sum_{i=1}^k w_if(x_i) \ge f\left(\sum_{i=1}^k w_ix_i\right)$. We wish to show
$\displaystyle \sum_{i=1}^{k+1} u_if(x_i) \ge f\left(\sum_{i=1}^{k+1} u_ix_i\right)$
for nonnegative reals $u_1, u_2, \ldots, u_{k+1}$ that sum to $1$. Well,
$\displaystyle f\left(\sum_{i=1}^{k+1} u_ix_i\right) \le u_{k+1}f(x_{k+1})+(1-u_{k+1})f\left(\frac{1}{1-u_{k+1}} \sum_{i=1}^k u_ix_i\right)$
by the definition of convexity. But since $\displaystyle \frac{1}{1-u_{k+1}} \sum_{i=1}^k u_i = \sum_{i=1}^k \frac{u_i}{1-u_{k+1}} = 1$, by our inductive hypothesis (the $k$ term case) we must have
$\displaystyle f\left(\frac{1}{1-u_{k+1}} \sum_{i=1}^k u_ix_i\right) \le \sum_{i=1}^k \frac{u_i}{1-u_{k+1}} f(x_i)$.
Combining this into the above inequality, we obtain
$\displaystyle f\left(\sum_{i=1}^{k+1} u_ix_i\right) \le u_{k+1}f(x_{k+1})+(1-u_{k+1})\sum_{i=1}^k \frac{u_i}{1-u_{k+1}} f(x_i) = \sum_{i=1}^{k+1} u_if(x_i)$
as desired, completing the induction. QED.
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Definition: The convex hull of a set $S$ is defined to be the smallest convex set containing $S$. It is the set of all points that can be written as $\displaystyle \sum_{i=1}^n a_ix_i$, where $n$ is a natural number, $a_1, a_2, \ldots, a_n$ are nonnegative reals that sum to $1$, and $x_1, x_2, \ldots, x_n \in S$.
--------------------
Definition: A vertex of a set $D$ is a point $v \in D$ such that for all $x \in D$ not equal to $v$ and $\lambda > 1$ we have $\lambda v+(1-\lambda)x \not\in D$.
--------------------
Theorem: Let $V_D = \{v_1, v_2, \ldots, v_k\}$ be the set of vertices of a compact convex set $D$. The convex hull of $V_D$ is $D$.
Example: The set of vertices of a convex polygon is, in fact, its vertices as traditionally defined in geometry. Any point inside the polygon can be written as a convex combination of its vertices.
--------------------
Theorem: If $f$ is a real-valued, convex function defined on a compact convex set $D$, then $\displaystyle \max_{x \in D} f(x) = \max_{x \in V_D} f(x)$, where $V_D$ is the set of vertices of $D$.
Proof: We will show that $\displaystyle f(x) \le \max_{x \in V_D} f(x)$ for all $x \in D$.
Let $\displaystyle x = \sum_{i=1}^k \lambda_i v_i$ where $\lambda_1, \lambda_2, \ldots, \lambda_k$ are nonnegative reals that sum to $1$ and $V_D = \{v_1, v_2, \ldots, v_k\}$. This is possible by the preceding theorem. Then by Jensen's Inequality we get
$\displaystyle \sum_{i=1}^k \lambda_i f(v_i) \ge f\left(\sum_{i=1}^k \lambda_i v_i\right) = f(x)$.
And since $\displaystyle \max_{x \in V_D} f(x) \ge \sum_{i=1}^k \lambda_i f(v_i)$, we have $\displaystyle \max_{x \in V_D} f(x) \ge f(x)$ for all $x \in D$. Furthermore, since $V_D$ is a subset of $D$, we know that this maximum is attained, thus
$\displaystyle \max_{x \in D} f(x) = \max_{x \in V_D} f(x)$
as desired. QED.
--------------------
Comment: This is a very useful result, as it allows us to limit our search for the maximum of a function to its set of vertices, which is usually a considerably smaller set, though it may still be infinite (think sphere). In any case, this works well for constrained optimization problems in which the domain is limited to a polygon, the easiest application of this theorem.
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Practice Problem: Let $x$ and $y$ be real numbers satisfying $|2x-y| \le 3$ and $|y-3x| \le 1$. Find the maximum value of $f(x, y) = (x-y)^2$.
## Tuesday, May 8, 2007
### A Square of Divisors. Topic: Number Theory. Level: AIME/Olympiad.
Problem: (1999 Canada - #3) Determine all positive integers $n > 1$ with the property that $n = (d(n))^2$. Here $d(n)$ denotes the number of positive divisors of $n$.
Solution: So, testing some small numbers yields $n = 9$ as a solution. We claim that this is the only such solution.
Clearly, since $n$ is a square, we can use a variant of the usual prime decomposition and say that $n = p_1^{2e_1} p_2^{2e_2} \cdots p_k^{2e_k}$.
Furthermore, again since $n$ is a square, we know
$d(n) = (2e_1+1)(2e_2+1) \cdots (2e_k+1)$
is odd, so $n = (d(n))^2$ must be odd as well, i.e. $2$ is not one of the $p_i$. Then we use the equation given to us to get
$p_1^{2e_1} p_2^{2e_2} \cdots p_k^{2e_k} = (2e_1+1)^2(2e_2+1)^2 \cdots (2e_k+1)^2$
$p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} = (2e_1+1)(2e_2+1) \cdots (2e_k+1)$.
Note, however, that by Bernoulli's Inequality (overkill, I know) we have for $i = 1, 2, \ldots, k$
$(1+(p_i-1))^{e_i} \ge 1+(p_i-1)e_i \ge 2e_i+1$
with equality iff $p_i = 3$ and $e_i = 1$. So
$p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} \ge (2e_1+1)(2e_2+1) \cdots (2e_k+1)$.
Since we want equality, we must have $p_i = 3$ and $e_i = 1$ for all $i$. But since the primes are supposed to be distinct we can have exactly one prime so that $n = 3^2 = 9$ is the only solution. QED.
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Comment: Another one of those problems that you kind of look at the result and you're like huh, that's interesting. But anyway, just throwing in some weak inequalities led to a pretty straightforward solution. As long as you know how to find the number of divisors of a positive integer it isn't too much of a stretch to figure the rest out, though it make take some time to get in the right direction since the problem is quite open-ended.
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Practice Problem: (1999 Canada - #4) Suppose $a_1,a_2,\cdots,a_8$ are eight distinct integers from $\{1,2,\ldots,16,17\}$. Show that there is an integer $k > 0$ such that the equation $a_i - a_j = k$ has at least three different solutions. Also, find a specific set of $7$ distinct integers from $\{1,2,\ldots,16,17\}$ such that the equation $a_i - a_j = k$ does not have three distinct solutions for any $k > 0$.
## Saturday, May 5, 2007
### Ready For AP Calculus? Topic: Calculus/S&S. Level: AIME/Olympiad.
Problem: Evaluate $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2 \cdot 2^n}$.
Solution: Let $\displaystyle f(x) = \sum_{n=1}^{\infty} \frac{x^n}{n^2}$. Then $\displaystyle f^{\prime}(x) = \sum_{n=1}^{\infty} \frac{x^{n-1}}{n} = -\frac{\ln{(1-x)}}{x}$, a well-known Taylor series. So we want to integrate this:
$\displaystyle \int \frac{\ln{(1-x)}}{x}dx = \ln{x} \ln{(1-x)}-\int \frac{\ln{x}}{x-1}dx$
by parts using $u = \ln{(1-x)}$ and $dv = dx/x$. Substituting $t = 1-x$ in the last integral, we have
$\displaystyle \int \frac{\ln{(1-x)}}{x}dx = \ln{x} \ln{(1-x)}-\int \frac{\ln{(1-t)}}{t}dt$.
So $-f(x) = \ln{x} \ln{(1-x)}+f(t)+C = \ln{x} \ln{(1-x)}+f(1-x)+C$. Thus
$f(x)+f(1-x) = C-\ln{x} \ln{(1-x)}$
for some constant $C$. Using our knowledge that $f(0) = 0$, $\displaystyle f(1) = \frac{\pi^2}{6}$, and $\displaystyle \lim_{x \rightarrow 1} \ln{x} \ln{(1-x)}= 0$ by L'Hopital twice, we see that
$f(0)+f(1) = C \Rightarrow C = \frac{\pi^2}{6}$
Then setting $x = \frac{1}{2}$ we obtain $\displaystyle 2f\left(\frac{1}{2}\right) = \frac{\pi^2}{6}-\ln{\frac{1}{2}} \ln{\frac{1}{2}}$ and $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2 \cdot 2^n} = f\left(\frac{1}{2}\right) = \frac{\pi^2}{12}-\frac{\ln^2{(2)}}{2}$. QED.
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Comment: This was a pretty tough problem that required you to compound a lot of calculus knowledge all into a single problem - series, integration by parts, limits. Recognizing all the steps was the first part; following through with the right computations was another. Still, there weren't really any super clever tricks, mostly just standard substitutions and approaches applied in a somewhat non-standard way. Makes for a very nice problem.
--------------------
Practice Problem #1: Show that $\displaystyle \lim_{x \rightarrow 1} \ln{x} \ln{(1-x)} = 0$.
Practice Problem #2: Evaluate $\displaystyle \sum_{n=1}^{\infty} \frac{x^n}{n}$. Can you also find $\displaystyle \sum_{n=1}^{\infty} \frac{x^n}{n^3}$? | 2019-06-19 10:01:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9481117725372314, "perplexity": 138.3546607663229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998943.53/warc/CC-MAIN-20190619083757-20190619105757-00222.warc.gz"} |
https://www.math3ma.com/blog/a-quotient-of-the-general-linear-group-intuitively | A Quotient of the General Linear Group, Intuitively
Over the past few weeks, we've been chatting about quotient groups in hopes of answering the question, "What's a quotient group, really?" In short, we noted that the quotient of a group $G$ by a normal subgroup $N$ is a means of organizing the group elements according to how they fail---or don't fail---to satisfy the property required to belong to $N$. The key point was that there's only one way to belong to $N$, but generally there may be several ways to fail to belong. This, then, is why the interesting/substantial/meaty part of the quotient is contained in the set of nontrivial cosets. It's also why I like to think of $G/N$ as
"all the stuff in $G$ that's not in $N$. Sorta."
To make the "sorta" a little more concrete, we took a look at the quotient $\mathbb{Z}/5\mathbb{Z}$, just to get our feet wet. We then explored the intuition behind the First Isomorphism Theorem and what's inarguably one of the most useful quotients out there: that of a group by the kernel of a homomorphism. And last week, we used the First Isomorphism Theorem to get an intuitive feel for another example, namely the quotient of a group by its center.
Today I'd like to close out this series by looking at one last example. It's a quotient of a likely familiar group of matrices by a special subgroup.
Example #3: matrices and their determinants
Suppose $F$ is any field and $GL_n(F)$ is the group of invertible $n\times n$ matrices, a.k.a. the general linear group. Recall that "$SL_n(F)\subset GL_n(F)$" means "You belong to $SL_n(F)$ (the special linear group) if and only if you're an $n\times n$ invertible matrix with determinant 1." As you might expect, I think it's helpful to view $GL_n(F)/SL_n(F)$ as consisting of those matrices in $GL_n(F)$ with determinant not equal to 1.
To see this, first note that two matrices $A$ and $B$ live in the same coset if and only if $\text{det}(AB^{-1})=1$ which is true if and only if $\text{det}(A)=\text{det}(B)$. In other words, each coset in $GL_n(F)/SL_n(F)$ is simply the set of all matrices with a given determinant. So for example, if $F=\mathbb{R}$, then all invertible $n\times n$ matrices with $\text{det}=3$ are in the same coset, all those with $\text{det}=\sqrt{2}$ are in the same coset, and so on. In particular, if your determinant is not equal to 1, then it must be some other non-zero number. Intuitively, then, for any field $F$, we should expect the cosets of $GL_n(F)/SL_n(F)$ to be in one-to-one-correspondence with the all of the nonzero elements of $F$.
And our intuition is correct! If we define a map from $GL_n(F)$ to $F^\times=F\smallsetminus\{0\}$ by $A\mapsto\text{det}(A)$, we can check that it's surjective and has $SL_n(F)$ as its kernel. So by the First Isomorphism Theorem, the quotient $GL_n(F)/SL_n(F)$ must be isomorphic to $F^\times$. And this was exactly our observation: either you have determinant 1 or you don't, and there are exactly $|F^\times|\smallsetminus 1$ (this is larger than one, so long as $F^\times\neq\{1\}$) ways to fall into the latter category. Voila!
By the way, if you've ever wondered, "What does the determinant actually mean?", here's a nice thread on Math StackExchange that may shed some light on the situation. (There's a geometric answer!)
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Related Posts | 2021-08-04 12:39:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8932474255561829, "perplexity": 130.10541508385785}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154805.72/warc/CC-MAIN-20210804111738-20210804141738-00072.warc.gz"} |
https://spark.apache.org/docs/3.2.0/api/python/reference/api/pyspark.sql.streaming.StreamingQuery.name.html | # pyspark.sql.streaming.StreamingQuery.name¶
property StreamingQuery.name
Returns the user-specified name of the query, or null if not specified. This name can be specified in the org.apache.spark.sql.streaming.DataStreamWriter as dataframe.writeStream.queryName(“query”).start(). This name, if set, must be unique across all active queries.
New in version 2.0. | 2022-08-08 12:41:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22132998704910278, "perplexity": 3604.9564654426426}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570827.41/warc/CC-MAIN-20220808122331-20220808152331-00547.warc.gz"} |
https://www.gerad.ca/fr/papers/G-97-60 | Groupe d’études et de recherche en analyse des décisions
# Control for Discrete-Time Linear Systems with Frobenius Norm-Bounded Uncertainties
## El-Kébir Boukas et Peng Shi
In this paper, we consider the problems of robust stability and control for the class of uncertain discrete-time linear systems with Frobenius norm-bounded parameter uncertainties in all matrices of the system and output equations. Necessary and sufficient conditions for the above problems are proposed. A linear static state feedback control law is designed, which is in terms of a Riccati inequality. The results obtained here show that the robust control problem of the uncertain system is equivalent to the ontrol problem for a corresponding uncertainty-free system.
, 18 pages | 2020-11-28 22:09:52 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8210472464561462, "perplexity": 731.2830830493738}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195929.39/warc/CC-MAIN-20201128214643-20201129004643-00203.warc.gz"} |
https://www.mysciencework.com/publication/show/degrees-freedom-siso-x-channel-alternating-csit-1b9348e5 | # On the Degrees of Freedom of SISO X-Channel with Alternating CSIT
Authors
Type
Preprint
Publication Date
Jul 31, 2014
Submission Date
Jul 31, 2014
Identifiers
arXiv ID: 1407.8348
Source
arXiv
In this paper, we establish the degrees of freedom (DoF) of the two-user single input single output (SISO) X-channel with alternating channel state information at the transmitters (CSIT). Three cases are considered for the availability of CSIT; perfect, delayed and no-CSIT. Each state is associated with a fraction of time denoted by $\lambda_P, \lambda_D$ and $\lambda_N$, respectively. We provide new results for DoF of the two-user SISO X-channel when the available CSIT alternates between these three cases under a certain distribution $\Lambda(\lambda_P, \lambda_D, \lambda_N )$. Specifically, we show that the X-channel with alternating CSIT for $\Lambda(1/8, 3/8, 1/2)$ can achieve $5/4$ DoF. The interesting thing about $5/4$ is that it represents a position of compromise or a middle ground between the channel knowledge that transmitters need to steer interference and the degrees of freedom that the network can achieve. Moreover, $5/4$ is strictly greater than $6/5$ which is the upper bound for the X-channel with \textit{fixed} delayed CSIT. | 2018-10-16 08:42:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7433509826660156, "perplexity": 440.38051645933314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510415.29/warc/CC-MAIN-20181016072114-20181016093614-00499.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/dft-finite-duration-sequence-corresponds-samples-z-transform-unit-circle-example-dft-10-po-q3900149 | Image text transcribed for accessibility: The DFT of a finite-duration sequence corresponds to samples of its z-transform on the unit circle. For example, the DFT of a 10-point sequence x[n] corresponds to samples of X(Z) at the 10 equally spaced points indicated in Figure P8.50-1. We wish to find the equally spaced samples of X (z) on the contour shown in Figure P8.50-2; i.e., we wish to obtain Show how to modify x[n] to obtain a sequence x1[n] such that the DFT ofx1[n] corresponds to the desired samples of X(z). | 2014-11-27 14:40:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9076246023178101, "perplexity": 921.6744933916092}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008720.43/warc/CC-MAIN-20141125155648-00247-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://brilliant.org/problems/interesting-sliding/ | # Interesting sliding
A $60\si{\kilo\gram}$ man running at an initial speed of $\SI[per-mode=symbol]{4}{\meter\per\second}$ jumps on a $120\si{\kilo\gram}$ cart initially at rest. After reaching the top of the cart, the person slides on the cart's surface and finally comes to rest relative to the cart. The coefficient of friction between the cart and the person's feet is $0.4$, while the friction between the cart and ground can be neglected.
How long (in seconds) does the frictional force act on the person?
Details and Assumptions:
• Take $g=\SI[per-mode=symbol]{10}{\meter\per\second\squared}$.
× | 2022-09-26 19:04:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41733962297439575, "perplexity": 473.01167842689046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334915.59/warc/CC-MAIN-20220926175816-20220926205816-00671.warc.gz"} |
http://taoofmac.com/space/blog/2005/06/08 | # Cooling Off
Well, it looks like the 40C weather we were having is finally going away, which should help my other machines survive a bit longer.
I arrived home after work, dragged a bean bag to my back veranda, and spent a most enjoyable hour reading until dinnertime.
As a sort of geek encore, I set up a VNC server on my surviving Fedora box as a sort of "roaming desktop" and am using it from my ancient Toshiba until my iBook gets fixed - not only does the laptop's ailing battery last a lot longer, it's also much cooler and dead quiet.
(I must try a Mac OS X VNC server later, it would be a neat way to get my very own Mac-on-Intel... Nah, just joking, all the gradients and subtle colors make using VNC to a Mac a rather annoying experience.)
In the meantime, here are a few interesting snippets of news:
• Kevin Marks has a keynote video with chapters, allowing you to skip to the interesting bits easily. This one's a keeper - computing history is seldom documented in video (via Joi Ito).
• People are benchmarking Rosetta, as if the results were meaningful at this stage.
• Apple set up a WebKit site, which should not only end all the pointless ranting from the KHTML side of the fence, but also strengthen the interesting possibility of someone actually coding a Windows version (it won't be trivial, but I bet someone will do it). Of course, iTunes for Windows is probably using a subset of this already..
• Extremely dumb patents strike again - am I infringing this patent if I use the Force to answer my phone?
• Michael Robertson is whining about Apple not allowing clones (something I bet he'd be all over as soon as he could...).
• Leander Kahney muses about DRM on Intel-based Macs (my guess is that the original rumor is mere FUD, and that none of this will pan out).
• Pythonistas complain about having to port Python to Mac OS X x86, and yet it turns out to be simple...
• Interesting gadgetry is afoot again: I don't care much for the iPAQ hw6515 (even if it does have GPS), but this is the first public mention of the Vodafone-branded K600.
Note: A few people dropped me a line about my feed not appearing in Asterisco. I have no idea why, and it isn't due to my (rather hasty) migration to this box - I tested all feeds soon afterward.
Update: My current guess is some delay in DNS updates. I must have removed the URL redirect too early (I did it this morning, convinced that if Argentinian ISPs had noticed the update, ours would have too), so Asterisco spent some time without reaching the feed.
And I'm still getting requests at my old IP...
66.147.154.3 - - [08/Jun/2005:22:36:11 +0100] "GET /space/RecentChanges HTTP/1.0" 404 299 "-" "http://www.almaden.ibm.com/cs/crawler [c12]" | 2017-01-24 07:02:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3398641049861908, "perplexity": 4596.986972825077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560284352.26/warc/CC-MAIN-20170116095124-00008-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://kerodon.net/tag/01P2 | # Kerodon
$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
Construction 4.6.1.14. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets, let $X$ and $Y$ be vertices of $\operatorname{\mathcal{C}}$, and let $e: q(X) \rightarrow q(Y)$ be an edge of the simplicial set $\operatorname{\mathcal{D}}$. We let $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{e}$ denote the fiber product $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y) \times _{ \operatorname{Hom}_{\operatorname{\mathcal{D}}}( q(X), q(Y) ) } \{ e\}$, which we regard as a simplicial subset of $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$. | 2022-11-28 19:27:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9988161325454712, "perplexity": 51.85437653262945}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00364.warc.gz"} |
https://physics.stackexchange.com/questions/467693/size-of-iron-sphere-with-mass-of-our-sun | # Size of iron sphere with mass of our sun [closed]
What would be the diameter of a sphere of iron with the mass of our sun? Use standard density of metalic iron. I realize it would then collapse into a star in its own right and become much smaller as it’s density increases. How does this relate to the large diameter that our sun will have when at its red dwarf stage? Thank you.
• The last part of your question is unclear. The Sun is in its "red dwarf" stage now. Do you mean its final white dwarf phase? – Rob Jeffries Mar 20 '19 at 19:50
• The first part of your question is simple arithmetic, not physics. What's the relevance of iron? FWIW, it'd take roughly 1000 stellar systems like ours to gather that much iron. I guess you could cheat & grab it from a large star in the silicon burning phase, but you have to be quick. That phase only lasts a few days, and generally ends in a type II supernova explosion. – PM 2Ring Mar 20 '19 at 21:31
• @PM2Ring The centre of a massive star is roughly a 1 solar mass ball of iron, shortly before core collapse... – Rob Jeffries Mar 20 '19 at 22:36
The object would shrink to become an "iron white dwarf", supported by electron degeneracy pressure.
If you want to assume that you have a cold sphere of iron supported by electron degeneracy pressure, then you can use the Nauenberg (1972) approximation for the radius of a cold$$^*$$ white dwarf with $$\mu_e$$ mass units per electron and a Chandrasekhar mass $$M_C = 5.816 M_{\odot}/\mu_e^2$$. $$R = \frac{2.45354}{\mu_e} R_{\rm Earth} \left(\frac{M}{M_{C}}\right)^{-1/3} \left[ 1 - \left(\frac{M}{M_c}\right)^{4/3}\right]^{1/2}$$
Thus for $$^{56}$$Fe, $$\mu_e = 2.15$$, $$M_c = 1.26M_{\odot}$$, and if the mass of your star is $$M=1M_{\odot}$$, we have $$R= 0.635R_{\rm Earth} \simeq 4045$$ km.
The Sun will end its life as a white dwarf with a mass of about $$0.5M_{\odot}$$ and will be made of a mixture of carbon and oxygen with $$\mu_e =2$$ and $$M_c = 1.45M_{\odot}$$. Putting this into the Nauenberg approximation we have an estimated radius for the end-of-life Sun as a cold white dwarf of $$R = 9700$$ km.
$$^*$$ "Cold" in this context means that the Fermi kinetic energy is much greater than $$k_B T$$. In practice this means $$T<10^9$$ K. A contracting iron ball roughly in hydrostatic equilibrium will never reach such temperatures because of highly efficient neutrino emission above $$10^8$$ K.
• FWIW, the radius for room temperature iron under no compression ($\rho=7.874 g/cm^3$) is just over 392,150 km. If you assembled this sphere from cold iron it would get very hot as it compresses into degenerate matter. (And even if there were no compression it could get hot from the heat of formation, unless you built it very carefully). But how hot could it get? I guess the total thermal energy can be calculated from the difference in gravitational potential of the initial & final spheres, but how long would it take to compress itself, and how much heat would be radiated away while it shrank? – PM 2Ring Mar 20 '19 at 21:19
• @PM2Ring a 1 solar mass ball of iron would shrink and heat up, but of course it would not become hot enough to avoid degeneracy - it would start emitting neutrinos long before that. It is no different at all in that respect from a 1 solar mass ball of carbon. – Rob Jeffries Mar 20 '19 at 22:25
• Ok, and from your edit I see the temperature is under a billion K. (BTW, I wasn't suggesting the heat would be sufficient to prevent degeneracy). – PM 2Ring Mar 20 '19 at 22:39
• @PM2Ring Cold and degenerate are synonyms in the study of compact objects. – Rob Jeffries Mar 20 '19 at 22:58
Hint: I'm assuming you know (or can find) the mass of the Sun $$m_\odot$$ and the density of solid iron on Earth $$\rho_{Fe}$$. Now, you just need to know the relation between density, mass and volume.
Regarding what happens after someone created such a sphere, I don't know for sure. The mass is below the Chandrasekhar limit of $$1.4 M_\odot$$, so it will not become a neutron star. (If it was the case, the diameter would be significantly reduced because its density would become around $$10^{14}$$ larger than the density of the Sun.) Nevertheless, the extra pressure due to the mass would decrease the diameter of the iron sphere since it's density would rougly be $$10^6$$ the density of the Sun.
If it had enough energy (e.g, from approaching the iron to create a sphere), we may get a white dwarf. In time it would cool down and it's colour would go to yellow, red, and brown, since the colour depends on the surface temperature (hotter means whiter and brighter). However, red dwarfs and brown dwarfs are different types of object.
• The answer has nothing to do with the density of solid iron on Earth. The object would not become a neutron star because it is below the Chandrasekhar mass for an iron white dwarf. – Rob Jeffries Mar 20 '19 at 19:47
• @RobJeffries: you're right, I was thinking about neutron degeneracy pressure. I'll edit my answer. – Ertxiem - reinstate Monica Mar 20 '19 at 19:51 | 2020-07-14 20:08:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5684829354286194, "perplexity": 562.4459671004344}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151197.83/warc/CC-MAIN-20200714181325-20200714211325-00198.warc.gz"} |
http://mathoverflow.net/questions/42114/when-a-morse-function-is-also-a-moment-map | # When a Morse function is also a Moment map…
Are there any interesting results, if a Morse function $M \rightarrow \mathbb{R}$ happens to be the moment map, for some $S^1$ action on $M$ (equipped with $\omega$) as well? Thank you very much.
-
A moment map is always Morse-Bott, so being told it's actually Morse is just saying that the S^1-fixed points are isolated. – Allen Knutson Oct 21 '10 at 2:01
In this case, if you pick a $S^1$-invariant metric, the Morse flow will commute with the $S^1$ action, and so you can think of them together as an action of $\mathbb{C}^*$ where the unit circle acts by the original $S^1$, and the real line acts by Morse flow.
In particular, the critical points will be the fixed points of the action, and the Morse index of a fixed point will be determined by how many of the $S^1$-weights on the tangent space at the point are positive, and how many are negative. | 2014-03-12 05:40:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8325772881507874, "perplexity": 204.49534737691837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021384410/warc/CC-MAIN-20140305120944-00057-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://itprospt.com/num/3791082/suppose-that-an-insurance-company-classifies-people-into | 5
# Suppose that an insurance company classifies people into one of three classes: good risks, average risks and bad risks. The company' s record indicates that th...
## Question
###### Suppose that an insurance company classifies people into one of three classes: good risks, average risks and bad risks. The company' s record indicates that the probabilities that good- , average- and bad-risks persons will be involved in an accident over a one- year span are; respectively, 0.1,0.2 and 0.30. Suppose that 20 % of the population is a good risk, 50 %an average risk and 30 % percent a bad riskWhat proportion of people have accidents in a fixed year?b) If policy holder A had no
Suppose that an insurance company classifies people into one of three classes: good risks, average risks and bad risks. The company' s record indicates that the probabilities that good- , average- and bad-risks persons will be involved in an accident over a one- year span are; respectively, 0.1,0.2 and 0.30. Suppose that 20 % of the population is a good risk, 50 %an average risk and 30 % percent a bad risk What proportion of people have accidents in a fixed year? b) If policy holder A had no accidents over the last year; what is the probability that he or she is a bad risk?
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https://physics.aps.org/synopsis-for/10.1103/PhysRevC.79.054304 | # Synopsis: Getting closer to the Bohr model
An algebraic version of Bohr’s collective model is shown to be an effective tool for the analysis of rotational and vibrational spectra in nuclei.
In the algebraic collective model, the five variables define the quadrupole moments of a nucleus. A group theoretical approach is used to separate the variables into a “radial” coordinate ($\beta$) and four angular variables. The radial wave functions can be chosen corresponding to a specific mean deformation in $\beta$ while calculations involving the angular coordinates are made simple by group theoretical techniques. This leads to huge computational savings over calculations in a spherical basis ($\beta =0$), used in some previous models, for which a very much larger set of basis functions is required. The Bohr Hamiltonian can now be solved for virtually any assumed potential.
In a paper appearing in Physical Review C, David Rowe and Trevor Welsh of the University of Toronto in Canada and Mark Caprio of the University of Notre Dame in the US demonstrate the practical utility of the algebraic collective model when applied to various well-known solvable limits of the Bohr model. In several cases, they find a substantial amount of centrifugal stretching (elongation of the nucleus with increasing angular momentum), which is neglected in adiabatic approximations to the Bohr model.
They argue that, as in the case of the interacting boson model, the ease of carrying out collective model calculations for a wide range of Hamiltonians can be used to quickly characterize a large body of nuclear phenomena and test for limitations of the Bohr model. – John Millener
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A laser-based fusion experiment demonstrates that liquid fuel capsules could rectify problems encountered with ice-based fuel capsules. Read More » | 2017-05-27 06:15:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.655955970287323, "perplexity": 1146.0179700193105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608870.18/warc/CC-MAIN-20170527055922-20170527075922-00200.warc.gz"} |
http://physics.stackexchange.com/questions/22613/lowest-gravity-on-earths-surface/39112 | # Lowest gravity on Earth's surface?
I am trying to determine which on Earth's surface has the lowest gravity. Googling is not finding anything concrete. My natural inclination would be to think of Mount Chimborazo in Ecuador, being on the equator (centripetal force) and also being the furthest point from the Earth's center. However, the GRACE gravity map has the area listed in red for high gravity, presumably due to local mineral anomalies or mantle structure.
Is there any definitive source for information on the topic?
-
What is wrong with the color coding of Grace? en.wikipedia.org/wiki/File:Geoids_sm.jpg . Lowest gravity is over oceans, and that is reasonable since the gravitational field depends on the mass below, and the smaller the radius the less mass there, not more as you seem to assume. – anna v Mar 20 '12 at 11:36
The colour coding of GRACE is fine. The lack of an X to mark the lowest point is my question. – dotancohen Mar 20 '12 at 11:44
Programmers solution: fetch GRACE data by running scripts on an interactive map. Find lowest point. I'll try this later :) – Manishearth Mar 20 '12 at 12:01
It is the darkest blue, and it is not one point but several, all under water: csr.utexas.edu/grace/gravity – anna v Mar 20 '12 at 12:05
Relevant article – dotancohen Sep 16 '13 at 14:55
Lowest gravity on earth surface is near Sri Lanka based on the articles below.
-
Thank you Dimuthu! – dotancohen Oct 12 '12 at 9:09
According to http://en.wikipedia.org/wiki/Gravity_of_Earth#Comparative_gravities_in_various_cities_around_the_world Mexico City has the lowest gravity of any city. However the article doesn't mention mountain tops.
-
Thank you. I did see that, but as you mention it does not pertain to the entire Earth's surface but rather only to the relatively small portions of the Earth's surface which constitute large human population centers. – dotancohen Mar 20 '12 at 11:30
Given the analysis you linked to it's surprising that someone hasn't worked out the answer to your question, but Googling has failed to find it. If someone finds an authoritative answer I'd be very interested to hear it. – John Rennie Mar 20 '12 at 11:36
Probably Mt. Chimborazo has the MOST gravity, as being in the "fattest" part of the planet and as one of the highest mountains you will have LOTS of mass generating more gravity (remember the more mass, the more gravity).
-
But the higher you go up a mountain the farther you are from the rest of the Earth and $1/r^2$ is pretty significant dropoff. Which one wins? More mountain mass or being closer to the surface of the Earth? – Brandon Enright Nov 26 '13 at 22:22 | 2015-08-05 08:37:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6291090846061707, "perplexity": 978.1516180322132}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438043062723.96/warc/CC-MAIN-20150728002422-00211-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://grossack.site/2020/11/30/automorphisms-dont-extend.html | # Automorphisms Don't Extend
### 30 Nov 2020 -
I was on mse last night (later than I should have been…) when I saw a really interesting question. In the interest of keeping the blog post self contained, I’ll transcribe the question here (with some notational edits):
Let $\text{Aut}(G)$ denote the group of automorphisms of $G$, and let $A$ be a subgroup of $B$.
Is $\text{Aut}(A)$ a subgroup of $\text{Aut}(B)$?
If not, is there a necessary and sufficient condition for this to hold?
I think automorphism groups are really interesting. They’re a very natural operation on groups, and yet they seem to be quite difficult to understand in general. I haven’t done any extensive work with them, but the fact that they’re so difficult to compute surprises and excites me. Moreover, if a group $G$ measures the symmetries of an object $X$, then in some sense $\text{Aut}(G)$ measures the “symmetries among the symmetries”. This seems like an interesting topic of study, analogous to the study of Syzygies in ring theory1. I’ve actually asked a question about this myself, though I didn’t phrase the question as clearly as I could have so I didn’t get any answers. It’s also possible the problem is Hard™️, which would be another reason there’s no answers. In general, automorphism groups are one of many objects I’d like to learn more about, so I got excited to see this question about them.
My instinct, upon seeing this problem, was to answer “no”. That is, there’s no reason $\text{Aut}(A)$ should be a subgroup of $\text{Aut}(B)$. After all, it’s possible for $A$ to be some very symmetric object living inside some less symmetric object $B$. Then there’s no reason why a symmetry of $A$ should extend to a symmetry of the larger object $B$.
One picture you might have in mind is this2:
The circle has LOTS of symmetries, but the deathly hallows logo3 has only two. The “do nothing” symmetry, and the “reflect horizontally” symmetry. Most of the symmetries of the circle don’t extend to symmetries of the entire object, and there’s no reason to expect symmetries of groups to behave any differently. Mark Bennet phrases this well in his comment under the original question.
Gerry Myerson asked if I could give a counterexample, rather than informally arguing that such a theorem shouldn’t be true. It’s a good question, but he asked it around 2am, so when I couldn’t immediately think of one (again, I’m not very comfortable with computing automorphism groups myself) I told him I’d think harder (and ask sage) in the morning.
By the time I checked again, there were already some counterexamples floating around. Ancientmathematician mentions $\mathfrak{S}_6 \leq \mathfrak{S}_7$, and uses some “well known” facts about their orders (which happened to be not-so-well-known to me :P). Moreover, in a comment on my answer, Derek Holt mentions $C_2 \times C_2 \leq D_8$, where again the automorphisms can’t work out (though again this wasn’t immediately obvious to me).
I was still interested in verifying this by hand, and since sage doesn’t seem to have a way to compute automorphism groups directly4 I decided making calls to gap.eval() every other line was too much of a hassle (also it kept weirdly segfaulting?)… If I wanted to do this, I was going to have to do it directly in gap. It took me some experimenting to get the syntax right, but at the end of the day, it really wasn’t too hard to get some (naive) code working:
You can uncomment either of the tests at the bottom to verify that the counterexamples mentioned above are actually counterexamples. You can also ask this same question of any group you’re interested in. It raises some warnings along the way (something about my code being inefficient for large subgroups), but it’s good enough for right now.
You might try to add a loop to this code to run TestGroup on every group of order $\leq 100$.
Being able to test a conjecture on all the “small” groups is obviously a useful skill, so if you aren’t sure how you would go about doing this, give it a try! It’s not too hard, and you can even test your code out in the sage cell above.
1. I’m not sure how precise this analogy can be made, however. It’s certainly an informally similar idea, but it clearly doesn’t align with the notion of a $\mathbb{Z}$-syzygy for abelian groups.
2. Taken from here
3. I know, I know, she’s cancelled. The books were still impactful on me, and this is a good and fairly fun example.
4. I’m not crying, you’re crying. | 2021-06-12 22:53:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7566604614257812, "perplexity": 399.5094971221644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487586465.3/warc/CC-MAIN-20210612222407-20210613012407-00302.warc.gz"} |
https://im.kendallhunt.com/HS/students/2/1/6/index.html | # Lesson 6
Construction Techniques 4: Parallel and Perpendicular Lines
• Let’s use tools to draw parallel and perpendicular lines precisely.
### 6.1: Math Talk: Transformations
Each pair of shapes is congruent. Mentally identify a transformation or sequence of transformations that could take one shape to the other.
### 6.2: Standing on the Shoulders of Giants
Here is a line $$m$$ and a point $$C$$ not on the line. Use straightedge and compass tools to construct a line perpendicular to line $$m$$ that goes through point $$C$$. Be prepared to share your reasoning.
1. The line segment $$AB$$ has a length of 1 unit. Construct its perpendicular bisector and draw the point where this line intersects our original segment $$AB$$. How far is this new point from $$A$$?
2. We now have 3 points drawn. Use a pair of points to construct a new perpendicular bisector that has not been drawn yet and label its intersection with segment $$AB$$. How far is this new point from $$A$$?
3. If you repeat this process of drawing new perpendicular bisectors and considering how far your point is from A, what can you say about all the distances?
### 6.3: Parallel Constructions Challenge
Here is a line $$m$$ and a point $$C$$ not on the line. Use straightedge and compass moves to construct a line parallel to line $$m$$ that goes through point $$C$$
### Summary
When we write the instructions for a construction, we can use a previous construction as one of the steps. We now know 2 new constructions that are made up of a sequence of moves.
• Perpendicular lines are lines that meet at a 90 degree angle.
• Parallel lines are lines that don’t intersect. One way to make parallel lines is to draw 2 lines perpendicular to the same line.
### Glossary Entries
• angle bisector
A line through the vertex of an angle that divides it into two equal angles.
• circle
A circle of radius $$r$$ with center $$O$$ is the set of all points that are a distance $$r$$ units from $$O$$
To draw a circle of radius 3 and center $$O$$, use a compass to draw all the points at a distance 3 from $$O$$.
• conjecture
A reasonable guess that you are trying to either prove or disprove.
• inscribed
We say a polygon is inscribed in a circle if it fits inside the circle and every vertex of the polygon is on the circle. We say a circle is inscribed in a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.
• line segment
A set of points on a line with two endpoints.
• parallel
Two lines that don't intersect are called parallel. We can also call segments parallel if they extend into parallel lines.
• perpendicular bisector
The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it. | 2022-11-30 17:29:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5510630011558533, "perplexity": 306.7090255680699}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710765.76/warc/CC-MAIN-20221130160457-20221130190457-00160.warc.gz"} |
http://www.borovik.net/selecta/page/2/ | 09/1/18
# Tony Gardiner: Towards an effective national structure for teacher preparation and support in mathematics
A new paper at The De Morgan Gazette:
A. D. Gardiner, Towards an effective national structure for teacher preparation and support in mathematics, The De Morgan Gazette 10 no. 1 (2018), 1-10. bit.ly/2N9NU7W
Abstract:
The fragmented, learn-on-the-job English model for ITE is not working. About this there is little dispute. We analyse why such a system cannot possibly work for mathematics teaching. We also suggest the need for an improved national framework for teacher preparation and development, based on a limited number of specialist centres, which accumulate expertise over time, and through which planned programmes might be effectively delivered.
08/30/18
# Trigger reflex
When I see a statement like that, I just cannot stop myself from pulling the trigger:
Why does Wittgenstein want surveyability? He seems to think that to be capable of the specific use of a theorem which a new proof makes possible we must be able to reproduce its proof. This is just false, indeed perversely so — without understanding anything about Wiles’ proof of Fermat’s Last Theorem you can use it to rule out the truth of $$a^{17} + b^{17} = c^{17}$$ where $$a$$, $$b$$ and $$c$$ are any three integers, even hundreds of digits long — for example I know that $$123456789^{17} + 12233445566778899^{17}$$ can’t be equal to $$12345678901234567890^{17}$$ without needing to calculate any of the three powers. [Edwin Coleman, The surveyability of long proofs, Foundations of Science, 14, Issue 1–2pp 27–43.]
Indeed, I believe most mathematicians will make an instant observation that $$17$$ is a odd natural number, and therefore the last digit of $$9^{17}$$ is $$9$$, and therefore the last digit of $$123456789^{17} + 12233445566778899^{17}$$ is $$8$$ and does not equal to the last digit of $$12345678901234567890^{17}$$ , which is, of course, $$0$$. One does not need Fermat’s Last Theorem for that (and, for the sake of historical integrity of the narrative, the case $$n = 17$$ had been settled by Kummer in 1847).
08/22/18
# Do mathematicians need funding?
My answer to a question on Quora: Do mathematicians need funding?
There was a number of answers in this thread regurgitating the old joke about mathematicians and philosophers – apparently the latter require even less funding. What really matters, however, is that mathematicians really need (very modest, admittedly) funding for meeting regularly other mathematicians – either at conferences, or, which is much more important, in direct visits to their universities, or in various programs like “Research in Pairs” run by the famous Mathematisches Forschungsinstitut Oberwolfach. There are serious psychological and neurophysiological reasons why doing serious mathematics in isolation from the community of fellow mathematicians is very difficult, next to impossible. I served, for a number of years, on a committee of a learned society which was awarding quick, easy to apply, small grants for international collaborative research in mathematics (basically, short visits, for about a week) . Quality of papers arising from this research is astonishingly high, on the value for money count it beats any state-funded bureaucratic schemes.
08/17/18
# The effect of domestication on post-conflict management: wolves reconcile while dogs avoid each other
A fascinating paper by Simona Cafazzo, Sarah Marshall-Pescini, Martina Lazzaroni, Zsófia Virányi, Friederike Range in the Royal Society Open Science
Highly cooperative social species are expected to engage in frequent reconciliation following conflicts in order to maintain pack cohesiveness and preserve future cooperation. By contrast, in social species with low reliance on cooperation, reconciliation is expected to be less frequent. Here, we investigate the pattern of reconciliation in four captive wolf packs and four captive dog packs. We provide evidence for reconciliation in captive wolves, which are highly dependent on cooperation between pack members, while domestic dogs, which rely on conspecific cooperation less than wolves, avoided interacting with their partners after conflicts. Occurrence, intensity, latency, duration and initiation of wolf reconciliations appeared to vary as a consequence of a compromise between the costs (e.g. risk of further aggression) and the benefits (e.g. restoring relationship with opponents) of such interactions. Our results are in line with previous findings on various wolf packs living under different social and ecological conditions, suggesting that reconciliation is an important strategy for maintaining functional relationships and pack cohesiveness. However, current results on dogs are in contrast to the only other study showing that reconciliation can occur also in this species. Therefore, the occurrence of reconciliation in dogs may be influenced by social and environmental conditions more than in wolves. Which factors promote and modulate reconciliation in dogs needs to be further investigated.
08/14/18
# Understanding Mathematics
Question on a LinkedIn discussion group:
Which way do you learn and understand Mathematics in general? -> From the “forest” to the “tree” (-> first the Big Picture and then going into the details) or vice versa (-> seeing the Big Picture after learning and understanding some details) and explain why.
In learning mathematics, it definitely starts from a tree to a forest. I think only professional research mathematicians, or exceptional teachers of mathematics, can really think from a “forest” to a “tree”. I recall a recent conversation with my former MSc and PhD student who now works, in a senior position, in software development for a serious, and widely known, Internet company. I asked her: “Does it help you that you have a PhD in mathematics”. Her response: “When they have a project too big to handle, they come to me and I cut it in smaller more manageable parts”. This is thinking from top down. It remains a rare skill, hard to teach, and hard to learn. And the issue is of critical importance not only for mathematics, but for other walks of life, too. Just a few weeks ago I had a conversation about that with a lecturer of architecture (and she was also a very successful practicing architect).
07/10/18
# Why it matters that so many people became innumerate
BBC Capital published this post, Why it matters if we become innumerate. The article says:
“What we all need in daily life is quite simple maths,” says Mike Ellicock, chief executive of the charity National Numeracy. “But we also need a conceptual understanding applied to complex situations.” In essence, this understanding applies to a broad range of mathematical information that may be intricate, abstract, or embedded in unfamiliar contexts.
For instance, you might need to calculate the true cost of buying versus hiring a car; whether to use award points or money to buy an airline ticket; or how to adjust a recipe to feed six people instead of four.
In the first two examples, you deal with businesses which are not much interested in you being numerate. I have already said on a number of occasions that
If banks and insurance companies were interested in having numerate customers – as they occasionally claim – we would witness the golden age of school mathematics: fully funded, enjoying cross-party political support, promoted and popularised by the best advertising companies in all forms of mass and social media. But they are not; banks and insurance companies need numerate workforce – but even more so they need innumerate customers. 25 years ago in the West, the benchmark of arithmetic competence at a consumer level was the ability to balance a chequebook. Nowadays, bank customers can instantly get full information about the state of their accounts from an app on a mobile phone together with a timely and tailored to individual circumstances advice on the range of recommended financial products. This kind service can be described in a logically equivalent form: a bank can instantly exploit the customer’s vulnerability.
Growing innumeracy is a quite alarming socio-economic phenomenon, and it has very deep roots. Read mor on that in my papers:
Mathematics for makers and mathematics for users, bit.ly/2qYHtst
07/8/18
# Why does algebra have letters in sums?
My answer to a question on Quora:
Why does algebra have letters in sums?
One should not underestimate the influence of François Viète who was the first to use algebraic notation (letters) not only for unknowns but also for parameters (knowns) in a problem. He also used, as Wiki states, “simplification of equations by the substitution of new quantities having a certain connection with the primitive unknown quantities”. Importantly, Viète is the first cryptographer and cryptanalist know to us by name. His decryption of intercepted diplomatic correspondence had direct effect on European politics of his time. A really juicy bit from the Wiki:
In 1590, Viète discovered the key to a Spanish cipher, consisting of more than 500 characters, and this meant that all dispatches in that language which fell into the hands of the French could be easily read.
Henry IV published a letter from Commander Moreo to the king of Spain. The contents of this letter, read by Viète, revealed that the head of the League in France, the Duke of Mayenne, planned to become king in place of Henry IV. This publication led to the settlement of the Wars of Religion. The king of Spain accused Viète of having used magical powers.
At that time, encryption of texts mostly used substitution ciphers, and the idea of substitution of letters for numbers should be very natural for Vieta.
I modestly suggest that teachers could perhaps use this idea: teaching primary school children some basic substitution ciphers: it is fun, it is a natural spelling exercise, and, I believe, a good propaedeutic for later study of algebra and computer coding.
07/8/18
# No intrinsic gender differences in children’s earliest numerical abilities
Alyssa J. Kersey, Emily J. Braham, Kelsey D. Csumitta, Melissa E. Libertus & Jessica F. Cantlon. No intrinsic gender differences in children’s earliest numerical abilities. npj Science of Learning 3, Article number: 12 (2018).
Abstract
Recent public discussions have suggested that the underepresentation of women in science and mathematics careers can be traced back to intrinsic differences in aptitude. However, true gender differences are difficult to assess because sociocultural influences enter at an early point in childhood. If these claims of intrinsic differences are true, then gender differences in quantitative and mathematical abilities should emerge early in human development. We examined cross-sectional gender differences in mathematical cognition from over 500 children aged 6 months to 8 years by compiling data from five published studies with unpublished data from longitudinal records. We targeted three key milestones of numerical development: numerosity perception, culturally trained counting, and formal and informal elementary mathematics concepts. In addition to testing for statistical differences between boys’ and girls’ mean performance and variability, we also tested for statistical equivalence between boys’ and girls’ performance. Across all stages of numerical development, analyses consistently revealed that boys and girls do not differ in early quantitative and mathematical ability. These findings indicate that boys and girls are equally equipped to reason about mathematics during early childhood.
07/8/18
# What are some real-world uses of the determinant of a matrix?
My answer to a question on Quora:
What are some real-world uses of the determinant of a matrix?
At the time of writing, I am engaged in a small debate with a colleague on one of the LinkedIn discussion groups: he teaches students to solve systems of 2 linear equations with 2 variables using Cramer’s rule (that is, via determinants), without giving any justification or proof for it, but I personally prefer self-justified solutions: for systems of 2 linear equations with 2 variables, the honest Gaussian elimination is quick, and it is easy to explain to students why it gives the right solution. Moreover, every intermediate step of Gaussian elimination can be naturally interpreted in terms of the original system of equations.
And this goes to the heart of the matter: in life, determinants are almost never used in computation. Someone said that
mathematics is the art of avoiding calculations;
in that sense,
linear algebra is the art of avoiding calculations with matrices,
and the rule of thumb is
avoid calculations with determinants!
For example, you can invert a matrix in essentially the same time as compute its determinant; after that the use of the cofactor formula for the inverse of a matrix and Cramer’s rule for solving systems of linear equations becomes waste of time.
However, determinants provide extremely efficient tools for thinking about problems of linear algebra, including those in practical applications. Linear algebra in its development or exposition goes through more and more compressed expression of relevant mathematical meaning, and the value of the determinant: zero or not zero is perhaps the most compressed form of expression of linear dependence / independence of $$n$$ vectors in $$\mathbb{R}^n$$.
Determinants have wonderful algebraic properties and occupied their proud place in linear algebra because of their role in higher level algebraic thinking.
In this thread on Quora some uses of determinants were mentioned, for example, computation of eigenvalues of a matrix; I am not an expert in numerical linear algebra, but I have a feeling that most methods for computation of eigenvalues do not even mention the word “determinant”. Even at a theoretical level, determinants can be excluded from the standard treatment of linear algebra, see Sheldon Axler’s paper Down with Determinants!
So, let me summarise:
• If you need more that just application of existing computer programs for solving practical problems of linear algebra and have to think about the process of solution, you may find determinants very useful indeed.
• Determinants can be meaningfully used for compact formulation of mathematical models of physical phenomena (perhaps this applies not only to physics). This thread in Quora contains some nice examples.
• But is is best avoid calculation of determinants.
07/6/18
# Why is mathematical illiteracy socially acceptable?
My answer to a question on Quora, with some amendments:
Why is mathematical illiteracy socially acceptable?
Because what is known as “mathematical literacy” is economically redundant: having it, or not having it does not affect earnings of 95% of people. An ever decreasing pool of jobs which require “mathematical literacy” is filled (at least in Britain) by recruiting university graduates from mathematics-intensive disciplines, like mathematics, or physics, or electronic engineering. These jobs require no more than basic school level mathematics skills which are supposed to be given to every school leaver. However, big employers do not trust school marks, and rightly so.
However, a small number of professional occupations require knowledge of mathematics far beyond “mathematical literacy”. Critically, for many nations, this includes certain jobs in the defense and security sector.
The summary: everyone is taught mathematics at school not for his/her personal advancement and enjoyment, but for alleged future employment – which is a fiction for majority of learners. This is misselling of “educational product” on a grandiose scale. Wide acceptance of “mathematical illiteracy” is a natural, and healthy, reaction of the society to this scam.
I support the idea that mathematics has to be taught as music: for learner’s enjoyment and personal development, without any promise of future employment in “music-intensive industries”. This will make mathematics more popular — and much more expensive to teach, which, of course, kills this idea at its roots.
There are also crucially important skills which beg to be taught: mathematics for citizenship, mathematics for protection ones’ rights as a responsible human and a member of the society. Should I explain why this is not part of the curriculum?
A colleague wrote to me recently that “anti-math” campaign had reached his university and was pushed by the university administration. It is easy to explain: they see their task as training, on the cheap, future workforce for businesses; they are not interested in educating citizens or helping young people to boost their spiritual and intellectual potential.
I apologise for plugging my papers, but they contain more on that:
Mathematics for makers and mathematics for users, bit.ly/2qYHtst
As a taster, a quote from one of these papers:
If banks and insurance companies were interested in having numerate customers – as they occasionally claim – we would witness the golden age of school mathematics: fully funded, enjoying cross-party political support, promoted and popularised by the best advertising companies in all forms of mass and social media. But they are not; banks and insurance companies need numerate workforce – but even more so they need innumerate customers. 25 years ago in the West, the benchmark of arithmetic competence at a consumer level was the ability to balance a chequebook. Nowadays, bank customers can instantly get full information about the state of their accounts from an app on a mobile phone together with a timely and tailored to individual circumstances advice on the range of recommended financial products. This kind service can be described in a logically equivalent form: a bank can instantly exploit the customer’s vulnerability.
Perhaps I have to add a disclaimer:
Views expressed are my own and do not necessarily represent position of my employer, or any other person, corporation, organisation, or institution. | 2018-12-19 12:37:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3146679401397705, "perplexity": 1874.6818255102457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832259.90/warc/CC-MAIN-20181219110427-20181219132427-00089.warc.gz"} |
https://ltwork.net/a-walkway-forms-one-diagonal-of-a-square-playground-the--12402291 | # A walkway forms one diagonal of a square playground. The walkway is 32m long. How long is a side of the playground?Hint:
###### Question:
A walkway forms one diagonal of a square playground. The walkway is 32m long. How long is a side of the playground? Hint: Use the Pythagorean Theorem
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### .FreePoiNtS............................
.FreePoiNtS . . . . . . . . . . . . . . . . . . . . . . . . . . . . $.FreePoiNtS . . . . . . . . . . . . . . . . . . . . . . . . . . . .$... | 2022-12-01 20:30:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37862247228622437, "perplexity": 2405.375807093372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00107.warc.gz"} |
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Book%3A_Electromagnetics_I_(Ellingson)/05%3A_Electrostatics/5.06%3A_Electric_Field_Due_to_an_Infinite_Line_Charge_using_Gauss%E2%80%99_Law | $$\require{cancel}$$
# 5.6: Electric Field Due to an Infinite Line Charge using Gauss’ Law
Section 5.5 explains one application of Gauss’ Law, which is to find the electric field due to a charged particle. In this section, we present another application – the electric field due to an infinite line of charge. The result serves as a useful “building block” in a number of other problems, including determination of the capacitance of coaxial cable (Section 5.24). Although this problem can be solved using the “direct” approach described in Section 5.4 (and it is an excellent exercise to do so), the Gauss’ Law approach demonstrated here turns out to be relatively simple.
Example $$\PageIndex{1}$$: Electric field associated with an infinite line charge, using Gauss’ Law.
Use Gauss’ Law to determine the electric field intensity due to an infinite line of charge along the $$z$$ axis, having charge density $$\rho_l$$ (units of C/m), as shown in Figure $$\PageIndex{1}$$.
Figure $$\PageIndex{1}$$: Finding the electric field of an infinite line of charge using Gauss’ Law. (CC BY-SA 4.0; K. Kikkeri).
Solution
Gauss’ Law requires integration over a surface that encloses the charge. So, our first problem is to determine a suitable surface. A cylinder of radius $$a$$ that is concentric with the $$z$$ axis, as shown in Figure $$\PageIndex{1}$$, is maximally symmetric with the charge distribution and so is likely to yield the simplest possible analysis. At first glance, it seems that we may have a problem since the charge extends to infinity in the $$+z$$ and $$-z$$ directions, so it’s not clear how to enclose all of the charge. Let’s suppress that concern for a moment and simply choose a cylinder of finite length $$l$$. In principle, we can solve the problem first for this cylinder of finite size, which contains only a fraction of the charge, and then later let $$l\to\infty$$ to capture the rest of the charge. (In fact, we’ll find when the time comes it will not be necessary to do that, but we shall prepare for it anyway.)
Here’s Gauss’ Law:
$\oint_{\mathcal S} {\bf D}\cdot d{\bf s} = Q_{encl} \label{m0149_eGL}$
where $${\bf D}$$ is the electric flux density $$\epsilon{\bf E}$$, $${\mathcal S}$$ is a closed surface with outward-facing differential surface normal $$d{\bf s}$$, and $$Q_{encl}$$ is the enclosed charge.
The first order of business is to constrain the form of $${\bf D}$$ using a symmetry argument, as follows. Consider the field of a point charge $$q$$ at the origin (Section 5.5):
${\bf D} = \hat{\bf r}\frac{q}{4\pi r^2}$
We can “assemble” an infinite line of charge by adding particles in pairs. One pair is added at a time, with one particle on the $$+z$$ axis and the other on the $$-z$$ axis, with each located an equal distance from the origin. We continue to add particle pairs in this manner until the resulting charge extends continuously to infinity in both directions. The principle of superposition indicates that the resulting field will be the sum of the fields of the particles (Section 5.2). Thus, we see that $${\bf D}$$ cannot have any component in the $$\hat{\bf \phi}$$ direction because none of the fields of the constituent particles have a component in that direction. Similarly, we see that the magnitude of $${\bf D}$$ cannot depend on $$\phi$$ because none of the fields of the constituent particles depends on $$\phi$$ and because the charge distribution is identical (“invariant”) with rotation in $$\phi$$. Also, note that for any choice of $$z$$ the distribution of charge above and below that plane of constant $$z$$ is identical; therefore, $${\bf D}$$ cannot be a function of $$z$$ and $${\bf D}$$ cannot have any component in the $$\hat{\bf z}$$ direction. Therefore, the direction of $${\bf D}$$ must be radially outward; i.e., in the $$\hat{\bf \rho}$$ direction, as follows:
${\bf D} = \hat{\bf \rho}D_{\rho}(\rho)$
Next, we observe that $$Q_{encl}$$ on the right hand side of Equation \ref{m0149_eGL} is equal to $$\rho_l l$$. Thus, we obtain
$\oint_{\mathcal S} \left[\hat{\bf \rho}D_{\rho}(\rho)\right] \cdot d{\bf s} = \rho_l l$
The cylinder $$\mathcal{S}$$ consists of a flat top, curved side, and flat bottom. Expanding the above equation to reflect this, we obtain
\begin{aligned}
\rho_{l} l=& \int_{t o p}\left[\hat{\rho} D_{\rho}(\rho)\right] \cdot(+\hat{\mathbf{z}} d s) \\
&+\int_{s i d e}\left[\hat{\rho} D_{\rho}(\rho)\right] \cdot(+\hat{\rho} d s) \\
&+\int_{b o t t o m}\left[\hat{\rho} D_{\rho}(\rho)\right] \cdot(-\hat{\mathbf{z}} d s)
\end{aligned}
Examination of the dot products indicates that the integrals associated with the top and bottom surfaces must be zero. In other words, the flux through the top and bottom is zero because $${\bf D}$$ is perpendicular to these surfaces. We are left with
$\rho_l l = \int_{side} \left[D_{\rho}(\rho)\right] ds$
The side surface is an open cylinder of radius $$\rho=a$$, so $$D_{\rho}(\rho)=D_{\rho}(a)$$, a constant over this surface. Thus:
$\rho_l l = \int_{side} \left[D_{\rho}(a)\right] ds = \left[D_{\rho}(a)\right] \int_{side} ds$
The remaining integral is simply the area of the side surface, which is $$2\pi a \cdot l$$. Solving for $$D_{\rho}(a)$$ we obtain
$D_{\rho}(a) = \frac{\rho_l l}{2\pi a l} = \frac{\rho_l}{2\pi a}$
Remarkably, we see $$D_{\rho}(a)$$ is independent of $$l$$, So the concern raised in the beginning of this solution – that we wouldn’t be able to enclose all of the charge – doesn’t matter.
Completing the solution, we note the result must be the same for any value of $$\rho$$ (not just $$\rho=a$$), so ${\bf D} = \hat{\rho} D_{\rho}(\rho) = \hat{\rho} \frac{\rho_l}{2\pi \rho}$ and since $${\bf D}=\epsilon{\bf E}$$:
$\boxed{ {\bf E} = \hat{\rho} \frac{\rho_l}{2\pi \epsilon \rho} }$
This completes the solution. We have found that the electric field is directed radially away from the line charge, and decreases in magnitude in inverse proportion to distance from the line charge.
Suggestion: Check to ensure that this solution is dimensionally correct. | 2021-03-05 17:02:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9051688313484192, "perplexity": 159.66019301764968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373095.44/warc/CC-MAIN-20210305152710-20210305182710-00483.warc.gz"} |
http://www.lastfm.com.br/user/arrypottuh/library/music/Beth+Hart/_/Is+That+Too+Much+to+Ask?setlang=pt | Biblioteca
Música » Beth Hart »
Is That Too Much to Ask
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Is That Too Much to Ask 3:32 Nov 29 2013, 17h46
Is That Too Much to Ask 3:32 Set 22 2013, 21h54
Is That Too Much to Ask 3:32 Mai 7 2013, 22h32
Is That Too Much to Ask 3:32 Mar 12 2013, 0h47
Is That Too Much to Ask 3:32 Mar 10 2013, 18h22
Is That Too Much to Ask 3:32 Jun 7 2012, 22h46
Is That Too Much to Ask 3:32 Fev 17 2012, 22h10
Is That Too Much to Ask 3:32 Jan 4 2012, 17h59
Is That Too Much to Ask 3:32 Set 19 2011, 15h43
Is That Too Much to Ask 3:32 Set 14 2011, 19h31
Is That Too Much to Ask 3:32 Jul 2 2011, 16h29
Is That Too Much to Ask 3:32 Jun 17 2011, 20h32
Is That Too Much to Ask 3:32 Abr 11 2011, 20h02
Is That Too Much to Ask 3:32 Mar 7 2011, 13h22
Is That Too Much to Ask 3:32 Mar 3 2011, 19h33
Is That Too Much to Ask 3:32 Mar 3 2011, 14h35
Is That Too Much to Ask 3:32 Fev 3 2011, 21h49
Is That Too Much to Ask 3:32 Fev 3 2011, 20h57
Is That Too Much to Ask 3:32 Jan 13 2011, 14h08
Is That Too Much to Ask 3:32 Nov 23 2010, 18h46
Is That Too Much to Ask 3:32 Jul 8 2010, 13h02
Is That Too Much to Ask 3:32 Jul 5 2010, 20h57
Is That Too Much to Ask 3:32 Jul 5 2010, 20h57
Is That Too Much to Ask 3:32 Mar 24 2010, 17h33
Is That Too Much to Ask 3:32 Mar 10 2010, 16h35
Is That Too Much to Ask 3:32 Mar 3 2010, 17h24
Is That Too Much to Ask 3:32 Fev 26 2010, 16h34
Is That Too Much to Ask 3:32 Jun 7 2009, 21h49 | 2014-08-23 14:23:56 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8212275505065918, "perplexity": 6255.006184939563}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500826025.8/warc/CC-MAIN-20140820021346-00255-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=98-331 | 98-331 G. Gallavotti, G. Gentile, V. Mastropietro
Melnikov's approximation dominance. Some examples. (46K, TeX (as plain as it can be)) May 7, 98
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers
Abstract. We continue a previous paper to show that Melnikov's first order formula for {\it part} of the separatrix splitting of a pendulum under fast quasi periodic forcing holds, in special examples, as an asymptotic formula in the forcing rapidity.
Files: 98-331.tex | 2017-11-24 20:17:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9969459772109985, "perplexity": 11749.184850122068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934808935.79/warc/CC-MAIN-20171124195442-20171124215442-00060.warc.gz"} |
http://math.stackexchange.com/questions/27011/algebraic-versus-analytic-line-bundles | # algebraic versus analytic line bundles
If one has a quasiprojective complex variety X, there is a natural map from the algebraic Picard group to the analytic Picard group. Is this map either injective or surjective?
I assume the latter is not true, but couldn't think of an example (nor a definitive opinion for the former question) If you take a normal crossings projective compactification Xbar, then both notions coincide, but while an algebraic line bundle on Xbar that is trivial on X must be associated to the boundary divisor, I couldn't see if the same holds in the analytic setting.
-
Okay so a punctured higher genus curve shows that it isn't injective. Not sure about surjective. – grey Mar 15 '11 at 3:34
Here is an example of non-surjectivity. Let $X = \mathbb{A}^2 \setminus 0$. I claim that $Pic(X)$ is $0$, but $Pic(X^{an}) \neq 0$.
Proof that $Pic(X)= 0$: There is an affine cover $X = U_1 \cup U_2$ where $U_1 = \{ (x, y) : x \neq 0 \}$ and $U_2 = \{ (x,y) : y \neq 0 \}$. Note that $U_1$, $U_2$ and $U_{12}$ are all Spec's of PID's, so their Picard groups are trivial and we can compute $Pic(X)$ in terms of this open cover. The corresponding unit groups are $\{ \alpha x^i : \alpha \in \mathbb{C}^*, \ i \in \mathbb{Z} \}$, $\{ \alpha y^j : \alpha \in \mathbb{C}^*, \ j \in \mathbb{Z} \}$ and $\{\alpha x^i y^j : \alpha \in \mathbb{C}^*, \ (i,j) \in \mathbb{Z}^2 \}$. So the Cech complex is $$\left( \mathbb{C}^* \oplus \mathbb{Z}\right) \oplus \left( \mathbb{C}^* \oplus \mathbb{Z}\right) \to \mathbb{C}^* \oplus \mathbb{Z}^2,$$ which clearly has no cokernel.
Proof that $Pic(X^{an}) \neq 0$: We could mimic the above, but it is a little simpler to first use the exponential sequence $0 \to \mathbb{Z} \to \mathcal{O} \to \mathcal{O}^* \to 0$. Since $X \cong \mathbb{R}^4 \setminus \{ (0,0) \}$ retracts on $S^3$, we have $H^1(X, \mathbb{Z}) \cong H^2(X, \mathbb{Z}) \cong 0$ and $H^1(X, \mathcal{O}) \cong H^1(X, \mathcal{O}^*)$. Computing $H^1(X, \mathcal{O})$ from the Cech cover above, we get that it is spanned by the set of all sums $\{ \sum a_{ij} x^{-i} y^{-j} \}$ where the sum is convergent everywhere in $U_{12}$.
So the simplest example of a nontrivial class in $H^1(X, \mathcal{O})$ is the Cech cocycle $U_{12} \mapsto x^{-1} y^{-1}$, and the simplest nontrivial line bundle is to take trivial line bundles on $U_1$ and $U_2$ and glue them together by $e^{x^{-1} y^{-1}}$. | 2015-11-25 08:38:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9661964178085327, "perplexity": 136.75631563238915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398445033.85/warc/CC-MAIN-20151124205405-00108-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/electric-field-strength-at-a-point-between-charges.872439/ | # Electric field strength at a point between charges
1. May 19, 2016
### Ch3m_
1. The problem statement, all variables and given/known data
A +1.0 μC charge is placed at point X. A +4.0 μC charge is placed at point Y,
50 cm from X.
How far from X, on the line XY, is the point where the electric field strength is zero?
2. Relevant equations
E = Q/4πε0r2
3. The attempt at a solution
I know that the electric field is zero at the point where the magnitude of the field due to the 1.0 μC charge is equal to the magnitude of the field due to the 4.0 μC charge, but I have tried making the equations equal to each other and don't know how to find r
2. May 19, 2016
### Incand
If you write up the equation the distances have to satisfy how does it look?
One hint is that if you define the distance from $X$ along the line as $x$ the distance from $Y$ can be written as $(0.5-x)$ (in meters). | 2018-02-21 12:01:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7790471315383911, "perplexity": 291.47584408984807}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813608.70/warc/CC-MAIN-20180221103712-20180221123712-00778.warc.gz"} |
https://tex.stackexchange.com/questions/linked/235927 | 1k views
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Please save your time and energy on this task. It's partly solved. Step by step I am trying to solve this question xindy for ancient Egyptian transliteration. There are some interesting side problems,... | 2019-06-17 22:38:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8740784525871277, "perplexity": 4478.98022865841}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998581.65/warc/CC-MAIN-20190617223249-20190618005249-00118.warc.gz"} |
https://www.physicsforums.com/threads/a-seemingly-simple-triple-integral-has-me-stumped.288467/ | A seemingly simple triple integral has me stumped
1. Jan 29, 2009
Seda
1. The problem statement, all variables and given/known data
Essentially, do the volume integral of z^2 over the tetrahedron with vetices at (0,0,0) (1,0,0) (0,1,0) (0,0,1)
3. The attempt at a solution
There seems to be a ton(!) of brute-force algebra involved. Enough to make me question if I'm doing the problem right.
I set up the triple integral of z^2 in the order dzdydx with the following limits of integration.
z=0 to z= 1-x-y
y=0 to y= 1-x
x=0 to x=1
It didn't take to long for me to end up with trying to integrate a humongous polynomial in the second interval.
Evaluating z^3 / 3 at z = 1-x-y was fun enough.
But now after integrating again, I have to evaluate y/3 -xy-y^2/2+xy^2+x^2*y + y^3/3 + 1/3*x^3*y et cetera at y = 1-x seems to be a nightmare.
Am I tackling this the wrong way?
2. Jan 29, 2009
Dick
No, I think your approach is correct. Though I'm not sure I agree with your xy polynomial. You just have to work through the mess and be careful. If don't have to use a triple integral you can use a shortcut. If A(z) is the area of a cross section of the tetrahedron at a constant value of z, and you can use geometry to get a formula for that area in terms of z, then the triple integral is the integral of A(z)*z^2*dz. Hmm. That sort of suggests that you change the order of integration so you integrate over z last, it might be easier.
3. Jan 29, 2009
Seda
Yeah not only have I found a few mistakes, but i typed some parts in wrong, I was really just writing the polynomial to show how ugly.
Ill try integrating over x last then.
4. Jan 29, 2009
Dick
Z last, I think. You already did X last.
5. Jan 29, 2009
Seda
sorry, i meant z
6. Jan 29, 2009
Seda
Ok i have an answer now, thanks for the help.
Yes, integrating in the different order helped alot. Much cleaner algebra there.
7. Jan 29, 2009
Dick
Right. If your integrand depends on a subset of the variables, integrate over those variables last. It keeps them constants for as long as possible. | 2017-02-27 21:10:54 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8980048298835754, "perplexity": 818.4348199054598}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501173761.96/warc/CC-MAIN-20170219104613-00303-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://icml.cc/Conferences/2021/ScheduleMultitrack?event=13163 | Timezone: »
Hölder Bounds for Sensitivity Analysis in Causal Reasoning
Serge Assaad · Shuxi Zeng · Henry Pfister · Fan Li · Lawrence Carin
We examine interval estimation of the effect of a treatment T on an outcome Y given the existence of an unobserved confounder U. Using Hölder's inequality, we derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding (i.e., the strength of the connection U->T, and the strength of U->Y). These bounds are tight either when U⊥T or U⊥Y | T (when there is no unobserved confounding). We focus on a special case of this bound depending on the total variation distance between the distributions p(U) and p(U|T=t), as well as the maximum (over all possible values of U) deviation of the conditional expected outcome E[Y|U=u,T=t] from the average expected outcome E[Y|T=t]. We discuss possible calibration strategies for this bound to get interval estimates for treatment effects, and experimentally validate the bound using synthetic and semi-synthetic datasets. | 2022-08-10 01:16:32 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8160914778709412, "perplexity": 1404.4586164028078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571097.39/warc/CC-MAIN-20220810010059-20220810040059-00643.warc.gz"} |
http://tex.stackexchange.com/questions/41537/chemical-purity-and-siunitx-clash-when-putting-a-after-percentage | # Chemical purity and siunitx clash when putting a “+” after percentage
I'm using siunitx to describe some chemical purities. The purity I would like to describe is sold by the chemical company as 99.9+ % (not the best way of describing it I'm sure). When I try to describe this using siunitx it halts pdflatex.
\SI{99.9+}{\percent}
Is there a way around this problem with siunitx?
-
I don't get errors with \SI[parse-numbers=false]{99.9+}{\percent}, but it doesn't seem a mathematically correct way of writing this: why not at least \SI{99.9}{\percent}? – egreg Jan 18 '12 at 23:51
@egreg: That may be delving into political chemistry... of course, something we're removed from. – Werner Jan 19 '12 at 0:08
Instead of the unusual 99.9+ % notation, you could say \SI{>=99.9}{\percent}, which will give you the properly formatted and more mathematically correct output ≥99.9 %. But if you need to reproduce exactly what the manufacturer told you, egreg's suggestion of switching off the number parser is probably the way to go. – Jake Jan 19 '12 at 2:05
I (used to) work with noble gases. Some of these have a purity of 99.998% or 99.999%. This is a bit messy so a gas purity shorthand developed: 5.0 =99.999% and 4.8=99.998% ie 5 nines and and 4 nines and an eight. I have only seen it used with gases...Is there a 4.9? Does this equal 5.0???!!! – Leeser Jan 19 '12 at 14:15
Thanks for the help guys. Unfortunately the people at the chemical company state the purity as 99.9+%. As much as it hurts my eyes I need to state it as it is on the bottle. @egreg If you make that into an answer I'll accept it. Thanks. – Darling Jan 20 '12 at 0:20
The option to use is parse-numbers=false. However there are perhaps slightly better ways to render the symbol (or less bad):
\documentclass[convert,varwidth,border=2]{standalone}
\usepackage{siunitx}
\newcommand{\smallplus}{\raisebox{.3ex}{$\mkern1mu\scriptstyle+$}}
\newcommand{\smallerplus}{\raisebox{.45ex}{$\mkern1mu\scriptscriptstyle+$}}
\begin{document}
\SI[parse-numbers=false]{99.9+}{\percent}
\SI[parse-numbers=false]{99.9\smallplus}{\percent}
\SI[parse-numbers=false]{99.9\smallerplus}{\percent}
\end{document}
-
Another possibility would be to add the sign to the list of allowed symbols:
\documentclass{article}
\usepackage{siunitx}
\newcommand\plus{+}
% egreg's nicer versions:
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- | 2015-07-28 06:06:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8100437521934509, "perplexity": 1926.9277191760084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042981576.7/warc/CC-MAIN-20150728002301-00188-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=118&t=30770 | ## example 1.8
$E_{n}=\frac{h^{2}n^{2}}{8mL^{2}}$
Leslie Contreras 1D
Posts: 35
Joined: Fri Apr 06, 2018 11:02 am
### example 1.8
in this example, I am unclear what exactly the formula is to be used in these situations? What exactly are we trying to find?
Chem_Mod
Posts: 18023
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 418 times
### Re: example 1.8
Please provide the full details of the question in order for the question to be answered. | 2020-01-29 22:26:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2819567322731018, "perplexity": 1892.0411992460286}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251802249.87/warc/CC-MAIN-20200129194333-20200129223333-00268.warc.gz"} |
http://mattpap.github.io/scipy-2011-tutorial/html/summation.html | # Summing roots of polynomials¶
Let’s suppose we are given a univariate polynomial $$f(z)$$ and a univariate rational function $$g(z)$$, and we wish to compute:
$g(r_1) + g(r_2) + \ldots + g(r_n)$
where $$r_i$$ for $$i = 1 \ldots n$$ are the roots of $$f$$ (i.e. $$f(r_i) = 0$$).
In theory this is a very simple task. We just have to compute roots of $$f$$, using the roots() function, substitute those roots for $$z$$ in $$g$$ and add resulting values together.
Let’s consider the following polynomial and rational function:
>>> f = z**5 + z + 3
>>> f
5
z + z + 3
>>> g = 1/z
>>> g
1
─
z
Following the trivial approach, let’s compute the roots of $$f$$:
>>> roots(f)
{}
We got a very unfortunate result: no roots! By the fundamental theorem of algebra we should get five, possibly complex, roots, including multiplicities. Unfortunately, there is no way to express roots in terms of radicals of some polynomials of degree five and higher. For certain instances of polynomials of this kind it may be possible to compute their roots (e.g. roots() recognizes cyclotomic polynomials of high degree), but in general we will most likely be unlucky.
Instead, we could switch to numerical root finding algorithms and compute approximations of roots of $$f$$ and proceed with summation of roots. This can be done by using nroots():
>>> R = nroots(f)
>>> for ri, r in zip(numbered_symbols('r'), R):
... pprint(Eq(ri, r))
...
r₀ = -1.13299756588507
r₁ = -0.47538075666955 - 1.12970172509541⋅ⅈ
r₂ = -0.47538075666955 + 1.12970172509541⋅ⅈ
r₃ = 1.04187953961208 - 0.822870338109958⋅ⅈ
r₄ = 1.04187953961208 + 0.822870338109958⋅ⅈ
We can substitute those roots for $$z$$ in $$g$$ and add together:
>>> sum([ g.subs(z, r) for r in R ]).evalf(chop=True)
-0.333333333333332
It was necessary to evaluate this sum with evalf(), because otherwise we would get an unsimplified result. The additional parameter chop=True was necessary to remove a tiny and insignificant imaginary part. Next we can use nsimplify() to get an exact result from numerical approximation:
>>> nsimplify(_)
-1/3
Is this result correct? The best way is to figure out a purely symbolic method that doesn’t require computing roots of $$f$$. In SymPy it possible to represent a root of a univariate polynomial with rational coefficients using RootOf:
>>> RootOf(f, 0)
⎛ 5 ⎞
RootOf⎝z + z + 3, 0⎠
>>> _.evalf()
-1.13299756588507
We can obtain all roots using list comprehensions:
>>> R = [ RootOf(f, i) for i in xrange(degree(f)) ]
>>> for r in R:
... pprint(r)
...
⎛ 5 ⎞
RootOf⎝z + z + 3, 0⎠
⎛ 5 ⎞
RootOf⎝z + z + 3, 1⎠
⎛ 5 ⎞
RootOf⎝z + z + 3, 2⎠
⎛ 5 ⎞
RootOf⎝z + z + 3, 3⎠
⎛ 5 ⎞
RootOf⎝z + z + 3, 4⎠
Alternatively we can use Poly(f).all_roots() which gives the same result, but is much faster when $$f$$ is a composite polynomial, because the preprocessing step in RootOf is executed only once.
Unfortunately we can’t get anywhere from here, because SymPy is not yet capable of simplifying expressions with RootOf:
>>> G = sum([ g.subs(z, r) for r in R ])
True
>>> _ = simplify(G)
True
We can, however, evaluate sums of RootOf‘s using evalf():
>>> G.evalf()
-0.333333333333333
>>> nsimplify(_)
-1/3
which gave us the same result as before. The difference is that now numerical approximations of roots of $$f$$ were computed using a hybrid symbolic–numeric method, where first disjoint isolating intervals (rectangles) where computed for all roots of $$f$$ and then a numerical root finding algorithm was used in each interval.
Let’s approach this problem differently, using a purely symbolic approach. We know that a polynomial of degree $$n$$ has exactly $$n$$ complex roots, counting multiplicities. In our case $$f$$ has five roots:
>>> R = var('r:5')
>>> R
(r₀, r₁, r₂, r₃, r₄)
Let’s now substitute those “roots” for $$z$$ in $$g$$:
>>> [ g.subs(z, r) for r in R ]
⎡1 1 1 1 1 ⎤
⎢──, ──, ──, ──, ──⎥
⎣r₀ r₁ r₂ r₃ r₄⎦
>>> sum(_)
1 1 1 1 1
── + ── + ── + ── + ──
r₄ r₃ r₂ r₁ r₀
We got a sum of simple rational functions. The next step is to put those rational functions over a common denominator:
>>> G = together(_)
>>> G
r₀⋅r₁⋅r₂⋅r₃ + r₀⋅r₁⋅r₂⋅r₄ + r₀⋅r₁⋅r₃⋅r₄ + r₀⋅r₂⋅r₃⋅r₄ + r₁⋅r₂⋅r₃⋅r₄
───────────────────────────────────────────────────────────────────
r₀⋅r₁⋅r₂⋅r₃⋅r₄
We got very peculiar numerator and denominator, which are very specific functions of roots of $$f$$ (symmetric polynomials). Polynomials of this kind can be generated using viete():
>>> V = viete(f, R, z)
>>> for lhs, rhs in V:
.... pprint(Eq(lhs, rhs))
....
r₀ + r₁ + r₂ + r₃ + r₄ = 0
r₀⋅r₁ + r₀⋅r₂ + r₀⋅r₃ + r₀⋅r₄ + r₁⋅r₂ + r₁⋅r₃ + r₁⋅r₄ + r₂⋅r₃ + r₂⋅r₄ + r₃⋅r₄ = 0
r₀⋅r₁⋅r₂ + r₀⋅r₁⋅r₃ + r₀⋅r₁⋅r₄ + r₀⋅r₂⋅r₃ + r₀⋅r₂⋅r₄ + r₀⋅r₃⋅r₄ + r₁⋅r₂⋅r₃ + r₁⋅r₂⋅r₄ + r₁⋅r₃⋅r₄ + r₂⋅r₃⋅r₄ = 0
r₀⋅r₁⋅r₂⋅r₃ + r₀⋅r₁⋅r₂⋅r₄ + r₀⋅r₁⋅r₃⋅r₄ + r₀⋅r₂⋅r₃⋅r₄ + r₁⋅r₂⋅r₃⋅r₄ = 1
r₀⋅r₁⋅r₂⋅r₃⋅r₄ = -3
Viete formulas show the relationship between roots of a polynomial and its coefficients:
$V_{i-1} = (-1)^i \frac{a_{n-i}}{a_n}$
where $$f(z)=a_nz^n + a_{n-1}z^{n-1} + \ldots + a_1z + a_0$$ and $$i = 1 \ldots n$$. To obtain the final result it sufficient to take $$V_3$$ and $$V_4$$ and substitute in $$G$$:
>>> numer(G).subs(*V[3])/denom(G).subs(*V[4])
-1/3
Or we could simply use G.subs(V), but due to a bug in SymPy (#2552) this doesn’t work as expected, leaving the denominator unchanged.
We obtained the same result as before, just this time using purely symbolic techniques. This simple procedure can be extended to form an algorithm for solving the root summation problem in the general setup. SymPy implements this algorithm in RootSum:
>>> RootSum(f, Lambda(z, g))
-1/3
The choice of $$g$$ allowed us to recognize Viete formulas very easily in $$G$$, but is this the case also for more complicated rational functions? Let’s modify $$g$$ a little:
>>> g = 1/(z + 2)
1
─────
z + 2
Now let’s repeat the procedure for the new $$g$$:
>>> G = together(sum([ g.subs(z, r) for r in R ]))
>>> p = expand(numer(G))
>>> q = expand(denom(G))
>>> p
r₀⋅r₁⋅r₂⋅r₃ + r₀⋅r₁⋅r₂⋅r₄ + 4⋅r₀⋅r₁⋅r₂ + r₀⋅r₁⋅r₃⋅r₄ + 4⋅r₀⋅r₁⋅r₃ + 4⋅r₀⋅r₁⋅r₄ + 12⋅r₀⋅r₁ + r₀⋅r₂⋅r₃⋅r₄ + \
4⋅r₀⋅r₂⋅r₃ + 4⋅r₀⋅r₂⋅r₄ + 12⋅r₀⋅r₂ + 4⋅r₀⋅r₃⋅r₄ + 12⋅r₀⋅r₃ + 12⋅r₀⋅r₄ + 32⋅r₀ + r₁⋅r₂⋅r₃⋅r₄ + 4⋅r₁⋅r₂⋅r₃ + \
4⋅r₁⋅r₂⋅r₄ + 12⋅r₁⋅r₂ + 4⋅r₁⋅r₃⋅r₄ + 12⋅r₁⋅r₃ + 12⋅r₁⋅r₄ + 32⋅r₁ + 4⋅r₂⋅r₃⋅r₄ + 12⋅r₂⋅r₃ + 12⋅r₂⋅r₄ + 32⋅r₂ + \
12⋅r₃⋅r₄ + 32⋅r₃ + 32⋅r₄ + 80
>>> q
r₀⋅r₁⋅r₂⋅r₃⋅r₄ + 2⋅r₀⋅r₁⋅r₂⋅r₃ + 2⋅r₀⋅r₁⋅r₂⋅r₄ + 4⋅r₀⋅r₁⋅r₂ + 2⋅r₀⋅r₁⋅r₃⋅r₄ + 4⋅r₀⋅r₁⋅r₃ + 4⋅r₀⋅r₁⋅r₄ + \
8⋅r₀⋅r₁ + 2⋅r₀⋅r₂⋅r₃⋅r₄ + 4⋅r₀⋅r₂⋅r₃ + 4⋅r₀⋅r₂⋅r₄ + 8⋅r₀⋅r₂ + 4⋅r₀⋅r₃⋅r₄ + 8⋅r₀⋅r₃ + 8⋅r₀⋅r₄ + 16⋅r₀ + \
2⋅r₁⋅r₂⋅r₃⋅r₄ + 4⋅r₁⋅r₂⋅r₃ + 4⋅r₁⋅r₂⋅r₄ + 8⋅r₁⋅r₂ + 4⋅r₁⋅r₃⋅r₄ + 8⋅r₁⋅r₃ + 8⋅r₁⋅r₄ + 16⋅r₁ + 4⋅r₂⋅r₃⋅r₄ + \
8⋅r₂⋅r₃ + 8⋅r₂⋅r₄ + 16⋅r₂ + 8⋅r₃⋅r₄ + 16⋅r₃ + 16⋅r₄ + 32
This doesn’t look that familiar anymore. Let’s try to apply Viete formulas to the numerator and denominator:
>>> p.subs(V).has(*R)
True
>>> q.subs(V).has(*R)
True
We weren’t able to get rid of the symbolic roots of $$f$$. We can, however, try to rewrite $$p$$ and $$q$$ as polynomials in elementary symmetric polynomials. This procedure is called symmetric reduction, and an algorithm for this is implemented in symmetrize():
>>> (P, Q), mapping = symmetrize((p, q), R, formal=True)
>>> P
(32⋅s₁ + 12⋅s₂ + 4⋅s₃ + s₄ + 80, 0)
>>> Q
(16⋅s₁ + 8⋅s₂ + 4⋅s₃ + 2⋅s₄ + s₅ + 32, 0)
>>> for s, poly in mapping:
... pprint(Eq(s, poly))
...
s₁ = r₀ + r₁ + r₂ + r₃ + r₄
s₂ = r₀⋅r₁ + r₀⋅r₂ + r₀⋅r₃ + r₀⋅r₄ + r₁⋅r₂ + r₁⋅r₃ + r₁⋅r₄ + r₂⋅r₃ + r₂⋅r₄ + r₃⋅r₄
s₃ = r₀⋅r₁⋅r₂ + r₀⋅r₁⋅r₃ + r₀⋅r₁⋅r₄ + r₀⋅r₂⋅r₃ + r₀⋅r₂⋅r₄ + r₀⋅r₃⋅r₄ + r₁⋅r₂⋅r₃ + r₁⋅r₂⋅r₄ + r₁⋅r₃⋅r₄ + r₂⋅r₃⋅r₄
s₄ = r₀⋅r₁⋅r₂⋅r₃ + r₀⋅r₁⋅r₂⋅r₄ + r₀⋅r₁⋅r₃⋅r₄ + r₀⋅r₂⋅r₃⋅r₄ + r₁⋅r₂⋅r₃⋅r₄
s₅ = r₀⋅r₁⋅r₂⋅r₃⋅r₄
Here we performed the formal simultaneous symmetric reduction of the polynomials $$p$$ and $$q$$, obtaining their representation in terms of elementary symmetric polynomials, non-symmetric remainders, and elementary symmetric polynomials. Remainders are always zero for symmetric inputs.
We can zip this mapping and Viete formulas together, obtaining:
>>> [ (s, c) for (s, _), (_, c) in zip(mapping, V) ]
[(s₁, 0), (s₂, 0), (s₃, 0), (s₄, 1), (s₅, -3)]
Now we can take head of P and Q and perform substitution:
>>> P[0].subs(_)/Q[0].subs(_)
81
──
31
Let’s verify this result using RootSum:
>>> RootSum(f, Lambda(z, g))
81
──
31
The numerical approach also works in this case:
>>> sum([ g.subs(z, r) for r in Poly(f).all_roots() ]).evalf()
2.61290322580645
>>> nsimplify(_)
81
──
31
1. Repeat this procedure for:
• $$f = z^5 + z + a$$ and $$g = \frac{1}{z + 1}$$
• $$f = z^5 + z + a$$ and $$g = \frac{1}{z + b}$$
(solution)
1. Can this or a similar procedure be used with other classes of expressions than rational functions? If so, what kind of expressions can be allowed? | 2021-12-08 00:56:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8403978943824768, "perplexity": 3709.6373697175804}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363420.81/warc/CC-MAIN-20211207232140-20211208022140-00043.warc.gz"} |
https://golem.ph.utexas.edu/category/2011/10/spectra_of_operators_and_rings.html | ## October 16, 2011
### Spectra of Operators and Rings
#### Posted by Tom Leinster
There are many uses of the word ‘spectrum’ in mathematics, and most of them are related. (The main exception that I’m aware of is spectra in the sense of homotopy theory.) In particular, the spectrum of a linear operator on a finite-dimensional vector space — that is, its set of eigenvalues — can be seen as the spectrum of an associated commutative ring.
I’ll explain how that story goes. But let me state up front the question that I want to ask. Although it was motivated by my desire to link up the various notions of spectra, it doesn’t actually mention spectra at all.
Let $V$ be a finite-dimensional vector space over a field $k$. Let $T$ be an operator on $V$, in other words, a linear map $V \to V$. Write $\chi(x) \in k[x]$ for its characteristic polynomial. What is the significance of the ring
$k[x]/(\chi(x))?$
Let me explain the kind of answer I’m hoping for. Suppose we replace the characteristic polynomial $\chi$ by the minimal polynomial $m$. Then the ring
$k[x]/(m(x))$
can be seen as the ring of polynomials in $T$. Precisely: write $End(V)$ for the $k$-algebra of operators (endomorphisms) on $V$, with composition as its product. The homomorphism $k[x] \to End(V)$ sending $x$ to $T$ has $(m(x))$ as its kernel, and the image is the subalgebra of $End(V)$ generated by $T$. Hence $k[x]/(m(x))$ is isomorphic to this subalgebra, which consists of the polynomials in $T$.
But is there a nice way to think about $k[x]/(\chi(x))$?
I said that the spectrum of a linear operator $T$ was its set of eigenvalues, but it should really be thought of as a set with multiplicity. The multiplicities here are the algebraic multiplicities. I’ll write $Spec(T)$ for the spectrum of $T$.
Usually people define the algebraic multiplicity of an eigenvalue $\lambda$ as the power of $(x - \lambda)$ appearing in the characteristic polynomial. In the first post I ever wrote for the Café, Linear Algebra Done Right, I explained a more conceptual way to think about the algebraic multiplicity. It’s the dimension of the eventual kernel of $T - \lambda$, defined as
$evKer(T - \lambda) = \bigcup_{i \in \mathbb{N}} Ker((T - \lambda)^i).$
(I’m assuming that we’re over an algebraically closed field.) For that reason, I wanted to use the term ‘dynamic multiplicity’ instead. But I’ll just say ‘multiplicity’.
In any case, we can write the characteristic polynomial of $T$ as
$\chi(x) = (x - \lambda_1)^{\alpha_1} \cdots (x - \lambda_k)^{\alpha_k}$
where $\lambda_1, \ldots, \lambda_k$ are the distinct eigenvalues of $T$ and $\alpha_1, \ldots, \alpha_k$ are their multiplicities. We can form the ring
$R(T) = k[x]/(\chi(x)),$
which is commutative. So, starting from a linear operator $T$, we’ve defined a commutative ring $R(T)$.
Every commutative ring $R$ has a spectrum, $Spec(R)$. At its most basic, the spectrum of a ring is the set of prime ideals; but it also carries a topology and a sheaf of rings. In the jargon, $Spec(R)$ is a ‘ringed space’.
So: given a linear operator $T$, we get two things called ‘spectra’: the set-with-multiplicities $Spec(T)$ of eigenvalues, and the ringed space $Spec(R(T))$. How are they related?
The answer was worked out long ago, and I guess all algebraic geometers know it. Nevertheless, I think there are plenty of people who know both uses of the word ‘spectrum’, but aren’t aware that there’s a close connection between them. So here goes.
For our ring $R(T)$, the (mere) set $Spec(R(T))$ of prime ideals is
$Spec(R(T)) = \{ (x - \lambda_1), \ldots, (x - \lambda_k) \}.$
The points of $Spec(R(T))$ are, therefore, in natural, one-to-one correspondence with the points of $Spec(T)$. That’s an encouraging start.
As a topological space, $Spec(R(T))$ is discrete: every subset is open. A sheaf of widgets on a discrete space $S$ is just an $S$-indexed family of widgets (namely, the stalks of the sheaf). Here, ‘widget’ is ‘ring’. So, to describe the sheaf $O$ with which $Spec(R(T))$ comes equipped, we just have to describe one ring $O_p$ for each point $p$ of $Spec(R(T))$. And in fact, the ring associated to the point $(x - \lambda_i)$ of $Spec(R(T))$ is just
$k[x]/((x - \lambda_i)^{\alpha_i}).$
The point now is that you can recover the multiplicity $\alpha_i$ from this ring. At least, you can do so if you’re allowed to know its $k$-algebra structure: for $\alpha_i$ is just its dimension as a vector space over $k$.
Thus, even if you don’t know $T$, knowing $Spec(T)$ tells you what $Spec(R(T))$ is, and vice versa. In that sense, $Spec(T)$ and $Spec(R(T))$ contain equivalent information about the operator $T$.
This is satisfying, but one question remains. How do we understand the ring $R(T)$? As I said at the beginning, it would be easily understandable if we’d used $k[x]/(m(x))$ instead of $k[x]/(\chi(x))$; but then the spectrum would tell us the powers of $(x - \lambda_i)$ in the minimal polynomial, rather than the characteristic polynomial, and that’s not such important information.
Maybe an example will make the problem clearer. In fact, a really trivial example will do: $T = 0$. Say $dim(V) = N$. Then
$m(x) = x, \quad \chi(x) = x^N.$
Hence
$k[x]/(m(x)) = k, \quad R(T) = k[x]/(\chi(x)) = k[x]/(x^N).$
Conceptually, what is the process that turns the zero operator on $k^N$ into the ring $k[x]/(x^N)$?
Posted at October 16, 2011 1:58 PM UTC
TrackBack URL for this Entry: http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2447
### Re: Spectra of Operators and Rings
Deformation? Given a linear operator you can consider the moduli space of all linear operators with the same characteristic polynomial. Generically they should have minimal polynomial the characteristic polynomial, so an arbitrarily small deformation of a given operator (preserving its characteristic polynomial) will generate an algebra isomorphic to the quotient by the characteristic polynomial. I don’t know how satisfying this is, though.
Posted by: Qiaochu Yuan on October 16, 2011 6:47 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Thanks, Qiaochu, but I’m not sure I understand you.
First, I guess your opening sentence “Deformation?” is the answer to the closing sentence of my post. Is my guess right? If so, I’m not really sure how to assemble the grammar of your answer. “The deformation of the zero operator on $k^N$ is the ring $k[x]/(x^N)$” doesn’t really sound right.
Second, you wrote:
an arbitrarily small deformation of a given operator […] will generate an algebra …
What do you mean by “generate an algebra” here? That is, what process are you using to turn an operator into an algebra? My guess is that you’re assigning to an operator $S$ the ring $k[x]/(m_S(x))$, where $m_S$ is the minimum polynomial of $S$. Is that right?
Thanks!
Posted by: Tom Leinster on October 16, 2011 8:30 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Sorry, I guess I worded my reply confusingly. I think Andrew Stacey’s version of this argument probably has the best ratio of explanatory power to background necessary, so here’s my spin on it:
Given any linear operator T (I’ve forgotten how to typeset math here!) one can consider operators close to T, say in some matrix norm. Generically these operators have distinct eigenvalues, so their characteristic and minimal polynomials coincide. In particular we can find a sequence of such operators converging to T. Of course their characteristic polynomials converge to the characteristic polynomial of T, but it’s not necessary for their minimal polynomials to converge to the minimal polynomial of T; this is the sense in which the minimal polynomial behaves poorly as a function on the space of matrices.
So the characteristic polynomial is what the minimal polynomial “should be” if T had more room to move around, in the same way (as in Jason Starr’s response) that the intersection multiplicity of, say, two algebraic curves is what the number of intersections “should be” if the curves had more room to move around.
Posted by: Qiaochu Yuan on October 20, 2011 7:03 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Great; thanks.
I’ve forgotten how to typeset math here!
Just enclose it between dollar signs as usual. (There are a few quirks.)
The only thing to know is that when you’re writing your comment, you have to choose an appropriate “text filter” from the dropdown menu. I guess anything containing “itex” will work. I use “itex to MathML with parbreaks”.
Re characteristic and minimal polynomials, I get the point now. Thanks. But remember the original question: I feel like I have a good intuitive understanding of what algebraic multiplicity is, and therefore, for the most part, what the characteristic polynomial is. What I wanted to do was to transform that into a good understanding of what $k[x]/(\chi(x))$ is.
Posted by: Tom Leinster on October 20, 2011 9:15 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
I agree with Qiaochu Yuan. The assignment to every linear operator $T$ of the ring $k[x]/\chi_T(x)$ is the only assignment of quotient rings which “generically” is $k[x]/m_T(x)$ and which is “flat” in $T$. This is precisely the same issue as comes up in assigning multiplicities to non-transverse intersections in algebraic geometry. It might seem non-intuitive to “count” certain solutions with multiplicities, but it is the only way to count which is “continuous” in the parameters.
Posted by: Jason Starr` on October 16, 2011 8:08 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Thanks, Jason. By the way, to type Latex here, you need to select an appropriate option from the drop-down menu marked “Text filter” in the comment form. I use “itex to MathML with parbreaks”.
The message I’m getting is that you understand $k[x]/(\chi_T(x))$ by thinking not only about $T$ itself, but also about “nearby” operators. I don’t really know what “nearby” means, but I guess that’s because I don’t understand what “flat” means in this context. Let me see. The process
$T \mapsto k[x]/(\chi_T(x))$
takes an element of the endomorphism ring $End(V)$ and turns it into a ring. So, it’s an $End(V)$-indexed family of rings. (Or you could replace “ring” by “$k$-algebra” throughout the previous two sentences.)
If I understand you correctly, whenever $R$ is a ring and $(A_r)_{r \in R}$ is an $R$-indexed family of rings, there must be a definition of what it means for such a family to be “flat”. Am I warm?
Posted by: Tom Leinster on October 16, 2011 8:37 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
I searched for “flat family” in Wikipedia, but it just asked me if I meant “fat family”. Nope.
Posted by: Tom Leinster on October 16, 2011 10:31 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
I would recommend that you look in the index of any commutative algebra book under the word “flat”.
Posted by: Jason Starr on October 21, 2011 2:53 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Jason, your first comment was helpful, but this one not so much so.
I guess you think I’m being lazy, asking people to explain stuff that I could look up in any commutative algebra book. But you’re overestimating the clarity of your original comment.
I know the definitions of flatness for modules over rings, for homomorphisms of rings, and for algebras. Sure, a random commutative algebra book will include those definitions. But as far as I can tell, none of those three definitions covers the notion of flatness invoked in your comment:
The assignment to every linear operator $T$ of the ring $k[x]/\chi_T(x)$ is the only assignment of quotient rings which “generically” is $k[x]/m_T(x)$ and which is “flat” in $T$.
You’re saying, among other things, that the assignment $T \mapsto k[x]/(\chi_T(x))$ is “flat”. Now $T$ is an element of the endomorphism ring of $V$, and $k[x]/(\chi_T(x))$ is a ring, so I guessed that there was some definition of what it means for a ring-indexed family of rings to be “flat”. By a “ring-indexed family of rings” I mean a ring $R$ together with a ring $A_r$ for each $r \in R$. I asked you in this comment whether that was the correct interpretation of your comment, but I still don’t know the answer.
So, let me ask again: are you alluding to some notion of flatness of a ring-indexed family of rings? If so, what is that definition?
Perhaps there’s a canonical way of turning a ring-indexed family of rings into a module, and then it would be clear what it meant for it to be flat. Perhaps my guessed interpretation of what you wrote was wrong. In any case, if your second comment is correct, the notion of flatness used in your first comment must somehow be a case of the notion of flatness for modules.
But “look in the index of any commutative algebra book under the word ‘flat’” is simply unhelpful.
Posted by: Tom Leinster on October 21, 2011 4:22 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
You are correct: I think you could look this up in any commutative algebra textbook.
Posted by: Jason Starr on October 22, 2011 4:51 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Eisenbud? Atiyah-Macdonald? Schenck’s little blue book?
Posted by: Yemon Choi on October 22, 2011 5:35 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
I tried Matsumura, to no avail. I’m absolutely willing to look stuff up, but at present I don’t know what to look up in order to understand Jason’s original comment. If someone knows and can tell me, I’d be interested, and it would be good to get something positive out of this conversation.
All usages of “flat” appearing in your average commutative algebra book (e.g. flat homomorphism of rings, flat algebra) are derived from the notion of flatness for a module. So, Jason seems to be saying (i) that from the family
$\Bigl( k[x]/\chi_T(x) \Bigr)_{T \in End(V)},$
one can derive a module, and (ii) that module is flat. It’s (i) that’s a mystery to me, and which no one seems able or willing to explain.
On the other hand, David R’s brief comment suggests that one needs to invoke the notion of flat morphism of schemes, which certainly doesn’t appear in all comm alg books.
Posted by: Tom Leinster on October 22, 2011 6:02 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Let $S$ be the polynomial algebra generated by the vector space of all linear operators on a finite dimensional vector space $V$. Let $S[t]$ be the polynomial ring over $S$. This is a flat $S$-module. The only quotient $S[t]$ module which is $S$-flat and which agrees with $S[t]/m_T(t)$ over the generic point is $S[t]/\chi_T$.
Posted by: Jason Starr on October 22, 2011 7:30 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
OK, this is going nowhere. Let’s leave it there.
Posted by: Tom Leinster on October 22, 2011 12:55 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Try Flat morphism instead. You’ll need to know that a flat map of rings $R\to S$ is one that makes $S$ a flat $R$-module.
Posted by: David Roberts on October 17, 2011 1:34 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Hmm. Thanks, David, but this is getting pretty indirect. It looks as if, in order to understand what you’re saying, I’d have to do all of the following:
1. understand how a family $(A_r)_{r \in R}$ of rings indexed over a ring $R$ can be regarded as a morphism of schemes
2. understand what it means for a morphism of schemes to be flat
3. put these together to understand what it means for a ring-indexed family of rings $(A_r)_{r \in R}$ to be flat
4. specialize to understand what it means for the particular ring-indexed family of rings $(k[x]/(\chi_T(x)))_{T \in End(V)}$ to be flat
5. convince myself that it is indeed flat
6. convince myself that it’s the only flat family that’s “generically” the same as $(k[x]/(m_T(x)))$, which of course involves…
7. …understanding what “generically” means
8. take this knowledge that $(k[x]/(\chi_T(x)))$ is the unique flat family generically agreeing with $(k[x]/(m_T(x)))$, and somehow use it to improve my understanding of what $k[x]/(\chi_T(x))$ looks like, for any individual operator $T$.
I get the idea at the level of vagueness used in Jason’s first sentence. But I was really hoping to get some vivid picture of the ring $k[x]/(\chi_T(x))$. The algebraic-geometric intuition that Jason described seems to depend on thinking about a varying $T$. Evidently that can be helpful, but I’d like to be able to understand better what the ring looks like for an individual $T$.
As evidence that this might be possible, I do have a vivid picture of the algebraic multiplicities of $T$: they’re the dynamical quantities discussed in the post. But I haven’t managed to use that to get an equally vivid picture of $k[x]/(\chi_T(x))$.
Posted by: Tom Leinster on October 17, 2011 6:47 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
There’s a more explicit answer to the question, which of course is morally equivalent to that of Qiaochu and Jason, but has a proud history in representation theory (under names like “Kostant slice”). Namely, to any matrix we can attach a unique matrix up to conjugacy with the same characteristic polynomial but which is regular, i.e., all Jordan blocks have distinct eigenvalues <==> the dimension of its stabilizer is minimal <==> the matrix admits a cyclic vector (so can be written in “companion”/rational cyclic form with all 1’s on first subdiagonal and stuff on the last column). The scheme you write is the spectrum of this associated matrix. As Qiaochu and Jason explain this spectrum is the only well-behaved specturm one can attach to a general matrix, but the specific realization as the spectrum of a regular “replacement” for your matrix is used a lot in representation theory.
More formally, this describes a slice to the adjoint quotient map from the Lie algebra $g$ of matrices to $g // G = h /W$. The slice lands in the locus of regular matrices. Kostant generalized this construction to arbitrary semisimple Lie algebras (and quantized it to give a model for the center of the enveloping algebra of $g$), Steinberg has a group version, Slodowy generalized this to slices to nonregular nilpotent orbits (whose quantizations are known as W-algebras), Hitchin used it to construct a section for the Hitchin integrable system, etc…
Posted by: David Ben-Zvi on October 17, 2011 5:31 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
This makes one wonder if it can be done for, say, nilpotent $L_\infty$-algebras…
Posted by: David Roberts on October 17, 2011 8:12 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Thanks, David B-Z.
You and the others have said that the assignment
$T \mapsto k[x]/(\chi_T(x))$
is “well-behaved”, but the assignment
$T \mapsto k[x]/(m_T(x))$
is not. Is this an incarnation of the fact that the coefficients of $\chi_T(x)$ are polynomials in the entries of the matrix of $T$, but those of $m_T(x)$ are not?
Posted by: Tom Leinster on October 17, 2011 7:01 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Just thought I’d weigh in in favour with everyone else (nothing like a bandwagon for joining). When I teach about the characteristic polynomial then I first teach the minimum polynomial and then say that the characteristic polynomial is the “continuous minimum polynomial”. So it’s what you get if you want a continuous assignment $T \mapsto p_T(t)$ with the property that $p_T(T) = 0$ and if $T \mapsto q_T(t)$ is another such assignment then $p_T(t) | q_T(t)$.
I actually used this in a paper as I had a family of unitary operators depending on a parameter (in the circle as it happened). I could interpret these as a single operator acting on the loop space, $L\mathbb{C}^n$, and I had the condition that when I did so then the resulting operator had a minimum polynomial. I wanted to show then that the family of operators was constant, modulo similarity.
The argument went as follows. Suppose that $t \mapsto T_t$ is my family of unitary operators on $\mathbb{C}^n$ and write $T$ for the operator on $L \mathbb{C}^n$ defined by $\gamma \mapsto (t \mapsto T_t(\gamma(t))$. Let $m_T$ be its minimum polynomial (which exists by assumption) and let $m_{T_t}$ be the minimum polynomial of $T_t$ (which exists by finite dimensionality). Then $m_{T_t} | m_T$ so, using $c$ for the corresponding characteristic polynomials, $c_{T_t} | (m_T)^n$, since the missing multiplicities are of at most $n$. Now $c_{T_t}$ is a monic polynomial so is completely determined by its roots, but these must be drawn from the roots of $(m_T)^n$ (with multiplicity) and that is a discrete set. Thus since $c_{T_t}$ depends continuously on $t$, it must be constant. Since our operators were unitary, they were diagonalisable, and so their characteristic polynomial determines their similarity class.
That usefulness combined with my dislike of determinants (for similar reasons to you!) leads to my teaching of characteristic polynomial as a “continuous minimum polynomial”.
Posted by: Andrew Stacey on October 18, 2011 7:50 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Andrew wrote:
characteristic polynomial as a “continuous minimum polynomial”
I like it!
Posted by: Tom Leinster on October 20, 2011 9:16 PM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
In that case, I’ll add a couple of links. My lecture notes from last year on this are Lecture 20 (Polynomials) on http://www.math.ntnu.no/~stacey/Teaching/TMA4145h2010/lectures.html and the article where I used this argument was Finite dimensional subbundles of loop bundles, details at http://www.math.ntnu.no/~stacey/Research/Papers/looprep.html.
Posted by: Andrew Stacey on October 21, 2011 8:18 AM | Permalink | Reply to this
### Re: Spectra of Operators and Rings
Nice! Also, I’ve never seen so many colours used in a single formula.
Posted by: Tom Leinster on October 21, 2011 3:37 PM | Permalink | Reply to this
Post a New Comment | 2016-05-28 22:10:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 155, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8462452292442322, "perplexity": 393.15487160941524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278244.51/warc/CC-MAIN-20160524002118-00162-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/questions/39609/checking-whether-a-number-can-be-composed-from-the-cube-of-its-digit/39612 | # Checking whether a number can be composed from the cube of its digit
How to check whether or not the sum of the cube of each digit of a number is equal to the number itself?
In the following code, I tried to return the number in question whenever it matches the condition.
In[191]:= Func[x_]:=If[Total[Map[#^3& ,IntegerDigits[x]]]==x,x,0];
Func[300]
Out[192]= 300
Apparently the checking seems to be wrongly done. What caused this issue? How to fix it?
-
Func[300] returns 0 on my machine... – cormullion Dec 30 '13 at 15:30
Have you reset the Kernel before? Maybe there is some old definition for Func. p.s. you don't have to Map in such cases: Total[IntegerDigits[300]^3] will do too. – Kuba Dec 30 '13 at 15:40
@cormullion: Oh my ghost, I forgot to kill the kernel first. – kiss my armpit Dec 30 '13 at 15:40
We would like to find all integers x satisfying the following equation Total[ IntegerDigits[x]^3] == x (we don't have to map #^3& since Power is Listable).
Warning: Flexibility and polymorphism of Mathematica notation is restricted by Operator Precedence (see also When is f@g not the same as f[g]?). It appears to be the case here. One could suspect this was the problem defining Func initially.
f[x_] := Total[ IntegerDigits[x]^3] == x
however we might get incorrect results using this definition Total @ IntegerDigits @ x^3 == x while this one works fine Total[ IntegerDigits @ x^3] == x.
Select[ Range[0, 10^5], f @ # &]
{0, 1, 153, 370, 371, 407}
One can easily observe that we don't have to search for such integers anymore since Total[ IntegerDigits[x]^3] increases in a polynomial rate with the exponent in Range while x increases in an exponential rate and
Total[ IntegerDigits[99999]^3] < 10^5
True
Thus the above are all integers satisfying Total[ IntegerDigits[x]^3] == x.
Edit
Out of curiosity I have found how the solutions depend on the exponent. Defining:
f[x_, k_] := Total[ IntegerDigits[x]^k] == x
immediately we find with Select[ Range[ 0, 10^4], f[#, 2]&] that for k == 2 there are no solutions (besides 0 and 1).
ListPlot[
Append[
Table[ Log @ Total[ IntegerDigits[10^k - 1]^m], {m, 3, 9}, {k, 15}],
Table[ Log[ 10^(k - 1)], {k, 15}]], AxesOrigin -> {1, 0},
PlotMarkers -> {Automatic, Medium}, PlotRange -> All, Joined -> True,
PlotStyle -> Thick, PlotLegends -> Range[3, 9]]
With this plot it appears to be easier to estimate appropriate range of search space. We've got:
Select[ Range[10^6], f[#, 4]&]
{ 1, 1634, 8208, 9474}
Select[ Range[10^7], f[#, 5]&]
{ 1, 4150, 4151, 54748, 92727, 93084, 194979}
Select[ Range[5 10^7], f[#, 6]&]
{ 1, 548834}
-
It works as Artes showed, but here's, not faster but why not, another approach:
func = (1 - Unitize[Norm[IntegerDigits[#], 3]^3 - #]) # &
for clarification, see the documentation for Norm and it's second argument.
- | 2016-05-28 18:13:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.520803689956665, "perplexity": 3929.825712666713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278042.87/warc/CC-MAIN-20160524002118-00089-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://accessanesthesiology.mhmedical.com/content.aspx?bookid=2070§ionid=157604505 | Skip to Main Content
Chapter 51
### INTRODUCTION
An increasing number of patients are undergoing surgical procedures in hospital outpatient departments (HOPDs) or ambulatory surgery centers (ASCs).1 Outpatient surgical procedures have become more complex, and patients are presenting for surgery with a greater number of comorbid conditions than in the past.2 Regional anesthesia (RA) and peripheral nerve blocks (PNBs) can help meet the goals of caring for these patients in the outpatient setting.
In 1976, there were 67 Medicare-certified ASCs in the United States, and in 2011, there were 5,344.3 In 1982, 30 ambulatory surgical procedures were covered by Medicare; today there are hundreds.4 In an analysis of National Survey of Ambulatory Surgery (NSAS) data, Tighe et al. found that 15% of an estimated 4 million orthopedic outpatient cases implemented a “regional block” as part of the anesthetic used.6,7 Over 580,000 PNBs were performed in HOPDs or ASCs in 2006.5
From 2006 to 2010, outpatient services per Medicare enrollee increased by 5.7% annually. In 2011, the rate increased by 1.9%, accounting for $3.4 billion in charges, a 2.2% increase from 2010.3,4 Currently, about 57 million outpatient procedures (surgical and nonsurgical) are performed in the United States at a cost of$3.2 billion.4,8 In 2014, over 3 million of these cases are estimated to be orthopedic procedures.5 At some institutions, including the authors’, most PNBs are performed for orthopedic cases.9 Based on NSAS data from 1996 through 2006, arthroscopic knee procedures in the U.S. increased by 49%.10 As minimally invasive surgery becomes available for surgeries that require an inpatient stay due to the severity of postoperative pain, RA can allow for safe same-day discharge.11 A study by Koenig and Gu indicated that the growth of ASCs may reduce Medicare spending due to lower reimbursements relative to number of hospitals.12 There is preliminary evidence that outcomes at ASCs are better than those at in-hospital settings for similar otolaryngologic surgical cases.13 Future research in this area needs to be completed for other services.
With the growth in both complex outpatient surgeries and ASCs, there is a need for more anesthesiologists with specific training in the use of acute pain medicine with integrated RA and PNB techniques. With the use of these techniques, the first priority should be on safety, the second on reducing patient pain and minimizing opioid and general anesthesia (GA) side effects, the third on economics, and the fourth on efficiency.14,15
#### Outpatient Surgery Stakeholders
Patients, providers, payers, and “internal customers,” including anesthesiologists, nurses, and support staff,16 may have differing views on the value on the various outpatient operational and clinical outcomes. In healthcare, value is defined as patient outcome per costs used to achieve those outcomes.17,18 For payers, value consists of providing a service with good outcome at ...
### Pop-up div Successfully Displayed
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https://www.physicsforums.com/threads/replace-all-as-with-three-c.768240/ | # "Replace all As with three ***" (C++)
1. Aug 30, 2014
### Jamin2112
During my in-person interview yesterday, the interviewer asked me to write a function that takes a string and replaces all As with three As
Ex. "Abraham"--->"AAAbraaahaaam"
I did it, but it took me a while to get it right using the replace function (http://www.cplusplus.com/reference/string/string/replace/), because the documentation (which I was allowed to use) doesn't say how the string is re-indexed after using the function. I found it difficult to write the function by iterating through it with an iterator.
Anyways, I was wondering whether someone here could show me their most elegant solution, just so I can see what I could've improved on.
2. Aug 30, 2014
### AlephZero
Not tested, but no iterators were harmed in making this function:
Code (Text):
#include <string>
#include <regex>
string tripleA(string s)
{
return std::regex_replace(s, std::regex("([Aa])"), "$1$1\$1");
}
3. Aug 30, 2014
### Jamin2112
No boost library, please
4. Aug 30, 2014
### AlephZero
Not boost: standard C++11.
You didn't say it had to work with a legacy programming tools
5. Sep 6, 2014
### voko
Old school:
Code (Text):
void tripleA(std::string &s)
{
for (auto i = s.size(); i > 0; --i)
if (tolower(s[i - 1] == 'a')
s.insert(i, 2, s[i - 1]);
}
6. Sep 6, 2014
### D H
Staff Emeritus
C++11 has fallen into the status of "legacy programming tools". As of August 18, 2014, the current standard is C++14. | 2018-07-15 20:01:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4341356158256531, "perplexity": 6437.809503046456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676588961.14/warc/CC-MAIN-20180715183800-20180715203800-00415.warc.gz"} |
https://publires.unicatt.it/it/publications/linking-over-cones-and-nontrivial-solutions-for-p-laplace-equatio-7 | Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity
Marco Degiovanni, Sergio Lancelotti
Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review
60 Citazioni (Scopus)
Abstract
We prove that the quasilinear equation -\Delta_p u=\lambda V |u|^{p-2}u+g(x,u), with g subcritical and p-superlinear at 0 and at infinity, admits a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda in R. A minimax approach, allowing also an estimate of the corresponding critical level, is used. New linking structures, associated to certain variational eigenvalues of -\Delta_p u=\lambda V |u|^{p-2}u, are recognized, even in absence of any direct sum decomposition of W^{1,p}_0(\Omega) related to the eigenvalue itself.
Lingua originale English 907-919 13 ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE 24 https://doi.org/10.1016/j.anihpc.2006.06.007 Pubblicato - 2007
Keywords
• Critical point theory
• Differential equations
• Equazioni differenziali
• Teoria dei punti critici | 2021-04-11 15:48:34 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8548573851585388, "perplexity": 14508.248653167811}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00291.warc.gz"} |
https://www.autoitscript.com/forum/topic/16204-guibuilder/ | GUIBuilder
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This basenote will hold the most recent version of GUIBuilder, originally created by CyberSlug. All constructive feedback welcome.
Extract this to your Scite GUIBuilder directory (ex. "C:\Program Files\AutoIt3\Scite\GUIBuilder") if you like.
Thanks,
Livewire
***Note: Latest AutoIt beta version recommended for use.
Update History:
==================================================
GUIBuilder_9.4:
- Disabled Label control's FontColor, FontName, and Color buttons since
they are not implemented yet.
GUIBuilder_9.3:
- Added "Hint" and "ShowHint" functionality
- Added some extended properties for Edit control
- Added some extended properties for Input control
- Modified extended properties functionality (no more right click -> Properties)
GUIBuilder_9.2:
- Added "Hidden" properties for button and checkbox
- Added "Flat" property to Checkbox
- Updated "Picture" functionality to Checkbox (Can have picture w/ Checkbox not just picture button)
- Added extended properties for Group control
GUIBuilder_9.1:
- added command-line .agd file opening (just associate *.agd files with GUIBuilder) (Open-With -> GUIBuilder)
- added GUIBuilder.ini file (remembers last visited directory and Grid Ticks)
- added extended properties (Font, Color, Enabled, etc) for "Checkbox" control
GUIBuilder_9:
- added extended properties (Font, Color, Enabled, etc) ***currently for "Button" control only***...the rest coming soon
GUIBuilder_8:
- updated grid refreshing (check it out in Settings->SetGridTicks)
- GUIBuilder output (removed Exit and GUICreate style options)
- also other misc stuff.
GUIBuilder_9.4.zip
Edited by livewire
For me too
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Sure, next version will have version in the About window.
-Livewire
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I get this errors when i tyr to compile the script
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(3860,105) : ERROR: GUICtrlCreateMonthCal(): undefined function.
$returnValue = GUICtrlCreateMonthCal("MonthCal" & ($numCtrls + $num_of_deletes),$p[0], $p[1],$w, $h) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~^ D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4351,36) : ERROR: DllStructCreate(): undefined function. Local$p = DllStructCreate($struct) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^ D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4360,21) : ERROR: DllStructDelete(): undefined function. DllStructDelete($p)
~~~~~~~~~~~~~~~~~~^
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4370,45) : ERROR: DllStructGetSize(): undefined function.
DllStructSetData($p, 1, DllStructGetSize($p)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4370,46) : ERROR: DllStructSetData(): undefined function.
DllStructSetData($p, 1, DllStructGetSize($p))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4373,45) : ERROR: DllStructGetPtr(): undefined function.
DllStructSetData($p, 5, DllStructGetPtr($cc)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3(4384,46) : ERROR: DllStructGetData(): undefined function.
Local $color_picked = DllStructGetData($p, 4)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
D:\Profil\AutoIt3 scripts\GUIBuilder_9[1].1\GuiBuilder.au3 - 7 error(s), 0 warning(s)
My Autoit ver. is 31175, am i missing somthing in my autoit or ?
The only thing i have changede is that i'd put in a hotkey for properties (ctrl+p)
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Make sure that you are "running" the correct version of AutoIt.
Even though you downloaded the beta, it still gives you the option of running the stable version. If you are using Scite, go to Tools -> Beta Run. Otherwise, make sure that you are "pointing to" or selecting the right executable for AutoIt ("C:\Program Files\AutoIt3\beta\AutoIt3.exe").
For compiling, make sure you use: "C:\Program Files\AutoIt3\beta\Aut2Exe\Aut2Exe.exe"
-Livewire
Edited by livewire
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You are not running the latest version of Au3check and definition files.
Did you update your SciTE4AutoIT3 installation ?
Live for the present,
Dream of the future,
Learn from the past.
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You are not running the latest version of Au3check and definition files.
Did you update your SciTE4AutoIT3 installation ?
Yeps i have downloaded the latest installer (24-09-2005) (and installede it )
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Nice app:
1. Weird issue when resizing group boxes, keeps snapping to a small size when using handles to adjust group box size.
2. Would like option to lock group box & also lock controls with group box.
* Will add more as I find em / think of em.
~Projects~1. iPod Ejector 1.0 - Tool Used To Eject iPod in Windows - Uses DevEject.exe :P2. SmartFTP Close Popup Tool - Closes reminders from freeware SmartFTP.~Helpful Links For New Users~1. LXP's Learning AutoIT PDF Guide - <<< Go here for a PDF Guide on learning AutoIT from the ground up!<<<2. AutoIt 1-2-3 <<<Want to learn more about AutoIT quickly? Go Here<<<3. How To Install The Beta And Production Versions Of AutoIT / SciteAutoIT
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Nice app:
1. Weird issue when resizing group boxes, keeps snapping to a small size when using handles to adjust group box size.
2. Would like option to lock group box & also lock controls with group box.
* Will add more as I find em / think of em.
1. Left, Bottom, and Right sides of the rectangle are the only sides that "snap". The top side doesn't. Is this working correctly for you?
2. What do you mean by "lock"? (GUICtrlSetState @SW_LOCK)?
-Livewire
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1. Left, Bottom, and Right sides of the rectangle are the only sides that "snap". The top side doesn't. Is this working correctly for you?
2. What do you mean by "lock"? (GUICtrlSetState @SW_LOCK)?
-Livewire
1. The snapping is working but If I try to resize the group box it instantly resizes to it's smallest form I believe this to be only occuring when controls are over top ( within ) the group control causing issues.
2. By lock I mean lock all controls ( say input box / labels etc ) to a group box or to the position where you want them to remain. I thought this a basic feature.
~Projects~1. iPod Ejector 1.0 - Tool Used To Eject iPod in Windows - Uses DevEject.exe :P2. SmartFTP Close Popup Tool - Closes reminders from freeware SmartFTP.~Helpful Links For New Users~1. LXP's Learning AutoIT PDF Guide - <<< Go here for a PDF Guide on learning AutoIT from the ground up!<<<2. AutoIt 1-2-3 <<<Want to learn more about AutoIT quickly? Go Here<<<3. How To Install The Beta And Production Versions Of AutoIT / SciteAutoIT
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1. The snapping is working but If I try to resize the group box it instantly resizes to it's smallest form I believe this to be only occuring when controls are over top ( within ) the group control causing issues.
2. By lock I mean lock all controls ( say input box / labels etc ) to a group box or to the position where you want them to remain. I thought this a basic feature.
1. I know what you mean, but I can't reproduce that scenario...it's working fine for me...I'll have to test more.
2. You want to not be able to move the locked controls? Or you want it so that when you move the group box, the controls locked move also??? There's many definitions for lock, try explaining again without using the word lock.
-Livewire
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1. I know what you mean, but I can't reproduce that scenario...it's working fine for me...I'll have to test more.
2. You want to not be able to move the locked controls? Or you want it so that when you move the group box, the controls locked move also??? There's many definitions for lock, try explaining again without using the word lock.
-Livewire
2. Both, the ability to lock the group together and also the ability to lock the group within the parent box wherever you place it.
~Projects~1. iPod Ejector 1.0 - Tool Used To Eject iPod in Windows - Uses DevEject.exe :P2. SmartFTP Close Popup Tool - Closes reminders from freeware SmartFTP.~Helpful Links For New Users~1. LXP's Learning AutoIT PDF Guide - <<< Go here for a PDF Guide on learning AutoIT from the ground up!<<<2. AutoIt 1-2-3 <<<Want to learn more about AutoIT quickly? Go Here<<<3. How To Install The Beta And Production Versions Of AutoIT / SciteAutoIT
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New GUIBuilder version 9.2!
Let me know of any significant bugs...thorough error detection to come in the future.
GUIBuilder_9.2 info:
- Added "Hidden" properties for button and checkbox
- Added "Flat" property to Checkbox
- Updated "Picture" functionality to Checkbox (Can have picture w/ Checkbox not just picture button)
- Added extended properties for Group control
-Livewire
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New GUIBuilder version 9.2!
Looks pretty good so far!
I noticed that you changed the buttons in the preferences window for the elements that are currently changeable (like the combobox, etc) from "Update" and "Return" to "OK", "Apply" and "Cancel". However, the properties window is still modal and thus I cannot select a different control. Hopefully in the future it will be possible to select another control and have the properties window update with the properties of the new selected control (perhaps asking first if you want to apply the changes you made to the previous control).
Cheers,
Angel
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Recommendation: upgrate the properties menu option
GuiCreate("Modify Properties of [Wadeva]", 243, 322,(@DesktopWidth-243)/2, (@DesktopHeight-322)/2 , $WS_OVERLAPPEDWINDOW +$WS_VISIBLE + $WS_CLIPSIBLINGS)$Label_1 = GuiCtrlCreateLabel("Tooltip", 10, 270, 90, 21)
$Label_2 = GuiCtrlCreateLabel("Style", 10, 250, 100, 20)$Label_3 = GuiCtrlCreateLabel("State", 10, 230, 110, 20)
$Label_4 = GuiCtrlCreateLabel("Resizing", 10, 210, 110, 20)$Label_5 = GuiCtrlCreateLabel("Limit", 10, 190, 110, 20)
$Label_6 = GuiCtrlCreateLabel("Image", 10, 140, 110, 20)$Label_7 = GuiCtrlCreateLabel("Font", 10, 120, 110, 20)
$Label_8 = GuiCtrlCreateLabel("Cursor", 10, 100, 110, 20)$Label_9 = GuiCtrlCreateLabel("Data", 10, 50, 110, 20)
$Label_10 = GuiCtrlCreateLabel("Text Color", 10, 30, 120, 20)$Label_11 = GuiCtrlCreateLabel("Background Color", 10, 10, 120, 20)
$Input_12 = GuiCtrlCreateInput("Input12", 120, 270, 90, 21)$Input_13 = GuiCtrlCreateInput("Input13", 120, 250, 90, 20)
$Input_14 = GuiCtrlCreateInput("Input14", 120, 230, 90, 20)$Input_15 = GuiCtrlCreateInput("Input15", 120, 210, 90, 21)
$Input_16 = GuiCtrlCreateInput("Input16", 120, 190, 90, 20)$Input_17 = GuiCtrlCreateInput("N/A", 10, 160, 200, 20)
$Button_18 = GuiCtrlCreateButton("Browse...", 140, 140, 70, 20)$Combo_19 = GuiCtrlCreateCombo("Combo19", 120, 120, 90, 21)
$Combo_20 = GuiCtrlCreateCombo("Combo20", 120, 100, 90, 21)$Combo_21 = GuiCtrlCreateCombo("Combo21", 120, 50, 90, 21)
$Input_22 = GuiCtrlCreateInput("Input22", 10, 70, 100, 20)$Button_23 = GuiCtrlCreateButton("Add", 120, 70, 40, 20)
$Button_24 = GuiCtrlCreateButton("Delete", 160, 70, 51, 20)$Input_25 = GuiCtrlCreateInput("Input25", 120, 30, 90, 21)
$Input_26 = GuiCtrlCreateInput("Input26", 120, 10, 90, 20)$Button_27 = GuiCtrlCreateButton("Save Changes", 10, 300, 90, 21)
$Button_28 = GuiCtrlCreateButton("Discard Changes", 120, 300, 90, 20)$Label_29 = GuiCtrlCreateLabel("Label29", 240, 320, 1, 1)
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**New GUIBuilder version 9.3**
GUIBuilder_9.3 info:
- Added "Hint" and "ShowHint" functionality
- Added some extended properties for Edit control
- Added some extended properties for Input control
- Modified extended properties functionality (no more right click -> Properties)
I will probably start helping work on KODA with Lookfar and Lazycat...so depending on how that goes...there may not be a need for GUIBuilder. You can still let me know of bugs if you want.
-Livewire
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Thanks livewire. The KODA Team will be a super one
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Thanks livewire. The KODA Team will be a super one
May I ask what is KODA? I have not seen any mention to it in the forums...
Angel
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Register a new account | 2018-07-18 09:18:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1930166333913803, "perplexity": 11463.700673927846}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590074.12/warc/CC-MAIN-20180718080513-20180718100513-00181.warc.gz"} |
http://freethoughtblogs.com/pharyngula/2012/12/03/lounge-385/comment-page-1/ | # [Lounge #385]
This is the lounge. You can discuss anything you want, but you will do it kindly.
I remind you all: this is not the place for acrimony or argument. You can do that in practically every other thread on this site, but not here.
1. Portia, sporty and glam, pelted with pastries says
Good morning, everybody! Cute snowmen. Looks like a snow-free December ’round these parts. High of 69°F today. In December. In Illinois. What climate change?
2. says
3. rq says
Random mildly amusing story re: Christmas(Winterfest) trees:
The national forestry administration here allows the cutting of one Christmas(Winterfest) tree (this) per family every year, but only in state-owned forests, along roadsides or under powerlines. Cutting trees in municipal or privately owned forests can get you a fine of (the equivalent of) $2000 (CAD or USD), and up to four years in prison. My second Christmas-season here, with my sister visiting, we decided to go tree-hunting in the local forest. The entire time, we lamented the lack of (decent) spruces and in the end decided that that weedy one over there would do. Well, we did three things wrong that day: 1) the local forest is a municipal forest, which we found out after we’d arrived home with our booty; 2) the tree we cut was not the right sort of tree, being a juniper, a protected species (= extra fines for cutting) in the country (but to be fair, the junipers I knew looked like this, rather than this, which can resemble weedy spruces; the thought ‘What a strange spruce, with juniper-like needles!’ did cross my mind before putting the saw to that trunk); 3) apparently, since it’s a slow-growing species, we’d cut a really old and venerable juniper, one likely around since the beginning of the 20th century. Oops! Needles(s) to say, we escaped punishment that year, but every year around this time I get reminders about the extent of my botanical knowledge, and I haven’t lived it down yet. We did have a beautiful tree that year, though. +++ Hello, Portia! Indeed, what global warming? Ha. :P It’s only not snowing here, in contrast to most other years! :) +++ And to those seeking entertainment (Tintin, Asterix, Calvin and Hobbes), see here (should cut to #259 of previous thread, second page). 4. broboxley OT says rq remind me not to go mushroom picking with you :-) 5. Portia, sporty and glam, pelted with pastries says rq, Ha! Tramping through a forest in search of a tree sounds really fun. I still haven’t gotten one, though I had thought to. Seems odd to get one when I live alone and there really won’t be presents hanging around to put underneath. *shrug* I’ve decided that instead of getting SO’s kids something big for xmas (they get so much stuff from other family members) I’m going to stick stuff in their stockings throughout the month. My mom told us an “elf” brought us little gifts like that when I was a kid, and it was fun to see if there was a bulge in the stocking. 6. rq says broboxley There is definitely a reason I don’t do it in the first place. :) I’m good with berries, though – everything red is good, right? ;) But seriously. I’ve taken the time to study berries. Mushrooms? They’re all way too similar for me to risk liver transplantation and death. 7. In Canada, every berry that’s red when ripe is good—but how do you know if it’s ripe? Some pass though red on their way to blue or black. Some berries blue or black when ripe are good and no berries white when ripe are good. Anything green is not ripe. 8. Bro, you need to go mushroom-hunting with an experienced picker, that’s all. 9. Tony ∞2012 recipient of the coronal mass erection∞ says It’s the Argument from Frosty again. Those snowmen seem to be designed. Something more complex than them must have designed these snowpeople. Therefore_____? 10. Tony ∞2012 recipient of the coronal mass erection∞ says true atheists do not eat mushrooms (Yup, they’re on my list too) 11. says Good morning! My car is probably screwed, but I probably won’t know until tomorrow for sure. I have to figure out how much it is worth to me to fix it rather than abandon it an just rent a car for a few hundred dollars to get the rest of the way home. 12. broboxley OT says Markita #7 don’t fall for that old saw, sumac berries are red and you don’t want to eat many of those 13. rq says Markita Umm, I would beg to differ as well – not everything that is ripe-red will be good for you. Specifically, lily-of-the-valley is one example that comes immediately to mind. :) But you’re right, a lot of what’s blue or black when ripe (and good – blueberries, blackberries…) goes through a red phase. There’s a joke that works better in Latvian about blueberries: Q: Why are bluberries red? A: Because they’re green (unripe)! 14. Pteryxx says Joe, this is right after ‘we completely own our cars now!’ isn’t it? IRONY… 15. joed says Can anyone point me in the right direction to find authentic layman science sites. Basically, anthropology, archeology, paleo type human stuff that is authentic. If such sites are still available. Disapointing to read an article and come to a reference from the bible. 16. Beatrice says Lily of the valley is a pretty flower, but I get a horrible headache and have trouble breathing from their scent in a closed space. 17. Portia, sporty and glam, pelted with pastries says Oh, man, Joe, that sucks! === LOTV is my favorite flower scent. Daffodil is my favorite flower for the look of it. 18. blf says Don’t think they’d survive roasting very well. Besides, the screams are an essential part… </snark> Would work as “sashimi”… 19. Bro, you need to go mushroom-hunting with an experienced picker, that’s all. Ah! My wife walks through the woods looking at mushrooms while I look at the birds. She wants to learn the difference, and once tried talking to an obvious expert, out merrily plucking. The phrase “if looks could kill” was never more apt. 20. On TNG Troi rape Off top of my head 1) star baby impregnation 2) telepathically raped by the one of the memory archive species and they even called that one rape in the show 3) raped by Bane and Hellboy possessing Xanatos in Nemesis movie 21. jackiepaper says Just popping in to tell you all how much I’d love to gift you with cookies and beer. Have a happy day! 22. onychophora says The Troi-rape trope in so many TNG episodes was very, very annoying, to say the least. Anyone notice that the incidence really ramped up after Roddenberry died? The ‘soul’ was sucked out of the franchise when he passed. Alas. In other news and notes, I’m FREAKING OUT. I taught an online class last semester, and I had mejor problemos with a couple students. It got bad, involved deans, provost, etc. Aaaaand guess what? One of them (voluntarily) signed up to be IN MY CLASS next semester. Ahhhh! 23. cicely (fair-to-partly-cloudy) says We were able to get Roommate’s stuff moved, Huzzah! although I eventually had to hire a u-haul van to get it in. Bummer! Hope it wasn’t too expensive. Tony: Yeah, that’s just the sort of thing They would pull…if they thought They could get away with it; but it’s so hard to be incognito when you’ve got flames pouring outta your muzzle. Talk about your blown cover! *hugs* for Beatrice. Ready with a sympathetic…eyeball, if needed. Needles(s) to say, *snirk!* I saw that, rq. :) Joe: :( What can I say? OKC is a treacherous place. OK is a treacherous place. Escape while you still can! And hope that it doesn’t follow your trail. Joe, this is right after ‘we completely own our cars now!’ isn’t it? IRONY… More like planned obsolescence at work. 24. Anyone notice that the incidence really ramped up after Roddenberry died? The ‘soul’ was sucked out of the franchise when he passed. Alas. Sadly I disagree. Roddenberry’s vision and rules were ultimately a millstone that hampered creativity rather than promoting it. 25. says People are friendly in Oklahoma. There are worse places to be broken down than here. My credit card is in Declined City, so I can’t rent a car. Fuck. How am I supposed to get to the store to get beer and chips, not to mention pet supplies? UGH. 26. Portia, sporty and glam, pelted with pastries says It’s freaking hard to run a business like an actual professional when you have a landlord who can’t be arsed to fucking give you notice before sending repairmen to interrupt client meetings. /rage. 27. Janine: Hallucinating Liar says I will leave the jokes to people who know more about the goddamn Batman than I do. A cat that looks like Batman. I guess I have one question, would Catwoman want to own ormake out with cat Batman? Sorry. I had to try. 28. rq says Portia and Beatrice I also love the smell of lily-of-the-valley (Diorissimo, anyone?). And I get headaches from just lilies, lily-of-the-valley doesn’t bother me, so I feel for you, Beatrice. :( +++ Improbable Joe That sucks. Poor you, no beer and chips. :( /snark I hope you get everything sorted out soon, though!!! +++ cicely *all innocence* Saw what? *blink blink* 29. Portia, sporty and glam, pelted with pastries says rq I just added that perfume to my “someday” wishlist :) 30. Beatrice says rq, re:perfumes Have you tried “La petite robe noire” from Guerlain? I tried it only once, but I absolutely fell in love with it. 31. carlie says onychophora – ah, but you’ve expanded your syllabus to take into account any and all situations that have arisen lately, yes? So whatever they did before, they can’t pull again. 32. cicely (fair-to-partly-cloudy) says rq: Innocence? Ha! I do not believe it. After all, you are a self-confessed Advocate for Horses. 33. Janine: Hallucinating Liar says Bacon is one of the many memes of this place that I never played along with. Not sure if people will react with horror or find it intriguing. Perhaps both. Bacon Jello 34. rq says cicely No, not half-confessed. I’m pretty sure I confessed completely. But like you siad, it controls my mind, right, so I’m innocent, because I am not under my own control… Beatrice No, I hadn’t heard of that one, but I’ll be sure to check it out! Portia re: landlord My sympathies. :( Craptacular. 35. Beatrice says react with horror yes 36. Portia, sporty and glam, pelted with pastries says Thanks rq. On the bright side, my oven is repaired now, so that your regularly scheduled (holiday baking) programming can now resume. 37. Beatrice says Portia, Great! Make sure to share delicious recipes. 38. onychophora, Joe That sucks (differently for each of you, but still). USB brandy all round. Bummer! Hope it wasn’t too expensive. Looks like$40-50, plus I need to sort some things out with the carsharing outfit.
39. rq says
Portia
Yumyums!! :) Let the cookingstravaganza begin!
cicely
Also, I misread ‘self-confessed’ as ‘half-confessed’. I think it’s because there’s an open can of peas in the fridge. Messing with my reading.
40. cicely (fair-to-partly-cloudy) says
rq
That was self-confessed, not half-confessed. I hear that math is important, so that probably makes a difference.
I will concede that you are wholly under Their control, but it appears as if you are a willing participant in Their unholy machinations, rather than an unwilling victim of Their sinister Mind Control Powers.
41. cicely (fair-to-partly-cloudy) says
rq
Messing with your mind, you mean! See, once you let the Horses in, the peas insinuate their twisty tendrils into your unprotected brainmeatz.
You may not be who you are….
42. Pteryxx says
My credit card is in Declined City, so I can’t rent a car. Fuck. How am I supposed to get to the store to get beer and chips, not to mention pet supplies? UGH.
*whispers* called it. >_>
43. Beatrice says
I had risotto with carrots and peas today. It was good.
44. Portia, sporty and glam, pelted with pastries says
I made Cream Cheese cookies on Saturday at SO’s house, before his oven started emitting dangerous levels of CO^2. (What is it with ovens lately? Who’s sabotaging my cookie-making?) That’s identical to the recipe I used except I used almond extract instead of lemon peel (but lemon ones sound awesome). It doubles well.
45. rq says
cicely
I revel in the mind-control. Means I get to do a lot less thinking myself.
Ah, this is the life…!
Carrot?
46. says
Pteryxx,
You don’t get credit for a kind offer and then 10 pounds of snark… just saying. :P
47. cicely (fair-to-partly-cloudy) says
rq
Only if that sucker is baked as a cake, and covered in delicious cream cheese frosting.
48. Pteryxx says
Joe: idea… maybe you can find a rental agency that’ll let you use a pre-paid credit card? I don’t have a card either, but I’ve used pre-paid for hotels. Then, you just have to buy and activate the pre-paid card. Big-box stores have them, so do banks and credit unions.
(Also, y’know, me driving up there, still on the table…)
49. Pteryxx says
also re #47, sorry. That was supposed to be kinda-sympathetic-I’m-still-here irony, not snark, but I’m not very alert and missed big-time.
50. Beatrice says
Portia,
Looks nice. I’m still not sure what I will be making this year besides snickerdoodles and kuglof. Your cream cheese cookies are a definite possibility. SInce cookies will probably make a Christmas gift to my friend, I’ll have to make a lot of different kinds.
51. cicely (fair-to-partly-cloudy) says
There are a lot of Horses in OK, by the way.
52. Portia, sporty and glam, pelted with pastries says
Beatrice,
Your recipes look yummy, too. I’m baking as gifts, as well. Some for the ladies at the bank who are endlessly helpful with work stuff, and some for the support staff at the other office I freelance at. Etc, etc. Cream cheese ones are both light and rich, weirdly. I love them. Too much, probably;)
53. Menyambal --- son of a son of a bachelor says
rq, thanks for the Tintin. I am downloading now. My computer doesn’t presently extract .rar files, but I can download an extractor program, no problem. (I’m assuming if you have a program to make them, it comes with an extractor, but an extractor’s not included in my old computer—it came with a .zip extractor, though.)
54. Beatrice says
I don’t have a cookie press, so I won’t be able to make all the fancy shapes. Oh well, I’ll think of something, probably use a bag and try to make some nice swirly shapes.
55. says
Engine is blown, they want $2500 to fix it, I don’t have it. 56. says I remember now why I only ever sign up for counseling when I’m feeling the worst. I have no idea how it’s supposed to help me to be told that I need to learn to push through my anxieties, or to be told I need to develop more self-discipline, when I just finished explaining that I didn’t have the energy/willpower to both manage my depression and have self-discipline, and that the current level of “laziness” and disorganization is the balance I’ve worked out for myself between being self-disciplined and managing my depression. especially i don’t know how I’m supposed to be helped by being told I should try to show up to lectures far more regularly, when I just finished explaining that I’d tried that previously and that it only lead to even earlier burnout, and that the sporadic attendance is a coping mechanism without which I can’t make it through a semester at all. grrr 57. Ogvorbis says Threadrupt. I see a certain regular is now back on hir ‘I’m not advocating genocide, just killing those who I think might commit terrorist acts and why are you all accusing me of being a genocidal racist/bigot?’ kick. I have now had three people tell me that I look like Walt from Breaking Bad. Is this a good thing? I got my car back (I am so glad to be back in my car — that Nissan Quest was an epic POS). Happy Saturday to all. 58. ImaginesABeach says Not to brag or anything, but the kids and I have prepared and frozen 16 different kinds of cookies so far, and it’s only December 3. 59. Pteryxx says Holy shit Joe, I’m sorry about the car. 60. Tony ∞2012 recipient of the coronal mass erection∞ says Janine @34: Although I do love bacon, I’m going with HORROR. 61. Ogvorbis says Engine is blown, they want$2500 to fix it, I don’t have it.
Oh. Shit. Damn.
62. strange gods before me ॐ says
I see a certain regular is now back on hir ‘I’m not advocating genocide, just killing those who I think might commit terrorist acts and why are you all accusing me of being a genocidal racist/bigot?’ kick.
Yes, but, it’s already going on over in Thunderdome. Let’s not encourage spillover here?
I have now had three people tell me that I look like Walt from Breaking Bad. Is this a good thing?
I think so! In most episodes, especially after the first season, Walt is a sexy badass.
63. Tony ∞2012 recipient of the coronal mass erection∞ says
You both have my sympathies. So sorry.
****
At our Pharyngula commune, what say we all go horseback riding? I will be cicely’s White Knight and protect her from those sweet little carrot munchers. Then we can have a round of Pea Pelting with Portia…
64. Ogvorbis says
At our Pharyngula commune, what say we all go horseback riding?
Er, what? I mean, I do have some good cowboy boots and more than a couple of cowboy hats, but do you really want to ride the evil things? For pleasure? Then people will think they are useful and want to keep them around.
65. rq says
Portia
Cream Cheese cookies? Anything with cream cheese is a step towards heaven in my (cook)book. It even made pumpkin pie bearable, because now it was cheesecake with pumpkin, not pumpkin pie with cream cheese. :)
cicely
Indeed, I may not be who I am. I may be… you… DUNDUNDUNNNNN!!!
66. says
Hah! I have a credit card!
I thought it had been cancelled, but it wasn’t. I paid the full balance, and I should be able to rent a car tomorrow!
67. Pteryxx says
*cheers for credit-card powah*
68. rq says
Tony @64
We have a Pharyngula commune? Do the horses get homeopathic treatment? I’m all for the riding, but whatever happened to pelting Portia with pastries? We can pelt cicely with the peas. After we eat a cooked carrot with cream cheese icing on top for lunch.
Joe
I hope you manage to get through to your counsellor. :(
Ogvorbis
I don’t watch the show, but… if this is about right, then it can’t be a bad thing.
69. rq says
Improbable Joe
HA! YAY!! Happy for you! :D
*credit-card power* indeed!
70. cicely (fair-to-partly-cloudy) says
rqu
Nonono. I’m pretty sure that I’m Spartacus.
71. cicely (fair-to-partly-cloudy) says
rq‘, obviously.
72. Good evening
Joe
Oh shit, I’m sorry to hear
(((hugs)))
Argh, that sounds like Agony Aunt level to me. I’m sorry that they’re not more helpful.
+++
Nobody mention cookies until I manage to finish those whose dough has been sitting in my fridge since Wednesday and for which I need a special meat-grinder with cookie-gadget which I have to return to my mum in law tomorrow.
But maybe it will be a good distraction from the merry roundabout in my head. My dear family is short of bursting into flames -again.
Some time this week my mum’s psychiatrist will get a letter from us telling him a few things he probably doesn’t know.
So, in that house in which I fortunately don’t live there is my old gran who needs to be taken care of 24/7, my sister who does 90% of the caretaking, my mum who does 2% but who causes an extra 10% of work and cliams to be the one doing all the work, and my dad who picks up the rest of the tab.
My sister is there because she doesn’t want to leave gran, my dad is there because he doesn’t want to leave my sister alone*, and my mum who’s wondering what’s the matter with the rest of us.
*Which is remarkable, because the two of them are about as close as Switzerland and Turkey.
73. broboxley OT says
74. rq says
Giliell
I vote make cookies. Sometimes a bit of manual labour can help calm things down/sort things out in your head. :( *HUGS*
75. Janine: Hallucinating Liar says
Tony, I saw that you left this at Ashley Miller’s blog. I did not want to derail there and you are here often.
I can’t fathom how a parent could do such a thing to their child.
I guess I have to agree that I cannot fathom this either. But it happens all the time. Think of all of the homeless LGBT youth, most were thrown out of their childhood homes by their parents. While many parents do come around to accepting their children, many will allowed learned behavior to destroy relationships and lives.
I am sure that you are aware of all this but, damn, I had to say something.
76. Tony ∞2012 recipient of the coronal mass erection∞ says
Janine:
It would have been better for me to say that I cannot understand it. Rejecting a loved one on the basis of who they love is incomprehensible to me. You are correct, I am more than aware of how some parents do not change.
Before he died, M told me his father told him point blank that if any of his kids turned out gay, he would shoot them.
77. rq says
cicely
Clearly, if you say you are Spartacus, then you can’t be Spartacus.
Clearly.
78. says
I am most certainly NOT Spartacus! How you like me now?
79. Menyambal --- son of a son of a bachelor says
Improbable Joe, you might want to get a second opinion on your car repair. I’ve had a few times where strange mechanics told me that I needed engine work, but all I needed was a new radiator cap, or I when I managed to get it home with duct tape. (There’s also been a time I just left the car to die.) I am glad you have a credit card. 80. rq says Imrpobable Joe I like you anyway. And you just might be Spartacus…. 81. Tony ∞2012 recipient of the coronal mass erection∞ says rq: we joked earlier this year about forming a Horde commune somewhere away from the sexism, racism, homophobia etc of both the ‘Net and IRL. Last I checked, this fantasy (which really is just that, and not one I truly want…who wants to be isolated from the rest of the world? As a place to escape to and reboot/relax–> good thing) is in Alaska. **** Ogvorbis: Yes, we will have a blast riding horses. You can rid a pony instead if you want. 82. ImaginesABeach says You can rid a pony instead if you want. I’m guessing cicely will only be happy if we rid ourselves of all ponies (and horses). 83. says Menyambal, I know enough to know that the engine was pretty bad off, and somehow lost all the oil all at once, so the diagnosis seems not-unreasonable. Beyond that… what can you do? I’m going to get a cheeseburger and some onion rings. 84. rq says No, ImaginesABeach, the real question is, rid a pony of what? Perhaps the pony would like to be rid of cicely? Tony I’d join that commune, and I’d bring the family, too. Alaska seems fine, I’m a winter person, but… No other options? That’s still the US (technically, even though you can see Russia from it). 85. Ogvorbis says Good to hear about the credit card. Worst. Move. Ever. Maybe. I remember trying to poop after being on morphine for ten days and that was a really really bad move. :) You can rid a pony instead if you want. Good idea. If I ride a pony, when I fall off it won’t hurt as much. ======== 86. Tony ∞2012 recipient of the coronal mass erection∞ says rq: Of course it must be the U.S. we are like, TOTES the most awesomest, amazingest, bestest, most successfullest, goodest country in the world… 87. So, I have 5 baking trays of grandma’s Spritzgebäck. When I made them the first time last year I was in awe at the apparent ease with which grandma used to produce endless rows of S’s and O’s. I mostly made I’s. 88. Beatrice says Giliell, The last time I made something like that, I tried to squirt the dough into a round shape. After I brushed them with chocolate, they ended up looking like little piles of shit. At least you went for Is. Note to self: don’t make the same mistake with Portia’s cream cheese cookies 89. Jadehawk I wonder, have they given you a counselor, or an actual psychiatrist, i.e. someone with medical training? In either case, they’re wretchedly failing at their job, and you have my sympathies. Joe At least you’re able to finish your move. I wish I could help. That said, this has been an amazing adventure for me; after all, adventure is someone else having a really awful time of it somewhere far away, right? *ducks* rq Cream Cheese is an abomination, and I can’t conceive why anyone would ruin perfectly good cookies by putting it in them. I made cheese-filled sourdough rolls last night, myself. I was going to fill them with bacon too, but the bacon ends and tips were frozen, so it’ll have to wait until next time. 90. cicely (fair-to-partly-cloudy) says rq, you are semi-transitively Spartacus. The Pony wants rid of me, I want rid of the Pony—best for us both that we never meet in the first place. 91. says Pteryxx: also re #47, sorry. That was supposed to be kinda-sympathetic-I’m-still-here irony, not snark, but I’m not very alert and missed big-time. No worries. It is all going to work out in the end, plus or minus one more night in this hotel. I may need 24 hours to secure a one-way vehicle. 92. rq says Ogvorbis By the way, did you get Asterix alright? Menyambal About the .rar thing: I’ll try to remember for the next time (if there be one), because I can just as easily ZIP the files as RAR them. :) But I’m glad you’re looking forward to the reading. Giliell It sounds delicious!! Beatrice HA! This is why I have never sprinkled anything with chocolate. I have yet to try making formed cookies (I’ve only ever made cookie-cutter ones). I’ll make a note not to sprinkle with chocolate. Tony Right, you own the world. I keep forgetting. Dalillama Cream cheese? An Abomination?? You can’t possibly be serious. cicely Make a pony happy? You? You? Best not to meet, indeed. We’ll put you on the donkey, then. Mule, if you prefer – they’re bigger. +++ Tomorrow I dig out recipe for bacon rolls, because there have been too many cookies on this thread. Time for something healthy. With bacon. +++ Good night to everyone! A round of hugs, cookies, happy thoughts, encouragement, as appropriate! 93. Beatrice says rq, Do sprinkle or brush with chocolate! Just not after you’ve made swirly round cookies with a peak in the middle. 94. Beatrice says rq, good night! 95. Esteleth has eaten ALL the gingerbread! Suck it! says Holy hell am I threadrupt! Thanks for the links to Asterix and Calvin and Hobbes! ^_^ A few comments: Tea I went to Teavana not long ago. I bought 50 of tea in a sampler. Conclusions thus far: “Golden Monkey” is delicious. “Yunan Golden Pu’eh” is intriguingly delicious. Their English Breakfast is an ordinary English Breakfast. Good, as EB’s go, but rather blah. Car Insurance So Progressive has decided that the proper reward for 12 months of no tickets, incidents, claims, or anything, plus paying everything on time, is to jack my bill up. Did some googling, discovered that Progressive is vastly overcharging me, compared to what Geico and Allstate have to offer (seriously: that “15 minutes will save you 15% or more” thing for Geico could get me saving 57%). So I said to myself, “Okay. My insurance agent is an independent who deals with 10-15 companies. I’ll go see him, and see what he can get me. After all, many of my problems last year were that I was a first-time car buyer and hadn’t been listed on anyone’s insurance since my parents dropped me 6 years previously, so I was an unknown quantity.” His hours: M-F 9-4:30. Closed Sat and Sun. Which means that if I’m going to go in I have to go during work hours. (╯°□°）╯︵ ┻━┻ 96. says Ogvorbis, One time, in the Marine Corps…. I was out in the field playing GI Joe in the woods, and I went 9 days without pooping. I think they design the field rations to discourage diarrhea but DAMN. When the dam burst, I thought I was going to die. Good times !! Speaking of which, being back in Oklahoma brings back memories. If I had a car and money, I know a few strip clubs where I could be the sad old pathetic person. 97. Tomorrow I dig out recipe for bacon rolls, because there have been too many cookies on this thread. Time for something healthy. With bacon. Recipe? Make roll dough and wrap it around a glob of cheese and bacon before you proof it. (cook the bacon first). How much more of a recipe is called for? 98. Esteleth has eaten ALL the gingerbread! Suck it! says Oh, also: How is it that it took me until I was 27 years old to realize that pomegranates are fucking delicious?! 99. Ogvorbis says By the way, did you get Asterix alright? Haven’t been able to get into that email. Sometimes I wonder if it is ever possible for me to not fuck something up. Did some googling, discovered that Progressive is vastly overcharging me, compared to what Geico and Allstate have to offer (seriously: that “15 minutes will save you 15% or more” thing for Geico could get me saving 57%). I have geico. And from when the deer hit us to when I picked up the car this morning they have been fantastic. And going from a ‘special deal’ through the union to geico saved me about 700 a year. One time, in the Marine Corps…. I considered joining the USMC. Dad is still recovering from his stint back in the 1950s. They wouldn’t take me because I knew both of my parents . . . Nine days? Damn. When I’ve had MREs at fires, I’m lucky if I can hold it in for 1/2 hour. 100. says Joe’s bacon roll recipe: Cook bacon until not quite done. Roll it up. Finish cooking. Eat. 101. BTW, today in the lecture a young couple sat behind me. The guy raised all of my red flags and the hair on my neck. If it had been any good I would have turned and told the young woman to drop that manipulating dipshit. He was constantly negging, telling her in the “stupid little woman” voice that noo, dearie, the Hobbit takes place before the LotR, you know when Bilbo, Frodo’s father (!) sets out to find the ring! And oh I’m so sad you can’t sleep over at my place tonight and yes I know where that is stop talking, while all the time having his arm around her neck. You know, not around her shoulders, but really around her neck. 102. says Ogvorbis, no talking shit about the Marines, elsewise I’ll have to make ridiculous cyber-posturing comments or something. :) The USMC is an interesting mix of us low-class folks though. Some people, you assume they joined for the free dental, but I also worked with some obscenely smart people, that managed to make me look like just a normal-level genius. One roommate apparently managed to get kicked out of the UK and his dual citizenship suspended/revoked when he went to live with his mom after discharge, for too many bar fights in his first few months there… but he had most of the relevant manuals all but memorized, and could work a slide rule like a Heinlein hero. He could also pass the physical fitness test running backwards (and did!) and had a back so broad you could project movies onto it. 103. Ogvorbis says The USMC is an interesting mix Not just Uncle Sam’s Misguided Children. The Army, Navy, Air Force and Coast Guard are an amazing mix of people. One kid I went to high school with has a PhD in nuclear physics paid for by the Navy — he’s been in since 1984. 104. says have they given you a counselor, or an actual psychiatrist, i.e. someone with medical training? counselor; pretty sure the actual psychiatrists cost actual money to talk to. though I do have an appointment at the actual health clinic later this week 105. says Ogvorbis, My father-in-law was a submariner in the nuclear fleet from basically the birth of nuclear power (he lied about his age and enlisted at 15) and up until earlier this year he has been doing consulting work for between 90 and 120 an hour all over the country. Poor and no formal education but just the smartest man in almost any room. 106. Ogvorbis says Joe: One of the smartest people I ever met was a VW mechanic down in Maryland. He was a member of one of the more conservative Christian sects (not Mennonite, not Amish, but the same general idea) and he loved history. But it annoyed him when translations were ‘off’. So he taught himself to read German, Italian, Latin, Hebrew, Polish, Russian, Yiddish, Portuguese, Spanish, and Gaelic. Couldn’t speak anything but English and German, but he could read those languages fluently. The bookshelf in his garage was one-third VW manuals, one-third dictionaries and one-third history books in lots of languages. His ‘specialty’ was pogroms, crusades and religious wars. He had a 7th grade education. And was an incredible VW mechanic (he could rebuild a VW air-cooled engine and have no parts left over). 107. Tony ∞2012 recipient of the coronal mass erection∞ says Long Post Ahead. Crossposted from the Thunderdome:Ok, Internet access is MINE. MINE. MINE. No one else may partake of it. :0 In all seriousness, when scholars look back into the mists of time looking for evidence of a teal deer, this post shall be it. No, I’m not full of myself. Yes, I am giving warning that this post will be long. Do not despair. There shall be paragraph breaks. How religion fucked my sex life I sat across from him, not five feet away, yet it felt like a vast gulf between us. I could see the pain in his eyes. You could cut the pain and anguish with a knife. He sat there in that state just before crying. You know that state. It’s the “I’ve got to be strong. I can’t give in. I can’t show this emotion. If I break down crying now, I will be a complete mess” state. I sat there wishing with every fiber of my being that I could do something to help him out. Yet there was nothing I could do other than offer my advice and my support. So I told Jim (obviously this is not his name, but since he is in the closet, I’m not about to out him in any way, shape or form): “There is nothing wrong with you. You are a good person. What we did was consensual. We both wanted it. No one was hurt. There is no need to feel guilty or shameful. I enjoyed myself. I would like to do it again. But I can’t do that until you are more comfortable in your skin. I can tell the pain that you’re in. You are struggling tremendously and I hate that. I hate that you’re having to choose between your faith and your very identity. I wish you could know what it is like to not have that guilt. I wish you could know the freedom that comes with accepting and being happy with who you are. I’m not saying I’m better than you. I don’t believe that. No one is better than anyone else. But I do feel that I am more comfortable in my skin than you are currently. I look at you and I see the problem. You’re struggling with your religious belief and currently, that belief is winning. And you’re in pain. I can’t command you-nor would I want to-but I hope that you don’t lose my phone number. It seems to me that you don’t have many people to talk to. Few, if any people to open up to and discuss what’s going on in your head, without fear of judgment. I want you to know that if you need to talk…if you need to cry…call me. Text me. I will listen. I won’t judge you.” With that, I left the hotel, with my head hung low. Thursday of last week, I was bored and searching around online for something to do. At that point (and currently), I’m struggling financially. The job that I have is unable to provide enough money to pay my bills. Hell I’m writing this on my laptop from a bar where Wi Fi is available because my cable (thus my Internet access) has been cut off. I have no clue when I will be able to afford to reactivate it. Meh. First World problems. Anyways, I was checking out Adam4Adam, which is an online gay site for guys meeting guys. It serves to bring men together in search of dating, sex, threesomes. Whatever the heck they’re looking for. By and large, I’ve gotten past the desire to hook up for sex. At 37, I’m *beyond ready* to have something meaningful with another guy. But I haven’t had sex in almost a year. Enter Jim. I got a message from him saying he was intrigued by my profile and pictures (in short, my profile mentioned my appreciation for logic, reason, science and freethinking). He, however, had no pictures. I politely told him that while I appreciated the compliments, without a picture, I had no way of knowing if I was attracted to him. His response was to say that he was in the closet and was unable to come out at the time. I responded back that I take no issue with that, and that I wouldn’t judge him because he wasn’t out. I let him know that I’m well aware that people have their reasons for either staying in the closet or coming out of it, and given that I am not him and I’m not aware of what’s going on in his life, it is not my place to judge his decisions (even if I knew all the details-it is still not my life, it was his). After exchanging emails, he decided to send me pictures. To be honest, I was pleasantly surprised (in my experience, those without pictures for me to view don’t turn out to be my type): I found him attractive. We agreed to meet up Saturday night. He informed me that he would rather meet at a hotel instead of my house because even though I seemed like a nice guy, he couldn’t be too sure. I took no issue with that. It’s an entirely reasonable position. Saturday rolled around and I met him at a hotel here in town. It was clear from the moment we entered the hotel room that Jim had not had any attention or contact in some time. He later told me that he hadn’t had any sexual interaction since the summer of 2011. Damn. Fast forward through the fun. We finished up and I looked at him and his demeanor had changed. His face was sunken. His head was tilted down. He looked lost in thought. I asked him what was wrong. He told me that he felt guilt. He felt ashamed. When I asked why, he told me it was because we did something he wasn’t supposed to do. Even though I *knew* what he was referring to, I asked anyways. He said because of his religious beliefs-Christianity to be exact-that what he did was wrong. Tears didn’t appear to be far behind. Interlude: I’ve never had any deep religious conversation with someone in meatspace. The ensuing conversation took up more time than the sex. end Interlude We hadn’t talked much about our chose occupations prior to meeting. I mentioned that I was a bartender, but he didn’t talk about his job. As we began chatting, I asked him what he did (at this point, given the guilt that I saw on his face, and the shame he felt, I suspected he was a priest). He asked me not to make fun of him or to laugh and I promised not to. He told me he worked at a daycare center. I looked at him and said “so what”. I let him know, in no uncertain terms that there was nothing wrong with that. There is no reason to shame someone for their job. If that’s what he’s chosen to do, who the fuck am I to judge him for it. Moreover, when he told me that he enjoys his job, I told him that I thought that was great. There are many people who do NOT enjoy their job. People that are miserable. That he *has* a job and it’s one that he enjoys is a good thing. I let him know my opinion of people who judge others based on their job. They can suck the shit out of my asshole. Moving on, he began to give details of his life and upbringing (it turns out he’s familiar with the city in Alabama that I lived in before I moved to Florida; small world, eh?). He waffled between telling his stories and feeling shameful. I made a point-multiple times-of letting him know that he did nothing wrong. No one was hurt. We both wanted to have sex. We both enjoyed ourselves. What is wrong with that. Of course, he replied with “it’s against the Bible”. After a short time, I told him I was an atheist. It didn’t really seem to affect him much. No shock. No derision. No criticism. No judgment. I was rather surprised. Over the course of our conversation, I was able to explain many reasons why I am an atheist. I was able to channel the wonderful, intelligent, witty Greta Christina when I told him that supernatural explanations for the world have consistently been replaced by scientific ones over the course of human existence. I told him that I felt Christianity does not have the market cornered on religion…that there are many other religions. I told him that I don’t believe in *any* of the thousands of gods that humanity has created (and was able to mention that he is an atheist WRT all religions BUT one). He was unable to offer any proof of his god. He was unable to discuss why he believed what he did. I mentioned that one of the reasons many people have their religious beliefs was due to indoctrination from youth. He confirmed that he never really decided to be a believer, but rather, that it was just always there. It turns out that Jim is one of those believers that *has* read the Bible. I asked him point blank-twice-if he had read the Bible. He said he’d read it cover to cover. Given his responses, I’m inclined to believe him. He was able to quote various portions of the Bible (not unlike joe 4060). He was able to locate-quickly-passages in the Bible that supported his position. We actually talked specific stories in the Bible. When I brought up how genocidal his God is, we discussed the story of the flood of Noah. I flat out told him that it’s ridiculous that we criticize Adolph Hitler and the Nazi’s for committing genocide, yet God is able to get a free pass. And that it doesn’t matter what the reason was. The end result was that countless people…innumerable living beings-from plants to animals and bacteria-were killed in a worldwide flood because of God. I told him that it makes *no* sense for God to punish humanity for actions that he created us to do. I asked Jim if God was omnipotent, omniscient, omnibenevolent, and omnipresent. His response was yes. To which I said, “why the hell did he punish humanity for doing something he created us to do?” No answer. I followed up with “It makes no sense that God punished humanity for doing the things he knew we were going to do…things he created us to do…things he knew in advance that we were going to do.” Now don’t get me wrong. Jim didn’t sit there and look gobsmacked as I presented all this logic and lack of evidence. He was refuting. He made some counter examples to my criticisms of the Flood. He even made some interesting observations about *logic* that I, in my lack of experience, was unable to counter. He made an “argument” that I was countering his faith with logic, but that I was using logic on the same basis he used faith. I.E. that I was using logic as some sort of foundational principle, without being able to explain *why* logic is better than faith. I actually had to bow out of that argument. I agreed that logic makes more sense than faith, but I wasn’t able to explain why arguing logically makes more sense than arguing from faith. Again, this was all in the wake of having sex. I wasn’t exactly prepared to make arguments for atheism. Despite being at FtB for a few years and listening to the great argument provided by the bloggers and commenters here. For a few seconds, I felt like a failure. It didn’t last long. I told him that I didn’t feel confident enough to pursue that line of reasoning. I couldn’t argue his point. I conceded. Only to my lack of knowledge. (at this point, I was metaphorically kicking myself in the ass because I felt I *should* have been better) At one point he brought up…THE ARGUMENT FROM COMPLEXITY. He started saying “Imagine if you were walking along on a deserted island and you came upon…” To which I said “oh hell no! You are not bringing up the Argument from Design”. He said that’s what he was doing. It’s so damn funny, because I was exploring that very argument last week. I was able to refute his point. I was able to point out that if a watch requires a more complex designer to create it…and that creator is God…then something more complex had to design God. Of course he issued the standard response “God is eternal and requires no creator”. My response was that if it’s possible for something to exist without a creator, why can’t it be the universe. Crickets chirping. We also discussed other Christians. He couldn’t understand how some xtians were able to rationalize their beliefs and their sexuality. He felt they were trying to have their cake and eat it too. He even told me they weren’t *true Christians*. At which point, I yelped “Oh no you didn’t pull an No True Scotsman Fallacy??!” He was unfamiliar with this. My brain kicked in enough to pull out my cellphone and bring up Wikipedia’s definition, which I read off to him. He didn’t have much to say. We discussed how religious beliefs are justified by people for a variety of reasons, but no reason is superior to another, especially since there is no proof of any of them. Proof was something else he wasn’t able to offer. When I asked him why he believed in his religion but no others, he had no defense. At this point, I need to mention that he frequently displayed uncertainty about his beliefs. Sometimes he would say “I believe in the Bible” or “I believe in the truth of the Bible”. Other times, he would say “IF I believe what the Bible says is true.” Those times were quite telling. It told me that he wasn’t completely confident in his beliefs and was searching for a way to retain his beliefs while being gay. I think I shocked him more than once. At one point, he attempted an analogy. He tried to compare our enjoyable night or pleasure with the actions of a serial killer. Yeah. You read that right. I shut shit down FAST. I told him that the actions of a serial killed have a negative, detrimental impact on other human beings. Serial killers KILL people. What we did hurt no one. There is no comparison. Moreover, the very comparison is wrong and insulting. This was the only time where I came across as trying to “know better”. Because making that comparison was FUCKED UP. He accepted that it was a faulty analogy and backpeddeled. Which was good. I was saddened further when I noticed him grabbing his clothes. He had informed me that he’d never woken up to a guy and how much he looked forward to doing so. He even asked me when I arrived if I wanted to. My response was “of course”. To see him gathering his clothes, I could see how much things changed. I asked him if he wanted to leave and his response was yes. I didn’t try to stop him. I didn’t try to change his mind. I just reminded him that there was nothing wrong with what we did. I reminded him that his God created everything and nothing happens or will happen against his will. I told him “Remember, you turned out the way your God wanted.” I also told him literally, that everything we talked about cemented in my mind that activism is where I need to focus my energies. To see him sitting there struggling…nearly crying… …I’m not joking when I say that even as I type this, I’m having a hard time NOT crying. I told him that I feel religion is bad. That while religion has some good aspects to it, I feel that religious belief is detrimental and hurts humanity far more than it benefits us. I told him that because he was able to bring things down to Earth…that he was able to make things more personal for me in a way that I’d never done before. It was different this time. Despite this, I made a point of saying that while I’m against religion, I want to persuade people out of religion. I told him that I don’t want to force or coerce people out of their beliefs. I want to convince people to abandon their superstitious beliefs. I want to do so with no bloodshed. No violence. No manipulation. I just. want. to. talk. I hadn’t discussed religious beliefs with someone THIS deeply before. I hadn’t been able to see the harm in religious belief on a personal level before this. Now, I had. Now, I was able to see how fucked up religion makes people. Now, I was able to see, without any doubt, that I need to do my part to rid the world of religion. **** At various points during this conversation, I was having flashbacks to the discussion in the Thunderdome with joe4060. I even referred to it a few times. So many of the regulars here are so good at arguing their point. They have the scientific knowledge. They have the experience arguing. I’m not there yet. I want to be one day. I hope that at some point in the future, I’m able to refute the argument I faced this weekend with the strength, knowledge and confidence I see from so many of you. Fuck. I’m about to cry again. This site has changed my life. This weekend has given me a renewed focus and drive. There are so many people to thank. So many influential people. Thank you PZ Myers. Thank you Ed Brayton. Thank you to all the regulars at FtB. Thank you to all the bloggers at FtB. You have all made a difference. Never forget that. I know I never will. 108. Jadehawk Hopefully they can be a little more helpful there. I’m not at all convinced that ‘counselors’ are actually any more competent or useful for this type of thing than bartenders. Maybe less; the barkeep can at least pour you a drink. 109. Menyambal --- son of a son of a bachelor says Uncle Sam’s Confused Group had some interesting mixes of people. At on place, we all wanted to take some test or other, most of the guys just to get the day off. I wanted to take it because, hey, it was a test. The guys somehow found out my score, and I got some odd respect after that. But one of those guys had a Civil War replica cannon, and could tell you everything about it and every engagement the original had been used in, and could serve and fire that thing like a machine. I still remember the day he trailered it up to a very secure Coast Guard base and said he was there to visit me. 110. Esteleth has eaten ALL the gingerbread! Suck it! says I wish there was a way to save comments or like them or something. Because wow, Tony, that was amazing. All I can say is that I hope you planted some sort of seed in his mind that will help him. And that maybe someday he’ll call/email you. 111. says the boyfriend bought me a full set of dice (d4-d20) made of chocolate i wonder how well-balanced they are 112. Menyambal --- son of a son of a bachelor says Hugs for Tony. 113. Tony ∞2012 recipient of the coronal mass erection∞ says Esteleth: Thank you. My fondest wish is that Jim is able to attain the inner peace that he is searching for. 114. Ogvorbis says the boyfriend bought me a full set of dice (d4-d20) made of chocolate Just don’t use them in a really hot game of D&D. 115. says Tony, Easily comment of the month. You have my sympathy and my empathy and my best wishes… and most of all my thanks, for being brave and strong enough to share that with us. 116. opposablethumbs says I already said what I think over at the ‘dome, but there’s no harm in repeating – that I think you’re a really great person, Tony, and that Jim was lucky to meet you. And I hope that even if he can’t take it all in now, someday he manages to really hear everything you had to say to him. And that you probably gave him the best and most needed support he ever got in his life. And also ♥! 117. Nerd of Redhead, Dances OM Trolls says Just don’t use them in a really hot game of D&D. Dang, I don’t think I can top that retort. Have some swill…. 118. says OK. So I logged in recently after being away for a long time and, on the first page, I saw an ad from Christian Mingle. You can see it here . Has something changed? 119. carlie says made of chocolate i wonder how well-balanced they are Well, as long as you also eat some fruits and fiber-rich foods with them, it would be perfectly balanced. ;) Sorry the counselor sucked – if you have an appt. with someone else next, you can tell them exactly how much the first one sucked. If their triage people don’t even know what to do about depression, they’re training them wrong. Tony, I commented at the other thread, but I LOVE YOU YOU’RE AWESOME. Oh, wait, did I write that out loud? Joe, so sorry about the adventure. Now I feel like crap complaining about my car window and how I have to get a new tire this week. stupid fucking transportation. I bought this for my cousin’s baby. I’m not sure what the animal is – it looks kind of like Pooh, but also kind of like a hybrid between a seal and a penguin, but it does look festive. The site is very God-heavy, but eh, it had the cutest stuff. I bought some ornaments last week from another online store, and when they came in I realized the logo was “CHRISTmas store”, and there were Bible verses all over everything. I was annoyed that I hadn’t noticed that online, but was amused because they sell beer and margarita ornaments. Keeping Christ in Christmas, indeed. 120. Tony ∞2012 recipient of the coronal mass erection∞ says @121: Nothing has changed. 3rd party advertisers. FtB has no control over the ads. Still, it is funny to see xtian advertisements here, no? 121. thunk, cold air advection says Portia: Yes, it is TOO DAMN HOT. I want snow. Now. Tony: Well done, indeed. Very thought-provoking. Joe: Sorry about the car. :( 122. birgerjohansson says Boardgame Review: “Beer & Vikings” http://scienceblogs.com/aardvarchaeology/2012/12/02/boardgame-review-beer-vikings/ — — — — — — — — Tony That you for your comment. P.S. I like horses. That is why I don’t sit on them. — — — — — — — — Having a conscript army means there is a full mix of talents in any group. It is good to have a car mechanic or a professional driver along with you. The diversity was amazing. Where I did my eleven months in the Swedish air force I met several who were familiar with science fiction authors that were “obscure”, such as Stanislaw Lem. One of the guys who served at the same meterological office after me eventually became one of Sweden’s most successful musical artists. — — — — — — — — — — — — Ogvorbis “But it annoyed him when translations were ‘off’” Once I learned a smidgeon of English early at school, I started reading English-language detective paperbacks. I unintentionally picked up enough skill to routinely read stuff in the original language, important if you want to really appreciate the skills of Pratchett and others. There is only so much even the best translator can do. — — — — — — — — I have come to realise that I was priviliged to grow up where I did. Big forests within walking distance, a big river with rapids bordering the farm, yet close enough to a sizable city for my parents to drive there in just a quarter of an hour. (plus, 3000-year-old rock carvings at the river, but I did not know it back then). But I never learned to tell which mushrooms were safe. 123. ednaz says Tony – Thank You for sharing that. You are an amazing person. *hugs* and <3 124. Tony ∞2012 recipient of the coronal mass erection∞ says thunk, birgerjohanssen, ednaz: Thank you. **** My self worth has been in the toilet lately. There have been times that I feel like I am taking up space on this planet better used by someone else. Then come those times where people respond to something I’ve said or done and their responses fill me with renewed vigor. Too often, I’m stuck inside my head, feeling worthless or useless. Support from others reminds me that I can and DO have a positive impact on people around me. To be able to help others in some way…what more can I ask? 125. Ogvorbis says Comas can save lives. It can be the difference between ‘Let’s eat, Grandma,’ and ‘Let’s eat Grandma’! 126. Esteleth has eaten ALL the gingerbread! Suck it! says Comas are useful, and so are commas, Oggie :p 127. Ogvorbis says Comas are useful, and so are commas, Oggie :p er, umm, all hail Tpyos? 128. broboxley OT says Tony, you seem like a good person to me. Hopefully your self esteem will catch up with the high regards that others hold you in. 129. Ogvorbis says Sometimes I worry about Boy. This just came out of his mouth: “I wonder if you can deep fry mayonnaise? 130. Tony from Thunderdome: I’ve been feeling useless lately. Not being able to pay bills or hang out with friends or take vacations…having to ask for financial help from my parents–> it has been stressful. I’m right there with you, man. *Hugs* are all I can offer, though. My self worth has been in the toilet lately. There have been times that I feel like I am taking up space on this planet better used by someone else. You kick ass, Tony. You’re a caring and compassionate person, and you make the Lounge (and other threads) brighter by your presence. BTW, since your bday is coming up/recently passed, I thought I might send you a print from L’s photography portfolio, if there’s a way I could get your address. @110 Hell of a post. Thank you for sharing that, and I’m offering both props and sympathies. 131. Nerd of Redhead, Dances OM Trolls says Dang, tell me AGW isn’t happening…second night in week where the temperature above 60 ºF at 8pm in early December. 132. Portia, sporty and glam, pelted with pastries says thunk Portia: Yes, it is TOO DAMN HOT. I want snow. Now. You hush, or I’ll drive the three hours to Chicago just to scowl at you in person. Harumph. Ogvorbis Er, what? I mean, I do have some good cowboy boots and more than a couple of cowboy hats, but do you really want to ride the evil things? For pleasure? Then people will think they are useful and want to keep them around. Yes. Riding horses is nice. I miss it. rq Cream Cheese cookies? Anything with cream cheese is a step towards heaven in my (cook)book. It even made pumpkin pie bearable, because now it was cheesecake with pumpkin, not pumpkin pie with cream cheese. :) Mmmm yes the rich goodness of cream cheese makes anything awesome. I made an excellent pumpkin cheesecake last year. This year I just didn’t have the energy. Ah well. I’m all for the riding, but whatever happened to pelting Portia with pastries? OM NOM NOM Pelt away! Tony *hugs* and congratulations on conducting yourself wonderfully. It seems like it came out a little disappointing for you, but you did excellently. Thank you for sharing that with all of us. I’ll add my voice to the chorus that thinks you are a stellar human being. I enjoy sharing a thread with you. Your thoughtful comments are heartwarming, and your cheerful comments are, well, cheering. Thanks for sharing your great personality and person with us. 133. carlie says Sometimes I worry about Boy. This just came out of his mouth: “I wonder if you can deep fry mayonnaise? The answer is: of course you can, if you try hard enough. After all, if you can deep fry kool-aid, I think you could deep fry anything. 134. thunk, cold air advection says Nerd: Yeah it’s crazy all right. One hot day does not make a pattern, but a whole string of them all year for 50 years do. 135. Esteleth has eaten ALL the gingerbread! Suck it! says Whargarble. My brain is all buzzy with thoughts and bouncy ideas. I’ve been trying to unpack a single paragraph from God Emperor of Dune and am getting nowhere. Anyone read them and willing to hash this crap out? 136. Ogvorbis says After all, if you can deep fry kool-aid, I think you could deep fry anything. Boy now wants to make deep-fried Jager Bombs. He is in college (Russian history major (yeah, that’s useful (says the guy who majored in modern European military history))) so I guess it makes sense. 137. Ogvorbis says Whargarble. My brain is all buzzy with thoughts and bouncy ideas. I’ve been trying to unpack a single paragraph from God Emperor of Dune and am getting nowhere. Anyone read them and willing to hash this crap out? Which paragraph? 138. After all, if you can deep fry kool-aid, I think you could deep fry anything. I question the claim that you can meaningfully deep fry koolaid. People mix koolaid powder into hush puppy batter and deep fry that, but those are koolaid flavored hushpuppies, not deep fried koolaid. 139. Esteleth has eaten ALL the gingerbread! Suck it! says Which paragraph? The one where Leto explains to Duncan why the Fish Speakers are all women. 140. Ogvorbis says The one where Leto explains to Duncan why the Fish Speakers are all women. Gong upstars to chek my own bok. 141. says Tony/#110: Awesome doesn’t do you justice. Doesn’t even touch you. I wish now for a better world. You, at least, deserve one. 142. Ogvorbis says I know we probably have different editions, but what page are we talking about? 143. cicely (fair-to-partly-cloudy) says Ogvorbis, no talking shit about the Marines, elsewise I’ll have to make ridiculous cyber-posturing comments or something. :) Seconded. (And no, I’m not blind to the scandals; just narrow your brush, ‘mkay?) My father was a Marine, my mother was a Marine, my brother and sister were Marines, my nephew is a Marine this very minute (if not, IMO, a sterling example of one), and I’d probably have been a Marine if the recruiter hadn’t told me I wouldn’t be allowed to drive a tank. (Or pack a rifle in the infantry; I managed to restrain my disappointment, there.) Diss indiviudual Marines if you must (and my nephew is a sociopathic little fink, and I won’t hear any different, and you may diss him at your pleasure), but not the whole Corps. Tony: I commented on your teal deer in the [Thunderdome]. I still remember the day he trailered it up to a very secure Coast Guard base and said he was there to visit me. :) :) :) Chocolate dice….*drooooool* Save vs. Nomnomnom at -4. 144. Ogvorbis says Diss indiviudual Marines if you must (and my nephew is a sociopathic little fink, and I won’t hear any different, and you may diss him at your pleasure), but not the whole Corps. note to self: Self, no more humour is allowed that is directed in any towards, or even near, the USMC. Got it. 145. cicely (fair-to-partly-cloudy) says Good. ;) 146. cicely (fair-to-partly-cloudy) says Esteleth, I’ve read it, but I’d have to see the paragraph in question. 147. Ogvorbis says cicely: please not that I did NOT ‘dis’ the USMC. Joking about is not the same as disrespecting unless you are coming at this from a direction my stupid little US Army 98GL brain cannot comprehend. 148. cicely (fair-to-partly-cloudy) says Ogvorbis, it is important that you remember at all times that I am a completely humorless person. (And that Horses are Eeeeeeevil.) 149. cicely (fair-to-partly-cloudy) says More seriously (because I am without humor), I feel that my nephew’s being in the USMC is an example (one of many) of how having quotas in recruiting can be a Massively Bad Idea. Religiously and racially bigoted, and wanted to join up, as he said, so he could kill people. I cannot diss him enough. But I’m willing to try…. 150. Esteleth has eaten ALL the gingerbread! Suck it! says I know we probably have different editions, but what page are we talking about? Page 104 of the 1981 Putnam hardback. Duncan is having breakfast with Moneo, who paraphrases the explanation (couched in endless “As Lord Leto says…”) 151. Ogvorbis says “The Lord Leto says that when it was denied and external enemy, the all-male army always turned against its own population. Always.” This one? 152. Esteleth has eaten ALL the gingerbread! Suck it! says Yes. And the bit that follows about rape. 153. Ogvorbis says Well, the part about the adolescent attitudes, including the strongly sublimated homosexuality, within the military certainly seems right to me (based on my limited experience and studies). What are you wondering about? 154. Richard Austin says Esteleth: Erm, you aren’t going to like the answer. I’m not sure if it’s all in that paragraph, but the whole reason why Leto’s army is led by women is that a man-dominated army leads to homosexuality and violence. Women are the ones who have to “pick up the pieces”, as it were, so they tend to be less violent. Putting them in charge means that the army will avoid violence if possible. Additionally, he gets to “marry” all of them and bind them to him through that. As a final step, the sublimated made violence will come out as creativity and invention once his reign is done, basically in “the Scattering”. I think that’s most of it. Moneo is the one who actually states, “An all-male army always turns against its own population.” Also, “the all-male army has a strong tendency towards homosexual activities.” The paragraph: The homosexual, latent or otherwise, who maintains that condition for reason which could be called purely psychological, tends to indulge in pain-causing behavior – seeking it for himself and inflicting it on others. 155. Esteleth has eaten ALL the gingerbread! Suck it! says (1) This totally ignores the issue of sexual predation/rape by soldiers against their comrades, which anyone who has a passing knowledge of the military has heard of (in fact, statistically speaking, a female soldier is more likely to be attacked by a comrade than by an enemy, even if she is in a war zone). (2) Given that Leto is depicted as more-than-a-little sociopathic, and more-than-a-little insane, and the deliberate way in which the Fish Speakers (Nayla, natch) we meet are presented as fanatics who are, despite their discipline and efficiency, somewhat lacking in the brains department (and how later books have them utterly collapse as a power and be openly mocked), I can’t shake the notion that this idea is being presented in order to be poked at. (3) The non-or-less-rapeyness of women I’m going to accept. Likewise the argument about how less rape of civillians -> less angry civillians -> less and shorter revolts -> greater overall stability, at least in the broad strokes (I think this is an oversimplification, but is largely true). (4) I’m troubled by the “women are more mature then men because pregnancy” thing. Also, there’s some troubling gender essentialism. (5) Given that God Emperor also has Leto opining that the Fremen (a society where wives could be won in knife fights) were truly egalitarian and had equality of the sexes, this casts a further pall. Of course, Leto is a consummate liar and possibly a sociopath, so… *flail* 156. StevoR says Dry but good solid informative analysis of the key facts and figures on Human Induced rapid Global Overheating here : ‘Data crunching for Doha and beyond’ written by Dr Pep Canadell from the Global Carbon Project. Comments section there is being predictably plagued by Climate Change deniers too if anyone is interesting in helping out there. 157. broboxley OT says apparently Moneo never was up close and personal with Berber, Apache and pre-salafist Afghan women. 158. Richard Austin says Leto’s goal explicitly isn’t a stable society. He’s enforcing peace, not bringing it about naturally. That’s why all creativity or newness must be sublimated into other things. He’s deliberately clamped the boiler lid shut to make the whole pot explode. So, you’re right, the idea is there to be deliberately poked at. Also remember that the Reverend Mothers are a purely matriarchical society that also uses religion as a tool. That isn’t to say Leto’s likeable, or that Herbert’s ideas aren’t horribly -ist in a lot of ways. He’s very much an “ends justify the means” character, and he hates himself for doing what he’s doing, but he sees it as the Golden Path as the only solution to prevent humanity’s extinction. 159. Ogvorbis says Yes. And the bit that follows about rape. When I reread this section just now, I was struck by the accuracy of the military rape description and medieval Europe. The soldiers — the successful soldiers, especially the cavalry — transformed from protecting the farmers from an external predator to being the predator themselves, consuming production and even the idea of droit de signeur seem to fit in with Herbert’s view of the military. They became the ruling class, the knights, the dukes, the earls, and became the primary predator for most of the population. Even in war, the search for, or denial of, provisions by either army did far more damage to the producing class than the battles and sieges ever did. Here in the modern US, the military (which is sexually integrated but the model is still that developed in an all-male army) is now consuming an inordinate amount of the US economy. And the US military is, to me, an adolescent male society complete with the practical jokes, the ‘bonding’ exercises, the joyful infliction of pain, small unit loyalty, the ideal of shared pain, shared sacrifice as a way to create internal loyalty. Your (1) The paragraph about the willing infliction of pain within practical joking, the loyalty only to one’s pack mates, feeds into this for the male soldiers (in Leto’s estimation). Those within the unit who are viewed as weak, as outsiders, as different, are subjected to ‘othering’ activities which enforces the small unit loyalty of those who are not ‘others’. (2) Herbert does this frequently. Well, not frequently, but there are elements of satire in many of his works. Perhaps Nayla is a Fish Speaker who has become too much of a male to be truly effective? (3) Definitely an oversimplification on Herbert’s part but, then, we don’t actually know yet as we have no example in history or extant of an all-female army, or even an army that is free of male adolescent ideals. (4) I agree with you. Herbert does flesh out the argument but that one struck me as odd the first time I read it (when I was in high school). (5) Women can be won as war prizes but they also retain property rights, the right to divorce, and an economic place within the sietch that gives (gave?) a woman within Fremen society far more freedom, far more rights, far more opportunity than women in the Houses Minor, the Great Houses, or those in trading families. 160. Esteleth has eaten ALL the gingerbread! Suck it! says Yes, yes. Basically, the central issue with God Emperor is that we, the reader, are dependent on what Leto says to guide us to the facts. And Leto is a liar. He also has sociopathic tendencies. Yes, the Golden Path is there to ultimately free humanity from stagnation, but it also comes at a terrible cost. Your answer to (5) is true. But that is hardly egalitarian. I’d accept “more egalitarian than other societies at the time,” certainly, but Leto’s statement that they had gender equality is a bit much. In any case, God Emperor is the only book of the series I struggle with (the others are much more clear-cut), mostly because of how mind-boggling unreliable the narrator is and my struggles to unpack stuff like this. Because yeah, I can totally see the point being made about homosocial conditioning in all-male armies and the inherent dangers of all-male armies. But I can’t get over a sense of ick. Maybe it is my own social conditioning. 161. ImaginesABeach says Commas can save lives So can periods. At Thanksgiving, my mom had a card on the table that said “Love people. Cook them good food.” I read it with a period after “them”. 162. Richard Austin says I hope it doesn’t need to be pointed out that Frank Herbert was pretty homophobic. He considered homosexuality at best an adolescent experimentation, both for men and women, and something that would be grown out of. The only actively gay character in the books was the Baron Harkonnen, who was also a sadist and a pedophile as well as a dispicable person all around. The one time Duncan catches fish speakers kissing, he flips out and Moneo blows it off as “youth”. Frank also practically disowned his own son for being gay. So, that’s all useful to remember when he’s discussing homosexuality. 163. Esteleth has eaten ALL the gingerbread! Suck it! says Well, yes, Richard. The homophobia that runs through the books (all of them, I think) is pretty glaring. The most icky section is in Children of Dune where Alia/Baron have random sex with some random d00d, and it is implied that the Baron half really liked it. 164. Ogvorbis says In any case, God Emperor is the only book of the series I struggle with (the others are much more clear-cut), mostly because of how mind-boggling unreliable the narrator is and my struggles to unpack stuff like this. The first couple of times I read it (I read the Dune series about once every three years (same for Harry Potter and (it looks like) Discworld)) the book confused the hell out of me. I realized, at some point, that the reason the book confused me is that Leto has mutually exclusive goals. He seeks to preserve his power (As Richard Austin pointed out, he enforces, through brute power, a period of minimalism in order to create the renaissance following his death) and, at the same time, create the necessary conditions so that his death will create the new future in order to save humanity. Leto must both foment revolution and create the stillness to ferment the future. It is still a weird book. 165. Esteleth has eaten ALL the gingerbread! Suck it! says One of the things I like about Herbert is that he actually tackles the issue of religion. Many authors have a tendency to either say “the religious patterns will be more-or-less identical to now” or “everyone is an atheist.” Herbert said, not necessarily. And while I think some of his ideas on the topic are a bit … odd … they have the benefit of being at least somewhat coherent. Though sometimes I laugh about the very concept of “Zen-sunni + worship of the horned Great Mother.” 166. Esteleth has eaten ALL the gingerbread! Suck it! says Leto has mutually exclusive goals. Yeah, that. In Dune Paul has a vision, and he’s simultaneously horrified and attracted to it. He thinks – wrongly – that he can create a godhead and then control it. But on a fundamental level, Paul is angry and driven by revenge, and he’s also more than a little scared of himself, the visions, and what it is he’s made. In Dune Messiah and Children of Dune, Paul’s completely fallen out of love with his vision and is now horrified by it because he sees the conclusion of it. He’s also broken by Chani’s death, which (of course) he sees coming and is helpless to prevent. I do think it is interesting that Paul sees the Golden Path and he rejects it. Because it horrifies him and, even though he knows the consequences, both good and bad, he cannot accept the bad in order to achieve the good. Initially, Leto is determined to avoid it as well. It takes Jessica and the Bene Gesserit to shove him down that path. And, ultimately, it is only because Leto is not (nor was he ever, really) human that he is capable of going that route. 167. Ogvorbis says Esteleth: My senior term paper in high school was a study of the historical parallels between the people and religions of Dune and the people and religions of our real history. Paul as both Christ and Muhammad, for instance. I managed a 65-page paper with over 100 sources. My English teacher declared that Dune (along with anything by, or about, Faulkner) were on her ‘never again’ list. And the next year, she started limiting the papers to no more than 40 pages (double-spaced, typed, with footnotes). It was a fun paper to research and write but, damn, was my understanding superficial. Richard Austin: I’m not all that familiar with Herbert’s life but his active homophobia helps explain a few things. Thanks. 168. Esteleth has eaten ALL the gingerbread! Suck it! says Oggie, by any chance to you still have a copy of that paper? I’d love to read it. In trade, I offer a paper I wrote as an undergraduate on day/night imagery in five generations of women in Tolkien’s mythology. 169. Tony ∞2012 recipient of the coronal mass erection∞ says Dalillama, broboxley, AJ Milne, Portia: Thank you for the kind words. **** Dalillama, it’s on the 16th of this month. Email- I’m on yahoo. tanthonyv@ 170. Richard Austin says There were a few ideas I first encountered in the Dune series that I liked. One of them was the notion that “he who can destroy a thing controls the thing,” which sounds self-evident to me now but wasn’t necessarily then. I re-read the series – the 6 prequels and then Frank’s novels – once every year or two. There are definitely things to watch out for, and I would by no means claim it to be the best sci-fi series ever, but – like Card and Asimov – there are elements that are worth revisiting (Card’s “Speaker for the Dead” concept is pretty nifty in my estimation, even if it doesn’t make up for the horrors of his books). 171. broboxley OT says In trade, I offer a paper I wrote as an undergraduate on day/night imagery in five generations of women in Tolkien’s mythology. /me want! all I have to trade is some pictish tales I would have to whip out at short notice :-( 172. Ogvorbis says Oggie, by any chance to you still have a copy of that paper? I’d love to read it. Nope. Long gone. It started my habit, continued in college, of coming up with at least one totally bizarre source. In my Dune paper, titled “Back to the Future: Frank Herbert’s Dune“, I managed to include a quote from, believe it or not, Bloom County. 173. Ogvorbis says In trade, I offer a paper I wrote as an undergraduate on day/night imagery in five generations of women in Tolkien’s mythology. Girl did a paper in high school on the light/dark imagery of Tolkien her Junior year. 174. Azkyroth, Former Growing Toaster Oven says (3) The non-or-less-rapeyness of women I’m going to accept. “Less.” Definitely “less.” >.> 175. Esteleth has eaten ALL the gingerbread! Suck it! says Broboxley, if you really want it I can try to dig it up. But I am pretty sure that my only electronic copy is on the hard drive of a computer that I am not entirely sure will boot. But I have been meaning to clone that HD (for the sake of some other data). I’ll try tomorrow, okay? Oggie, you give me the sads. :( 176. Esteleth has eaten ALL the gingerbread! Suck it! says Girl did a paper in high school on the light/dark imagery of Tolkien her Junior year. Tolkien does not use light/dark or day/night as subtext. He slaps it all over. He also would spend 5 pages on something that adds up to wow, look at that tree. 177. Richard Austin says Tolkien does not use light/dark or day/night as subtext. He slaps it all over. He also would spend 5 pages on something that adds up to wow, look at that tree. The one I remember is him going on for pages about the rolling hills near the barrow-wights. 178. cicely (fair-to-partly-cloudy) says Sometimes I worry about Boy. This just came out of his mouth: “I wonder if you can deep fry mayonnaise? The whole carnival and fair industry exists for the purpose of proving that you can deep fry anything. I hope it doesn’t need to be pointed out that Frank Herbert was pretty homophobic. He considered homosexuality at best an adolescent experimentation, both for men and women, and something that would be grown out of. I recall something, I think out of The Dosadi Experiment, where our Saboteur viewpoint-character (I cannot for the life of me remember his name) asks if the shock troops of last resort, within the resistance inside Dosadi, were homosexual…and shudders at the implicit, “Yes”. One of the things I like about Herbert is that he actually tackles the issue of religion. From another of his books, “Gods are made, not born!” Esteleth, your Tolkien paper sounds interesting. I have nothing to offer in exchange, though. :( 179. Esteleth has eaten ALL the gingerbread! Suck it! says Okay, okay. I shall dig out my portable hard drive, see if I can get the running-XP computer to boot, and then see if I can’t clone the HD and then see what I can find on it. 180. says The author Volter Kilpi is famous and infamous for his novel Alastalon salissa, which is held as a landmark in Finnish literature. In one famous scene, a character’s journey to the mantelpiece to fetch a pipe is told in over seventy pages. I haven’t read it. I tried, but got really, really bored maybe 50 pages into it. 181. Therrin says Dalillama, just saw your post (last thread), I’ve got access to a minivan if you have need again. I think I’m across town from you, but I usually have time to help out with things. Email is notechasing with either yahoo or Google for next time. Fyi, I was the quiet one at Crip Dyke’s place. 182. Esteleth has eaten ALL the gingerbread! Suck it! says But for now, I’m going to bed. 183. Fucking Vacula is here. Fuck this shit. I have an empty bag of shits to give. I’m gone until he is. Night all 184. Ogvorbis says Heading for bed. G’night, all. 185. Therrin Thank you for the offer, I’ll keep it in mind in future, although I hope that in future I’ll have a little more lead time. This was a totally last-minute thing, we didn’t find out until Saturday night, so Sunday was it as far as collecting the stuff. 186. chigau (無) says I cannot catch-up tonight. But Tony should have an old-fashioned Molly. (not a comment-Molly) 187. Tony ∞2012 recipient of the coronal mass erection∞ says Thanks chigau :) 188. Menyambal --- son of a son of a bachelor says Oy, the drama. We’ve been hosting an extra teen, as he’d had some difficulty with his family. The difficulties he was causing in our family were getting to be overwhelming, and tonight it all went bloowiee. He’d made himself sick with his antics, and wanted to see a doctor. We got him to the emergency room, but had to get his own dad to come sign him in. To over-simplify a bit, I snuck home, packed his stuff, drove back up and dumped it into his dad’s truck, then scooted for home. My grateful family had bought me some pistachios, and I’m washing out his bedding and listening to the rain. The window is open, there’s thunder out there, and it is December. That’s not unprecedented, but it is unusual. 189. Beatrice says Tony, You heard this from everyone else already, but I’ll repeat it anyway: you are an amazing person. You gave Jim support and understanding, without giving harmful religious belief a pass. You were great. I’m glad the conversation also helped you. Thanks for sharing this with us. 190. Tony ∞2012 recipient of the coronal mass erection∞ says Beatrice: Thank you very much. 191. rq says Good morning! Thumbs up, hugs, good thoughts, chocolate cakes for Tony! You are one amazing person. Thank you for sharing. *more hugs* +++ Sunshine today. In more than a week. Yay! 192. Tony ∞2012 recipient of the coronal mass erection∞ says rq: The hugs and kind words are quite appreciated. 193. birgerjohansson says Robert Zubrin critique of the new NASA plans: “Mars the Hard Way” http://www.spacenews.com/article/mars-the-hard-way In NASA, planning exists to justify past bad decisions. (a typo originally made it “planning exits” which is strangely appropriate for the lack of foresight) — — — — — — — I remember The Dosadi Experiment. The underlying premise for the need to set up this glass-box city state was not credible (I don’t recall the details). His “Whipping Star” had an even more ridiculous premise. BTW the otherwise excellent Jack Vance was* also homophobic, and often let the bad guys be homosexuals, or other non-standard sexual habits. — — — — — — — *He must be well into his eighties, but is still alive. I am currently reading an anthology of stories set in the “Dying Earth” setting, written by various authors as a tribute to Vance. — — — — — — — The “Speaker for the Dead” trilogy was pretty good. Apart from that, I do not like the Ender novels. — — — — — — — “but not the whole Corps” While not dissing USMC more than the rest, I am seriously worried that nations with a professional army/ armed force have a cadre of people sworn to obey orders, even when going into foreign lands for very shady reasons. Once they have shot up everything, and received horrible prychological or physical traumas in return, they will slowly realise it was all because some asswipe wanted to secure his re-election. — — — — — — Thunk, you can have our snow once you have solved the logistic difficulties. 194. says Sorry the counselor sucked – if you have an appt. with someone else next, you can tell them exactly how much the first one sucked. If their triage people don’t even know what to do about depression, they’re training them wrong. but they’ve ALL been like that. every single counselor/therapist I’ve ever talked to has tried to get me to change the behaviors that were a consequence of me coping with it, rather than helping me figure out how to not be depressed 195. carlie says Dam, I’m sorry, Jadehawk – it does sound like they just suck all around. Is anyone there allowed to prescribe antidepressants? I’ve heard sometimes that’s a good way to start, to get the person to the point where they can start doing other things. 196. says it does sound like they just suck all around. Is anyone there allowed to prescribe antidepressants? that’s part of the health center appointment. but let’s just say that i’m skeptical as to whether psychmeds will work as advertised. but i’m willing to try, simply because i’m sick of these unmanageable episodes and the counselors are useless 197. John Morales says Jadehawk, FWIW, chemicals do their thing whether you’re skeptical or not. (Worth a try) 198. I question the claim that you can meaningfully deep fry koolaid. People mix koolaid powder into hush puppy batter and deep fry that, but those are koolaid flavored hushpuppies, not deep fried koolaid. You is strange people. Hushpuppies are shoes… *need lunch* 199. says Jadehawk: I remember now why I only ever sign up for counseling when I’m feeling the worst. I have no idea how it’s supposed to help me to be told that I need to learn to push through my anxieties, or to be told I need to develop more self-discipline, when I just finished explaining that I didn’t have the energy/willpower to both manage my depression and have self-discipline, and that the current level of “laziness” and disorganization is the balance I’ve worked out for myself between being self-disciplined and managing my depression. It sounds like your counsellor is using an unhelpful approach. I know it’s disappointing when you’re exhausted and you’ve turned to someone as a last resort and they just don’t understand. This may be a stupid question but have you told them that you feel their approach is unhelpful and you want to try a different strategy? They’re supposed to be using client centred therapy. especially i don’t know how I’m supposed to be helped by being told I should try to show up to lectures far more regularly, when I just finished explaining that I’d tried that previously and that it only lead to even earlier burnout, and that the sporadic attendance is a coping mechanism without which I can’t make it through a semester at all. Also, before they get you to try and change your behaviour they’re supposed to help you identify some of the negative thoughts and feelings that lead you to use those behaviours (like avoidance). Have they asked you about your thoughts and feelings in attending lectures and why it’s making you more stressed? Please keep trying. I’m seeing a counsellor too and I’m pretty happy with how it’s going. I’m sure it seems tough now but I believe you can survive the dark periods. I believe in you. Hell, if I can do it, I’m sure anybody can. 200. Tony, Easily comment of the month. QFT. I often get bored with long texts, even when the subject is about something I am interested in. I read your piece all the way through, a great post. Tolkien does not use light/dark or day/night as subtext. He slaps it all over. He also would spend 5 pages on something that adds up to wow, look at that tree. Indeed. I start to read LOTR on a regular basis (every winter or so) but seldom finish it. The Tom Bombadil section is normally the first hurdle, after the rescue from Mount Doom is normally the biggy, though. The Silmarilion is not a problem once I have got over the singing spirits at the start. 201. *comes home* *looks around* Where’s that damn houseelf? *looks in the mirror* Ah, right… Tony Wonderful comment. I’m sorry your pleasure encounter ended like this, but I’m even more sorry for Jim. I guess for him the “serial murder” comparison feels valid, I guess he really feels like a serial killer who must kill time after time after time. How awefull must it be to live in a world where your most inner self makes you feel like a horrible criminal just for doing consensual stuff with other adults. 202. Beatrice says Back from a job interview. Not bad, but I doubt I’ll get it. There were more qualified people there, I applied just to try my luck. Another one tomorrow, now, for that one I would be a good candidate. I hope I handle the interview as well as today’s. There’s also another job I should get an answer about this week. I’d really really like that one. It’s in a place I used to dream about working at, not in the position I applied for, but what the hell. There would be science and books all around me. 203. rq says Beatrice Good for you! That sounds like a good strategy, to apply for as many jobs as possible and to go to the interviews – even if they’re positions you don’t actually want, at least the practice will do you good! And I’ll cross some thumbs for the science-and-books job. ;) (Yes, I have a stack of random thumbs to cross for people… Don’t ask; I could just say it’s part of my job…) 204. Beatrice says rq, I will remember not to ever cross you, so that my thumbs don’t join your stack. There aren’t many jobs these days, so I apply for everything that I have basic qualifications for. It’s not my fault if someone made a position suited for someone who studied agriculture open for economists and mathematicians. The interview tomorrow is at the same place, so I’m counting today as a rehearsal for the real thing. 205. rq says Ooh and the latest evo-psych post reminded me of something I’ve been thinking about since the previous collection of evo-psych posts, specifically – the one that had the chart with the division of labour on it. The one line of that that had me thinking was the ‘Childcare’ one, with ‘easy’ under the heading ‘foraging’ and ‘hard’ under the heading ‘hunting’. And Rebecca Watson mentions that in her talk, too, about taking children shopping (because shopping = foraging, remember?). And then there’s the whole does-trapping-count-as-hunting-or-gathering aspect. Anyway. The point (and no, it’s not much of one). Childcare isn’t easy under any circumstances (in my opinion). It can be easier, but not easy (unless you have textbook-perfect-kids, a nanny, a cook, a personal chauffeur, a large house with a large backyard, and a heck of a lot of time just for your kids). And I wonder, how many of these evo-psych people (are they mostly guys?) have ever even tried to take care of children? How many of them have actually tried to take a child (let’s make it easy :P) foraging? Hunting? The modern equivalents? I’m going to go out on a limb here and guess that most of them wouldn’t even think about trying such a thing, because it is too hard for them. Which brings out the irony, because they see childcare as something easy or easily done (yeah yeah I know by women who have evolved for it right), and yet they can’t really say that they have ever tried it, to see if it actually is easy, because, you know, children, that’s hard. So it’s hard for them, but it must be easy for women, because, you know, women – so, foraging with children would also be easy, because hey, how hard can it be to hold down a few kids while you dig up some roots? Personally, I think they’re afraid of children and cover that up by shoving them off on the women. But it just felt strange that it was so simple and straightforward for them to label childcare as ‘easy’. And I think that lack of thought, more than anything, is what has turned me off of the gendered evo-psych stuff completely. +++ FtB … has changed my life. No, has ruined (and by ruined I mean has made obvious to me a lot of things that were subtly wrong with the way the world should work) my life and my capacity to enjoy movies. Used to be, a 90% male cast – nothing wrong with that! Women-to-be-rescued – super! Kickass-woman ends up in stereotypical relationship – great! No same-sex couples? Same-sex couples as something weird and quirky? Same-sex couples as evil? Yeah wonderful, I know they’re not like that… It’s just a movie anyway. But NOW. Oh boy do these things jump out at me. Like a lot. Watched two movies over the weekend, and I kept thinking, why couldn’t they have had at least one woman doing all of that? (The movies were, for the record, Equilibrium and Looper.) I actually found it annoying (as much as I love Christian Bale – but they really should give Sean Bean a role where he doesn’t die via injury to the head/neck area) that both movies, while supposedly set in the future, had mostly male casts, with women in fairly typical, passive fair-maiden or motherly roles. I’d started operating under some misguided idea that the creative writers in Hollywood were better than that. *sigh* Note on Equilibrium: what was rather telling was the fact that there were more women present (no speaking roles, though) in the resistance part of the population, while the fascist-type surface population was definitely dominated by men. +++ Sorry that was all a bit long. But I wanted to get it out before the migraine actually arrives. :/ Currently taking preventative measures (coffee) but I don’t know if I’m too late. 206. rq says Beatrice Dammit, I meant hold some thumbs for you… But really, it comes down to much the same thing (and yes, you may now picture me with a handful of thumbs). :) 207. Beatrice says … in a jar on your work desk. 208. rq says Beatrie That’s where I store them, but when someone needs some of the long-distance super-natural superstitious good luck vibe, I take them into my hands and hold them. Soft and gentle-like. :P 209. rq hold thumbs /cross fingers? beatrice Good luck for your applications. As for the agricutural job: many years ago a friend of mine (acounting/economist) ended up in one of those by chance and it was kind of a very lucky move. His boss figured out that in order for him to run the financial part of the business he would need to understand the agricultural part as well and gave him the training. Makes him awesomly qualified for some jobs. rq, again Well, everything that women do has to be easy. That’s why you leave it to the poor fragile women, you know? And because women are on average weaker and smaller they get to do the easier jobs! Quod erat demonstrandum. It’s a bit like with teachers: At least here everybody complains about how lazy teachers are, what a good life they have, lots of holidays, reasonable pay, moochers in short. But if you ask them if they want to be one they tell you they’re not crazy, of course not! As for ruining everything: Sadly yes. Can’t watch any TV-show, especially not the kids’ without noticing that shit, like being able to count all female charaters using my feet… 210. Beatrice says rq Awww, that’s so sweet. 211. rq says Giliell Yeah, crossed my language wires there for a bit. :) And yeah, the part about kids’ shows really struck home last weekend, when I realized that most of the books we have and the things we watch have boys in lead roles. And since I’m the only girl in this household, the boys don’t get much exposure. What brought this to my attention? Ha. Eldest was afraid to go to a girl’s birthday party because it would be full of girls. And when we ask him about his friends from kindergarten, he never lists any girls, even though his teacher assures us that he’s one of the fewer boys who actually does play regularly with the girls. So I’ve asked my sister to send some strong-female-character books from Canada, and I’ll probably go out and buy Pippi Longstocking, but also I have to find more children’s movies with main girl characters. Most of the ones out there are pretty stereotypical, but better than nothing… Beatrice :) If I’m too rough with the thumbs, I might break them. 212. says Rick Santorum is going to be a writer for the WND :-D 213. Beatrice says Jadehawk, Heh. Now you just have to find out who predicted it here first so that we know who’s getting us the next round of grog. 214. carlie says rq – what age group are you talking about? 215. Tony ∞2012 recipient of the coronal mass erection∞ says Giliell, Cosmic Teapot: Thank you both for the kind words. 216. jackiepaper says rq, My older daughter overheard my youngest son telling his little sister that she was losing a certain video game because, “Boys are better at fighting than girls.” So older sister walked over, borrowed little sister’s controller and whipped his butt. Then they had a talk about how maybe beating a younger kid at a game had nothing to do with gender. We don’t know where he got that. School? Movies? Made up on the spot to mess with his sibling? All I know is it creeped me out. 217. rq says carlie Five and three, in round numbers, but rapidly getting older. :) The three-year-old does what his brother does and reads what he reads (or is read to him). You have suggestions? :) 218. rq says jackiepaper It’s weird how they hold these ideas, even when we’ve done nothing specific to help them. :( I was surprised, too, but I’m pretty sure it’s a combination of kindergarten, TV and inadvertent boy-programming through the children’s books we have. Not that we have violent, fighting, machine-wielding characters only, but… I guess it’s enough that most of the main characters are boys. :/ Have to work on fixing that! 219. broboxley OT says should the police bear some responsibility for that murder suicide in Kansas City? http://www.nypost.com/p/news/national/chief_other_girl_uULWUcuM7p4tJb2PLeaITP After dinner and drinks Friday night at a local tavern, the former Long Island high-school star took the woman, Brittni Glass, to her home, but spent the next several hours asleep in his Bentley outside her building, neighbors said. After cops roused him from his drunken slumber at about 2:30 a.m., Belcher went inside Glass’ building and re-emerged about four hours later. in Georgia he would have been woken up, put into the back of a cruiser and charged with DUI. He wouldn’t have been out and about with a weapon. Since he had his keys with him, he is considered in control of a motor vehicle while impaired. You dont have to have the motor running around here. 220. Portia, sporty and glam, pelted with pastries says rq Sorry that was all a bit long. But I wanted to get it out before the migraine actually arrives. :/ Currently taking preventative measures (coffee) but I don’t know if I’m too late. I hope it works to head it off. : ( Re: Kids’ media. I read that Tamora Pierce has some great female lead characters, so I went and got Wild Magic for SO’s oldest (she’s 12). Is anyone familiar? I’ll probably read it myself, because it sounds good. Even though I’m not normally into fantasy. Maybe the bug will bite me. Beatrice Good luck with the job. You are braver than I am. I have/had a defeatist attitude about jobs I probably wouldn’t get. (Which is why I’m self-employed, ha.) jackiepaper That’s sad that your boy said something like that but this: So older sister walked over, borrowed little sister’s controller and whipped his butt. Then they had a talk about how maybe beating a younger kid at a game had nothing to do with gender. is AWESOME. Both that she demonstrated how wrong he was and that she talked to him about it. Good show on her part. === I haven’t been drinking much coffee (finally kicked the caffeine addiction) but I think I might need some this morning. Whew. 221. Esteleth has eaten ALL the gingerbread! Suck it! says Today is the 4th of December. And it is 65 fucking degrees Fahrenheit. What the fuck is this shit? 222. Portia, sporty and glam, pelted with pastries says What the fuck is this shit? Awesome. This shit is awesome. 223. Esteleth has eaten ALL the gingerbread! Suck it! says This shit is awesome. Less awesome is the forecast for the next few days. Namely: Today: high of 65. Tomorrow: high of 35. 60% chance of snow. Thursday: high of 37. 20% chance of rain. Friday: high of 45. 30% chance of rain. YUCK 224. Portia, sporty and glam, pelted with pastries says Yuck indeed. Here we have 60° today then 40s for the rest of the week, with clouds. 225. Esteleth has eaten ALL the gingerbread! Suck it! says On my way to work, the radio announcer read the weather report, stopping after each given temperature to say, “yes, that’s right, [number].” She sounded irritated. 226. Rey Fox says Oh feh. Let winter be winter. I’m irritated that I couldn’t sleep with my comforter the last couple of nights. 227. thunk, cold air advection says Portia, Esteleth: Today is the 4th of December. And it is 65 fucking degrees Fahrenheit. What the fuck is this shit? really, really unusual weather. That makes me gripe about how it’s way too hot. 228. birgerjohansson says “Gases from grasses: Simulations on Ranger supercomputer help researchers understand biofuel reaction” http://phys.org/news/2012-12-gases-grasses-simulations-ranger-supercomputer.html Medical issues: “Rewarding people to live healthier lives is acceptable if it works, study reveals” http://medicalxpress.com/news/2012-12-rewarding-people-healthier-reveals.html Study explains why some teenagers more prone to binge drinking http://medicalxpress.com/news/2012-12-teenagers-prone-binge.html Study reveals autism treatment clues http://medicalxpress.com/news/2012-12-reveals-autism-treatment-clues.html Researchers find fungus has cancer-fighting power through nanoparticles http://phys.org/news/2012-12-fungus-cancer-fighting-power.html Faster, safer method for producing stem cells http://phys.org/news/2012-12-faster-safer-method-stem-cells.html 229. rq says I like my comforter. But yes, I haven’t had much reason to use it yet, this season. +++ Portia We’ll see how awesomely you like the warm weather when the fire-ants move north. ;) Thanks for the good wishes re: migraine. It’s at some weird half-way point right now that’s annoying but not debilitating. :/ Hopefully the children will co-operate and I can get more than 1.5 hrs sleep at a time tonight (teething issues with youngest :/). Good for you for kicking caffeine in the ass. My sister did it, too, finally. I’ve never been a big coffee drinker, but I definitely like it now and then. And if I catch it early enough, it can get rid of my migraines (weird… that, or really dark chocolate). I’m more of a black-tea person myself. 230. I swear, some days the biggest challenge of raising kids is not to kill them. Not only did it take me well over 60 min to collect them from kindergarten, also they have been crying and shouting and trying to kill each other for shits and giggles ever since. jackiepaper I blame kindergarten. Until #1 went there she liked all colours and many things, but since then it’s “girl’s colours” and “girls games” and “pretty”. Pretty, pretty, pretty. 231. Portia, sporty and glam, pelted with pastries says Eek! Ants! But you know me, I have lots of insect repellant :) That middle ground before the headache really hits you is like an uncomfortable purgatory. I’m always trying to do things that help and walking on eggshells when I’m feeling like that. Hope it retreats. Poor little thing with the sore mouth, hope they get some peace so you can too. Lack of sleep is my biggest migraine trigger, I think. Funny you should mention black tea, because that’s exactly how I (unintentially) kicked the caffeine. I had a cold and so didn’t want to irritate my throat with cream and coffee a few months back. Switched to homebrewed chai tea, then just a few days ago realized I didn’t get a headache at all when I skipped my morning tea. Not to say I don’t still love coffee, though. I worked in several different coffeehouses in college. (Leading to a proposed autobiography title: Barista to Barrister :)) Come to think of it, SO brought me a chai just a few minutes ago. Mmmm. 232. Portia, sporty and glam, pelted with pastries says Giliell, More power to you. I couldn’t handle it. SO’s oldest’s favorite pasttime is dragging her feet, and it drives me bonkers. 233. rq says Giliell Definitely with you there. :/ Portia I like the title. I hope the rest of it is just as good. Because no other lawyer has worked the coffeeshop circuit prior to making it big in law. ;) :D Black tea might have helped because it has caffeine in it (just not as much), so instead of dropping it cold, you’ve weaned yourself off. :) Excellent work, Iago! 234. says Congress Promotes Dangerous Anti-vaccine Quackery — Phil Plait of Bad Astronomy was picked up by Slate when he wrote an article updating news from the antivax wars, including the disastrous attitudes coming from mostly Republican forces in the US Congress. I doubt that Phil’s opening plea will be heeded: This is not my first vaccine rodeo, and I expect some interesting remarks in the comments section. As always, I have copiously linked key phrases in this article to more information backing up my claims. Please read them before commenting. … The Committee on Oversight and Government Reform held a hearing trying to look into the cause and prevention of autism. Rep. Dan Burton (R-Ind.) launched into a several-minute diatribe [see video at the link] that starts off in an Orwellian statement: He claims he’s not antivax. Then he launches into a five-minute speech that promotes long-debunked and clearly incorrect antivax claims, targeting mercury for the most part. Burton has long been an advocate for quackery; for at least a decade he has used Congressional situations like this to promote antiscience. In the latest hearing, Burton sounds like a crackpot conspiracy theorist, to be honest, saying he knows—better than thousands of scientists who have spent their careers investigating these topics—that thimerosal causes neurological disorders (including autism). He goes on for some time about mercury (as does Rep. Dennis Kucinitch (D-Ohio) starting at 21:44 in the video), making it clear he doesn’t have a clue what he’s talking about. For example, very few vaccines still use mercury, and the ones that do use it in tiny amounts and in a form that does not accumulate in the body…. This is what we get when we elect willfully ignorant people. These ill-informed idiots should be outed — and then they should be booted. 235. Portia, sporty and glam, pelted with pastries says Right, those nicotine gums are right on with their step-down approach to weaning :) I’m not going to be the one to write the book, the title was a friend’s suggestion. I’ll need a ghostwriter, ha. (Though come to think of it, a friend did ask me to co-author a book a while back…I should follow up on that). …no one has likened me to Iago in quite some time! === Yesterday, I listened to another attorney (that one I have to work with) call a 13 year old a slut over and over for alleged sexual activity. I finally snapped, and he said “Oh, do you not like that word? Cindy doesn’t like another particular word, so I avoid that one. I’ll stop saying slut, too.” Couldn’t really explain that it’s not the word, it’s the whole fucking attitude. I did manage to put together a syllogism pointing out that he was essentially calling a rape victim a slut, because any sexual activity a 13 year old engages in is not legally consented to. He didn’t have much to say to that. 236. Portia, sporty and glam, pelted with pastries says YAY JOE!!! 237. Yay, Joe! Oh dear, I’m working through the evopsych thread. Vacula is cupcake par excellence 238. rq says Improbable Joe YAY!!!!!!!! Portia You mean, you resemble Iago…? And good for you for standing up to the slut-shaming. Sounds like you work in a tough job! Giliell I’m going to attempt tomorrow. Don’t have the energy tonight. :/ 239. broboxley OT says Giliell I swear, some days the biggest challenge of raising kids is not to kill them. Not only did it take me well over 60 min to collect them from kindergarten, also they have been crying and shouting and trying to kill each other for shits and giggles ever since. wait until you come home from work and the 21yo and 18yo are doing exactly that :-( crying and shouting and trying to kill each other for shits and giggles 240. says While we’re giving anti-science congresscritters the boot, let’s get rid of stupid judges as well. A Nevada judge twisted his regressive attitudes into monster knots in order to uphold a ban on gay marriage: To rule last week that it was constitutional for Nevada to bar gay couples from getting married, U.S. District Judge Robert Jones had to determine that there was a “reasonably conceivable state of facts that could provide a rational basis” for the state to reserve marriage to straight couples. Here’s what he came up with: Marriage is important to maintaining a stable society, and if it is expanded to include gays, “it is conceivable that a meaningful percentage of heterosexual persons would cease to value” marriage because “they no longer wish to be associated with the civil institution as redefined.” Nice photo of gay cowboys dancing accompanies the article. As as being so disgusted by gay marriage that one abandons the idea of marriage entirely, I think this attitude should be extended to sex. If gay people are having sex, then that is certainly something I’m never going to do again. /sarcasm 241. Esteleth has eaten ALL the gingerbread! Suck it! says So people keep mentioning Vacula in the context of the evopsych thread. Am I to take that as “Vacula shows up”? 242. Portia, sporty and glam, pelted with pastries says rq, I’m not as diabolical as I used to be, but… and thanks for the moral support :) === Lynna, If gay people are going to eat liver and onions, I’ll just have to never eat them. As a self-respecting hetero and all. 243. says If gay people are going to eat liver and onions, I’ll just have to never eat them. As a self-respecting hetero and all. If most of the gay men I know exhibit really fine grooming habits, I am never going to shower again. Combing my hair is out too. Come to think of it, those decisions should take care of any marrying-like-those-damned-gays issues. No grooming, no marrying, no fucking. I’m not doing anything that might make me look gay. 244. esteleth More kind of shitting all over the place rehashing E-gate A-fucking-gain broboxley Don’t destroy my hopes… 245. Pteryxx says I’m not doing anything that might make me look gay. Guess that means serving in the military, playing pro ice hockey, and weightlifting are right out. 246. carlie says Yay Joe!!! rq – For tv, Legend of Korra/Avatar the last Airbender, the cartoons. Very strong female characters. The storylines might be a little too old for them right now, but they can see girls kicking butt. Also, actually, Arthur the cartoon on PBS. There are strong girl characters in there and it’s a slightly younger group. Backyardigans is even younger and also has strong girls.Charlie and Lola is ok; very cute, Lola is a little sister, has a big part. Movies – Spirited away, um… hm. I’ll have to think about that. Books – Frannie K. Stein, mad scientist. Think Captain Underpants, but with a girl and science and funny. Paper Bag Princess, also the Free to be You and Me storybook. Music – The Princess Who Saved Herself by Jonathan Coulton. There are several cute videos of it; this is one Coulton retweeted a few weeks ago. 247. says I’m not exactly looking for deep sympathy here or nothin’, as it’s pretty First World Problem, at least in terms of its immediate impact on me, and there’s probably lots of people sleeping on the streets who are (relatively) relieved that it’s not -20 or something (as against the people in low lying coastal regions soon to be under water if this kind of thing keeps up), but seriously, yeah, about this freakin’ weird weather… I’m just going to sit here on the step in my snowboarding boots and pout and hold my breath until I turn blue or it snows. That’s what I’m going to do. (Pause…) ‘Kay. So I did turn blue first. Holding it again then… (/And, I suppose, on the bright side, if this keeps up, I’ll be able to plant some vineyards and a open proper winery up here, any season now. And sure, presumably the windsurfing on the coming inland sea will be awesome, so long as I stay around the edges of the passing hurricanes…) 248. says Guess that means serving in the military, playing pro ice hockey, and weightlifting are right out. Yep. So many avenues are now closed to me. Including preaching an anti-gay message to a mega-church audience. Hiring luggage-lifters is out. I also can’t write a book about being cured of the gay, followed by a book-signing tour of Uganda. 249. chigau (無) says Yay! Improbable Joe! 250. Pteryxx says Oh wait – Things Gays Do includes … serving in state legislatures and in Congress! Hey wingnuts, here’s a thought… 251. opposablethumbs says Guess that means serving in the military, playing pro ice hockey, and weightlifting are right out. … and having friends or lovers or family, or breathing … hey, come to think of it, if we could persuade homophobes that breathing is right out because it’s something that gay people do … eh? ::iz insanely hopeful:: 252. opposablethumbs … and having friends or lovers or family, or breathing I think you’re onto something there… Yes, I brushed up my nastiness lately, why do you ask? 253. cicely (fair-to-partly-cloudy) says I haz a rental SUV, and I will be home TONIGHT! Huzzah! 254. Emrysmyrddin says Just popping in to drop this link. After the regressive vote on women bishops a few weeks ago, is anyone really surprised at this public direction from ‘lay’ groups? 255. Tony ∞2012 recipient of the coronal mass erection∞ says As I type this, I am standing outside in 75 degree weather and I love it. It is normally in the 40s even in NW FL. I despise cold weather more than peas. 256. rq says Portia I have added some thumbs to your portion, for extra luck and support. :) AJ Milne Oh you. You have to put away those boots before the snows come. Preferably at the very back of the garage/attic/storage space, and put everything else in front of it. Then sigh hopelessly, shrug your shoulders in that the-snow-will-never-come way, and voila! Instant blizzard! carlie THANK YOU for the suggestions. I’d found some books with which to inoculate them, and a few of those I’ll have to file away for future reference, but I feel less ignorant now. :) More capable of passively providing some good examples. Thanks! 257. rq says opposablethumbs I’m sitting here and wondering, Is there anything that gays don’t do? It’s amazing how versatile they are! /snark Tony You and my best friend (and all those other folks who can’t take the cold). Could never convince her that winter is a good thing. I find it much easier to warm up than find a way to cool down (but then, physically, I handle heat poorly, so that’s probably part of it). 258. broboxley OT says wondered about all the fooferaw on the evopsych read some of vacula’s stuff. Not for nuffin but from his self identifation, single male, lives on campus, hmm could make me some evopsych out of that. 259. rq says broboxley Write it up and get it published in Nature and he might think about changing his ways. :P (Or just have evolutionary justification for why he is the way he is.) 260. Beatrice says Cold weather is better than hot. That’s my objective observation. 261. Azkyroth, Former Growing Toaster Oven says You and my best friend (and all those other folks who can’t take the cold). Could never convince her that winter is a good thing. I find it much easier to warm up than find a way to cool down (but then, physically, I handle heat poorly, so that’s probably part of it). Can’t we just put the damn poikilotherms in terrariums with heat lamps instead of setting the thermostat for the whole building to “Bessemer process?” 262. cicely (fair-to-partly-cloudy) says In theory cold seems like the better proposition; after all, it’s easier to pile more clothing on to get warm, than it is to peel down past the skin to get cool. In practice, though, the colds seem colder to me than the hots seem hotter. I cannot find it in me to be upset that we are snow-free and in the mid-50s in December. But then, this is the time of year when I generally choose my seating with an eye to the availability of basking surfaces, and begin to wait miserably for the Spring Thaw, when feeling returns to my fingers and toes. 263. Tony ∞2012 recipient of the coronal mass erection∞ says And once again, cicely for the win. She is totes correct @ 270. 264. Beatrice says It’s snowing. First snow this year. 265. rq says Azkyroth If it were up to me, YES. Because the apartment heating bill would be a lot less, too. Poikilotherms. I’d forgotten the term; remind me to use it more often as an insult. cicely You have obviously never worn enough layers of wool to fully enjoy the cold. 266. Beatrice says Er, this winter, not this year. 267. Tony ∞2012 recipient of the coronal mass erection∞ says Giliell: Your comment @206 reminded me of one thing I didn’t elaborate on sufficiently. Jim made a comparison between us deriving pleasure from having sex and a serial killer deriving pleasure from killing people. That just goes to show how twisted morality can be twisted by religious beliefs. He was having a hard time understanding that sexual activities between consenting adults is not *wrong*. In his eyes, the very act of having sinful gay sex and enjoying it makes one no different than a serial killer. 268. Tony ∞2012 recipient of the coronal mass erection∞ says I hear the gays like to celebrate Christmas, Thanksgiving, Halloween, July Fourth, Memorial Day weekend, Easter, New Years… I guess those homophobes can celebrate holidays either. What does that leave them? 269. Beatrice says From the looks of it, if it keeps snowing the whole night there will be some serious snow on the ground tomorrow. 270. rq says Tony That’s a horrible comparison!!! But I have to confess, I haven’t witnessed this kind of religious conditioning in real life, either. Must have been a shock to you! Wow. It sounds so hard to believe (and yet I know it’s true). Also, the gays have now taken away everything meaningful to me! What am I to do?? Next thing I know, they’ll be after my husband! 271. Tony ∞2012 recipient of the coronal mass erection∞ says Given the recent chatter about evolutionary psychology, I am mildly interested in understanding it more. However, it seems *waaaaay* above my head. Is there a cite or book that can give the layman an understanding of EP? Is the Wikipedia entry sufficient? 272. Tony ∞2012 recipient of the coronal mass erection∞ says “Is there a cite website or book…” Sheesh. 273. cicely (fair-to-partly-cloudy) says rq I do not believe that enough layers of wool exist for me to enjoy the cold, particularly in the fingers and toes area. (Oh, yes; also, nose.) The best I can hope for is to tolerate the cold. And enough layers to make the cold tolerable seriously interfere with movement (again, particularly the fingers and toes) and balance. You’ve possibly seen/heard the jokes about the kid whose mother bundles hir up so much as to be an immobile, undifferentiated lump? Like that. With no enjoyment possible at all. 274. Beatrice says (first world problem) I like having long fingernails. That doesn’t go well with gloves. Especially mum’s old leather ones which I really don’t want to ruin. (first world problem) 275. Janine: Hallucinating Liar says Dealing with two racists on Ashley Miller’s blog reminds yet again how much I hate threaded comments. 276. says I’m in the ‘can’t ever really get comfortable in the heat’ category, too. Sometimes the ‘just feel like sludgy, dazed crap in the heat’ category, even. It seems to have eased a bit, in recent years, tho’ I’m not sure it’s much. Might have something to do with slightly better cardio fitness, of late. Or maybe I just acclimate really, really slowly. And re rq‘s bury the boots thing, thanks. I may try that. Also, I guess I could probably put summer tires back on a car, drive it somewhere remote and potentially dangerous… That always brings snow, too, right? … Yes, I know, putting winter tires on in the first place was probably a mistake. Quite possibly, this whole damned thing is my fault. What was I thinking? 277. Esteleth has eaten ALL the gingerbread! Suck it! says Jesus tapdancing Christ, I thought the racist herpaderp on Ashley’s thread was going to be bad, until i actually read it. How is it, that I, raised in a small super-racist town in the rural Midwest, am shocked by how blatant that was? You’d think nothing would surprise me any more. 278. rq(and others who may be looking.) So I’ve asked my sister to send some strong-female-character books from Canada, and I’ll probably go out and buy Pippi Longstocking, but also I have to find more children’s movies with main girl characters. I can only be of limited help on the movie front, but for books, husband recommends A Sky So Close. Also Two Moons in August, and the works of Martha Brooks generally, and also Gloria Whelan, particularly Homeless Bird. I’d add Pratchett’s Tiffany Aching books, satrtinf with The Wee Free Men. His Equal Rites also features a young female protagonist, as does Monstrous Regiment. The eponymous hero of Wen Spencer’s Tinker is also a young woman. For movies, L recommends Lilo and Stitch, and Pepper Ann (TV series). 279. Tony ∞2012 recipient of the coronal mass erection∞ says Whoa! Are we talking about the same thread at Ashley’s where she discusses her father disowning her? Oh hells no. ::cracks knuckles:: On my way. 280. ImaginesABeach says I HATE being cold. I grew up in St. Paul, Minnesota. All the way through high school, I swore I would go south for college. I ended up going about 50 miles south to a college on a hill surrounded by sod farms (to maximize the wind chill). All the way though college, I swore I would go somewhere warm for law school. I even researched it and found that the University of Hawaii at Manoa had an excellent nautical law program. I figured I could be interested in nautical law. I ended up at the University of Minnesota Law School. And I swore that when I graduated, I would move somewhere warm. I now live about 5 miles from where I grew up. Apparently my issues with change are stronger than my hatred of cold. 281. rq says Go, Tony, go!! (And all others trying to bring sense on that and other threads bringing out the terrible in people.) *brings out cheerleading pom-poms* Today I am not brave enough even to read any racism and/or evo-psych supporters, but I will educate myself tomorrow. In the meantime, I shall dance the Courage-and-Support Dance for all of you. And I’ll hold a lot of thumbs. In the palms of my hands. And I am obviously running on little sleep, for talking like that. Thank you, Dalillama, for the book suggestions – a lot of them seem a bit advanced for our current age, but I’ll file them away for future reference (or just buy them now and have them sitting around!). +++ Good night, all! 282. Portia, sporty and glam, pelted with pastries says ImaginesABeach, you just described the last ten years of my life. Tony, I’m enjoying the fact that this white supremacist asshole uses “factoid” to describe his racist assertions. A factoid is a questionable or spurious (unverified, false, or fabricated) statement presented as a fact, but with no veracity. http://en.wikipedia.org/wiki/Factoid *pedant snicker* 283. Portia, sporty and glam, pelted with pastries says Night, rq! Hope you get a good solid rest tonight. 284. birgerjohansson says Winter (used to) kill off ticks and other parasites. Also, useful if you live in Russia and Wehrmacht is coming. — — — — — — — I suspect the powers that be at FTB is stalling the arrival of blogger Near-Earth Object to allow Bruce Willis to sneak in. — — — — — — — Gender debate sparks UK-Sweden media spat http://www.thelocal.se/44824/20121203/ Brit tabloids prove we have DNA in common with some sludgy life forms. — — — — — — — A new promising approach in the therapy of pain http://medicalxpress.com/news/2012-12-approach-therapy-pain.html — — — — — — — Anger may play larger role in anxiety disorders, study shows http://medicalxpress.com/news/2012-12-anger-larger-role-anxiety-disorders.html I know laypersons should not read about symptoms, but there areso many things here that fit me that it cannot be just hypocondria — — — — — — — Fish oil helps heal bed sores of the critically ill http://medicalxpress.com/news/2012-12-fish-oil-bed-sores-critically.html 285. Esteleth has eaten ALL the gingerbread! Suck it! says While I’m sure it is relevant somehow, I’m rather baffled that the largest and most prominent picture on the “Vervet” Pffft! page is a close-up of testicles and penis. And the caption helpfully informs me that the balls are a lovely shade of blue. 286. I gratefully thank those people who invented microwaves. I gratefully thank those people who inveted microwave dinners. I gratefully thank the Italians for spaghetti and evolution for shrimp. night rq 287. Esteleth has eaten ALL the gingerbread! Suck it! says Gilliel, you forgot to thank the Americans, for domesticating the tomato, and for figuring out that it is tasty. 288. says Winter (used to) kill off ticks and other parasites. Also, useful if you live in Russia and Wehrmacht is coming. Or, in Finland, and the Red Army is coming. :) It worked both ways for the mighty Soviet war machine. At the moment, however, I don’t like this -20ish °C (or worse) weather at all. Expected to get warmer towards the end of the week. 289. Janine: Hallucinating Liar says Giliell, if I could, I would send you to a world without shrimp. 290. carlie says I hate being too hot. When I am at melting temperature, I can’t do anything but lie around and gasp like a beached carp. But in the cold, I get into a half-frozen hibernation like state in which I can’t even bear to move. So I guess I’m pretty lazy either way. :) (but yes cold is worse) More than cold, what I hate about winter is darkness. Miserable, awful darkness. 291. Esteleth Gilliel, you forgot to thank the Americans, for domesticating the tomato, and for figuring out that it is tasty. Generally speaking: yes In this case: no White wine and cream sauce. Janine Why? It would be less tasty 292. Janine: Hallucinating Liar says Buffy joke. It could be a world of shrimp. 293. birgerjohansson While not dissing USMC more than the rest, I am seriously worried that nations with a professional army/ armed force have a cadre of people sworn to obey orders, even when going into foreign lands for very shady reasons. Once they have shot up everything, and received horrible prychological or physical traumas in return, they will slowly realise it was all because some asswipe wanted to secure his re-election. General Smedley Butler, one of the most decorated Marines in history (Behind Chesty Puller, apparently), definitely caught on eventually: (Warning, mild wall of text.) I spent thirty-three years and four months in active military service as a member of this country’s most agile military force, the Marine Corps. I served in all commissioned ranks from Second Lieutenant to Major-General. And during that period, I spent most of my time being a high class muscle-man for Big Business, for Wall Street and for the Bankers. In short, I was a racketeer, a gangster for capitalism. I suspected I was just part of a racket at the time. Now I am sure of it. Like all the members of the military profession, I never had a thought of my own until I left the service. My mental faculties remained in suspended animation while I obeyed the orders of higher-ups. This is typical with everyone in the military service. I helped make Mexico, especially Tampico, safe for American oil interests in 1914. I helped make Haiti and Cuba a decent place for the National City Bank boys to collect revenues in. I helped in the raping of half a dozen Central American republics for the benefits of Wall Street. The record of racketeering is long. I helped purify Nicaragua for the international banking house of Brown Brothers in 1909-1912. I brought light to the Dominican Republic for American sugar interests in 1916. In China I helped to see to it that Standard Oil went its way unmolested. During those years, I had, as the boys in the back room would say, a swell racket. Looking back on it, I feel that I could have given Al Capone a few hints. The best he could do was to operate his racket in three districts. I operated on three continents. There’s more like it in his book War is a Racket 294. Nerd of Redhead, Dances OM Trolls says Shrimp are on the high cholesterol list. The Redhead is having a blood lipid test at the end of the month, and is wigging out over it, so I’ve been online finding out the naughty/nice lists. 295. Janine Buffy joke. It could be a world of shrimp. Ahhh, that makes sense. No, I still don’t understand the joke, but I understand now what that whooshing noise over my head was. 296. Azkyroth, Former Growing Toaster Oven says I thought a factoid was a fact that hadn’t entered the atmosphere yet. O.o 297. Portia, sporty and glam, pelted with pastries says I have eaten about 9 cream cheese cookies today and I don’t regret a thing. Also, I have been freezing all damn day. I hate being cold. There are times where I just can’t bundle enough. My nose always gets really cold. I love being hot, because it means I’m not cold. Cold is terrible, awful, and uncomfortable. And I was born and raised in Michigan of all places. People tell me I should be used to the Midwestern winters, but I tell them it just means I know how to bundle, not that I enjoy the cold. *shiver* 298. birgerjohansson says I gratefully thank those who invented indoor plumbing. Imagine going to the outhouse in temperatures of -20 C and discovering a bear has chosen to hibernate there*. *As Magrat, the third of the Lancre witches did once. Pratchett has a weird imagination. — — — — — — Weird film titles; Cockneys and Zombies. Some Dude Killing People. The Killer Condom (the last one -a German detective spoof set in New York- has the best reviews). — — — — — — The moon is up, the temperature is down. And the copies of Science arrive two weeks after the publishing date. Me is grumpy. 299. thunk, cold air advection says Portia: Speaking of tea, it was surprisingly powerful in influencing world events. Brits wanted tea. China had it, and they set the rules. Which led to the British selling opium, and an eventual war which saw the East crumble. 300. thunk, cold air advection says I don’t mind the cold. I’m so used to my extremities being this way; it’s become commonplace. I just can’t sleep in Hot. I hate Hot. It’s miserable. But then again, I come from St. Petersburg. What do you expect? 301. Tony ∞2012 recipient of the coronal mass erection∞ says I feel dirty dealing with those racist fuckwits at Ashley’s blog. And I really hate nested comments. Trying to find the racist assholes and their comments was a little difficult. 302. Tony ∞2012 recipient of the coronal mass erection∞ says thunk: sleeping in heat is miserable, I agree. In the wake of Hurricane Ivan (back in ’04), we went without power for 11 days. This was in September. In NW Florida. It was miserable. Thankfully we still had water, so we were able to take cold showers before bed. We didn’t have the foresight to purchase the necessary items before the storm, so when the sun went down, we were sitting in near darkness. I remember going to bed as early as 9. Back then my bar job had me at work until midnight, so I was going to sleep around 3 or 4. Heck, even though I’m done at my current job no later than 10 (most nights), I still remain awake until 2 or 3. In fact, I’ve noticed that about the time I’m going to sleep, rq has begun posting here :) 303. Azkyroth, Former Growing Toaster Oven says But then again, I come from St. Petersburg. What do you expect? Resignation, cynical humor, and possibly a fur hat? 0:) 304. carlie says *crawls in* One more day of classes. One. More. Day. Speaking of tea, it was surprisingly powerful in influencing world events. History of the World in Six Glasses.Great book. Can I do a computer question – I have a new laptop, and it’s doing these weird cursor things (Windows 7, which I did have on my old machine as well). Sometimes when I’m typing it will jump to the middle of a word somewhere else, which I think might be a leaning on the freaking stupid gigantic track pad problem, but it also does this weird thing even with a keyboard attached where the little line that shows the cursor doesn’t move when you use the mouse and move it, so then you don’t know where the cursor really is. Like right now the cursor line is at the end of my words, but if I use the mouse to go up to the last paragraph to change something, the line doesn’t move with it even though if I start typing it shows up there. Very annoying. 305. thunk, cold air advection says Azkyroth: Resignation, cynical humor, and possibly a fur hat? 0:) Only the first two. Fur hats are too expensive to lose as often as I do. Cicely: History of the World in Six Glasses.Great book. Haven’t heard of that one, but I know another history course uses a lot of “The Sweetness of Power”. Sugar’s the same deal, especially when it goes into the tea. 306. Ogvorbis says I thought a factoid was a fact that hadn’t entered the atmosphere yet. And when it enters the atmosphere and starts to have an effect, it would be a factite? And when it actually hits, then it is finally a fact? Works for me. And I can think of a few people for whom a high speed fact upside the head would be a good thing. Many people suffer severe cases of factile dysfunction. Wife says they are taking liagra. ===== Wife bought some Seagram’s wine coolers to celebrate. And when we got home she discovered that they are flavoured beer. Yes, folks, strawberry beer. (I had a Harpoon Winter Ale). ===== For the past three years, I have been dealing with about 60k of unsecured debt. I was stupid enough to pay for medical bills with unsecured loans, credit cards, etc. Wife and I went through a company that does the debt negotiation bit. A little over three years of 1200 a month going into a bank account (minus fees). And we paid our last payment last week and are actually free of debt (well, except for mortgage, student loans for Kids, and car payment). It was scary as hell but if we hadn’t done it, we would still owe about 58k. After three years of payments. 307. Portia, sporty and glam, pelted with pastries says Ogvorbis: Congrats on getting out from under that. SO does bankruptcy law and sees lots of good people in tough situations because of predatory lending or unexpected difficulties like medical bills. I’m glad that a debt negotiation company worked out for you, so many of them are scams in sheep’s clothing. Cheers! I’ll raise a glass for you and Mrs. Oggie. 308. Portia, sporty and glam, pelted with pastries says *consumer bankruptcy, that is, he represents debtors, not creditors. 309. Ogvorbis says I’m glad that a debt negotiation company worked out for you, so many of them are scams in sheep’s clothing. First thing we did was check out BBB. This company had (I think) four complaints in the past 2 years and all had been settled to the satisfaction of the client. Of the ones we looked at, one had no BBB complaints at all (which I thought very suspicious) and another had about 100. We still have one debt out there but the amount in our account should cover the negotiated settlement. Scary but it worked. 310. Ogvorbis says SO does bankruptcy law Is that how the SO can afford a Portia? Sorry. I could not resist. Especially after the conversation a few weeks ago. I should have resisted but I’m not a resistor, I’m a conductor. 311. Portia, sporty and glam, pelted with pastries says That got a legit LOL, Og. (Sadly, neither of us are stereotypical rich lawyers. Though he has more disposable income now that he has told the ex he doesn’t want to give money to pay the Catholic church to indoctrinate his children anymore). 312. Esteleth has eaten ALL the gingerbread! Suck it! says Side gloat: I called my insurance agent today. He’s an independent agent, who sells coverage from a dozen different companies. I complained about my rates going up. Thirty minutes later, I had identical coverage for 40% of the cost. ^_^ *confetti* and *champagne* for Mr. and Mrs. Oggie on getting debt-free! 313. Tony ∞2012 recipient of the coronal mass erection∞ says Oggie @316: And when it enters the atmosphere and starts to have an effect, it would be a factite? And when it actually hits, then it is finally a fact? Works for me. And I can think of a few people for whom a high speed fact upside the head would be a good thing. Many people suffer severe cases of factile dysfunction. Wife says they are taking liagra. This was pure gold. You rock! And that’s a fact. 314. Portia, sporty and glam, pelted with pastries says Woot! for Esteleth! Way to go. 315. Tony ∞2012 recipient of the coronal mass erection∞ says -Ok, so I’m sure many of the Pharyngula regulars are familiar with the BP Oil Spill a few years ago. At the time of the spill, I worked at a seafood restaurant that’s literally on the gulf. It’s quite beautiful and is one of Pensacola’s tourist attractions. Once BP started having to compensate people for loss of money, I knew *so* many people that got pay outs. Some people were getting multiple checks varying anywhere from 3-30K. There didn’t seem to be a rhyme or reason to how people received money. At the time, I opted not to file a claim. I’ve recorded all my tips for the last 10 years or so (when I get off work, I mark it on my calendar, or enter the amount in my phone). That way I know how much money I’ve made on any given day of the year (it also allows me to have a good idea of which holidays are busier than others). I did not notice any significant difference in money following the oil spill versus the same time the prior year. My thinking was that despite the tremendous amount of money that BP was paying out that it wouldn’t be fair of me to file a claim and get money (I know several people who said they don’t think they were affected and just wanted free money) when there are people who actually *were* affected by the oil spill. I thought it would have been shitty of me to take money away from those who actually needed it. -Fast forward to a few days ago. A coworker mentioned that he was in the process of filing a claim (heck, I didn’t know BP was still paying people out). I told him all of the above, and his response made me completely rethink the situation. He framed it in terms of how many people would have come to this region had the oil spill not happened (this is likely a sizeable amount, as many hotels saw a tremendous decline in business for roughly a year following the spill). I may not have made less money than the year before, but how much *more* money would I have made had the oil spill not occurred? I still have no clue how one could figure out such a hypothetical amount. However, given my current financial status, I do plan to look into it. If I get back some funds, that would be stellar. If not, well I’m no worse off. 316. Esteleth has eaten ALL the gingerbread! Suck it! says The insurance guy also gave me cake. Good cake! And thanked me for calling, rather than just dropping the coverage and going to somewhere else. Says that as a small business owner, customer loyalty is how he stays in business. My heart got all soft. 317. Tony ∞2012 recipient of the coronal mass erection∞ says Oggie, Esteleth: Congratulations to both of you! 318. Tony ∞2012 recipient of the coronal mass erection∞ says Esteleth: What type of cake was it? *** Anyone familiar with this Tears in Rain book (the ads are all over FtB)? 319. Esteleth has eaten ALL the gingerbread! Suck it! says What type of cake was it? Chocolate fondant. With chunks of Oreos. 320. Tony ∞2012 recipient of the coronal mass erection∞ says Portia @306: It sucks having no hair in the winter. My head gets reeeeeeeally cold. So do my ears and toes. Of course the heat of the summer is no kinder to my bald head either. Imagine going out to eat with someone who orders spicy food. I’ve had to have extra napkins/linens for my head. People get a kick out of it. It doesn’t bother me, but it is annoying to be enjoying my meal and have to wipe sweat off my face before it hits my eye. 321. Portia, sporty and glam, pelted with pastries says I say take whatever you can from those asshats, Tony. Good for you. 322. Portia, sporty and glam, pelted with pastries says Huh, yeah I can’t imagine what it’s like to have to dab one’s scalp for perspiration. : ) On the other hand, you have no problem with hat hair in the cold! I’m looking into getting an electric heater to get myself through the winter. While I’m dreaming, I want an electric free-standing fireplace for my office. 323. Esteleth has eaten ALL the gingerbread! Suck it! says In an odd twist, the new insurance company wanted to run my driving history for the past 5 years. So they asked for my license number from before I moved to New York. I blanked. Who memorizes their license number, after all? I asked the agent if he had any suggestions. He asked if this was my first license. I said yes. He asked if I’d ever been on my parents’ insurance. I said yes. So he said to call them. Because my license number would have been listed on their policies as I was an insured driver. Cue a truly baffling conversation with my parents. Was exciting. 324. Janine: Hallucinating Liar says Here is your chance to be able to live with other Patriots™ when the economic collapse happens. If you are a patriotic American who believes in Jefferson’s Rightful Liberty, who believes in the Constitution as written, who believes in the Declaration of Independence, and who wishes to live in a beautiful, secure mountain town that bans Liberals from living among us, consider exploring the Citadel as we evolve and build. If you need to escape your suburban life and the vulnerabilities your family faces, consider the Citadel. …the Constitution as written…? Woo hoo! Can we keep slaves and allow only land owning white men a voice in civic affairs? 325. Richard Austin says Who memorizes their license number, after all? *blink* … I thought most people did? Like their credit cards and social security number? Then again, I memorize monologues for fun, so I may not be an accurate judge of “typical”… 326. Esteleth has eaten ALL the gingerbread! Suck it! says Let me rephrase, Richard: Who has the number for a license that expired 3 years ago memorized? 327. cicely (fair-to-partly-cloudy) says Cicely: History of the World in Six Glasses.Great book. carlie, not cicely. I can always tell the difference! And we paid our last payment last week and are actually free of debt (well, except for mortgage, student loans for Kids, and car payment). Huzzah! And, Ogvorbis, the more I think about it, the more sure I am that I owe you an apology. I definitely over-reacted to the USMC thing. It’s a bit of a knee-jerky spot for me, so I was a bit jerky. (And I think everyone here is already familiar with my knees.) I’m sorry. 328. Richard Austin says Let me rephrase, Richard: Who has the number for a license that expired 3 years ago memorized? Still living in my birthstate, so I can’t say I do. I still remember all the license plate numbers for my parents’ cars when I was growing up, does that count? :) 329. Azkyroth, Former Growing Toaster Oven says Thunk, you’re still in high school, right? 330. Azkyroth, Former Growing Toaster Oven says (Because otherwise I just received an email from my department about a summer internship related to atmospheric science…but it’s specifically for US citizens enrolled at a four year college D:) 331. mildlymagnificent says Yaaaay! Our solar panels are now seriously paying off! Just got the quarterly “bill” with a credit balance on it. A credit balance!! So for a cash outlay of less than 3000 dollars we’re now expecting 2 entirely free quarters a year and it’ll depend on how cold winter is, how hot summer is, (and how good the new, extra insulation is) how much we’ll pay for the other two quarters. (Sorry to brag – Australia’s subsidy/bonus/feed in tariffs seem to be better than in USA – and we have much cheaper and easier installation to keep the costs down. But whoopee!) 332. Rey Fox says Janine: But they’ll have a Firearms Museum! 333. broboxley OT says scored a huge win. Few days ago son asked me to order “Girl who kicked over a hornets nest” for his SO for christmas. Decided to buy my xmas present for myself at the same time. Ordered a few pratchett’s I haven’t read. Read the blurb for “the last hero” put it on the list. Books arrived today. That book IS THE FULLY ILLUSTRATED VERSION!! supersized glorious looking pictures. Will enjoy this one in many different ways. 334. broboxley OT says shit, a facebook entry just landed in my inbox “So my best friend gets in the car and says, ya know, I think onions, think they are ugly. I asked her why, she said because you get them naked and start crying. If you got me naked, and started crying, I’d be offended.hahahahhaha omg.” the best friend in question is my 14yo dottir sigh 335. says Hey folks… Made it home safe! This place is HUGE!! 336. Menyambal --- son of a son of a bachelor says Improbable Joe, YAY!!! 337. ImaginesABeach says Yea Joe! Have a great reunion with BossNurse and enjoy a night in a home that finally feels safe. 338. cicely (fair-to-partly-cloudy) says YAY! 339. thunk, cold air advection says Cicely: C. Six. Letters. GAAAAAAAAAAHHHHHH!!! Azkyroth: Why yes I am in high school. But I’m curious anyway. 340. thunk, cold air advection says Joe: Hooray! You’re home! 341. I posted this on Facebook too but: any tips for getting good hotel deals? Specifically when you’ve already decided on a hotel (so none of those Priceline gigs where you basically say “give me someplace to stay, cheap”. Misterc and I are going for a weekend trip to the Big City for our anniversary next summer and I’d like to get as good a price as possible for a hotel with a wee bit of luxury. Said hotel chain already has a “lowest price guarantee” on their own website. 342. broboxley OT says double down on yays! for joe 343. Yay for Joe, Esteleth,Ogvorbis, and mildlymagnificent. @Broboxley AFAIK, all copies of The last Hero are illustrated, and it does indeed kick ass on many levels. rq The Tiffany Aching books are suitable for younger children, although the very young might need reading to. Other books that occurred to me: the Ramona Quimby books by Beverly Cleary. And yay for me, I just got upgraded to full time, which means I get health benefits now, and also a few hundred dollars more in my next paycheck, which will be an enormous help. 344. Nerd of Redhead, Dances OM Trolls says Good news here for a change: Joe, Oggie, and Esteleth, throws confetti in their general direction. 345. broboxley OT says #351 kristinc which big city? 346. Portia, sporty and glam, pelted with pastries says Awesome, Joe!!! === I ♥ Ramona 347. broboxley OT says kristinc, never mind, you already decided on the hotel… So for others DC area during the weekend Greenbelt courtyard marriot, take the train, good restaurants nearby NYC best western on the Jersey side of nyc at the base of GW bridge SanFran Top of the Mark weekdays ATL IHG perimeter YMMV 348. Azkyroth, Former Growing Toaster Oven says NYC best western on the Jersey side of nyc at the base of GW bridge SanFran Top of the Mark weekdays ATL IHG perimeter YMMV EIEIO? 349. Azkyroth, Former Growing Toaster Oven says Thunk: email text is as follows: 2013 NASA Student Airborne Research Program (SARP) June 9 – August 2, 2013 The NASA Airborne Science Program invites highly motivated junior and senior undergraduates to apply for participation in the NASA Student Airborne Research Program (SARP 2013). SARP provides students with hands-on research experience in all aspects of a major scientific campaign, from detailed planning on how to achieve mission objectives to formal presentation of results and conclusions to peers and others. Participants will fly onboard the NASA DC-8 aircraft where they will assist in the operation of instruments to sample and measure atmospheric gases and to image land and water surfaces in multiple spectral bands. Along with airborne data collection, students will participate in taking measurements at field sites. Students will work in multi-disciplinary teams to study surface, atmospheric, and oceanographic processes. Each student will develop his/her own individual research project. Many students have gone on to present their results at conferences such as AGU, AMS, and ASLO. Instrument and flight preparations, and the research flights themselves, will take place at NASA’s Dryden Aircraft Operations Facility, in Palmdale, CA. Post-flight data analysis and interpretation will take place at the University of California, Irvine. Applicants must have a strong academic background in any of the physical, chemical, or biological sciences, or engineering and an interest in applying their background to the study of the Earth system. We especially encourage applications from students majoring in Earth, environmental or atmospheric sciences and related disciplines. SARP participants will receive round-trip travel to California, housing and transportation during the 8-week program, a 3000 stipend and a 2500 meals allowance. The deadline for all applications is Feb. 8, 2013. Applicants must be US citizens currently enrolled in a four-year college or university. For more information and to download the program application, visit: http://www.nserc.und.edu/learning/SARP2013.html. To watch a video about the program, visit http://www.youtube.com/watch?v=B2-jqE43PG0 Please also see the attached flyer. Specific questions about the program should be directed to SARP2013@nserc.und.edu. Emily Schaller, Ph.D. Science and Education Coordinator National Suborbital Education and Research Center 701-317-0789 e.schaller@nserc.und.edu 350. Portia, sporty and glam, pelted with pastries says In case anyone wants to know how, I learned how to remove an alternator from a diesel engine tonight. And by learned how, I mean I held the light and asked intermittent questions. 351. Tony ∞2012 recipient of the coronal mass erection∞ says Joe: Awesome. Happy for you buddy. 352. thunk, cold air advection says Azkyroth: Aight. I presume there’ll be some in future years. 353. Portia, sporty and glam, pelted with pastries says G’night everybody, hope everyone is as well or better in the morning. 354. Menyambal --- son of a son of a bachelor says A few years back, when Prince William was still unmarried, I posted somewhere that the United Kingdom needed to change the royal inheritance laws. If the first-born royal child was a girl, and greeted as third in line to the throne (making it Chucko, William, William’s child), that would be all fine and dandy, until a boy child was born and took precedence in the line to the throne, displacing the female. Then several kinds of heck would break out, with women everywhere rightly taking umbrage. So it turns out that the UK and the Commonwealth figured out the same thing (or read my post), and have enacted that as law, and back-dated it, even, to make it more legal. If the first child of the now-pregnant Kate formerly-Middleton is a girl, that girl is 3rd-heir to the throne, and her little brother cannot bump her out. The interesting thing to me is that the ancient and medieval law that they had to overturn, after untold centuries of male-privileged Dark-Age patronage, was only enacted in 1701. Apparently, before that, the first-born got the job, regardless of the shape of their plumbing. But in 1701 the menz took care to take precedent. I may research that a bit, but I thought it was odd. 355. chigau (無) says Yay for everything good! Especially Improbable Joe and BossNurse. (how are the critters taking it?) Hugs and rum for everything ungood. 356. I HAVE A NEW BEHBEH NEPHEW! That is all. Carry on. 357. *scrolls up* HOORAY FOR JOE!! 358. chigau (無) says Anyone awake I’m at comment #157 on the “It’s a good idea…” thread should I keep reading or skip to the end? 359. mildlymagnificent says Well done Joe. Happiness all round. And for all other good news. Menyambal – 1701. I see the pernicious hands of the two Jameses here. Succeeding Elizabeth they set about reversing all the advantages of education and trade that women had previously had – even before Elizabeth’s time women could own and run businesses http://www.antithetical.org/restlesswind/plinth/wimguild2.html (just my first googly hit). I haven’t the book handy, but I remember reading a quote from one noblewoman lamenting the loss of rights during this period, particularly education for her class, that nowadays a “woman needs only wit enough to tell her husband’s bed from any other” – that isn’t accurate in the words used but it is in content/tone. 360. Anyone awake I’m at comment #157 on the “It’s a good idea…” thread should I keep reading or skip to the end? There’s pot brownies and kumbaya with lurkers at the end… I recommend skipping. 361. Beatrice says good morning Congrats Sally, Joe, Ogvorbis and whoever else had something good happen to them! 362. chigau (無) says SallyStrange #370 I read to the end and snuck some brownies. *The InterNets is Hard!* and I have seven more threads to do catch-up… I know moar beer! 363. Good morning I think I have an appointment at 9 am with my dentist. I don’t know for sure. I’m pretty sure I’m not going to make 9… Yay! For all those great news. Portia How come I know a bunch of lawyers but no rich ones? OK, I know one who’s doing pretty well… 364. chigau (無) says I really like graham crackers. 365. rq says Good morning! No sun again today. Ah well, at least we made it outside yesterday. +++ *fur hat for Tony, should he ever decide to go North* Hoorays, confetti, chocolate cakes and beer for Ogvorbis and wife, and for Improbable Joe and BossNurse. Hoorays, general cheering, and sparkling champagne for all those whose insurance has been lowered (Esteleth), those coming into some money (via promotion/status change at work) (Dalillama), those whose investments are starting to pay off (mildlymagnificent – my aunt took advantage of the same program, and is expecting some returns around this time, as well!). Hugs, moral support, mulled wine and/or hot chocolate and gingerbread to those needing some warmth. +++ I’m adding myself to the ‘coming into money’ group, because I received another sudden unexpected translating (side)job which will triple my usual monthly translating income for January. This is on top of the one I did in October that has a quadruple effect and the one I just finished with a double effect. Yes, I am gloating a little bit. Because house. Now approaching faster than a well-aimed factoid. 366. Speaking of financial bonuses, I also indirectly got a check from my last employer. I say indirectly because the check was my share of a class action settlement against them for wage theft, and some law firm actually sent the check. 367. rq says chigau So do I. At least, I did. It’s been years. 368. rq says Dalillama Sweeeeeet. For me, it’s just a bit weird to realize that my side-job/hobby is now earning me almost twice as much as my ‘real’ job does. :/ With a minimum of effort. If I didn’t love the lab so much, I know what I would do. And no, forensic lab work here isn’t super-lucrative (like it should be). It’s pretty low down the list, which is why I need the translating in the first place… 369. ednaz says JOE IS HOME!! Hooray! No one deserves it more! mildlymagnificent – Hooray for solar panels! I am so jealous! I wish the U.S. would get with the solar panel program. Esteleth – Hooray for a better insurance deal! Portia – Good Job Assistant Auto Mechanic! chigau – I brought more rum for all the celebrating! hee hee SallyStrange – Hooray for the New Bebeh Nephew! I bet Auntie is so happy! rq – Hooray for more income! Anyone I have missed – have some rum! I brought plenty! : D : D : D : D 370. rq says Today’s excitement is provided by the fire engine and ambulance pulling up outside of the building, and a whole lot of bustle and discussion between firemen, paramedics and the building’s caretaker. :/ 371. rq I just remembered some more books, younger ones this time: Half Magic by Edward Eager and The Boxcar Children by Gertrude Chandler Warner. Both have several sequels, as well. 372. Beatrice says Another congrats to everyone getting some unexpected boost in income. rq, Someone got stuck in the elevator? The interview today went really well. The interviewer told me that a board makes the final decision, but I’m her candidate. And there were only 5 of us. On the other hand… I think there is something about my eager face that makes people tell me “you’re my best candidate”, “I would give you the job immediately”, “I hope the board chooses you” and similar. So that kind of encouragement leaves me more and more doubtful. 373. rq says Dalillama Oh, I remember the Boxcar children! That was a good series. Which automatically leads me to The Saddle Club (cicely‘s favourite!). Which, if I recall correctly, were also pretty decent and with lots of sequels. Beatrice That’s my guess, too. re: interviews One of those times they’ll actually give it to you. Eager faces in interviews are supposed to be good, yes? :) I have added more thumbs to your pile! :) 374. rq says Make that two fire engines – one with a ladder. But it was parked on the other side of the building, so the boys didn’t see it until it was driving away. They seem disappointed. (And yes, it was either a renovations incident with the neighbours upstairs (their fervent drilling and sawing was suddenly cut short shortly before the arrival of emergency vehicles), or somebody got stuck in the elevator. Since we’re right next to it, and the firemen mostly sat in their truck after the initial conversation, I’m betting the former.) 375. beatrice How about this: I think there is something about my eager face that makes people tell me “you’re my best candidate”, “I would give you the job immediately”, “I hope the board chooses you” and similar. So that kind of encouragement leaves me more and more doubtful. understand that I’m really looking forward to that job and that my motivation is a huge plus. I think you have convinced yourself thoroughly that you’re really a failure and therefore every person who says something nice about you is just doing that: being nice so you don’t make sad puppy eyes, because, honestly, why would anybody think you’re really the best person* for that job? How do I know? Well, I have a mirror. Because I’m just the same. It took me a while to accept human kindness just as that and to believe people who sincerely expressed some compassion for me. When people said I really had a busy life, I would think they’re just being nice. (((hugs))) and good luck for the job. *There is no “best person” for a job. Within every group that applies there will be several people who are 100% able to do the job and the actual job-performance will vary a lot with factors no person doing an interview or reading resumees can tell in advance. 376. rq says Beatrice Giliell has once again put me to shame. What she said. Because you have to believe that sometimes, you are the best person for the job. True story: my cousin applied for a job (in Brussels) with one opening, 3 candidates. The interviewer loved her, told her so, and told her she’d push for her in the committee meeting. Unfortunately, she didn’t get the position. BUT. Two weeks later she got a call from the company, from the interviewer, with news that, because she liked her so much and put in a good word for her, they’d opened a second position just so they could hire her. True story. :) Anecdotal and all that, but – consider, as Giliell said, that they may actually be telling you the truth. And allow yourself to feel special for it. :) *hugs* 377. Beatrice says Giliell, Yeah, that definitely sounds like me. That’s why I also can’t take compliments. I immediately wonder why this person said this nice thing about me. What’s the deal, an agenda or I just looked pathetic? It’s really tiring, actually, always secondtenth(?)guessing everything. I’m glad you got better at this. There’s hope for me too, then. :) 378. opposablethumbs says Drive-by, sadly – just to say YAYYYYY for Joe and Esteleth and SallyStrange et al, and hugsandchocolate for any whose hugsandchololate metabolism needs a boost for any reason. Crossed tentacles for Beatrice. (also, wow that was a couple of unbelievably nasty shitstains on Ashley’s blog just now. The guy who drafted a letter of apology to her dad on her behalf actually gave me chills – the thought of having a smiling, self-satisfied psychopath like that as a father, exercising power over you and feeling so happy doing it … real horror-film grade chills. But worse, because he and those like him are so numerous, and are real) 379. beatrice There’s definetly hope. And believe me, life gets better then. But I admit that it’s hard work and that I’m still learning. You know when you have to practise saying things?Mine is “yes, thank you!” +++ What am i doing in the kitchen making cookie dough when I have a presentation to write? 380. rq says Giliell Procrastinating? opposablethumbs Agreed on the racist bigots on that thread. *shudder* You know what struck me about the second one? The fact that he constantly referred to Ashley’s boyfriend as ‘the black male’. Like he wasn’t even human. HOW DO PEOPLE DO THAT? :( +++ Also, I previously forgot SallyStrange in my list of Good Things for People with Good News, so wild applause, leaps of joy, and delicious, delicious pie (of your choice) with ice cream (your choice) in celebration of the Big Event! Spoil that nephew rotten. His parents deserve it, no doubt. ;) 381. rq says Oh and gift ideas for those with small children in the family. 382. Nick Gotts (formerly KG) says The interesting thing to me is that the ancient and medieval law that they had to overturn, after untold centuries of male-privileged Dark-Age patronage, was only enacted in 1701. Apparently, before that, the first-born got the job, regardless of the shape of their plumbing. – Menyambal Not true at all. Henry VIII was succeeded, in 1547, by his son, Edward VI, who had two older sisters (later Mary I and Elizabeth I). Edward IV was succeeded, in 1470, by his son Edward V, who also had two older sisters living. I’m sure there are other examples, given that no woman succeeded to the throne before Mary I. (Henry I tried to leave the throne to his daughter Matilda in 1135 – he had no living son – but her cousin Stephen displaced her.) What may well be true is that the rules weren’t written down until 1701, when the Act of Settlement made it explicit that Parliament had the power to specify the rules of succession. 383. rq Procrastinating? Partly. That’s why I prefer working in the library. I’m really bad at getting organized and doing something from start to finish and setting priorities. So at home with all the other things that have to be done, too, I will “quickly load the dishwasher”, “just do the laundry so it can run while I work on this” or just plain trip over something and then clean it up. In the library I’m forced to wirk on one thing… But I’ve done the biggest part of it now, so, lunch. 384. rq says Giliell That’s my problem working from home, too. There’s always something to pick up or clean. Ah well. Good luck with the presentation!! And put those chores down. 385. Well, I’m mostly going to take a shower now. I have the main part worked out intellectually. I need to get the materials scanned and included but not this afternoon. +++ mini-rant: My last name is spelled with an E. There’s no Ä in it, damn it. Why can’t even people with a PhD bother? +++ more rant: Reading over Ashley’s thread again, I often hope that, in absence of a just god, people who got such shit from their parents will in the end not be the bigger person and will just let them grow old and bitter alone, always aware that out there is your child, probably even your grandchildren, who would keep you company now, visit you, call you, love you, take care of you, but you, you alone drove them away by being a shitty asshole and sorry excuse for a human being. 386. rq says *fewf* Just made it through the straw thread. Wow. On to the evo-psych. 387. rq says Ah, I do so love it when all the children are napping and I set off the fire-alarm with my dinner preparations… 388. Portia, sporty and glam, pelted with pastries says Giliell How come I know a bunch of lawyers but no rich ones? OK, I know one who’s doing pretty well… Ha, don’t get me started ; ) rq Yes, I am gloating a little bit. Because house. Now approaching faster than a well-aimed factoid. Congratulations!!! SallyStrange *confetti* and *cigarsifyouwish* :D Beatrice Fingers crossed that the encouragement was sincere! Giliell What am i doing in the kitchen making cookie dough when I have a presentation to write? Because you need brain food. No procrastination guilt : ) rq That’s my problem working from home, too. There’s always something to pick up or clean. Ditto. Sigh. Re: children’s books. You all keep naming some of my favorites from growing up. 389. Esteleth has eaten ALL the gingerbread! Suck it! says Nothing like randomly keyboard mashing at PubMed and finding a 2008 paper that explains all of your experimental problems. *flail* 390. rq says Portia Just so you know, when I say ‘Iago’, I mean this one. :) 391. Portia, sporty and glam, pelted with pastries says I read that thread at Ashley Miller’s yesterday and checked again to see that letter. Fucking awful. What a terrible human being. Glad to see she banned them. Which reminds me… This morning, we had a higher up at our Rotary event. This lady mentioned she wanted to find ways to reach out to the growing Latin@ community to bring them into Rotary. A woman from our local chapter piped up that “We have one in our club, FirstName HispanicLastName. He was adopted by a Hispanic family.” Said guy is lily white. I wouldn’t be so skeptical of his ability to present a diverse perspective that we would gain from Latin@ members if he hadn’t gone on a protracted, disgusting, racist and sexist diatribe in the middle of a meeting a couple of weeks ago. And yet he’s apparently considered to be our token minority because his wife and his parents are Latin@. I’m not totally qualified to be the judge of the situation, being white, but it makes me uncomfortable. 392. Portia, sporty and glam, pelted with pastries says rq HA! I was thinking this one! I had totally forgotten the parrot’s name. 393. Beatrice says I made Olivier salad/Russian salad (no meat version)… which is Russian. Since we call it francuska salata (French salad) over here, I was convinced it was from France until today. Anyway. I forgot the peas. I blame cicely. 394. rq says Beatrice I think that’s what we call ‘rosols’. Never liked the stuff anyway, mostly because of the peas. Portia re:#401 Damn, that makes me uncomfortable just reading about it. And that letter is horrendous. Imagine? The most important relationship she should be having is with her dad? For her entire life? Yeah… Wow. And yes, that Iago, because he says ‘Excellent work, Iago’ in Jafar’s voice in that clip, and that’s the effect I was going for previously. Also, red. Not quite sporty-and-glam, but it’s a parrot. :) Pirates have them. :) 395. Beatrice says rq, So. You join the pea haters. Ok. Ok. 396. Portia, sporty and glam, pelted with pastries says rq, Thanks for catching me up on the joke. :) And I like how you are building on my alter-ego/internet persona! Red is my favorite color to wear, so it works out. Lots of people’s fathers are very important to them…but that is freaking up to the individual. That creepwad is so twisted. My own dad is a very nice guy and was a good dad growing up. But now, he clearly prioritizes his live-in girlfriend at every opportunity. To the point that it is impossible for me to have one-on-one time with him. But I’m sure that asshat would have me apologize to my father for that fact. The slightly less overt misogyny of Larry’s attitudes are what really makes my skin crawl. The racist stuff makes me want to punch him, but the misogyny makes me scared. I guess that’s why intersectionality is so important… /rant. 397. thunk, cold air advection says Beatrice: So that’s that funny-looking salad thing at the center of the table? (aside from that vinegret). 398. Portia, sporty and glam, pelted with pastries says Beatrice, That salad looks really tasty. 399. Tony ∞2012 recipient of the coronal mass erection∞ says SallyStrange: Congrats on the addition to your extended family! **** Dalillama: More money coming your way! Very, very good news **** rq: It’s going to be easier to buy xmas presents now, what with the additional money from your side job. **** Anyone have a link to this letter @ Ashley’s blog? I won’t be on my laptop til later and searching on phone= not easy. **** 400. Portia, sporty and glam, pelted with pastries says 401. Tony ∞2012 recipient of the coronal mass erection∞ says Beatrice: Please picture me as a mad scientist with a curly mustache: “YES. We have won another over. Pea lovers of the world shall one day tremble before our po–hey squirrel!” 402. Beatrice says On the radio: Some sort of quack (didn’t listen from the beginning so I don’t know her credentials), talks some idiocy about positive thoughts. Science has become a form of religious dogma. People are taught that our whole health is in our genes. That our parents are to blame if we get a tumor, and that people are literally taught that. Breast cancer awareness programs are harmful because they make women think negative thoughts. SHe has a dear friend who became obsessed with checking her breasts for lumps. Until one day she found one, it turned out to be malignant. Radio host* asks “So she created it herself?”. Answer: “Yes”. I turned the radio off then. *This particular radio host is such an idjit I don’t doubt for a moment she actually swallowed this shit hook, line and sinker. 403. hockeymonkey says If anyone would like to give me an opinion or advice on the following letter, it’d be much appreciated. It’s in regards to a prayer offered at a cheerleading banquet. The cheerleading organization is affiliated with our public school. My daughter LOVES this activity, and I don’t want to single her out as having a “trouble-making parent”. Text follows: “I want to express my appreciation for all your hard work during this year’s cheer season. My daughter xxx had a fabulous time cheering for yyy, and can’t wait to begin again next season. It must be an incredible work load for you and your team to ensure it all runs so smoothly. It couldn’t happen without all the hard work you & the other board members put in. Thank you so much for that. We also had a lot of fun at the banquet. Overall, it was a wonderful event, and the girls really seemed to appreciate the recognition. However, I was a little uncomfortable with the prayer before the festivities. Asking for a blessing from God/the Father excludes those families who don’t have a belief in that vision of God, or in any Gods whatsoever. There are some wonderful secular blessings out there that celebrate the spirit of giving and thankfulness without referencing any sort of deity. Or perhaps a moment of silence could be offered, where all could choose to pray or reflect in the manner they see fit. As our organization is affiliated with the school district and accepts girls from all faith backgrounds, I think it’s especially important to remain neutral in matters of religion. Please let me know what you think. I’d be happy to discuss this further with you. 404. Beatrice says My French/Russian salad usually has: carrots potatoes PEAS eggs pickles —— cooked (except pickles, of course) and cut into little cubes mayonnaise salt I don’t really like mayonnaise in large quantities, so is usually looks more colorful and less like vegetables drowned in a gallon of mayonnaise. 405. thunk, cold air advection says One of our teachers is doing an intersession activity simply titled “HORSE!” Enough said. 406. dianne says Does anyone else wonder, just a little, if “Larry” might actually be Ashley Miller’s father? He’s so obsessed with the idea that she’s rebellious and that reconciling with her father is her only possible path to happiness… 407. Tony ∞2012 recipient of the coronal mass erection∞ says Hockeymonkey: I think the letter is perfect as is. 408. says Yay, Joe! When’s the housewarming? And listen, Thread, I really thought I’d commented that in last night, and it seems to have disappeared entirely… So… Ummm… Probably something to do with the general flakiness of smartphones for longer comments threads (you don’t want to know how cranky mine gets about even giving me an edit window in those in the first place, once we’re up to a few hundred comments). But if it did appear somewhere and I’m just missing it somehow, no, this you’re not experiencing dèja vu. Just in case. 409. Tony ∞2012 recipient of the coronal mass erection∞ says Beatrice: Salad purist here–where are your greens? I know, salads are composed of all kinds of ingredients, and greens aren’t always part of the mix. I’ve just always associated salad with the leafy veggies (I am aware of chicken salad and pasta salad). 410. says hockeymonkey/#413: I find that very diplomatic. But my window may be in a pretty strange place, relative to many. Anyway, for what it’s worth. … oh, also, I’d go with no capital on the plural ‘gods’. Normally is. God with the capital is fine elsewhere (the singular ‘God’ referring specifically to the Abrahamic figure) since it’s treated like a proper name in this said context. 411. Beatrice says Tony, Leafy greens and mayo? No way. Greens are to be unsullied by anything but salt, oil and vinegar. 412. Tony ∞2012 recipient of the coronal mass erection∞ says No love for freshly fround black pepper? :'( 413. Tony ∞2012 recipient of the coronal mass erection∞ says Fround? Really?! razzum frazzum stooopid phone. or alternative explanation: Darnit big fingers! 414. says Leafy greens and mayo? No way. Greens are to be unsullied by anything but salt, oil and vinegar. I like my greens with black pepper. Anything from spinach to Buk Choy needs to have a generous serving of crushed black pepper on it. Salad, not so much I guess… 415. Beatrice says Possibly. I have to correct my above statement above leafy greens. It depends on the kind. This goes only with salt, oil&vinegar. And that’s the one I most often eat. Some others, like rucola or radicchio, may be combined with eggs or beans, and then pepper is permissible. But never mayo. Looks like I’m a worse salad purist than you. ;) 416. Rey Fox says Um…congratulations to everyone for everything. Also, sllrpnls? 417. rq says Tony Extra cash does not me a happy shopper instantly make. I’d still delegate to you, if there was enough time. Plus, that money’s going into the future-house-furniture fund, because if we don’t put it away, it’ll fritter away slowly into nothing. Because money has a short half-life in this household. As for salads, well, potato salad never has leafy greens. Why is it called a salad? Chicken salad? Nyah nyah. You said it yourself. That being said, I love green salads with a passion matched only by my love for horses. Or something. Yummy vit-amins. Beatrice I am only a fan of horses. I have never liked peas. I can bear with them, and I don’t jerk my knee like cicely does, but I’m not a fan. I’ll eat them in salads if covered in mayo, but that’s about it. hockeymonkey That letter sounds very good to me. But I don’t have any experience in these matters. For what it’s worth. Portia If I ever have the time, I will make you a picture of your internet persona. I love playing in photoshop; unfortunately, my free time is already all eaten up by all kinds of things. As for dads, Larry just freaks the hell out of me, because, because… Yes, the overt misogyny, and the threatening undertones, like Ashley’s a child who is misbehaving and will be punished eventually… It’s just scary reading, is what it is. Ick. 418. Rey Fox says One of our teachers is doing an intersession activity simply titled “HORSE!” Enough said. No, not enough said. Is it the basketball shooting game? Something different? Why the exclamation point? 419. Beatrice says And of course, spinach can go with all kinds of things. Er, spinach is a leafy green too. Ups. (Still not mayo) 420. Beatrice says So. Leafy greens and mayo? No way. GreensOne particular kind of leafy green which is the one I most often eat and apparently generalize onto everything are is to be unsullied by anything but salt, oil and vinegar. 421. rq says SPINACH. With mandarin slices, toasted almonds, and a raspberry-balsamic vinegar dressing. Salt and pepper obligatory. 422. Esteleth has eaten ALL the gingerbread! Suck it! says Oh, salad? My favorite: On a bed of fresh baby spinach, nice and green, add chopped hard-boiled egg, bacon, and feta cheese. Dribble honey mustard dressing over it all. (Also good: take all the aforementioned and put it inside a flatbread. OM NOM) 423. Beatrice says Spinach, salt, pepper, olive oil, balsamic vinegar and mozzarella. 424. Beatrice says A feta cheese salad: Fresh tomatoes, feta, cucumbers, peppers*, salt, pepper*, olive oil, lemon juice or a bit of vinegar *seriously, English? So many words, but then you have peppers and pepper 425. a_ray_in_dilbert_space says Crazy Climate Denialist quote of the week: “The advantage of my ignorance of the science is that I can offer an independent analysis of the data.” This was said in all seriousness after modeling Earth’s temperature as an unbounded random walk. One of the many reasons why this is WRONG, WRONG, WRONG is that it ignores conservation of energy. You really can’t make this stuff up. Unfortunately, you don’t have to. 426. says Spinach, finely chopped onion, creme fraiche, salt, pepper, walnuts. (And yes, I’m at work, it’s 0416am) 427. Portia, sporty and glam, pelted with pastries says Holy crap my phone is blowing up with new clients this week. I may be able to replace my junker before long after all. I went 3 for 3 with new client interviews who retained my services on Monday. More and more since then. I’ll need a paralegal if this keeps up… #bestproblemstohave 428. Matt Penfold says Spinach, new potatoes, black pudding, poached egg. 429. Beatrice says Portia, Yay! for getting lots of new clients. 430. Menyambal --- son of a son of a bachelor says Beatrice, back when I was researching the craziness of “alternative medicine”, I kept seeing a strong, strong emphasis on the value of positive thoughts. There were those who made it sound like the bogus meds were just there to give a focus to the positive thoughts, because mental attitude was everything. Yay for the power of the mind! Then every one of the bastards would start slagging conventional medicine, and say how it was useless and bad, and hospitals were bad and worse. Which was filling people with negative thoughts, and, if the power of the mind was so great, would probably lead to them …. no, I can’t think of anything to say except they were killing people. People would be lying in a modern hospital, getting the best of care, scaring themselves to death, and the “power of the mind” people would not see how they were responsible. 431. opposablethumbs says hockeymonkey 413 I also think the letter reads very well. Of course there may well be people who would have a fit and be up in arms over even so courteous an approach as this – but such people would perhaps find a way to feel “offended” by the mere suggestion that someone is querying them in the first place, so there’s no avoiding it! 432. Nepenthe says *taps mic* Is this thing on? 433. Nepenthe says Cool. Sorry for the intrusion. My posts haven’t been going through over at the anti-rape straw thread. 434. Portia, sporty and glam, pelted with pastries says thanks Beatrice: ) My fellow skeptics might have the same reaction I did to the following: I met with the tenant who lives in my grandfather’s house today. They are negotiating a sale and my grandpa asked me to be the go-between. The tenant is a really nice real estate agent. Four years ago, my grandmother passed away. Tenant asked me if she passed in the house. I said yes. He said, ok, that’s what we were thinking because we think she’s there. The table-top fake Christmas tree has been falling over, you see, and they couldn’t figure out why “her ghost” didn’t like the tree. Turns out, the lights on the table around the tree were getting to hot, and melting the feet the stree stood on. So, ergo, QED, her ghost is protecting them by alerting them the lights are dangerously hot by knocking over the tree. *facepalm* It was sweet, sort of, but kind of obnoxious in the way it was when everyone told me it was Gawd’s Plan™ when she passed away. (If a ghost can knock over a tree, why can a ghost not control a freaking pen and paper?!) 435. rq says Portia Yay! I don’t want to spoil the mood by calling it out, but today seems a general good-news day. That makes me happy. :) (I mean, this is if we ignore all those negative commenters on some rather gloomy and depressing posts…) Menyambal I’ve noticed that, too – as if actual medicine depresses eveyrone’s happy thoughts, and that’s why it doesn’t work, yet all the bogus stuff focuses happy thoughts and… magically magicks away disease? Yeah. +++ Speaking of magic, the boys’ current explanation for everything is ‘Magic!’ I hope it’s a phase. :P 436. Esteleth has eaten ALL the gingerbread! Suck it! says So today I said to myself, “Self, you pay 81.88 a month for TV cable service. And in the past six months, you watched MSNBC for 15 minutes, and have not otherwise touched your TV.” So I called Time Warner. Sat on hold, waded through their goddamn “tell the robot what you want” system, and got a customer service rep. Customer service rep first told me that TW had no record of me as a customer. (!!!) Then said that she’d transfer me to someone else who could help me. I then sat on hold for 20 minutes and then got hung up on. Stay classy, Time Warner. Stay classy. 437. Portia, sporty and glam, pelted with pastries says rq, you’re right. It has put me in a great mood :) 438. cicely (fair-to-partly-cloudy) says I really like graham crackers. Graham crackers really like Nutella. Congrats where due; behbehs,, etc.
“Faster than a speeding factoid!”
And once again, rq inadvertently catches my sister in her nets, as I swim freely away.
:D
The guy who drafted a letter of apology to her dad on her behalf[…]
I don’t wanta look.
I don’t.
.
.
.
Anyway. I forgot the peas. I blame cicely.
Indeed. Where ever there are peas to be forgotten, I will be there, in “spirit”, if not in corporeality.
O-o
Racist, patronising asswipe.
I am only a fan of horses. I have never liked peas. I can bear with them, and I don’t jerk my knee like cicely does, but I’m not a fan. I’ll eat them in salads if covered in mayo, but that’s about it.
1) Peas *hawwwwk! spit* are not improved by mayo, which has its own place on Nuggan’s List of Abominated Objects.
2) If I didn’t jerk my knees regularly, the damned things wouldn’t hardly get any exercise a-tall.
SPINACH.
With mandarin slices, toasted almonds, and a raspberry-balsamic vinegar dressing. Salt and pepper obligatory.
I can agree with you on this, except for the pepper. I avoid eating Painful Hot Objects. And the salt; these days, I get unpleasantly puffy feet and ankles if I get too much salt.
On a bed of fresh baby spinach, nice and green, add chopped hard-boiled egg, bacon, and feta cheese. Dribble honey mustard dressing over it all.
Also yummy.
439. broboxley OT says
(Guide to the Fundamentals of Culinary Arts) (1897) by P. Aleksandrova gave a recipe containing grouse, crawfish, potatoes, cucumber, lettuce, aspic, capers, olives and mayonnaise.
toss the lettuce and it sounds loverly
440. hockeymonkey says
Aww, thanks Tony, AJ Milne, rq, and opposable thumbs! I’m going to send it today. I will let you all know how it goes.
441. cicely (fair-to-partly-cloudy) says
Customer service rep first told me that TW had no record of me as a customer. (!!!) Then said that she’d transfer me to someone else who could help me.
“In that case, I need you to connect me with the Billing Department, or possibly Legal, so that we can discuss the refunding of all the money for which you’ve billed me, and which I’ve paid. Thank you!”
442. rq says
Portia
I like the Christmas tree story. :P I wonder, if the tree’s feet hadn’t been made of plastic, how your grandmother would have managed to signal that the lights were getting hot…? Burn the house down? Seems excessive.
But then, I suppose ghosts aren’t known for their self-restraint. :P
443. Portia, sporty and glam, pelted with pastries says
Ha, exactly, rq. What’s ridiculous is it’s so typical of that sort of credulous person. It was Tenant’s wife who came up with the ghost theory, and her husband who actually checked the physical reason that the tree wasn’t staying upright. And he still went with “zomg ghost” Before even doing the most basic investigation into why the tree fell over and over, the lady attributed it to supernatural causes.
444. rq
L also mentions the Babysitters Club with fondness.
445. Josh, Official SpokesGay says
Just had lunch. Macaroni and cheese, to which I added an ingredient to make it a complete and delicious meal.
Peas.
Suck it, haterz.
446. Portia, sporty and glam, pelted with pastries says
Good idea, Josh, I was just thinking about what to have for lunch. I think I have the stuff for mac n peas.
447. Azkyroth, Former Growing Toaster Oven says
So I called Time Warner. Sat on hold, waded through their goddamn “tell the robot what you want” system, and got a customer service rep.
Customer service rep first told me that TW had no record of me as a customer. (!!!)
Well, if they claim you’re not a customer it seems to me that you don’t owe them money for the service any more, since they’re obviously providing it out of the goodness of their hearts.
448. carlie says
Oh gods yes. Add in some canned tuna to the mix, and you have one of my favorite comfort meals.
449. carlie says
I see there were several foods discusses – I was referring to adding tuna to the mac and peas.
450. Beatrice says
I am soo sleepy amd it’s barely half past 7pm. I guess I’ll have to save the $\alpha$EP thread for tomorrow. It will probably be long enough to entertain me for some time, considering the topic.
451. rq says
I hate how these threads get so long and interesting that my time just disappears while delving into them. /snark
452. Azkyroth, Former Growing Toaster Oven says
Just had lunch. Macaroni and cheese, to which I added an ingredient to make it a complete and delicious meal.
Peas.
Suck it, haterz.
Ooh. I need to make this again :3
453. says
Esteleth/#446
We ditched cable like a year or more ago, now. Can’t remember exactly. It’s been video on demand and those mailed disk services, since. And I set up an antenna for digital/terrestrial broadcasts, just so we have backup/can watch local news live if there’s like a thing happening, emergency, whatever…
The paranoid in me thinks the cable people know the writing is on the wall, and doing the ISP thing (still lucrative, I’d expect, if less so, and you still provide the video, or just the link via which people acquire it) is all that’s going to be left to them, but they’re trying to make it as annoying as possible for people to leave as a ‘delay the inevitable’ tactic.
454. Esteleth has eaten ALL the gingerbread! Suck it! says
That’s my thinking, AJ. Between my Netflix account and my *cough* knowledge of the web *cough,* I don’t need cable service.
Now, internet is a different story. Not canceling that.
455. says
… oh, and when I say ‘video on demand’, I actually mean: download, paid services, things like iTunes. Again, not the cable company’s servers. They just give us the pipe…
(… and I’ll probably be switching that out for DSL, shortly, but shh, don’t tell them… Say, this is coming to you on their pipe, you don’t suppose they’d FZZT And cable is awesome! I love my cable! I’d never think of quitting! I’d give them MORE money, I tell you! Also, ask us also about our Cable For Life Don’t You Dare Leave Us Ever channel bundles! FZZT… )
(/In unrelated, but related to last week’s music/persistence will do wonders thing, I just had a downright epiphany level breakthrough on my bow hold (cello). Seriously. Like, geez, this is it, I get it, I can’t believe how much better this is, I could play for like hours now with way less grimacing on both sides–as in mine and the listeners’… And it was mostly about persistence, discipline, regular practice, I’m pretty sure making it even possible. I won’t go into the endless string player wonkish details, but anyway, we’re talking pretty awesome, and this was one of those things I was seriously beginning to fear I would just never get, like there was just something totally weird/mutant about my thumb and wrist or something. Apparently not. So, again: persistence.)
456. Esteleth has eaten ALL the gingerbread! Suck it! says
I count myself fortunate that my landlord (a stand-up guy) included high-speed internet in the utilities that are included in my rent. So I can walk away from TW without looking back.
457. says
I count myself fortunate that my landlord (a stand-up guy) included high-speed internet in the utilities that are included in my rent.
Sweet.
I begin to think the various places that are thinking in terms of everyone just getting the net as a sort of basic/necessary service have got it essentially right. So much of the world now, and it’s so crippling not to have it. But, y’know, I work for people who make a lot on server hardware, so I guess I should probably write some ‘financially interested party’ disclaimer in saying that.
458. says
Pfft. And I really have to get back to work, stop this comment burst thing… But anyway, vis à vis yesterday’s discussion of weather:
It’s SNOWING!.
Big white flakes. Lots of them. Something like four below freezing, I think…
(/… now do I dig out the boarding boots again, or do I wait for more accumulation before risking this?)
459. Menyambal --- son of a son of a bachelor says
My secret ingredient for mac-n-cheese is Worcestershire sauce. I don’t use it anywhere else, but I dash some over the mac. Used to, I mean. I’ve stopped eating cheese, so I need to find uses for the two big bottles that I bought at the bulk store.
Tuna is good, it almost makes a casserole out of mac-n-cheese.
The girl cat was eating mac-n-cheese the other day. I wonder how she’d like it with tuna?
460. rq says
AJ Milne
It’s like riding a bike, or a board – you can struggle and struggle and struggle, and then suddenly there’s a huge *CLICK* moment when your body gets what your brain has been trying to get it to get for so long… And then it’s just there. :) But without the struggle, you wouldn’t get it.
I’ve been there, with the violin – the bow-hold and vibrato. It just clicked at one point. And now it’s easy to pick it back up.
Yay for stringed instruments! I love the cello, but I’ve always had a soft spot for the viola. Seems underplayed.
461. broboxley OT says
wow a reason for peas
in fact, to accurately reproduce Soviet cuisine is the only legitimate use for canned peas
462. Beatrice says
Oh, now I remembered a delicious pasta salad:
pasta, sweet corn, tuna, mayo + salt, pepper
463. Tony ∞2012 recipient of the coronal mass erection∞ says
oh no he didn’t!
Come on cicely, we’ve got a spokesgay to whip with wet noodles or alternately: Jolting Josh w Jello!
464. Tony ∞2012 recipient of the coronal mass erection∞ says
AJ, are these special snowflakes?
465. says
… I’ve always had a soft spot for the viola. Seems underplayed.
Heh. Yeah. I know of a few folk now who wound up playing it initially primarily just because one was needed to round out a quartet or whatever, and it was the one thing missing.
466. Good evening
Penne
Delicious cocktail tomatoes
Feta cheese
Some
Ruccola
Olives
Mix a glass of pest a la Genovese (or some homemade pesto) with some mild vinegar.
Mix everything.
Enjoy.
+++++
Mum-post to follow, please, feel free to ignore if you’Re as fed up with the shit as I am…
So, tonight is St. Nick’s eve. According to the legend, St. Nick delivered the gifts during the night from the 5th to the 6th, so some people celebrate on the 5th, some on the 6th. We always celebrated on the 5th because that’s also the family-birthday. Seriously, we were so poor, they couldn’t even afford to give everybody their own birthday. So my gran’s sister was born on the 5th, her nephew, his niece, her nephew.
So, sister and I had agreed to make cookies with the kids and gran one afternoon, and today was the perfect day: I had some free time and it was St. Nick’s so we could really have a cosy family day.
Mum was present and agreed to this plan. We had even discussed that I would bring the dough (because I’m not so stupid to leave a crucial detail to her). Guess what, she managed to forget about St. Nick’s. Her lung-cancer ridden cousin didn’t forget. But no, their own grandma forgot. I know why I volunteered to get them the christmas presents…
And when I said “I’m going to take the phone and the phonebook down to gran so she can call Berlin (where the niece lives)”, she asked “why would she call them today?”.
But, and here’s the joke, she tore up her sick slip and wants to return to work on Monday. I guess her psychiatrist told her something she didn’t want to hear.
Well, I’m not going to feel sorry for her when they fire her for being drunk in a medical lab…
+++
Now I just hope the guy from Sophia doesn’t call tonight…
467. carlie says
I’ve stopped eating cheese, so I need to find uses for the two big bottles that I bought at the bulk store.
Pork chops. Particularly breaded pork chops. Mmmm.
468. cicely (fair-to-partly-cloudy) says
oh no he didn’t!
Come on cicely, we’ve got a spokesgay to whip with wet noodles or alternately: Jolting Josh w Jello!
*looking around wildly*
What?!? Where?!?
(The Cane was sucking to an unacceptable degree. I had to fix it. And now we’ve got…what? Horse Shrines? Paeans to Peas?)
I swear, I take my eye off the ball for one minute!
469. rq says
Beatrice
Add a touch of tomato sauce or mustard to that sauce, and yeah – great salad! (I ‘invented’ something similar one year when I didn’t know what to do with the leftover past and the last canned tuna in the cupboard.)
broboxley
I knew there was a purpose to peas! And to Soviet cuisine (because how else will we rid the world of canned peas?).
Giliell
**hugshugshugs**
And happy St Nick’s, tomorrow is eldest’s middle-name-day. So yes, candy for everyone!
+++
And, before I forget again, I present:
PIRAGI (warning: animal products (among those, bacon*))
Dough:
½ c. warm water
2 tsp. sugar
2 envelopes dry yeast
3 c. milk, scalded
¾ c. oil
2 tbsp. sugar
1 ½ tbsp. salt
2 eggs, slightly beaten
½ c. sour cream/yogurt
Bacon filling:
2 lbs. (1 kg**) lean bacon, chopped very fine
2 onions, diced very fine
salt & pepper to taste
In a hot pan, stir-fry mixture about 5 – 10 minutes. Remove separated fat. Cool mixture.
About 6 cups all-purpose flour, more or less.
Prepare yeast: in a small bowl mix sugar with water; sprinkle yeast on top; set aside in a warm place for 10 minutes. Yeast should bubble up to double the size.
Meanwhile, scald milk and put in a large mixing bowl. Add salt, sugar and oil and stir. Mix eggs with sour cream. When milk has cooled to lukewarm, add egg mixture; add yeast mixture and 2 cups of the flour. Beat thoroughly with a wooden spoon. Add another cup of flour and continue beating. Add more flour as necessary. When the dough begins to leave the sides of the bowl, turn it out onto a lightly floured board or counter. Keep working in enough flour so that it can be handled without sticking to your hands or the board. Knead the dough with the heel of your hands, slapping the ball down forcibly a few times.
Place the dough into a greased bowl; grease the top of the ball and cover with plastic wrap. Place in a warm spot to rise, about 1 ½ hours, or until doubled.
Punch dough down. Take a piece and roll out into a long strand. Cut into 1” pieces, flatten and fill with bacon mixture. Pinch sides together, place on a greased cookie sheet, brush with a beaten egg + milk. Bake at 400ºF until nicely browned.
*bacon may be substituted with fried onions, sauerkraut, cheese, chicken, ground beef, etc.
**From previous experience, MORE bacon is always better, because (a) some always disappears during the process and (b) there’s always too much dough.
Leftover dough can be used to make cinnamon rolls or caraway buns (make thin worm of dough, tie into knot, sprinkle with caraway seeds) or other treats needing white bread as a base.
470. says
Wow, lots of good news all around! Congrats to everyone, I’m going to be doing more reading than commenting because I’m on my cell phone data plan for at least a few more days up to a week.
471. Nick Gotts (formerly KG) says
Now, all you ailurophiles, admit it: this would not be remotely within the capabilities of cats!
472. Janine: Hallucinating Liar says
473. says
AJ, are these special snowflakes?
‘Kay… So I’ve been checking since you asked, and I still haven’t found two alike…
(/… I’ll keep checking.)
474. birgerjohansson says
Montgomery Burns explains the “fiscal cliff”
475. rq says
That poor man (Mr Burns).
+++
Ok, so I’m late to the party, but the gob-evo-psych comments have me giggling at the moment. Does it get bad? (I suppose I’ll find out.)
Aside: Males are supposed to bond over sports hunting, right? According to evo-psych and that vague recollection of an anthropology course in university way back? Anyway. I don’t recall ever hearing about female bonding, except once, when it was mentioned as some odd theory that maybe females have bonding rituals too, but they haven’t been studied blablabla. Or something.
But anyway, if hanging out at the mall foraging doesn’t allow women to bond, then I wonder – how did we ever evolve to be considered so damn talkative? Personally, I think it’s because all that lack of teamwork and communication during all that shopping foraging makes us thirsty for conversation, so when our man comes home from his sports game hunting trip, we’re just going to talk his ear right off.
Right?
Ok, I’m going back to that thread, and tomorrow I’ll try to catch up on the threads actually still active…
476. rq
So, your oldest shares a name with my friend’s oldest. So, does the middle boy have a name that means “man from Sebastos” and the youngest one that is about the patron Saint of firefighters? Or some apostel?
477. Tony ∞2012 recipient of the coronal mass erection∞ says
But in a meeting last year, Walmart officials decided against agreeing to pay suppliers more so that they could upgrade their manufacturing facilities and pay for the costs of safety improvements. “Specifically to the issue of any corrections on electrical and fire safety, we are talking about 4,500 factories, and in most cases very extensive and costly modifications would need to be undertaken to some factories,” Walmart officials said in documents obtained by Bloomberg News. “It is not financially feasible for the brands to make such investments.”
Ok, Fuck you Wal-Mart. They just keep adding reasons for me never to shop there. I was ignorant of a lot of the issues surrounding the company, but I’m not anymore. Wal-Mart is close to my house and one of the only places that I can buy groceries when I get off work late at night. I’ve since attempted to shop at different times so that I can patronize Publix or Winn Dixie.
****
Voter suppression in the Wisconsin state constitution? Mr. Vos, exactly what are the problems that necessitate forcing citizens of your state to have Photo ID’s to vote?
VOS: I do think that having photo ID is something that is broadly supported by the public. It’s something that I really hope we have in place by the next general election. If there were some serious issues raised by the Dane County court I’m looking to fix those, but ultimately I want to make sure photo ID is the law of Wisconsin.
478. rq says
Giliell
Nope. :) But it was on our list. Both of those, actually.
Eldest’s first name is a variation on the usual long form of his middle name (all of their middle names are short forms of their first names; Husband didn’t want two completely different names), but not the name of the saint celebrated tomorrow. (He’s in the Bible.) :)
Middle child’s name is also held by several saints, but my favourite is this one, mostly because of the writing/educational aspect.
Youngest child’s name is the patron saint of friendship, book sellers, publishers and editors, and yes, one of the apostles. Also oddly suitable for me.
(It seems your friend and I have followed a similar algorithm to naming children. :P)
It seems odd now to have such obviously religious names for them all, but it was difficult to choose – outright Latvian names are difficult in English, and rare is the English name that transfers well into Latvian (without horrible mangling). We went for the culturally religious aspect of the region from which most of our collective (i.e. mine and Husband’s) families originate historically, and got a whole bunch of Roman-Catholicism. But it works in both languages, plus we purposely looked for really old names rare in Latvia (if not elsewhere).
479. rq says
DRINKING GAME
Every time justinvacula writes ‘Rebecca Watson’ or indirectly mentions Elevatorgate in his comments, take a drink.
Oh wait…
480. Tony ∞2012 recipient of the coronal mass erection∞ says
Ord’s point is that if we care about what our money is doing, we should look for the most effective charities. (His group asks people to pledge to give 10 percent of income to the places where it will be most effective. He has decided he can live comfortably on $18,000 pounds (a little less than$30,000) per year and will give away everything he earns above that.)
What are the “most effective charities?” Ones that:
— Aim to solve the most serious problems (in the normal calculus, this means that providing bed nets to save children from malaria ranks above helping public radio stations or art museums).
— Use interventions that work.
— Employ cost-effective strategies (trachoma surgeries, rather than training guide dogs, to help the blind).
— Are competent and honest. The percentage of donations spent on overhead is one measure of these qualities.
— Can make good use of each additional dollar. This is the hardest point to assess, but it asks whether the group has the program on the ground to use your money well, and whether your donation will make something happen that otherwise wouldn’t.
http://opinionator.blogs.nytimes.com/2012/12/05/putting-charities-to-the-test/?ref=opinion
Food for thought. I know these are things I’m going to consider when I’m in a better financial position. I fully intend to donate to charities, and I think choosing a charity that is effective at achieving its goals is a good idea.
481. rq says
Alright, my work day is over.
Good night all around!
482. Mmm salads, I love them all. As long as the ingredients are good quality. Even the poor maligned iceberg lettuce has its place – crunchy and near flavourless, so handy as a base where you want other things to star. Today’s lunch is one of those mayo-glued salads: tuna, potato, egg, corn, pickles, 3-bean mix. With lime-chilli mayo, and a side of fresh greens.
Unfortunately for me, a hot lunch would be more appetising today. WTF, weather?? 35C on the weekend, 35F this morning??!
483. Tony ∞2012 recipient of the coronal mass erection∞ says
rq @491:
If I have to play that game, someone from *another* country will be driving me home…
484. Tony ∞2012 recipient of the coronal mass erection∞ says
rq:
I think some individuals throw the “findings” of evo psych so far out the window that they’re on another planet.
For instance, I’m a guy (he says, checking the equipment again to make sure). I *love* shopping. As I’ve said, I can spend an entire day in a mall. I go out of town and *want* to shop. I don’t mind lots of people in the mall. The bigger the mall, the better. I like to shop for clothes. I like to shop for electronics. I like to shop for food. I shop for all manner of items. I even like company when I shop, because I can discuss what the heck I’m interested and get different perspectives. I can also offer my opinion to someone I’m shopping with.
Contrast that with…
I have no desire to go hunting.
I’ve never gone fishing (except for that one time when I was a young one when my father took me. it didn’t last long and I caught nothing).
I don’t like watching sports. I’d rather play something.
I detest football. Too violent and too religion like.
I can’t work on cars for shit.
So how do gay men fit into evo psych explanations for gender differences?
485. Josh, Official SpokesGay says
So how do gay men fit into evo psych explanations for gender differences?
Girdles.
486. says
I know someone already linked to the wingnut-castle-project a while back, so I won’t bother re-linking. but I’d like y’all to admire the following sentence:
Living in a house, townhome or condo within the Citadel requires residents to voluntarily assume responsibilities for the common defense.
487. Khantron, the alien that only loves says
Sorry to be ignoring everything said in the lounge, but testing, testing, am I in the spam folder. Repeat, testing testing one two three four. I guess that wasn’t really a repeat.
488. Janine: Hallucinating Liar says
Jadehawk, that entire ad was an exercise in paranoid thinking and a glimpse into a way of life I am happy I am not a part of. | 2015-07-04 15:28:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2818606495857239, "perplexity": 3985.0926295087197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096773.65/warc/CC-MAIN-20150627031816-00265-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://socratic.org/questions/given-the-two-functions-f-x-2x-1-and-g-x-4-3x-9-how-do-you-determine-the-point-t | # Given the two functions f(x)=2x-1 and g(x)=-4/3x+9 how do you determine the point that lies in the solution set for both f(x) and g(x)?
Jan 7, 2017
Two find the point in the solution set for both these functions equation the two functions ($f \left(x\right) = g \left(x\right)$) and solve for $x$. See full process below.
#### Explanation:
Two find the point in the solution set for both these functions equation the two functions ($f \left(x\right) = g \left(x\right)$) and solve for $x$.
Therefore:
$2 x - 1 = - \frac{4}{3} x + 9$
We can now solve for $x$:
$2 x - 1 + \textcolor{red}{\frac{4}{3} x} + \textcolor{b l u e}{1} = - \frac{4}{3} x + 9 + \textcolor{red}{\frac{4}{3} x} + \textcolor{b l u e}{1}$
$2 x + \textcolor{red}{\frac{4}{3} x} - 1 + \textcolor{b l u e}{1} = - \frac{4}{3} x + \textcolor{red}{\frac{4}{3} x} + 9 + \textcolor{b l u e}{1}$
$2 x + \textcolor{red}{\frac{4}{3} x} - 0 = 0 + 9 + \textcolor{b l u e}{1}$
$2 x + \textcolor{red}{\frac{4}{3} x} = 10$
$\left(\frac{3}{3} \times 2\right) x + \textcolor{red}{\frac{4}{3} x} = 10$
$\frac{6}{3} x + \textcolor{red}{\frac{4}{3} x} = 10$
$\frac{10}{3} x = 10$
$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{10}} \times \frac{10}{3} x = \frac{\textcolor{red}{3}}{\textcolor{b l u e}{10}} \times 10$
cancel(color(red)(3))/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)))/color(red)cancel(color(black)(3))x = color(red)(3)/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)
$x = 3$ is the point which lies in the solution set for both functions. | 2019-09-19 08:41:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5758998394012451, "perplexity": 749.8753504651628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573465.18/warc/CC-MAIN-20190919081032-20190919103032-00043.warc.gz"} |
https://eprint.iacr.org/2020/980 | ## Cryptology ePrint Archive: Report 2020/980
SNARGs for Bounded Depth Computations and PPAD Hardness from Sub-Exponential LWE
Ruta Jawale and Yael Tauman Kalai and Dakshita Khurana and Rachel Zhang
Abstract: We construct a succinct non-interactive publicly-verifiable delegation scheme for any log-space uniform circuit under the sub-exponential Learning With Errors ($\mathsf{LWE}$) assumption. For a circuit $C:\{0,1\}^N\rightarrow\{0,1\}$ of size $S$ and depth $D$, the prover runs in time $\mathsf{poly}(S)$, the communication complexity is $D \cdot \mathsf{polylog} (S)$, and the verifier runs in time $(D+N) \cdot \mathsf{polylog} (S)$.
To obtain this result, we introduce a new cryptographic primitive: lossy correlation-intractable hash functions. We use this primitive to soundly instantiate the Fiat-Shamir transform for a large class of interactive proofs, including the interactive sum-check protocol and the $\mathsf{GKR}$ protocol, assuming the sub-exponential hardness of $\mathsf{LWE}$.
By relying on the result of Choudhuri et al. (STOC 2019), we also establish the sub-exponential average-case hardness of $\mathsf{PPAD}$, assuming the sub-exponential hardness of $\mathsf{LWE}$.
Category / Keywords: cryptographic protocols / delegation schemes, non-interactive, Fiat-Shamir, sum-check, GKR, PPAD, lossy, correlation intractability
Date: received 13 Aug 2020, last revised 18 Aug 2020
Contact author: jawale2 at illinois edu,yael@microsoft com,dakshita@illinois edu,rachelyz44@gmail com
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2020/980
[ Cryptology ePrint archive ] | 2021-04-20 19:52:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8056628704071045, "perplexity": 8068.711000128383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039490226.78/warc/CC-MAIN-20210420183658-20210420213658-00122.warc.gz"} |
https://aptitude.gateoverflow.in/2827/time-distance-speed?show=2829 | 303 views
A train takes 4/3 hours less for a journey of 528km . If its speed is increased by 11/2 km/hour from its usual speed . The usual speed of the train is ( in km/hour )
a. 44
b. 48
c. 52
d. 55
| 303 views
Let Speed of train= v km/hour
Time taken to complete journey= t hour
$Time=\frac{Distance}{Speed}$
$v \times t =Distance$
$v \times t =528 \dots\dots(1)$
Given that if speed increased by $\frac{11}{2} km /hour$ from its usual speed then train takes $\frac{4}{3}$ hour less.
$(v+\frac{11}{2}) \times (t-\frac{4}{3}) =528 \dots\dots(2)$
$(vt-\frac{4}{3}v+\frac{11}{2}t-\frac{44}{6}) =528$
From (1)
$(528-\frac{4}{3}v+\frac{11}{2}t-\frac{44}{6}) =528$
$(-\frac{4}{3}v+\frac{11}{2}t-\frac{44}{6}) =0$
$33t-8v=44$
$33\times \frac{528}{v}-8v=44$
$8v^{2}+44v-17424$
v=44 , $-\frac{99}{2}$
Hence,Option (a)44 is the correct choice.
by (11k points) 7 12 97
edited | 2019-09-17 02:46:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9528477191925049, "perplexity": 6227.368097705352}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573011.59/warc/CC-MAIN-20190917020816-20190917042816-00234.warc.gz"} |
https://www.coursehero.com/file/45025234/Slide-71pptx/ | # Slide 7.1.pptx - Integration by Parts Integration by Parts...
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This preview shows page 1 - 10 out of 10 pages.
Integration by Parts
Integration by Parts Let’s learn how to evaluate integrals of functions such as ln(x), xe x , x 2 cos(x) and more… [f(x)g(x)]’ = f(x)g’(x) + g(x)f’(x) ∫f(x)g’(x)dx = ∫[f(x)g(x)]’dx - ∫g(x)f’(x)dx = f(x)g(x) - ∫g(x)f’(x)dx
Selecting u and dv Rules for choosing u and dv: For dv: Choose the most complicated integrand that can be readily integrated. For u: Choose something that becomes simpler when differentiated *Tip: Choose u based on which of these comes first: I (inverse trigonometric), L (logarithmic), A (algebraic), T (trigonometric), E (exponential).
Example 1 Evaluate u = x → du = dx dv = e 3x dx → v = e | 2021-12-05 02:25:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9455528259277344, "perplexity": 5091.846442918058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363134.25/warc/CC-MAIN-20211205005314-20211205035314-00090.warc.gz"} |
https://blog.listcomp.com/math/2018/06/07/gradient-field | Yao Yao on June 7, 2018
$\newcommand{\icol}[1]{ \bigl[ \begin{smallmatrix} #1 \end{smallmatrix} \bigr] }$
## Gradient Field: a better way to interpret
Gradient and Directional Derivative 举了 $z = f(x,y) = 4x^2 + y^2$ 这个例子，但是举得并不好，因为它混淆了 function 的 gradient 和图形的 gradient，虽然它后面是用 level set 去解释的，相当于用平行于 $x \text{-} y$ 平面的平面去切这个椭圆抛物面，但是理解起来还是有点麻烦。
$\nabla f(x,y) = \langle 8x,2y \rangle = \icol{8x \newline 2y}$ 其实是这么一个 vector field (以下都是 Wolfram 代码)：
VectorPlot[{8x, 2y}, {x, -3, 3}, {y, -3, 3}]
VectorPlot3D[{8x, 2y, 0}, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}]
# Wolfram 类似 IPython Notebook，%2表示第二个 cell 的 output，即上图
Show[%2,ViewPoint->{0,0,\[Infinity]}]
## Clairaut’s Test
Given a vector field $\vec F(x, y) = \langle P(x, y), Q(x, y) \rangle$, how do you tell whether it’s a gradient field, i.e. $\exists G(x,y)$ such that $\nabla G = \vec F$?
Clairaut Test: if $P_y(x, y) = Q_x(x, y)$ always holds, then $\vec F(x, y) = \langle P(x, y), Q(x, y) \rangle$ is a gradient field.
Note that $P_y(x, y) = \frac{\partial P(x, y)}{\partial y}, Q_x(x, y) = \frac{\partial Q(x, y)}{\partial x}$, just a different set of notations.
Clairaut’s Test orginates from Clairaut’s theorem on equality of mixed partials:
Suppose $f$ is a real-valued function of two variables $x,y$ and $f(x,y)$ is defined on an open subset $U$ of $\mathbb{R}^2$. Suppose further that both the second-order mixed partial derivatives $f_{xy}(x,y)$ and $f_{yx}(x,y)$ exist and are continuous on $U$. Then, we have $f_{xy} = f_{yx}$ on all of $U$.
## Hamiltonian Vector Field
If $H(x, y)$ is a function of two variables, then $\langle H_y(x, y), −H_x(x, y) \rangle$ is called a Hamiltonian Vector Field.
An example is the harmonic oscillator $H(x, y) = x^2 + y^2$. Its vector field $\langle Hy(x, y), − Hx(x, y) \rangle = \langle y, −x \rangle$.
The flow lines of a Hamiltonian vector fields are located on the level curves of $H$ | 2021-04-18 11:00:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7782652974128723, "perplexity": 603.2789815956698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038476606.60/warc/CC-MAIN-20210418103545-20210418133545-00306.warc.gz"} |
http://mathoverflow.net/questions/93275/bijection-between-cm-points-and-orbits | # Bijection between CM points and Orbits
I am reading the paper "AN ARITHMETIC FORMULA FOR THE PARTITION FUNCTION" by Kathrin Bringmann and Ken Ono. In the proof of Proposition 4.2 they make reference to the existence of a bijection between the solutions to the Diophantine equation with $k,c>0$
$b^2-24kc=1-24n$
and the points of the orbits
$\displaystyle \bigcup_{Q\in Q_{24n-1}^p/\Gamma_0(6)}\lbrace{ A\tau_{Q}:A\in \Gamma_0(6)/\Gamma_{\tau_Q}\rbrace}.$
They do give some reasons why this exists but I am having trouble filling in the details. Does anyone know how to fill in the details that I think I am missing?
-
May be you can say something more on the notations... Or a more precise reference (I guess you have a misprint in the title). – Filippo Alberto Edoardo Apr 6 '12 at 9:32
Link to the paper: mathcs.emory.edu/~ono/publications-cv/pdfs/097.pdf – B R Apr 6 '12 at 13:48 | 2015-04-28 16:32:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6665830612182617, "perplexity": 396.6624562228813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246661733.69/warc/CC-MAIN-20150417045741-00264-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/595129/latex3-clist-put-inside-an-environment-definition | # latex3 clist put inside an environment definition
I'm puzzled as to why the following doesn't work:
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\clist_new:N \l_test
\clist_set:Nn \l_test {a,b,c}
\NewDocumentCommand{\putitem}{m}{
\clist_put_right:Nn \l_test {#1}}
\NewDocumentEnvironment{foobar}{mm}{ FOO }{ BAR \putitem{##1}}
\NewDocumentCommand{\giveitems}{}{\clist_map_inline:Nn \l_test {\fbox{##1}}}
\ExplSyntaxOff
\begin{document}
\putitem{xyz}
\putitem{asdf}
\giveitems
\begin{foobar}{abab}{baba}
XXX
\end{foobar}
\giveitems % output is the same as the earlier call
\end{document}
So as part of making the environment, an additional string should be added to the clist. But it doesn't work. I would expect the second \giveitems to have an additional item, namely abab. Replacing \putitem with its definition inside the new environment doesn't make any difference. What am I missing here?
Environments form groups, which means you'll need a global variable to see the result outside. At the same time, you need #1 not ##1 when using the argument from your environment.
\ExplSyntaxOn
\clist_new:N \g__seamus_test_clist
\clist_set:Nn \g__seamus_test_clist {a,b,c}
\NewDocumentCommand{\putitem}{m}{
\clist_gput_right:Nn \g__seamus_test_clist {#1}
}
\NewDocumentEnvironment{foobar}{mm}
{ FOO }
{ BAR \putitem{#1}}
\NewDocumentCommand{\giveitems}{}
{\clist_map_inline:Nn \g__seamus_test_clist {\fbox{##1}}}
\ExplSyntaxOff
• I've tided up the variable name here to follow standard expl3 conventions Apr 30 at 15:00
• Thanks for the quick answer! what convention requires double underscores after the g in the clist? Apr 30 at 15:09
• @Seamus Double underscores mean “private variable”, so not to be used by third parties. Apr 30 at 15:35 | 2021-09-27 01:47:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.856118381023407, "perplexity": 4618.409563288837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058222.43/warc/CC-MAIN-20210926235727-20210927025727-00564.warc.gz"} |
https://cstheory.stackexchange.com/questions/46487/what-research-is-being-done-in-classical-complexity-theory | # What research is being done in classical complexity theory?
As far as I'm aware, classical complexity theory is being replaced by more recent forms of complexity theory, such as communication complexity and quantum complexity. What happened to results such as Savitch's $$\textrm{NTIME}[S]\subset\textrm{DTIME}[S^2]$$ and the famous PPST result that $$\textrm{DTIME}[T]\neq\textrm{NTIME}[T]$$?
Is there any new research that I am unaware of with the goal of developing a deeper theory of complexity that could one day solve problems $$P$$ vs $$NP$$, just as the theory of modular forms was developed to solve problems like Fermat's last theorem in number theory? And if not is it simply that we have run out of ideas to prove theorems like this, or have we turned to other measures of complexity for different reasons?
• I'm unqualified to write a full answer, but as much work in classical complexity theory was motivated by solving $P\neq NP$, so looking into Scott Aaronson's survey on that problem may be useful. One might say that Geometric Complexity Theory is precisely the area you're looking for, but I'm unsure if it has developed any new complexity-theoretic results yet (instead of providing an alternative perspective on past results). Note that the issue isn't simply we've "run out of ideas", but that we can prove many of our common tricks don't work. – Mark Mar 17 '20 at 16:54
• I'll just quickly mention that this area is typically known as "Structural Complexity theory". $P\neq\mathsf{NP}$ is clearly a large open question, but so is $\mathsf{VP}\neq\mathsf{VNP}$ (often referred to as the "permanent vs determinant" problem), which geometric complexity theory tries to attack. There are other unrelated questions though, such as $\mathsf{P} = \mathsf{BPP}$ (relevant authors are Wigderson and Impagliazzo), which is generally summarized as the "Hardness vs Pseudorandomness" research program. There are additional questions in circuit complexity, but the ones I know are... – Mark Mar 17 '20 at 18:26
• ... simply stepping stones to proving $P\neq NP$ (and covered in the aforementioned survey). I know other students in my office have been working on things like extensions to the Easy Witness Lemma, or trying to get improved/generalized Karp Lipton lemmas, which I'm unclear if constitute answers to your question --- on one hand, they're current research in structural complexity theory. On the other hand, I do not know if the research is done with the goal of being a stepping stone to $P\neq NP$ (whereas this is the motivation for GCT). – Mark Mar 17 '20 at 18:34
• Have you looked at the list of recent preprints on ECCC? And the less recent ones? You have results on VP v. VNP, arithmetic circuits lower bounds, NP-Hardness of Circuit Minimization, circuit lower bounds... all the above in the past couple months. (If you go earlier, you'll get more.) – Clement C. Mar 17 '20 at 23:16
• I was looking at arxiv, which did not have many helpful results. I actually was not aware of ECCC (which is a little embarrassing), so this was really helpful. I’m a little concerned of the focus on circuits, but at least some research is being done. – exfret Mar 18 '20 at 1:54 | 2021-07-27 12:57:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6451130509376526, "perplexity": 528.3358386848142}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153391.5/warc/CC-MAIN-20210727103626-20210727133626-00009.warc.gz"} |
http://mathhelpforum.com/calculus/117043-integral-question-answer-confirmation-please-print.html | • Nov 27th 2009, 01:10 PM
shmayer
I am suppose to evaluate the indefinite integral of
dx / square root of (1 - x^2 +2x)..
I first broke down 1-2^x + 2x into 2-(x-1)^2
I then took the antiderivative of dx/(2-(x-1)^2) and came up with the answer of [sin^-1(x-1) / 2] + C
Can someone please tell me if this is correct, or what i can do to make it right? I took the derivavtive and it seems i might have made a small error somewhere in finding the antiderivative but im not soo sure where...
Also, if someone can help me solve this question, thatd be great, thanks!!(Rofl)
Compute the integral from -1 ->3 of the square root of (6-2x^2 +4x)dx .
I can't find the antiderivative of this function...and substitution doesnt seem to work...
• Nov 27th 2009, 02:39 PM
skeeter
Quote:
Originally Posted by shmayer
I am suppose to evaluate the indefinite integral of
dx / square root of (1 - x^2 +2x)..
I first broke down 1-2^x + 2x into 2-(x-1)^2
I then took the antiderivative of dx/(2-(x-1)^2) and came up with the answer of [sin^-1(x-1) / 2] + C
Can someone please tell me if this is correct, or what i can do to make it right? I took the derivavtive and it seems i might have made a small error somewhere in finding the antiderivative but im not soo sure where...
Compute the integral from -1 ->3 of the square root of (6-2x^2 +4x)dx .
I can't find the antiderivative of this function...and substitution doesnt seem to work...
I thought I saw these two exact problems before ...
http://www.mathhelpforum.com/math-he...gral-help.html
... did you even bother to look?
• Nov 27th 2009, 02:42 PM
Abu-Khalil
$\int\frac{dx}{\sqrt{1-x^2+2x}}=\int\frac{dx}{\sqrt{2-(x-1)^2}}=\frac{1}{\sqrt{2}}\int\frac{dx}{\sqrt{1-\left(\frac{x-1}{\sqrt{2}}\right)^2}}=\arcsin \left(\frac{x-1}{\sqrt{2}}\right)+C$
PD: Ups. Late post. | 2017-02-26 21:37:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.955109715461731, "perplexity": 1023.1937397409334}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172077.66/warc/CC-MAIN-20170219104612-00619-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.canadaka.net/video/6-canadian-humour/page3 | 88 videos
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## Facetime WIth The Giant.
The Motorleague's "Video" (and we use that term lightly) made by recycling footage of some of The CBC's finest.
added: Fri Oct 2010 | Length 00:00 | Views: 1129 | Comments: 0
## Great White North II - Episode One
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## Hilarious Magic Show
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## I am not American
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## John Wing - I'm Canadian
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## Kiefer Sutherlands Cameo on Corner Gas
Jack Bauer makes a comedic appearance on Canadian comedy "Corner Gas."
added: Mon Jan 2011 | Length 00:00 | Views: 922 | Comments: 0
## Michael Bublé on Corner Gas
Michael Bublé makes an appearance on Candian comedy "Corner Gas" as a jazz enthusiast.
added: Mon Jan 2011 | Length 00:00 | Views: 1373 | Comments: 0
## Monty Python - I'm a lumberjack
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## Nardwuar vs. Alex Burrows (2011)
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## Donate!
June´s Goal: $150.00 Amount in:$0.00 Left to go: \$150.00 | 2020-06-07 08:13:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6028364300727844, "perplexity": 14820.445280233713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348526471.98/warc/CC-MAIN-20200607075929-20200607105929-00356.warc.gz"} |
https://www.manueluberti.eu/emacs/2020/09/23/flymake/ | There was a time when I just didn’t trust Emacs. This lack of confidence was the result of mixing good and evil: listening to other reliable Emacsers’ opinions while being too lazy to see for myself what Emacs could do. The outcome of this endeavour was a frenetic copying-and-pasting of code snippets in my init.el, blindly dragging in more and more external packages.
Don’t get me wrong, external packages made Emacs what it is today for me. I can’t even imagine using it without the likes of Magit or CIDER. However, ignoring what is already there and reaching for MELPA every time I have an itch to scratch has made me overlook built-in niceties like project.el.
Flymake did fell prey of this line of reasoning. Flycheck has always seemed like the way go, so much so that I have barely registered João Távora’s and other Emacs developers’ efforts to improve Flymake. Since my recent experiments with project.el have turned my eyes inwards again, I wanted to see if I can live without Flycheck.
There are three places where I need on-the-fly syntax checking:
Kind people took care of Emacs Lisp and Clojure for me: package-lint-flymake comes with package-lint and flymake-kondor is a valid alternative to flycheck-clj-kondo. But I wasn’t able to find an existing integration with proselint, so I decided to provide one.
My first tries with flymake-easy didn’t go very well. I asked for help on Emacs StackExchange, before realizing I could use flymake-quickdef like flymake-kondor does and answer to myself. The next step was making the solution available to everyone in the form of a package, and so I published the little flymake-proselint.
Flymake may not have the extensive support for checkers that its bigger brother has, and it doesn’t seem to have the same huge community behind, but it’s still a great library to play with. There is a comparison between the two projects on the Flycheck website, so have a look there before making your choice. Note that the comparison doesn’t mention flymake-quickdef, which I find easier to use for extending Flymake.
As for me, my requirements for on-the-fly syntax checking are met by Flymake. At the end of the day it’s good to know that after all these years together Emacs can still surprise me. | 2021-04-18 10:44:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3070968687534332, "perplexity": 2876.3562122067483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038476606.60/warc/CC-MAIN-20210418103545-20210418133545-00218.warc.gz"} |
https://www.mimiframework.org/Mimi.jl/dev/faq/ | ## What's up with the name?
The name is probably an acronym for "Modular Integrated Modeling Interface", but we are not sure. What is certain is that it came up during a dinner that Bob, David and Sol had in 2015. David thinks that Bob invented the name, Bob doesn't remember and Sol thinks the waiter might have come up with it (although we can almost certainly rule that option out). It certainly is better than the previous name "IAMF". We now use "Mimi" purely as a name of the package, not as an acronym. | 2022-12-09 06:49:24 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.863388180732727, "perplexity": 1545.810988738435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711390.55/warc/CC-MAIN-20221209043931-20221209073931-00468.warc.gz"} |
https://plainmath.net/18482/find-derivatives-for-the-functions-assume-and-constants-equal-frac-plus | # Find derivatives for the functions. Assume a, b, c, and k are constants. f(z)=\frac{z^{2}+1}{3z}
Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}$$
$$\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{{3}{z}}}}={\frac{{{1}}}{{{3}}}}{\left({z}+{z}^{{-{1}}}\right)}$$
$$\displaystyle{f}'{\left({z}\right)}={\frac{{{1}}}{{{3}}}}{\left({1}-{z}^{{-{2}}}\right)}={\frac{{{z}^{{{2}}}-{1}}}{{{3}{z}^{{{2}}}}}}$$ | 2021-07-24 23:45:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6845982074737549, "perplexity": 971.9705280624813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151531.67/warc/CC-MAIN-20210724223025-20210725013025-00716.warc.gz"} |
https://math.stackexchange.com/questions/356260/ball-falls-from-ledge-at-a-rate-of-32-fracfeetsec2-after-4-seconds-how/356268 | # Ball falls from ledge at a rate of 32 $\frac{feet}{sec^2}$. After 4 seconds, how far did it fall?
My first step is to do something with this:
$32 \frac{feet}{sec^2}$.
From browsing through solutions, I know $$\int_0^4 32 \,t \, \mathrm d t$$ will provide the solution for distance.
I also know that $$\frac{d (32\,t^2/2)}{dt} = 32t$$.
Where did $32t^2/2$ come from?
• read the sections in your text with the formula $y=a/2 t^2$ where $a$ is acceleration. – Maesumi Apr 9 '13 at 19:24
The formula for the distance covered by a body moving at uniform acceleration is given by:
$$s = ut + \dfrac12 at^2$$
Where $s$ is the displacement, $u$ is the initial velocity, $t$ is the time and $a$ is the acceleration. Since the initial velocity is 0, we get:
$$s = \dfrac12 (32)t^2$$
You differentiate this to get the velocity of the ball after time $t$ seconds, since differentiating displacement gives velocity.
But you're looking for 'how far the ball fall', which means you simply take $s = \dfrac12 (32)t^2$ and put $t = 4s$.
Acceleration is the derivative of velocity which is the derivative of position.
In other words
a = v' = x'' v = x'
where a : acceleration v : velocity x : displacement.
With this relation we can derive all the formulas you need.
v = ∫a dt = a*t + C where t in this case is time and C is an arbitrary Constant.
By setting t = 0 we get C = V_0 where V_0 is initial velocity
Now we have the formula v = a*t + V_0
using the relationship v' = x we can derive a formula for position
x = ∫a*t + V_0 dt = (1/2)a*t^2 + v_0*t + C, setting t=0 we get x = X_0 where X_0 is initial velocity
Therefore we are left with the equations:
x = (1/2)a*t^2 + v_0*t + x_0 and v = a*t + V_0 | 2021-07-24 10:49:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9085206985473633, "perplexity": 659.5713404353091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150264.90/warc/CC-MAIN-20210724094631-20210724124631-00454.warc.gz"} |
https://www.tutorialexample.com/understand-numpy-random-permutation-randomly-permute-a-sequence-numpy-tutorial/ | # Understand numpy.random.permutation(): Randomly permute a sequence – Numpy Tutorial
By | September 22, 2019
numpy.random.permutation() can return a sequence randomly, which is very helpful in random two or more sequences. In this tutorial, we will introduce how to use this function correctly.
## Syntax
numpy.random.permutation(x)
## Parameter
x : int or array_like, if x is a integer, this function will return the random sequence of range(x)
## Return
A random sequence
Here are some examples on how to use this function.
## x is a integer
import numpy as np
x = 5
seq = np.random.permutation(5)
print(seq)
The random sequence is:
[3 4 2 0 1]
it is created based on range(5).
## x is an array
import numpy as np
#create a 3 * 3 matrix
x = np.array(range(9)).reshape(3,3)
print(x)
seq = np.random.permutation(x)
print(seq)
The sequence is:
[[0 1 2]
[3 4 5]
[6 7 8]]
The random sequence is:
[[3 4 5]
[6 7 8]
[0 1 2]]
From the result we will find, numpy.random.permutation() will randomly permute a sequence by its first aixs.
## Permute two sequences by the same random order
This is very helpful when you are generating random data, the example code is:
Create two sequeces with the same shape
import numpy as np
x1 = np.array(range(9))
print(x1)
x2 = x1+3
print(x2)
The x1 and x2 is:
[0 1 2 3 4 5 6 7 8]
[3 4 5 6 7 8 9 10 11]
Create a random order sequence
inx = np.random.permutation(9)
Get the same random sequences
random_x1 = x1[inx]
random_x2 = x2[inx]
print(random_x1)
print(random_x2)
The random sequences are:
[0 5 4 7 8 6 2 3 1]
[3 8 7 10 11 9 5 6 4]
From the result we will find, the random order of random_x1 and random_x2 is the same. | 2021-10-20 23:39:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41199827194213867, "perplexity": 1661.1291814295796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585353.52/warc/CC-MAIN-20211020214358-20211021004358-00476.warc.gz"} |
https://sciencehouse.wordpress.com/2009/02/ | # Systematic fluctuation expansion for neural networks
A new paper “Systematic fluctuation expansion for neural network activity equations“, by Michael Buice, Jack Cowan and myself has just been uploaded to the q-bio arXiv. The paper arose from a confluence of my desire to adapt moment hierarchy approaches from kinetic theory to studying fluctuations in neural networks and Michael and Jack’s field theory formulation of stochastic neural dynamics (see here). In this paper, we show that the two approaches are identical and give a systematic scheme to derive the equations. We give an example for self-consistent equations for the first two moments.
Classically, neural networks have been described either by rate equations, such as the Wilson-Cowan equation of the form $\dot{a_i} = -r a_i + f(\sum_{j} w_{ij} a_j + S_i)$ (and the continuum version) or networks of (more biophysical) spiking neurons. Although rate equations average over neural spikes, they have been extremely successful in describing many neural phenomena. Wilson and Cowan, Grossberg, Amari, Hopfield, Ermentrout, and many others, have used these types of equations to describe phenomena as diverse as associative memory, working memory, persistent activity, hallucinations, orientation tuning, and neural activity waves. In fact, the term neural network, has essentially been co-opted to imply a network of rate equations (i.e., multi-layer perceptron) with a back propagation learning rule for the weights to perform supervised learning.
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# Why can’t biology or economics be more like physics?
February 12 was the 200th anniversay of Charles Darwin and Abraham Lincoln. I’m not going to comment on either of the two directly in this post (given the large amount of press devoted to them recently) even though their impact on our lives cannot be overstated. What I do want to talk about is whether or not biology and economics can be more like physics. I will do this in two parts, with this post focusing on biology. By “not like physics”, I mean that there is not a more quantitative and unifying approach to biology. I think many physicists feel that biologists miss the big picture and that much more could be gleaned if they only started to think like physicists. This attitude is perfectly represented in biophysicist Bob Austin’s letter to Physics Today a decade ago, which can be found here. I think this view has evolved recently as more physicists work on biology but I still see it.
Although I am a former physicist, I’m going to take the side of the biologists. I’m not saying that biology couldn’t be more quantitative and better understood. I’m also not saying that ideas from physics couldn’t be useful. These are all probably true. What I am saying is that the reason biology is not more like physics isn’t because biologists are misguided (or as Bob Austin puts it “can’t reason their way out of a paper bag”) but because biology is different from physics. | 2017-11-25 05:48:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4946146309375763, "perplexity": 1485.7060494804036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934809419.96/warc/CC-MAIN-20171125051513-20171125071513-00682.warc.gz"} |
https://www.physicsforums.com/threads/charge-rearrangement-on-conducting-spheres.990731/ | # Charge rearrangement on conducting spheres
FranzDiCoccio
Homework Statement:
A conductive sphere of radius ## R ## carries a free charge ## Q_0 ##. A second conductive sphere is neutral. The spheres are brought into contact. Find the charge on each sphere when they are separated again.
Relevant Equations:
The formula giving the electric potential outside a charged isolated sphere
Hi,
I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in the preview).
So my reasoning is the following.
1. In the "experiment" involved in the problem the two spheres actually touch. The charged sphere will loose some of its charge, which will transfer onto the previously neutral sphere.
2. While touching, the two spheres form a singular conductor. The charge stays on the surface of this conductor and rearrange so that the electric field inside the conductor vanishes.
3. Since all the charge has the same sign, it tends to spread. It won't spread uniformly, though. I expect that there is basically no charge in the vicinity of the contact point.
4. When the spheres are separated again, the amount of charge on each of them stays the same. I see no reason for some charge migrating from one sphere to the other.
5. The key step is now to assume that the amount of charge on each sphere is the same as in a different "experiment". where the spheres are infinitely apart and are connected through a conducting wire.
6. Since there is an "escape route", some charge leaves the originally charged sphere and moves onto the originally neutral one. Another key assumption is that the wire is so thin that the amount of charge that remains on it is negligible.
7. Since the spheres are connected, they form a singular conductor, and are therefore at the same potential.
8. Since the spheres are infinitely apart, the charge onto their surfaces spreads uniformly. Therefore electric potential on their surface is the same as that of a suitable point charge placed at the center of the sphere. Such potential is proportional to the point charge and inversely proportional to the surface radius.
9. Equating the potentials one obtains that the ratio of the charges on the spheres is the same as the ratio of their radii. The final charges are obtained from this condition, along with the fact that their sum should give the original charge.
I think this works, but I'd like to have a stronger argument for the assumption in 5.
Also, I wonder whether there is a simpler overall argument. A crucial part of my argument is that the potential on the surface of each sphere is the same when they are infinitely apart. But what is the reason of that, if there is no connecting wire?
Of course the potential on the surface of the spheres (and inside them) is the same when they touch. But in that case (and, in general, when they are not infinitely apart) the charge distribution on their surfaces is far from uniform. Also, I'm not sure the surface potentials stay the same when the sphere are separated.
Thanks for any insight
etotheipi and Delta2
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What's the radius of the second sphere?
If I understand correctly, the experiment you are doing involves bringing the spheres together so that they touch, and then bringing them back to infinity (with no wire involved).
This is as opposed to the other example you mention, where you would bring them together so that they touch, connect a conducting wire between them so that they are constrained to be at equal potential until you've brought them back to infinity, and then cut the wire.
I think it is a good question. If the spheres have different radii, I don't think it is obvious that the line integral of the electric field from infinity either sphere at any given point during the separation process has to be the same for both spheres! Even though this seems like it would make sense.
It seems to only be obvious when the spheres have equal radii, because of symmetry considerations (i.e. suppose one ended up at a higher potential than the other; we would have no way of "choosing" such a favourite, so they must be at the same potential).
But I am also interested to see if anyone has a good answer for the case where the radii are not equal!
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Two charged conducting spheres in proximity can be handled by an iterative version of the method of images, but it is not for the faint-hearted.
https://arxiv.org/pdf/0906.1617.pdf addresses two noncontacting spheres at unequal potentials. Not sure how readily it can be adapted to contacting spheres.
etotheipi
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Yeah, the problem is simple if the spheres stay connected 'till they're infinity apart. Much less so otherwise. @haruspex, that Maxwell paper you once sent me - doesn't that address the latter contingency?
etotheipi
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Yeah, the problem is simple if the spheres stay connected 'till they're infinity apart. Much less so otherwise. @haruspex, that Maxwell paper you once sent me - doesn't that address the latter contingency?
I couldn't find the paper that led me to the Maxwell one. Did just find this: http://www.hep.princeton.edu/~mcdonald/examples/twospheres.pdf, which does discuss equipotent spheres and links to a copy of a Maxwell paper, but a paywalled one. Can probably find free access copies with a suitable search.
Edit:
This looks like the paper I found previously https://royalsocietypublishing.org/doi/10.1098/rspa.2012.0133.
It deals specifically with the case of touching spheres.
A key claim of the paper is to show that conducting spheres of like charge will attract if close enough, except for the case where their charges are already in the ratio they would have when in contact. In that special case they will repel.
Now, that doesn't make sense to me. Surely the force between them, at a given distance, varies continuously with the charge ratio. How can it jump suddenly from attraction to repulsion when the charge ratio hits the magic value?
But I have not attempted to find an error in the paper.
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etotheipi
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Though this problem doesn't seem to have an exact analytical solution, i believe that up to a very good degree of approximation the solution presented in the OP(that the ratio of charges equals the ratio of the radius of the two spheres) is the solution of the problem.
First of all we going to work in the quasi-static approximation where the E-field is conservative at all times. This means that the line integral of the E-field is the same between two end points regardless of the path between the two points. So let's consider a point A on the surface of sphere with radius ##r_1## and a point B on the surface of the sphere with radius ##r_2##. It will be
$$V_A=\int_{\mathbf{r_A}}^{\infty}\mathbf{E}\cdot d\mathbf{l}=\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}+\int_{\mathbf{r_B}}^{\infty}\mathbf{E}\cdot d\mathbf{l}=\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}+V_B$$
Now if we could only prove the ##\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}=0## or equivalently that $$\int_C\mathbf{E}\cdot d\mathbf{l}=0 \text { (1)}$$ where ##C## is the straight path that connects the centers of the two spheres, then we would have that ##V_A=V_B##
I think we can prove (1) as long as we assume that the charges on the two spheres are such that $$\frac{Q_1}{r_1}=\frac{Q_2}{r_2}\text{ (2)}$$ and the mild assumption that the electric field in the straight path that connects the centers of the two spheres is that of two points charges ##Q_1## and ##Q_2## that lie at the centers of the two spheres respectively, (and also that the electric field is zero in portion of the straight path that corresponds to the interior of the two spheres).
So under the charge distribution of (2) and this mild assumption we ll have that ##V_A=V_B## always as we move the spheres away from each other, without the need for them to be connected by a thin wire.
etotheipi
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Though this problem doesn't seem to have an exact analytical solution, i believe that up to a very good degree of approximation the solution presented in the OP(that the ratio of charges equals the ratio of the radius of the two spheres) is the solution of the problem.
First of all we going to work in the quasi-static approximation where the E-field is conservative at all times. This means that the line integral of the E-field is the same between two end points regardless of the path between the two points. So let's consider a point A on the surface of sphere with radius ##r_1## and a point B on the surface of the sphere with radius ##r_2##. It will be
$$V_A=\int_{\mathbf{r_A}}^{\infty}\mathbf{E}\cdot d\mathbf{l}=\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}+\int_{\mathbf{r_B}}^{\infty}\mathbf{E}\cdot d\mathbf{l}=\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}+V_B$$
Now if we could only prove the ##\int_{\mathbf{r_A}}^{\mathbf{r_B}}\mathbf{E}\cdot d\mathbf{l}=0## or equivalently that $$\int_C\mathbf{E}\cdot d\mathbf{l}=0 \text { (1)}$$ where ##C## is the straight path that connects the centers of the two spheres, then we would have that ##V_A=V_B##
I think we can prove (1) as long as we assume that the charges on the two spheres are such that $$\frac{Q_1}{r_1}=\frac{Q_2}{r_2}\text{ (2)}$$ and the mild assumption that the electric field in the straight path that connects the centers of the two spheres is that of two points charges ##Q_1## and ##Q_2## that lie at the centers of the two spheres respectively, (and also that the electric field is zero in portion of the straight path that corresponds to the interior of the two spheres).
So under the charge distribution of (2) and this mild assumption we ll have that ##V_A=V_B## always as we move the spheres away from each other, without the need for them to be connected by a thin wire.
The Royal Society link I gave in my edit to post #6 states that a good approximation to the charge ratio of unequal conducting spheres in contact is ##(\frac ba)^2(\frac{\pi^2}6)^\frac{a−b}{a+b}##;
etotheipi
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The Royal Society link I gave in my edit to post #6 states that a good approximation to the charge ratio of unequal conducting spheres in contact is ##(\frac ba)^2(\frac{\pi^2}6)^\frac{a−b}{a+b}##;
They might be right, it turns out when I tried to do the math, i couldn't prove (1) given (2) and the "mild" assumption. (1) holds only exactly when the spheres are of equal radius, and it holds as a vague approximation when the spheres are of unequal radius.
FranzDiCoccio
What's the radius of the second sphere?
Hi rude man,
you're right, I forgot to specify that. In general the second sphere has a radius ## r \neq R ##.
Of course if it was ## r=R ## it would be reasonable to conclude that the two spheres equally share the initial charge. I was planning to include these considerations in my OP, but in the end it slipped my mind.
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Hi rude man,
you're right, I forgot to specify that. In general the second sphere has a radius ## r \neq R ##.
Of course if it was ## r=R ## it would be reasonable to conclude that the two spheres equally share the initial charge. I was planning to include these considerations in my OP, but in the end it slipped my mind.
Thass' alright!
@haruspex, I think I retained the Maxwell (or Maxwell-based) paper you sent , will look for it soon.
EDIT: If it's the Royal Soc. paper you cite I won't bother.
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FranzDiCoccio
[..]
I think we can prove (1) as long as we assume that the charges on the two spheres are such that $$\frac{Q_1}{r_1}=\frac{Q_2}{r_2}\text{ (2)}$$ and the mild assumption that the electric field in the straight path that connects the centers of the two spheres is that of two points charges ##Q_1## and ##Q_2## that lie at the centers of the two spheres respectively, (and also that the electric field is zero in portion of the straight path that corresponds to the interior of the two spheres).
So under the charge distribution of (2) and this mild assumption we ll have that ##V_A=V_B## always as we move the spheres away from each other, without the need for them to be connected by a thin wire.
Hi Delta2,
if I'm getting it right, you are using the fact that the potential "outside" a charged sphere is
$$V = k \frac{Q}{r}\quad\text{(1)}$$
i.e. the same as a point charge ##Q## at the center of the sphere. But this is rigorously true only if the charge distribution on the surface of the sphere is uniform, right?
In general this is not the case, since che charges move freely throughout a conductor. The charge on the other sphere would disrupt the uniformity of the distribution, unless the spheres are very very far apart.
etotheipi said:
If I understand correctly, the experiment you are doing involves bringing the spheres together so that they touch, and then bringing them back to infinity (with no wire involved).
Yes, but bringing them back to infinity is just a trick to solve the problem.
The problem asks to find the final charge on each sphere. When the spheres are separated after touching the charge they carry stays the same, irrespective of the distance between the spheres. Bringing them very far apart results in such charges spreading uniformly on their surfaces, which makes the problem more symmetric, allowing e.g. to use equation (1).
The only way I can think of solving this problem without resort to ugly looking calculations is stil through the "thought experiment" involving the thin wire.
The key point of my reasoning is that the charge rearranges in the same way whether the spheres are brought in contact or connected through a thin wire.
We perhaps could think that when they are brought apart after touching, a very thin conducting wire keeps connecting them. This wire extends indefinitely as the distance between the spheres increases.
I see no reason for the charges on a sphere migrating to the other sphere during this process.
When the spheres are very far the problem is simple, because the potential on their surface is the same, and described by eq (1).
We can then think of severing the wire.
Perhaps another way of thinking about this is assuming that initially the spheres are separated but carry the same charges that would result from the situation where they are connected by a very long and thin wire.
What would happen if they are brought into contact. Would the charge ratio change?
Last edited:
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Hi Delta2,
if I'm getting it right, you are using the fact that the potential "outside" a charged sphere is
$$V = k \frac{Q}{r}\quad\text{(1)}$$
i.e. the same as a point charge ##Q## at the center of the sphere. But this is rigorously true only if the charge distribution on the surface of the sphere is uniform, right?
In general this is not the case, since che charge move freely throughout a conductor. The charge on the other sphere would disrupt the uniformity of the distribution, unless the spheres are very very far apart.
Yes you are absolutely right here at your comments. I tried to use this as a simplifying assumption in order to prove that the potential of the two spheres remains approximately equal even after we move them apart, but i couldn't prove it. My conclusion is that we can't prove that the two experiments outlined in the OP are equivalent in terms of the resulting charge ratio. They are approximately equivalent if the two spheres have approximately the same radius. That's all i can say. @haruspex paper link at post #6 claims that when we bring two spheres in contact then the charge ratio is approximately $$\left ( \frac{r_1}{r_2}\right )^2\left (\frac{\pi^2}{6}\right )^\frac{r_1-r_2}{r_1+r_2}$$
which is quite different than ##\frac{r_1}{r_2}## . The two quantities are approximately the same if we take ##r_1\approx r_2##.
etotheipi
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I see no reason for the charges on a sphere migrating to the other sphere during this process.
There is one. When close, the potential on each sphere is altered by its proximity to the other sphere. The effect will be greater for the smaller sphere.
According to the approximation in post #6 (which is reckoned to be good both when the spheres are similar in radius and when very different) and taking the case where the ratio of the radii is 1+x, small x, the ratio of the charges approximates 1+3x/2.
etotheipi
FranzDiCoccio
Uhm my book (the Italian version of "Physics", by Cutnell and Johnson) has examples and exercises where charged conductive spheres are "brought into contact" and share their charge. The final charges are always calculated assuming
$$\frac{q_1}{q_2} = \frac{r_1}{r_2}$$
At this point this seems to be correct only if "brought into contact" means "connected via a very thin conductive wire while infinitely far from each other".
I guess that the textbook should give a bit more detail on what it means by "brought into contact", because the above situation is definitely not what one pictures in his/her mind.
This seems to be a problem of the Italian version of the book only. I skimmed through its original version, and could not find the examples and exercises involving the conducting charged spheres with different radii.
I think that the Italian translators overlooked the fact that the charge distribution is not uniform, in general.
Delta2
FranzDiCoccio
There is one. When close, the potential on each sphere is altered by its proximity to the other sphere. The effect will be greater for the smaller sphere.
According to the approximation in post #6 (which is reckoned to be good both when the spheres are similar in radius and when very different) and taking the case where the ratio of the radii is 1+x, small x, the ratio of the charges approximates 1+3x/2.
Uhm no wait.
I'm thinking of the situation where the spheres touch and then are brought apart, but a "thin extensible wire" maintains them in electrical contact.
This means that the surfaces of the two spheres have always the same potential. This potential probably varies with the distance between the centers of the spheres. Still, I cannot wrap my head around the fact that in the process some charges migrate from one sphere to the other.
From another point of view: start with the two spheres far apart, and connected by the wire. I think that it's safe to say that the charges are uniformly distributed and their ratio equals the ratio of the radii.
Now imagine the wire shortening, and the spheres becoming closer and closer.
My intuition is that the charges on each spherical surface tends to move away from the other sphere, kind of accumulating on the "external" emispheres, and leaving the facing emispheres progressively less charged.
This is all the more true when the spheres touch each other (i.e. when the wire is extremely short, or disappears altogether).
Where does this scenario break, and produce the distribution predicted by Maxwell?
Perhaps the device of the "very thin and long wire" does not really work. But this is kind of an established trick, isn't it?
etotheipi
From another point of view: start with the two spheres far apart, and connected by the wire. I think that it's safe to say that the charges are uniformly distributed and their ratio equals the ratio of the radii.
Now imagine the wire shortening, and the spheres becoming closer and closer.
My intuition is that the charges on each spherical surface tends to move away from the other sphere, kind of accumulating on the "external" emispheres, and leaving the facing emispheres progressively less charged.
This is all the more true when the spheres touch each other (i.e. when the wire is extremely short, or disappears altogether).
Yes I also think it is non-intuitive. We "expect" the charges to "repel each other" to the outer sides, but evidently if the formulae presented here are correct there must be a transfer of charge across the wire whilst the separation is being reduced from infinity.
If the distance between the centres of the conducting spheres connected via a conducting wire is changed by a small amount, then we will for a tiny amount of time get a non-zero electric field inside the conductor that will redistribute the surface charges so that the electric field again goes to zero and the volume is again equipotential. But I cannot see anything mathematically stopping charges redistributing through the wire.
So it would appear our intuition is only correct to small order .
FranzDiCoccio
FranzDiCoccio
Right... the charges repel each other, but on the other hand they "want" to distribute so that the potential inside both spheres is uniform (and the same, if the spheres are electrically connected).
These two effects might be competing.
As you suggest, probably some charges have to redistribute trhough the wire, against the repulsive force, in order to keep the potential uniform inside both spheres.
Right... the charges repel each other, but on the other hand they "want" to distribute so that the potential inside both spheres is uniform (and the same, if the spheres are electrically connected).
These two effects might be competing.
As you suggest, probably some charges have to redistribute trhough the wire, against the repulsive force, in order to keep the potential uniform inside both spheres.
Even though the surface charges might be skewed to the outer hemispheres, during an infinitesimal time until electrostatic equilibrium is again reached the distribution could still cause an electric field to appear inside the wire (pointing in the direction from one sphere to the other), that causes charges to transfer across it.
This isn't so far fetched; in the wire in equilibrium the electric field from the charges on one sphere exactly balance that from the charges on the other sphere. A small change to the configuration would appear to cause a net electric field in the wire for a tiny duration.
Though I am still working through the maths myself, so I do not know if this is a correct interpretation.
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Where does this scenario break
Let sphere A be very small.
They start a long way apart, same positive potential. No connecting wire.
Bring them close, but for the moment treat them as insulators, so the charges do not migrate. Each gains in potential from proximity to the other. The potential is uneven on sphere B, but the potential at its centre is the same as that on A.
Now let the charges migrate. Redistribution of the charge on A matters little because it is small, but on B charge moves away from A. This does not change the potential at the centre of B because its charges are still all the same distance from its centre, but it lowers the potential on A.
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Even though the surface charges might be skewed to the outer hemispheres, during an infinitesimal time until electrostatic equilibrium is again reached the distribution could still cause an electric field to appear inside the wire (pointing in the direction from one sphere to the other), that causes charges to transfer across it.
This isn't so far fetched; in the wire in equilibrium the electric field from the charges on one sphere exactly balance that from the charges on the other sphere. A small change to the configuration would appear to cause a net electric field in the wire for a tiny duration.
Though I am still working through the maths myself, so I do not know if this is a correct interpretation.
It doesn't sound as though you are using the difference in radii, which must be critical.
etotheipi
It doesn't sound as though you are using the difference in radii, which must be critical.
Yes I didn't make specific reference there, I was just trying to say something along the lines that we can still have a transfer of charge between them even if it looks like "intuitively" the charges on each sphere would try to get as far away from each other as possible.
Though I have been messing around with the problem all morning and it has been quite soul-crushing... all I get are integrals that I cannot calculate. I am trying to discard some HOT and get an approximation but now I think I need to have breakfast 😆 | 2023-03-25 01:23:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8137457966804504, "perplexity": 350.50025940665506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00386.warc.gz"} |
https://www.physicsforums.com/threads/stedy-state-of-damped-system.602014/ | Stedy State of damped system
1. May 1, 2012
FHamster
1. The problem statement, all variables and given/known data
Find the steady-state solution having the form https://webwork3.math.ucsb.edu/webwork2_files/tmp/equations/e1/348e8eb8a4ddf62dd06b46276196e71.png [Broken] for the damped system x'' + x' + x = 2cos(3t)
2. Relevant equations
Acos3t + bsin3t
3. The attempt at a solution
To be honest, I wasn't sure how to do this problem, so I just tried undetermined coefficients and got (-16/73)cos(3t)+ (6/73)sin(3t), which was wrong :< muuu
Last edited by a moderator: May 6, 2017
2. May 1, 2012
sharks
Why is (-16/73)cos(3t)+ (6/73)sin(3t) less than the variable "muuu"? :surprised
3. May 1, 2012
ehild
It is the correct steady-state solution, but you need to convert it to the given form xss=Ccos(3t-δ).
ehild
Last edited by a moderator: May 6, 2017
4. May 1, 2012
HallsofIvy
Staff Emeritus
$$Acos(\omega t- \delta)= Acos(\delta)cos(\omega t)- Asin(\delta)sin(\omega t)$$
With $\omega= 3$. What are A and $\delta$?
5. May 1, 2012
andrien
yo need to calculate the particular integral of it.
WHICH WILL BE
2cos(3t)/(D^2+D+1)
where D is what I think you can guess.multiply and divide by D^2-D+1 on left.the denominator will contain only even powers of D.put D^2=-9 in denominator and carry out the differentiation in numerator after that to find the result and if you don't get it see any book on differential eqn to find out the P.I. of it.C.F.will not contribute because it will be zero in steady state. | 2017-08-20 22:20:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7492920756340027, "perplexity": 1550.867859244788}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106990.33/warc/CC-MAIN-20170820204359-20170820224359-00061.warc.gz"} |
https://www.vedantu.com/question-answer/permanent-hardness-is-due-to-presence-of-soluble-class-11-chemistry-cbse-5f5fbe3c68d6b37d163699b2 | Question
Permanent hardness is due to presence of soluble salts of Mg and Ca in the form of chlorides and sulphates in ${H_2}O$. It can be removed by (A) Boiling (B) Clark’s method(C) Treatment with $N{a_2}C{O_3}$(D) All of these
Hint: The hardness of water is due to the presence of soluble bicarbonates, chlorides and sulphates of calcium and magnesium water which does not give lather with soap in hard water.
Types of hardness of water : The hardness of water can be classified into two types
a) Temporary hardness
b) Permanent hardness
a) Temporary hardness – It is due to the presence of magnetism and calcium bicarbonates. There are two methods for removal of temporary hardness.
(i) By Boiling – Ca and Mg bicarbonates are converted into insoluble carbonates which are removed by filtration.
For example – When we boil water then we see that there is a deposition at the bottom of the vessel. The deposition is actually insoluble carbonates of Ca and Mg. Now filter the water of the cooling.
(ii) By Clark Method – Calcium hydroxide is used in this process. It removes the hardness of water by converting bicarbonates and carbonates.
For example – It is an old method. Calcium hydroxide (Lime water) is added to water and remains it undisturbed for some hours then carbonates of Ca and Mg settle down, which are removed by filtration.
b) Permanent hardness – It is due to the presence of sulphate and chloride salt of calcium and magnesium.
Permanent hardness can be removed by using $N{a_2}C{O_3}$. The salt of Ca and Mg convert into their carbonates, which are insoluble in water.
$CaC{l_2} + N{a_2}C{O_3} \to CaC{O_3} \downarrow + 2NaCl$
$MgC{l_2} + N{a_2}C{O_3} \to MgC{O_3} \downarrow + 2NaCl$
So, from the above discussion, we can say that permanent hardness can’t be removed by the boiling clark method. Only $N{a_2}C{O_3}$ can remove permanent hardness.
Here, the correct answer is (C).
Note: Sometimes students get confused and think that all methods are used to remove hardness of water. But different methods are used to remove both types of hardness. Temporary hardness can be removed by simple methods whereas permanent hardness cannot. | 2020-09-23 13:06:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3779090344905853, "perplexity": 2075.657721825164}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400210996.32/warc/CC-MAIN-20200923113029-20200923143029-00621.warc.gz"} |
https://webdesign.tutsplus.com/tutorials/a-deeper-look-at-less-mixins--cms-22882 | Unlimited Wordpress themes, plugins, graphics & courses! Unlimited asset downloads! From $16.50/m Advertisement # A Deeper Look at LESS Mixins Difficulty:IntermediateLength:MediumLanguages: This post is part of a series called LESS: Beyond the Basics. A Few Things You Might Not Know About LESS Creating Color Schemes with LESS Color Functions Our discussion about LESS continues–this time we’re going to look into LESS mixins. With mixins we can define a group of style declarations once and then reuse them throughout the stylesheet. It helps keep our code DRY as well as producing CSS in a more efficient way, particularly when dealing with complex CSS3 syntax. LESS provides different types of mixins with their very own purpose; they can be straight-forward mixins, or they can work as a (sort of) function. Nonetheless, before we dig deep down into the subject, let’s begin with the basics of how a LESS mixin works, shall we? Tutorial thumbnail created by Paul Slowinsky from the Noun Project. ## The Mixins LESS always tries to keep its syntax and features so that it closely mimics CSS. Hence a mixin in LESS is declared in the same way as we declare a CSS style rule using a class or an ID selector. Both of the following examples are valid LESS mixins: Then we can include these mixins into another style rule, for instance: When compiled, you will have the style declarations from both mixins output within the.header style rule. ### Nested Mixins As you’ve seen above, LESS mixins and (class and ID) selectors appear the same; a LESS mixin is not defined with a special directive like the $ which you’ll find in Sass. LESS gives more flexibility in terms of creating and applying mixins, and it allows us to reuse a nested selector as a mixin as well. Bootstrap uses this approach to construct its gradient mixins
Now, let’s take our previous .border and extend it with a couple of nested selectors, this way:
Assuming you would like to apply the border bottom style you would first need to use the .border, then follow it with the .bottom selector. You can use the nested selector using a > combinator (the same way as we do to select direct child elements in CSS) a space combinator, or compounding the two selectors.
All the above methods will result in the same output:
## Parametric Mixins
LESS mixins can also be extended into sort of functions by which they accept one or more parameters, hence being called Parametric Mixins. Through these parameters you are able to customize the mixin output in accordance with what’s passed through the parameters.
The above code snippet shows our previous .border mixin has now turned into a Parametric Mixin with three parameters. Now we are able to customize the border property values, namely the border-width, the style, and the color, for instance:
The output from the above example would be:
### Parameter Defaults
Please keep in mind that you would always have to set the values of the parameters explicitly when using a .border mixin like the one shown above. If you don’t LESS will throw an error when you try to compile it.
This error occurred because LESS expected the value of the parameters to be set. We can suppress this error by giving the parameter a default value, as follows:
Now, if the parameter’s values are left empty LESS will fall back to the default values.
### @arguments
Additionally, LESS has a special variable named @arguments which will pass the default values all together. This is a useful shortcut that makes our code looks neater, particularly when dealing with multiple parameters and lengthy values. Take our previous example: we can replace these lengthy variables @border-width @border-style @border-color to simply@arguments.
## Mixins Guard
In a nutshell, Mixins Guard is the LESS answer to conditional statement. For many entry users however it may take sometime to grasp and get used to the concept of Mixin Guards, since LESS retains the Mixin form to perform conditional statement and uses the when keyword instead of using the if keyword like one that in many popular programming languages.
So, let's take a very simple example:
The first to the third line of the above code snippet is our Mixin Guard which says: when the.border parameter, @text-color, is set to "red" it should produce border: 1px solid #000;. We use the .border() Mixin into the rule set that follows with the @text-colorincluded as the parameter. The @text-color value is set to "red", hence when compiled the style declaration from the Mixin should be output as the condition is met.
Sass uses != operator to negate the condition. In LESS, you can do so with the when notkeyword, like so:
This time the style declaration of .border Mixin will not be generated given the same example as above.
### Generating Default Output of Mixin Guard
Previously, we created a Mixin Guard with single evaluation. This Mixin Guard will not generate any output, unless the evaluation returns true. But, what if you still want to generate an output when the inceptive Mixin Guard condition is not met; you want to generate a default output.
To do this, you will need to create a new Mixin right after the first Mixin Guard.
The evaluation goes this way: If the value passed on the @a variable in the initial Mixin is not "red" it will fall to the next Mixin which will produce border: 1px solid #f3f3f3;. In the other language, say, JavaScript, this would equate to some the following code snippet using the if and else keyword.
When we compile it, we would have the border color to be #f3f3f3 since the variable passed is "red".
## Mixins as a Function
What makes this behavior different from parametric mixins? This type of mixin will return output that is reusable within the style rule where it is included, rather than taking values through parameters. Before we immediately jump on the subject, let’s take a look at how a similar idea is done in JavaScript.
Here we have two JavaScript functions: color() and header(). When executed the color()function will produce the value from the color variable. We then include the color()function into the header() and store the output in a new variable, bgColor, which we are now able to reuse in the header() function scope.
In LESS, we are also able to do this, limiting the variables’ and mixins’ scope where they can be reused.
The above code snippet resembles our JavaScript precedent. We created a .color() function and included it in the .header() that follows, which is why we are able to use the @color variable for our background-color. The code will give us the following when compiled:
Mixins as functions can also contain mixins or parametric mixins, for instance:
...which will result in the following:
## Final Thought
LESS provides different types of Mixins which allow us to produce CSS smartly. LESS is rather unique in this regard; it adopts programming traits such as a function, whilst retaining the form of CSS syntax. Hopefully this tutorial has helped you grasp how they work. | 2021-04-23 09:13:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4160666763782501, "perplexity": 1275.9909345752214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039568689.89/warc/CC-MAIN-20210423070953-20210423100953-00268.warc.gz"} |
https://cs.stackexchange.com/questions/71554/most-efficient-way-to-compute-number-of-anagrams-of-a-string | # most efficient way to compute number of anagrams of a string
This is a question from Hackerrank.
Given a string S, find the number of "unordered anagrammatic pairs" of substrings. In other words, find the number of unordered pairs of substrings of S that are anagrams of each other.
Two strings are anagrams of each other if the letters of one string can be rearranged to form the other string.
Here is an example:
For S = "abba" , anagrammatic pairs are $$\{ S[1,1], S[4,4] \},\;\; \{ S[1,2], S[3,4] \},\;\; \{ S[1,3], S[2,4] \},\;\; \{ S[2,2], S[3,3] \}$$
where the $[i, j]$ represents the starting and ending index of each substring (indexing starts at 1)
My solution got accepted but I think it's really slow (I don't know how to analyse the time complexity of it). So I looked in the editorial, and I didn't understand the approach used by the problem setter
Editorial:
How to check anagrams
We need to check if string S1 and S2 are anagrams, we first build frequency table where frequency[i] stores the frequency of character i+a. If two strings have same frequency table they are anagrams.
Approach 1
Traverse over all $O(N \times N)$ substrings and for each substring in $O(N)$ build the frequency table and store after hashing. For each $key$ in hashtable, we add $\frac{value \times (value-1)}{2}$ pairs to answer. A factor of $26$ arrives in complexity due to hashing of frequency tables. Overall complexity: $O(N^3 \times 26)$
Approach 2
Starting for $i=1$ to $N$, we dynamically build frequency for substring $S[i, j]$ where $j$ ranges from $i$ to $N$. So, overall complexity here would be $O(N^2 \times 26)$.
Can someone explain both approach 1 and 2?
• What specifically don't you understand, and what parts do you understand? Have you tried working through some small examples by hand, to see what each approach is doing? – D.W. Mar 15 '17 at 17:50
• I don't really understand how to "store after hashing." Or why we add value*(value-1)/2 pairs to the answer for each key in hashtable. Or how to "dynamically build frequency for substrings s[i, j]..." in approach 2. I only understand how to create a normal frequency table, the maps each character to number of occurrences. – Rockstar5645 Mar 16 '17 at 15:34
• Please edit the question to incorporate the information into the question. We want questions to be self-contained, so people don't have to read the comments to understand what you are asking -- comments exist only to help you improve your question, and comments can disappear at any time. Also note that the usual rule is that we prefer that you ask only one question per post. You can ask one question, then absorb the answer, and ask the next question separately. – D.W. Mar 16 '17 at 16:20
• For why you add that many pairs, what analysis have you done? How many pairs do you think will be added? Try working through some examples, then show your analysis and what you think the expression should be and why, before asking us to explain why that is the right number. You might find that you're able to answer the question on your own; or, showing your work might enable us to help point out your misconception or where you want wrong. – D.W. Mar 16 '17 at 16:20
• okay, let me try analysing it myself. – Rockstar5645 Mar 17 '17 at 15:37 | 2019-06-25 01:59:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.561100959777832, "perplexity": 632.0193959049205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999783.49/warc/CC-MAIN-20190625011649-20190625033649-00458.warc.gz"} |
http://stats.stackexchange.com/questions/26678/using-gpml-in-matlab-for-multiclass-classification | # Using GPML in Matlab for MultiClass Classification
I am using Rasmussen's GPML code in Matlab R2011a_student. I have training data (2560x29707) w/ labels (6 classes), and test data (640x29707). To prep the data I have
1. converted from sparse to full,
2. binarized the classes (ie. All classes that = 1 are 1, everything else is -1).
I planned on running this 6 times to accommodate all the classes.
I ran the following code (taken right from the documentation, but replaced the x,y,t values with my data):
meanfunc = @meanConst; hyp.mean = 0;
covfunc = @covSEard; ell = 1.0; sf = 1.0; hyp.cov = log([ell ell sf]);
likfunc = @likErf;
hyp = minimize(hyp, @gp, -40, @infEP, meanfunc, covfunc, likfunc, x, y);
[a b c d lp] = gp(hyp, @infEP, meanfunc, covfunc, likfunc, x, y, t, ones(n, 1));
I get the following error, and I'm not sure what it means. Any help would be greatly appreciated.
??? Error using ==> gp at 76
Number of cov function hyperparameters disagree with cov function
Error in ==> minimize at 75
[f0 df0] = feval(f, X, varargin{:}); % get function value and gradient
Error in ==> ds1pleasework at 7
hyp = minimize(hyp, @gp, -40, @infEP, meanfunc, covfunc, likfunc, full_TrainSet_feature, L_train);
Thanks so much.
-
## 1 Answer
The problem is that you are not supplying the right number of initial hyper-parameter values for the covariance function you are using. In the example the data set has two attributes, so in that case the ARD covariance function needs three hyper-parameters (two scale parameters, one for each attribute and an overall scale factor for the covariance). For this covariance function (covSEard), you need one more hyper-parameter than the number of attributes.
I would suggest changing covfunc to @covSEiso and hyp.cov to log([ell sf])
For a dataset with as many attributes as yours I would forget trying to use an ARD covariance, there are just so many hyper-parameters that you will just end up over-fitting the marginal likelihood in model selection and end up with a very poor model.
I just wanted to add, GPML is a great piece of kit, I'd strongly recommend it to anyone interested in non-linear regression or machine learning approaches to pattern recognition. Rasmussen and Williams book is similarly excellent.
-
Incredible, worked like a charm though Matlab seems to struggle with the volume of data. Really appreciate the help. – BryanH Apr 18 '12 at 14:48
no problem, datasets of that size will take a while, but hopefully the results will be worthwhile! – Dikran Marsupial Apr 18 '12 at 14:54
Actually, Matlab ran for a bit, then threw a major error. Looking at scaling the features down now with relieff. – BryanH Apr 18 '12 at 17:22 | 2015-07-29 20:03:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4929572343826294, "perplexity": 4517.195659498539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042986625.58/warc/CC-MAIN-20150728002306-00013-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/751083/the-implicit-function-theorem | # The implicit function theorem
Prove that if the functions $f_1,...f_n$ in the statement of the implicit function theorem are assumed to be $k$ times differentiable (i.e., all partial derivatives of order k exist and are continuous), then the same is true of all the component functions $\varphi_1,...,\varphi_n$ of $\varphi.$
I know I should differentiate $f(x,\varphi(x))=0$ and express the Jacobi matrix of $\varphi$ in terms of the Jacobi matrix of $f$ and then explain why the Jacobi matrix of $\varphi$ is continuously differentiable.
• I know I should differentiate f(x,p(x))=0 and express the Jacobi matrix of p in terms of the Jacobi matrix of f and then explain why the Jacobi matrix of p is continuously differentiable. – user142691 Apr 12 '14 at 21:01
• p should be phi in the above comment... – user142691 Apr 14 '14 at 19:45 | 2019-05-25 03:20:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8120919466018677, "perplexity": 127.01201644133751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257847.56/warc/CC-MAIN-20190525024710-20190525050710-00533.warc.gz"} |
https://tex.stackexchange.com/questions/222475/article-example-inside-beamer-frame | # Article example inside beamer frame
Let us assume that we have the following example code for an article
\documentclass{article}
\title{Sample title}
\author{Sample author}
\date{}
\begin{document}
\maketitle
\section{Sample section}
\end{document}
I wish to include the output of the above code as a minipage in my beamer frame. How can I do that? I would prefer a vector output rather than a PNG / JPG screenshot.
• Compile to PDF. \usepackage{pdfpages} and \includepdf{filename}?
– cfr
Jan 10, 2015 at 2:36
The easiest would be to create a separate document that contains the article content and include it as an image. Here's an example:
\documentclass{beamer}
\let\Tiny\tiny% http://tex.stackexchange.com/a/94159/5764
\usepackage{fancyvrb}
\usetheme{Warsaw}
\begin{document}
\begin{SaveVerbatim}{CodeBox}
\documentclass{article}
\title{Sample title}
\author{Sample author}
\date{}
\begin{document}
\maketitle
\section{Sample section}
\end{document}
\end{SaveVerbatim}
\begin{frame}[fragile]
\frametitle{\LaTeX{} code}
\begin{columns}
\begin{column}{.5\linewidth}
\UseVerbatim{CodeBox}
\end{column}
\begin{column}{.5\linewidth}
\includegraphics[width=\linewidth]{article}%
\end{column}
\end{columns}
\end{frame}
\end{document}
If you want to include a specific page from article.pdf, use the key-value page=<num> to include page <num> from article.pdf. You could also frame the page by using instead
\fbox{\includegraphics[width=\dimexpr\linewidth-2\fboxsep-2\fboxrule]{article}}
Note that code is stored in a box using fancyvrb and recalled inside the frame. Since you're dealing with beamer containing verbatim-like content, set the frame properties to [fragile].
Creating a separate document for the article is the easiest way. It has to be compiled only once and output plus source code can be included in the beamer frame.
But if you prefer to have only one source document which starts the compilation of the article, you can use the following (based on tcolorbox):
\documentclass{beamer}
\usepackage[skins,listings,raster]{tcolorbox}
\usetheme{Warsaw}
\begin{document}
\begin{frame}[fragile]
\frametitle{\LaTeX{} code}
\begin{tcblisting}{
enhanced,oversize,lower separated=false,
colframe=red!50!black,colback=yellow!10!white,
interior style={top color=yellow!5!white,bottom color=yellow!20!white},
listing side comment,
listing options={style=tcblatex,texcsstyle=*\color{red!70!black}},
pdf comment,
compilable listing,
run pdflatex,
raster columns=1}
\documentclass{article}
\usepackage{lipsum}
\title{Sample title}
\author{Sample author}
\date{}
\begin{document}
\maketitle
\section{Sample section}
\lipsum[1-3]
\end{document}
\end{tcblisting}
\end{frame}
\end{document}
Since the compilation of the article has to be started during compilation of the beamer frames, you have to use the -shell-escape option.
pdflatex -shell-escape mybeamerfile.tex
The example contains just one page. To select e.g. a possible page 3, you could use
comment style={drop lifted shadow,graphics pages={3}}
You can also show more than one page of output, but the size of each will shrink:
\documentclass{beamer}
\usepackage[skins,listings,raster]{tcolorbox}
\usetheme{Warsaw}
\begin{document}
\begin{frame}[fragile]
\frametitle{\LaTeX{} code}
\begin{tcblisting}{
enhanced,oversize,lower separated=false,
colframe=red!50!black,colback=yellow!10!white,
interior style={top color=yellow!5!white,bottom color=yellow!20!white},
listing side comment,sidebyside gap=5mm,
listing options={style=tcblatex,texcsstyle=*\color{red!70!black}},
pdf comment,
compilable listing,
run pdflatex}
\documentclass{article}
\usepackage{lipsum,tikz}
\title{Sample title}
\author{Sample author}
\date{}
\begin{document}
\maketitle
\section{Sample section}
\lipsum[1-12]
\begin{center} | 2022-08-16 14:16:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5749016404151917, "perplexity": 4708.868719864933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00782.warc.gz"} |
https://www.physicsforums.com/threads/laplacian-nabla-x-v.235712/ | # Laplacian(Nabla x v)
## Homework Statement
In cylindrical:
Get $$\frac{1}{\rho} \frac{d}{dp} \left( \rho\frac{d^2 v}{d\rho^2}\right) - \frac{1}{\rho^2}\frac{dv}{dp} = 0$$
Out of $$\nabla^2\left(\nabla \times \vec{v}\right) = 0$$
where $$\vec{v} = v(\rho)\hat{z}$$
## The Attempt at a Solution
I get $$\nabla \times \vec{v} = -\frac{dv}{dp}\hat{\theta}$$
But how do I apply the Laplacian? I can't even get that out of Maple.
Last edited:
Related Calculus and Beyond Homework Help News on Phys.org
Last edited:
Its a pain, but doable. You only have a theta direction, as a function of radius - so it'll simplify. Plug and chug.
http://en.wikipedia.org/wiki/Laplacian
So I should be applying $$\nable^2 f = \frac{1}{\rho} \frac{d}{d\rho}\left(\rho\frac{df}{d\rho}\right) + \frac{1}{\rho^2}\frac{d^2f}{d\theta^2} + \frac{d^2f}{dz^2}$$ (all should be partials)
to simply $$f = -\frac{dv}{d\rho}\hat{\theta}$$?
and use the derivatives of the unit vectors here http://mathworld.wolfram.com/CylindricalCoordinates.html?
Last edited:
I got $$\left[ \frac{1}{\rho^2}\frac{dv}{dp} - \frac{1}{\rho} \frac{d}{dp} \left( \rho\frac{d^2 v}{d\rho^2}\right) \right] \hat{\theta} = 0$$
This making sense anyone? Thanks
Thats exactly what you were looking for right?
Yeah. I guess applying the Laplacian to a vector messed me up a bit.
I also wonder why they don't give the answer in vector form... | 2020-02-19 08:19:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.736854612827301, "perplexity": 1943.1157645785363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144058.43/warc/CC-MAIN-20200219061325-20200219091325-00443.warc.gz"} |
https://bitbucket.org/sethdh/msu-latex-etd | # Overview
%% Readme file for MSUstyle.cls and example tex files.
%%
%% MSUstyle.cls was started by Seth Humphries in Jun-2007. Last updated 09-May-2012
%% Usage is described below
%%
%% Copyright (c) 2007-2012 Seth D. Humphries
%% or, (b) send a letter to Creative Commons, 171 2nd Street, Suite
%% 300, San Francisco, California, 94105, USA.
%%
%%
%%
%%
%% EXAMPLE USAGE AND IMPORTANT INFORMATION ARE GIVEN BELOW
%%
%%
%% There are many things in this guide and in the text that you may want to know how to do in your
%% ETD. Look at what I have done here in. There are things like citations in figure captions,
%% side by side figures, figure rotation, equations, subscripts in titles, figure sizing
%% and placement, tables, citations in tabe captions, referencing labeled objects, linking
%% values with there units so they do not end up separated on multiple lines, etc that may
%% really help you and if you see what I have done may shorten your time to get this done.
%%
%%
%% !!!!!!!!!!!!!!!!
%% When you make changes, run pdflatex at least twice before viewing the output. Sometimes LaTeX
%% misses things when only run once. !!!!!!!!!!
%%
%%
%% When using this style guide use the commands \msusection, \msusubsection and \msusubsubsection
%% instead of \section, \subsection and \subsubsection. The msu specific commands render the
%% formatting for section titles that DGE requires.
%%
%% Add nonumreset as an input if you want numbering to be contiguous throughout ETD.
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NOTE:
%% I use this package on a Linux platform using the texlive LaTeX package. I have used this
%% on SusE 10.1 through 10.3 and also on Ubuntu and ArchLinux without any issues. If you
%% are using a Microsoft operating system with MikTex you may need additional packages
%% to compile via pdflatex. If you let me know, I will add a note about that here for
%% future users.
%% Several others have used this on a Microsoft operating system with MikTex.
%% Some using TeXnic Center and others with winEdit. The only trouble that may arise is
%% you must have the software setup to automatically find needed packages via network
%%
%%
%% email me at sethdh@gmail.com with any questions and to let me know you are using this.
%% I would simply like to track how many are using this style guide and email you when I
%% have updates. Thanks and good luck!!
%%
%% NOTHING!!! in the MSUstyle.cls file should be changed or modified unless the DGE changes
%% the required style or format of a submitted thesis or dissertation
%%
%%
-- turn off a "List of ..." page
If you do not want or need a "List of Tables" page or a "List of Figures" page put \tablespagefalse or \figurespagefalse somewhere shortly after the \begin{document} in your main tex file. They are turned on by default but not everyone needs them.
--- numbering changes ---
DGE approved having numbers like 1.1, 1.2, .. 2.34, 2.35, 3.1, etc. for figures, table, equations and algorithms. This is now the default option. If you want to return to the old numbering scheme simply put 'numreset' as an input parameter to the class like "\documentclass[numreset]{MSUstyle}" at the top of your main tex file.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
EXAMPLE text for the MYmsuETD.tex file
%%
%% Example of use inside the file called mydissertation.tex or whatever you desire to call it:
%% \documentclass[12pt,oneside,doublespaced,normalmargins,dissertation,final]{MSUstyle}
%% in place of the word "dissertation" above use the word "thesis" and it will automatically
%% adjust for the differences between Master's Theses format and the PhD dissertation format.
%%
%% \documentclass[12pt,oneside,doublespaced,normalmargins,dissertation,final]{MSUstyle}
%% %or \documentclass[11pt,twoside,oneandahalfspaced,normalmargins,thesis,draft]{MSUstyle}
%% %or variations there on ... see Option Declaration Section below for more options
%%
%%\documentclass[]{MSUstyle}
%% This is MYmsuETD.tex. At Montana State University, ETD stands for electronic thesis/dissertation''.
%% Created by Seth Humphries
%%
%% The default options:
%% \documentclass[12pt,letterpaper,oneside,openright,%
%% doublespaced,normalmargins,dissertation,final,numreset]{MSUstyle}
%% will generate a document that conforms to the MSU division of graduate studies
%% guidelines. Switch thesis for dissertation if you are doing a Masters thesis. This
%% switch will make adjustments to the front matter according to DGE style rules that
%% are different for a thesis than for a dissertation.
%% can use such input options as singlespaced, 10pt, draft, thesis, twosided, openleft, etc
%%
%% options 10pt, singlespaced and draft allow you to require less number of pages for editting
%%
%%
%%
%%%%%%%%%%%% IMPORTANT %%%%%%%%%%
%% \nofiles %uncomment this line when you need to make adjustments to the .toc, .lof
%% or .lot files when they cover multiple pages. See the accompanying
%%
%%%%%%%%%%%%%%%%%%%% Definitions %%%%%%%%%%
%% define stuff for dissertation or thesis
%% change definition of name to your name and keys to key words you want searched
%% by the likes of google and such ilk. This information shows up in the pdf file properties
%% \newcommand{\name}{Yo fullname Candidate} %PUT your full name here
%% \newcommand{\DocTitle}{Carbon Dioxide Sequestration Monitoring and Verification Via Laser Based
%% Detection System}
%% \degreedepart{Engineering}
%% \department{Electrical and Computer Engineering}
%% \committeechair{Dr. So Ann Dso}
%% \submitdate{August, 2008}
%%
%% \newcommand{\keys}{Electrical Engineering, PhD, Dissertation, Tunable, Lasers, Laser Diode, DFB, Optics,
%% Lidar, Carbon Dioxide, CO2, Carbon, Sequestration, CCS, Carbon Storage, Monitor, Verify, Global Warming,
%% Montana, Montana State} %put searchable words that you want searched here
%%
%% \bibfiles{gwarm,laser,sequestration,monitor} %your .bib files, files containing bibliographic
%% %% information/references that you are going to cite in your ETD.
%% %%
%%
%%
%% %%%%%%%%%%%%%%%%%%%% Packages and preparations %%%%%%%%%%
%% \usepackage{graphicx} %for the \includegraphics command and figures
%% \usepackage{color} %for changing text color in chapters
%% \usepackage{subfigure} %to be able to have multiple plots in one figure
%% \usepackage{varioref}
%% \usepackage{listings} %used for formatting code...see appendices
%% \lstset{%set listings styles
%% language=Matlab, % program language for keywords and comments styles
%% basicstyle=\tiny, %font size and style
%% identifierstyle=\color{red}, %variable name style
%% stringstyle=\ttfamily, %string style
%% keywordstyle=\color{blue}\bfseries, %language keyword style
%% breaklines=true, % sets automatic line breaking
%% breakatwhitespace=false, %break line not just at whitespaces
%% }
%% \usepackage[pdftex,
%% pdfauthor={\name},pdfsubject={\degreetype \ for \name},pdfkeywords={\keys},pdfcreator={PDFLaTex
%% via \name},bookmarks=true,plainpages=false, pdffitwindow=true]{hyperref} %the \ is to give a space
%%
%%
%%
%% %%%%%%%%%%%%%%%%%%%% actual Document %%%%%%%%%%
%% \begin{document}
%% \bibliographystyle{IEEEtran.bst} %I like the IEEEtran bib style, you can use any you or your advisor likes.
%% %% \algorithmspagetrue %uncomment this line if you desire a list of algorithms'' page.
%%
%%
%% \begin{preliminary} %preliminary take care of all the front matter...before your text
%% \begin{dedication}
%% \input{dedication} %change or remove this, dedication is not necesary
%% \end{dedication}
%% \begin{acknowledgements}
%% \input{acknow} %change acknow to the file containing your acknowledgements
%% \end{acknowledgements}
%% \contents %do the contents type pages. Do not change this!
%% \begin{abstract}
%% \input{abstract} %change this to your abstract file
%% \end{abstract}
%% \end{preliminary}
%% %% end making front matter
%%
%% % dissertation chapters, change the file names to the ones that you want
%% \input{introduction}
%% \input{theory}
%% \input{new_instrum}
%% \input{initial_outdoor}
%% \input{release2007}
%% \input{release2008}
%% \input{conclusion}
%% %
%%
%% %% start formatting the end matter.
%% \begin{postliminary}
%% \Appendtrue %comment this out if you have no appendix
%% \references %do not change this
%% \end{postliminary}
%%
%% \appendix% put appendix chapters here.
%% \input{appendixWedge}
%% \input{appendixFigs}
%% \input{appendixCode}
%% \end{document} %%%%%%%%%% do not put anything after this
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% for backwards compatability, if anyone is using one of the older versions this is how you make changes to the list of tables, figure and toc.
%%% below this line is old an dnot necesary after Jun-2010.
When you compile the main code, MymsuETD.tex, it calls the functions \tableofcontents, \listoftables, and \listoffigures. LaTeX generates files MymsuETD.toc, MymsuETD.lot, and MymsuETD.lof, respectively. In these files are the LaTeX sources for these blocks of text. If you don't like the way they look by default (maybe too much space around some symbols, or no bold on math symbols in Chapter titles) you can edit these files.
So here's what to do from command line:
1. pdflatex MymsuETD.tex
2. bibtex MymsuETD.tex
3. pdflatex MymsuETD.tex (this is the usual gotta-LaTeX-twice...)
4. Edit the MymsuETD.[toc|lot|lof] files...see #4 below for details!
5. Now, if I run pdflatex again, it will over-write your edited files! So, you can:
* insert the \nofiles command in the preamble of the source file. This suppresses the output of new files. This is already at the top of the example code but with a comment sign "%" in front of it. After making adjustements to the .toc, .lof or .lot files just uncomment out the "\nofile" (aka remove the beginning "%") and recompile using "pdflatex MymsuETD.tex"
#4 DETAILS
So, what you do is look at the latex output after #3 above where the page breaks from one page of the TOC (lot or lof) to the second. If you have more than 2 pages then you should repeat these steps enough times for each page as adding the title will shift things down. Now open the .toc file and at location you just found insert this code:
\par \par \vfil \penalty -\@M \write \m@ne {}\vbox {}\penalty -\@Mi \par \hskip 1em\relax \hfill TABLE OF CONTENTS -- CONTINUED \hfill \hskip 1em\relax \hskip 1em\relax \vspace {.2in} \hskip 1em\relax \par
now recompile as in #5 above.
This is the code for secondary pages for the lot and lof respectively.
\par \par \vfil \penalty -\@M \write \m@ne {}\vbox {}\penalty -\@Mi \par \hskip 1em\relax \hfill LIST OF FIGURES -- CONTINUED \hfill \hskip 1em\relax \hskip 1em\relax \hskip 1em\relax \\ Figure \hfill Page \vspace {.15in}
\par \par \vfil \penalty -\@M \write \m@ne {}\vbox {}\penalty -\@Mi \par \hskip 1em\relax \hfill LIST OF TABLES -- CONTINUED \hfill \hskip 1em\relax \hskip 1em\relax \hskip 1em\relax \\ Table \hfill Page \vspace {.15in} | 2018-09-18 18:24:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8267655968666077, "perplexity": 13852.836261739758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267155634.45/warc/CC-MAIN-20180918170042-20180918190042-00057.warc.gz"} |
https://astronomy.stackexchange.com/questions/28214/what-would-our-night-sky-look-like-if-the-solar-system-was-100-light-years-from/28225 | # What would our night sky look like if the solar system was 100 light years from the centre of the Milky Way
When we look at photo's of the centre of the Milky Way, it looks extremely bright due to the concentraion of star systems...
If our solar system was only 100 light years from the centre of the Galaxy, would we still have a dark night sky?
• It's a great question. And don't forget we have our kickass supermassive black hole at the middle of our galaxy - astronomy from your 100 ly position would be fantastic! – Fattie Oct 30 '18 at 10:06
• Somewhat related. Just alter the density of stars to suit, though the stellar population in a globular cluster is also quite different. astronomy.stackexchange.com/questions/1241/… – ProfRob Oct 30 '18 at 19:13
• OP an interesting point - are you aware that, simply within our own solar system, once you get to the planets like Uranus .. it is VERY DARK. There's no real "daylight" as you and I thin of it. Our Sun becomes more like a "bright moon". (You can google any number of simulations of this example ... even if other stars were very close indeed on stellar scales ... really I think the sky would be pretty much pitch black as usual! – Fattie Nov 1 '18 at 3:04
I have tried to collate some info from various other answers.
Density of stars where we are:
# About 0.15 per cubic parsec
Density of stars "at the middle of the galaxy". Unfortunately I don't know how "100 ly" affects this. It's probably about this figure.
# About 50-100 stars per cubic parsec
So in this QA it's "about 500x as dense".
It would seem that this is in fact:
# Not very bright. About the same amount of light overall as when there's a full moon.
However the overwhelming factor is
# If one particular star was "very close" to us?
How likely would it be, in the region under discussion, that another star is "very" close to us - close enough that that one particular star is extremely bright?
# No, the stars there are not so close that you'd typically be close enough to a really bright star that it would be bright.
That seems to be the bottom line.
(There's a completely pointless, if pretty, image here showing what it's like "inside a star cluster" {where? At what depth?} here Unfortunately that image does not simply state the star density they are simulating - so it is of no help at all to this excellent QA!)
the bottom line then:
# "If our solar system was only 100 light years from the centre of the Galaxy, would we still have a dark night sky?" Answer, yes, there would just be "more stars". It would be hardly any brighter.
To improve on this answer, the next thing we need to quantify is one piece of information:
# What actually is the star density at "100 ly from the center"?
Is it 50, 100, 25, 300, 72.275 stars per cubic parsec?
I don't know.
• A fun point, would it be different (slightly? a lot?) if inside the galactic bar? IDK.
• @/fattie: thank you for this excellent and well thought out answer...of course I am disappointed that we would still have a night sky :) – Our Man in Bananas Oct 31 '18 at 11:48
• Distance to the nearest star scales as $\rho^{-1/3}$, so if the star density is 1000 times higher than our neighbourhood we should expect it to be about 1/10th of the distance to our nearest star. The same is true for the rarer bright stars; we should hence expect a Sirius-like star about 1 light-year away (hence apparent magnitude −6.46) and an Arcturus-like star about 2.5 ly away. While the night sky might still be dark, it would be pretty spectacular and some stars would likely cast faint shadows. – Anders Sandberg Oct 31 '18 at 16:44 | 2021-06-21 01:56:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3901498317718506, "perplexity": 1173.2928411287567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488259200.84/warc/CC-MAIN-20210620235118-20210621025118-00292.warc.gz"} |
https://plainmath.net/5070/find-the-four-second-partial-derivatives-of-f-x-y-equal-x-2y-3 | # Find the four second partial derivatives of f(x, y) = x^2y^3.
Find the four second partial derivatives of $f\left(x,y\right)={x}^{2}{y}^{3}$.
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Step 1
Given function:
$f\left(x,y\right)={x}^{2}{y}^{3}$
The four-second partial derivatives of $f\left(x,y\right):{f}_{xx},{f}_{yy},{f}_{xy},{f}_{yx}$
Step 2
Now,
Apply the Power Rule: $\frac{d}{dx}\left({x}^{a}\right)=a\cdot {x}^{a-1}$ to find the partial derivatives:
${f}_{xx}=\frac{\partial }{\partial x}\left(\frac{\partial f}{\partial x}\right)$
$=\frac{\partial }{\partial x}\left(\frac{\partial {x}^{2}{y}^{3}}{\partial x}\right)$
$=\left(\partial \frac{2x{y}^{3}}{\partial x}=2{y}^{3}$
${f}_{yy}=\frac{\partial }{\partial y}\left(\frac{\partial f}{\partial y}\right)$
$=\frac{\partial }{\partial y}\left(\frac{\partial {x}^{2}{y}^{3}}{\partial }y\right)\right)$
$=\left(\partial \frac{3{x}^{2}{y}^{2}}{\partial }y\right)$
$=3{x}^{2}×2y$
$=6{x}^{2}y$
${f}_{xy}=\frac{\partial }{\partial y}\left(\frac{\partial f}{\partial x}\right)$
$=\frac{\partial }{\partial y}\frac{\partial {x}^{2}{y}^{3}}{\partial x}\right)$
$=\left(\partial \frac{2x{y}^{3}}{\partial y}\right)$
$=6{x}^{2}$
${f}_{yx}=\frac{\partial }{\partial x}\left(\frac{\partial f}{\partial y}\right)$
$=\frac{\partial }{\partial x}\left(\frac{\partial {x}^{2}{y}^{3}}{\partial y}\right)$
$=\left(\partial \frac{3{x}^{2}{y}^{2}}{\partial x}\right)$
$=6x{y}^{2}$ | 2022-06-26 14:10:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 25, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8015881180763245, "perplexity": 1466.4599131167909}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00303.warc.gz"} |
https://physics.stackexchange.com/questions/379899/relative-motion-electromagnetism | Relative motion + electromagnetism
We say that Force exerted by a current carrying wire on charge $q$ moving with velocity $v$ is: $F=qvB\tag*{}$ (Where $B$ is the magnetic field , and electric Force is 0 because wire is neutral.)
But an observer moving in the direction of charge, with velocity $v$, would see the charge at rest. So, in this frame, no Force should act on the charge?
Please tell me where am I wrong?
If charge $q$ in a system $S$ moves with velocity $v$ in a direction perpendicular to a magnetic field $B$ (and there is no electric field in $S$), it experiences in $S$ a Lorentz force $$F=qvB$$ If you are in an inertial system $S'$ moving with the charge at constant velocity $v$ then you see an electrical force on the charge $$F'=qvB'$$ where $$B'=\frac{B}{\sqrt{1-v^2/c^2}}$$ is the magnetic field in $S'$ in the same direction as in $S$. For small velocities $v<<c$, the magnetic field in $S'$ is approximately $B'=B$. This means that, in this approximation, the Lorentz force $F$ on $q$ in $S$ is equal to the electrical force $F'$ on $q$ in $S'$ $$F=F'$$ Thus what is a magnetic force on the moving charge in $S$ appears as a purely electrical force in $S'$. This follows from the Lorentz transformation of electric and magnetic fields in inertial systems moving with velocity $v$ relative to each other. See, e.g., Chapter 12.3 Relativistic Electrodynamics, in D.J. Griffiths, Introduction to Electrodynamics, 3rd edition, 1999.
• If you change to $S'$, why do you use $v$, not $v'$ in the expression for force? In the question exactly this point is not understood. – queezz Mar 2 '18 at 5:18
• @queezz - Because it was assumed that the charge doesn't move in $S'$. See the text above.. – freecharly Mar 2 '18 at 17:32
• I just think it could be much more obvious if you explicitly state the transformation of the electromagnetic forces. – queezz Mar 2 '18 at 19:18
• @queezz - You are right, I just wanted to keep the answer short. – freecharly Mar 2 '18 at 20:27
Let us have two frames, $S$ where charge is moving and $S'$ where it is at rest. Then for $S'$ we can wright down $$\mathbf{E_\parallel}' = \mathbf{E_\parallel} \\ \mathbf{B_\parallel}' = \mathbf{B_\parallel} \\ \mathbf{E_\bot}' = \gamma \left( \mathbf{E}_\bot + \mathbf{v} \times \mathbf{B} \right) \\ \mathbf{B_\bot}' = \gamma \left( \mathbf{B}_\bot - \frac{1}{c^2} \mathbf{v} \times \mathbf{E} \right)$$ where $\gamma \ \overset{\underset{\mathrm{def}}{}}{=} \ \frac{1}{\sqrt{1 - v^2/c^2}}$, see Wiki for more details.
Important part now is $\mathbf{E_\bot}' = \gamma \left( \mathbf{E}_\bot + \mathbf{v} \times \mathbf{B} \right)$, even if $\mathbf{E} = 0$ in the frame $S$, in the frame $S'$ electric field would not be zero. Assuming velocity of the charge $v<<c$, in your case $\mathbf{E}' = \mathbf{v}\times \mathbf{B}$.
So if $\mathbf{v} \perp \mathbf{B}$, the force in $S'$ will be defined as follows: $$F' = qE = qvB = F$$
Force would not change, though the electromagnetic field in frame $S'$ will. And it will have an electric component now, which will act on the charge at rest.
Quote from undergraduate physics textbook from Knight: Basically, when you trying to observe in a "moving" reference frame, $E$ and $B$ field started to rotate by an imaginary angle. In this case, $B$ field became $E$ field, thus in stead of the magnetic force, there ought to be a equivalent electronic statics force. | 2020-02-18 16:51:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9025747179985046, "perplexity": 159.5556442925559}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143784.14/warc/CC-MAIN-20200218150621-20200218180621-00421.warc.gz"} |
https://twodee.org/blog/16047 | # teaching machines
## CS 1: Lecture 6 – String
Dear students,
If this class was a book, the chapter we’re in right now is Computer as Calculator. I’d mentioned that computers got their start in the world of mathematics. Why exactly did computers start with the mathematicians?
The good news is that numbers are not the only thing that computers are good at crunching. They are also really good at crunching communication. They can send out our words (and propaganda) as fast as electricity travels. So, today we’ll talk about text. We introduce the String class, which stands for a String of characters.
First, we should make it clear that there are two types of citizens in Java: primitives and objects. Primitives are the dregs of society, they are simple numbers or letters or trues or falses. Their type names are all lowercase. Objects are bigwigs, having their type names capitalized. We create them in slightly different ways:
Type myObject = new Type(...);
type myPrimitive = ...;
We also act upon them in different ways. Primitives are bullied about with operators like + and %. Objects are deferentially asked to do things through their methods:
prim1 + prim2 + prim3 // operators
object.pleaseDeleteAllMyFiles() // method call
So, we can make this analogy:
operators : primitives :: methods : objects
The data type of an object is its class. We’ve formally met one object class so far: Scanner. Now it’s time to meet String. Based on our discussion above, we create a String like this:
String name = new String("Frank Lee");
The thing is, we use Strings so often, the Java folks have allowed us to say it more compactly:
String name = "Frank Lee";
Now, we could jump immediately into describing the superpowers that String confers to you, but I’d rather we get a feel for what kinds of things we do with text. Let’s play a little game. Here goes. I’m thinking of a String. You need to figure out what it is by asking only yes or no questions. Can you do it?
It’s likely you are going to ask me questions that correspond to methods in the String class. If so, we have achieved our purpose.
We’ll discuss how Strings are laid out in memory, how we can index into them, extract substrings and so on, through a few example problems:
• You ask the user for a credit card number. Print it back to the console with all but the last four digits as asterisks.
• Students and teachers get a discount at your website. How can you tell if someone’s a student or teacher?
• You ask 125 people for their UWEC username—and username only. All of them append @uwec.edu anyway. How can you clean up one such input?
• You are writing a MUD and want to respond only to the commands north, south, east, and west. But the players are entering in all sorts of perversions of this like NORTH and east (with trailing spaces). How can you “canonicalize” their input to what you expect?
• Display at most 10 characters of a customer’s first name.
• Ask the user for a mod problem (100 % 3) and compute its value.
Notice that calling methods on Strings is different than calling methods of the Math class:
char first = name.charAt(0);
double score = Math.floor(points);
In the case of length, we call this method on an instance of the String class. There may be many instances of Strings in our program, and length will give back a different result for each one. With floor, there’s no instance of Math. We call it directly on the class.
This difference is what static refers to. Math.floor is a static method. String.charAt is not.
If something is static, like static electricity, it is not moving. It is in stasis. The Math class is not moving behind the scenes. Strings, however, are a moving target, as each String will have different contents.
Here’s your TODO list of things to complete before next class:
• Homework 1 is due before Friday. I will grade Friday. Visit office hours now, both mine and the TAs, if you need to think out loud with someone. You are likely to encounter SpecChecker and Git issues—resolving them is as much a part of the homework as writing the code. Give yourself enough time to actually learn the ideas of the assignment. Do not wait until the last minute; I will not be around to support last-minute scrambling.
• Lab 2 is posted. You are always invited to work ahead.
See you next class!
Sincerely,
P.S. It’s time for a haiku!
They’re just trolls, but still
The comments of the web burn
Leaving us in chars
P.P.S. Here’s the code we wrote together in class…
#### CreditCard.java
package lecture0918;
import java.util.Scanner;
public class CreditCard {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.print("Watz ur #? ");
String ccn = in.nextLine();
String last4 = ccn.substring(12);
System.out.println("************" + last4);
}
}
#### EduDiscount.java
package lecture0918;
import java.util.Scanner;
public class EduDiscount {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.print("Email: ");
System.out.println(isDiscounted);
}
}
#### EmailCleanerUpper.java
package lecture0918;
import java.util.Scanner;
public class EmailCleanerUpper {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.println("Email: ");
}
}
package lecture0918;
import java.util.Scanner;
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
String ccn = in.nextLine();
ccn = ccn.replace(" ", "");
ccn = ccn.replace("-", "");
ccn = ccn.replace(".", "");
// ccn = ccn.replaceAll("\\D", "");
String last4 = ccn.substring(12);
System.out.println("************" + last4);
}
}
#### MUD.java
package lecture0918;
import java.util.Scanner;
public class MUD {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.print("> ");
String command = in.nextLine();
command = command.toLowerCase().trim();
// command = command.trim();
System.out.println("|" + command + "|");
}
}
#### Modulator.java
package lecture0918;
import java.util.Scanner;
public class Modulator {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.print("> ");
String expression = in.nextLine();
int whereModAt = expression.indexOf('%');
String left = expression.substring(0, whereModAt);
String right = expression.substring(whereModAt + 1);
int a = Integer.parseInt(left.trim());
int b = Integer.parseInt(right.trim());
System.out.println(a % b);
}
} | 2019-09-15 18:40:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17522838711738586, "perplexity": 3031.314500005432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572235.63/warc/CC-MAIN-20190915175150-20190915201150-00466.warc.gz"} |
http://www.dcs.kcl.ac.uk/?search=au:Jorgen%20au:Ostensson | Found 1 result(s)
08.05.2007 (Tuesday)
Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendent
Regular Seminar Jorgen Ostensson (Leuven)
at: 16:00 Brunel U.room M128 abstract: I will discuss a recent work which concerns the critical behavior of eigenvalues in ensembles 1/Z(n,N) det M(2 alpha) exp(-N Tr V(M)) dM with alpha greater than -1/2, where the factor det M(2alpha) induces critical eigenvalue behavior near the origin. Supposing that the limiting mean eigenvalue density associated with V is regular, and that the origin is a right endpoint of its support, one can compute (using the Deift-Zhou steepest-descent method) the limiting eigenvalue correlation kernel in the double scaling limit as n, N to infinity such that n(2/3) (n/N-1) = O(1). It turns out that the limiting kernel can be described through a distinguished solution of the thirty fourth Painleve equation. This solution is related to a particular solution of the Painleve II equation, which however is different from the usual Hastings-McLeod solution. The talk is based on joint work with Alexander Its and Arno Kuijlaars. | 2018-02-21 20:40:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8961758017539978, "perplexity": 1780.8997216544283}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813803.28/warc/CC-MAIN-20180221202619-20180221222619-00235.warc.gz"} |
https://newproxylists.com/reference-request-stone-weierstrass-theorem-for-modules-of-non-self-adjoint-subalgebras/ | # reference request – Stone-Weierstrass theorem for modules of non-self-adjoint subalgebras
In “Weierstrass-Stone, the Theorem” by Joao Prolla, there is a Stone-Weierstrass theorem for modules, stated as the following:
Let $$mathcal{A}$$ be a subalegebra of $$C(X, mathbb{R})$$ and $$(E, |cdot|)$$ be a normed space over $$mathbb{R}$$. Let $$Wsubset C(X, E)$$ be a vector subspace which is an $$mathcal{A}$$-module. For each $$fin C(X, E)$$ and $$epsilon>0$$, there exists $$gin W$$ such that $$|f-g| if and only if for each $$xin X$$, there exists $$g_xin W$$ such that $$|f(t) – g_x(t)| < epsilon$$ for all $$tin (x)_{mathcal{A}}$$, where $$(x)_mathcal{A}$$ is the equivalent class of $$x$$ under $$mathcal{A}$$.
I know that the above theorem can be extended to $$mathcal{A}subset C(X, mathbb{C})$$ with $$mathcal{A}$$ being a self-adjoint subalgebra. I wonder whether there are some similar results for modules of non-self-adjoint algebras.
I’m interested in generalizing the above theorem into the following case. Let $$mathcal{S}$$ be a finite subset of $$C((0, 1), E)$$, denoted as $$S:={s_1, ldots, s_m}$$, and $$mathcal{A}subset C((0, 1), mathbb{C})$$ be a subalgebra (not necessarily self-adjoint). Then $$W := mathrm{span}{as : ain mathcal{A}, sin mathcal{S}}$$ is a vector subspace which is an $$mathcal{A}$$-module. Shall we still claim that $$fin overline{W}$$ if and only if $$fbigvert_{(x)_{mathcal{A}}} in overline{W}bigvert_{(x)_{mathcal{A}}}$$? Or is there any counter-example to this statement? | 2020-10-28 00:01:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 27, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7626891136169434, "perplexity": 1455.2083218247685}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894890.32/warc/CC-MAIN-20201027225224-20201028015224-00066.warc.gz"} |
https://wiki.kidzsearch.com/wiki/Cosmic_dust | kidzsearch.com > wiki Explore:web images videos games
# Cosmic dust
Porous chondrite interplanetary dust
Cosmic dust (also known as star dust and space dust) is a type of dust. It is very small crystals sent out from stars.[1][2]
It is formed when a star, such as the Sun, sends out atoms.[1][2] Some of the atoms become ions by gaining or losing electrons and becoming negatively and positively charged.[1][2] These oppositely charged ions form an ionic bond, sticking together in tiny crystals,[1][2] a few thousand nanometres across,[1] to form cosmic dust.[1][2]
Cosmic dust is found in various locations.[3] Intergalactic dust is found between galaxies.[1][3] Interstellar dust is found between stars.[1][3] Dust clouds in these places are found by their blocking light from stars behind them, and by their own infrared radiation. Circumplanetary dust is found around planets and in planetary rings[1][3] Interplanetary dust can be found between planets,[3] and is seen as gegenschein and zodiacal light.
The coming together of large amounts of dust over time leads to the creation of planets, the Earth, for example.[1][2][4]
## References
1. "What is cosmic dust?", How it Works (Imagine Publishing) (22): 58, 2011-06-16
2. "Cosmic Dust". Penny Press. 2010. Retrieved 2011-08-18.
3. "What is Cosmic Dust?". wiseGEEK. Retrieved 2011-08-18.
4. "Cosmic dust". Herschel Space Observatory. Retrieved 2011-08-18. | 2021-06-14 03:11:44 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8111397624015808, "perplexity": 9610.074403984492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611320.18/warc/CC-MAIN-20210614013350-20210614043350-00420.warc.gz"} |
http://specialfunctionswiki.org/index.php?title=Digamma_at_z%2Bn&printable=yes | # Digamma at z+n
The following formula holds for $n=1,2,3,\ldots$: $$\psi(z+n)=\dfrac{1}{z} + \dfrac{1}{z+1} + \ldots + \dfrac{1}{z+n-1} + \psi(z),$$ where $\psi$ denotes the digamma function. | 2020-10-19 15:22:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998934268951416, "perplexity": 491.46873519640735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107863364.0/warc/CC-MAIN-20201019145901-20201019175901-00525.warc.gz"} |
https://www.clutchprep.com/chemistry/practice-problems/138611/what-is-true-if-ln-k-is-1-a-g-rxn-is-positive-and-the-reaction-is-spontaneous-in | # Problem: What is true if ln K is 1?A. ΔG°rxn is positive and the reaction is spontaneous in the reverse direction.B. ΔG°rxn is positive and the reaction is spontaneous in the forward direction.C. ΔG°rxn is negative and the reaction is spontaneous in the forward direction.D. ΔG°rxn is negative and the reaction is spontaneous in the reverse direction.E. ΔG°rxn is zero and the reaction is at equilibrium.
###### FREE Expert Solution
We’re being asked to determine Gibb's Free energy when K is 1.
Recall that ΔG˚rxn and K are related to each other:
$\overline{){\mathbf{\Delta G}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$
###### Problem Details
What is true if ln K is 1?
A. ΔG°rxn is positive and the reaction is spontaneous in the reverse direction.
B. ΔG°rxn is positive and the reaction is spontaneous in the forward direction.
C. ΔG°rxn is negative and the reaction is spontaneous in the forward direction.
D. ΔG°rxn is negative and the reaction is spontaneous in the reverse direction.
E. ΔG°rxn is zero and the reaction is at equilibrium.
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Gibbs Free Energy concept. You can view video lessons to learn Gibbs Free Energy. Or if you need more Gibbs Free Energy practice, you can also practice Gibbs Free Energy practice problems. | 2020-10-25 16:09:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46618229150772095, "perplexity": 1554.0165723474329}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107889574.66/warc/CC-MAIN-20201025154704-20201025184704-00283.warc.gz"} |
https://handwiki.org/wiki/Equivariant_topology | # Equivariant topology
Short description: Study of spaces with group actions
In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps $\displaystyle{ f: X \to Y }$, and while equivariant topology also considers such maps, there is the additional constraint that each map "respects symmetry" in both its domain and target space.
The notion of symmetry is usually captured by considering a group action of a group $\displaystyle{ G }$ on $\displaystyle{ X }$ and $\displaystyle{ Y }$ and requiring that $\displaystyle{ f }$ is equivariant under this action, so that $\displaystyle{ f(g\cdot x) = g \cdot f(x) }$ for all $\displaystyle{ x \in X }$, a property usually denoted by $\displaystyle{ f: X \to_{G} Y }$. Heuristically speaking, standard topology views two spaces as equivalent "up to deformation," while equivariant topology considers spaces equivalent up to deformation so long as it pays attention to any symmetry possessed by both spaces. A famous theorem of equivariant topology is the Borsuk–Ulam theorem, which asserts that every $\displaystyle{ \mathbf{Z}_2 }$-equivariant map $\displaystyle{ f: S^n \to \mathbb R^n }$ necessarily vanishes.
## Induced G-bundles
An important construction used in equivariant cohomology and other applications includes a naturally occurring group bundle (see principal bundle for details).
Let us first consider the case where $\displaystyle{ G }$ acts freely on $\displaystyle{ X }$. Then, given a $\displaystyle{ G }$-equivariant map $\displaystyle{ f:X \to_G Y }$, we obtain sections $\displaystyle{ s_f: X/G \to (X \times Y)/G }$ given by $\displaystyle{ [x] \mapsto [x,f(x)] }$, where $\displaystyle{ X \times Y }$ gets the diagonal action $\displaystyle{ g(x,y)=(gx,gy) }$, and the bundle is $\displaystyle{ p: (X \times Y)/G \to X/G }$, with fiber $\displaystyle{ Y }$ and projection given by $\displaystyle{ p([x,y])=[x] }$. Often, the total space is written $\displaystyle{ X \times_G Y }$.
More generally, the assignment $\displaystyle{ s_f }$ actually does not map to $\displaystyle{ (X \times Y)/G }$ generally. Since $\displaystyle{ f }$ is equivariant, if $\displaystyle{ g \in G_x }$ (the isotropy subgroup), then by equivariance, we have that $\displaystyle{ g \cdot f(x)=f(g \cdot x)=f(x) }$, so in fact $\displaystyle{ f }$ will map to the collection of $\displaystyle{ \{[x,y] \in (X \times Y)/G \mid G_x \subset G_y\} }$. In this case, one can replace the bundle by a homotopy quotient where $\displaystyle{ G }$ acts freely and is bundle homotopic to the induced bundle on $\displaystyle{ X }$ by $\displaystyle{ f }$.
## Applications to discrete geometry
In the same way that one can deduce the ham sandwich theorem from the Borsuk-Ulam Theorem, one can find many applications of equivariant topology to problems of discrete geometry.[1][2] This is accomplished by using the configuration-space test-map paradigm:
Given a geometric problem $\displaystyle{ P }$, we define the configuration space, $\displaystyle{ X }$, which parametrizes all associated solutions to the problem (such as points, lines, or arcs.) Additionally, we consider a test space $\displaystyle{ Z \subset V }$ and a map $\displaystyle{ f:X \to V }$ where $\displaystyle{ p \in X }$ is a solution to a problem if and only if $\displaystyle{ f(p) \in Z }$. Finally, it is usual to consider natural symmetries in a discrete problem by some group $\displaystyle{ G }$ that acts on $\displaystyle{ X }$ and $\displaystyle{ V }$ so that $\displaystyle{ f }$ is equivariant under these actions. The problem is solved if we can show the nonexistence of an equivariant map $\displaystyle{ f: X \to V \setminus Z }$.
Obstructions to the existence of such maps are often formulated algebraically from the topological data of $\displaystyle{ X }$ and $\displaystyle{ V \setminus Z }$.[3] An archetypal example of such an obstruction can be derived having $\displaystyle{ V }$ a vector space and $\displaystyle{ Z = \{0\} }$. In this case, a nonvanishing map would also induce a nonvanishing section $\displaystyle{ s_f:x \mapsto [x,f(x)] }$ from the discussion above, so $\displaystyle{ \omega_n(X \times_G Y) }$, the top Stiefel–Whitney class would need to vanish.
## Examples
• The identity map $\displaystyle{ i:X \to X }$ will always be equivariant.
• If we let $\displaystyle{ \mathbf{Z}_2 }$ act antipodally on the unit circle, then $\displaystyle{ z \mapsto z^3 }$is equivariant, since it is an odd function.
• Any map $\displaystyle{ h:X \to X/G }$ is equivariant when $\displaystyle{ G }$ acts trivially on the quotient, since $\displaystyle{ h(g\cdot x)=h(x) }$ for all $\displaystyle{ x }$.
## References
1. Matoušek, Jiří (2003). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry. Universitext. Springer.
2. Goodman, Jacob E., ed (2004-04-15) (in English). Handbook of Discrete and Computational Geometry, Second Edition (2nd ed.). Boca Raton: Chapman and Hall/CRC. ISBN 9781584883012. | 2022-09-26 18:16:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.956774115562439, "perplexity": 274.44320932199946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334915.59/warc/CC-MAIN-20220926175816-20220926205816-00094.warc.gz"} |
https://www.techwhiff.com/issue/which-statement-describes-the-process-of-budding--92175 | # Which statement describes the process of budding
###### Question:
which statement describes the process of budding
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https://agentfoundations.org/item?id=1613 | by Tom Everitt 9 days ago | link | parent That is a good question. I don’t think it is essential that the agent can move from $$s_1$$ to $$s_2$$, only that the agent is able to force a stay in $$s_2$$ if it wants to. The transition from $$s_1$$ to $$s_2$$ could instead happen randomly with some probability. The important thing is that the human’s action in $$s_1$$ does not reveal any information about $$s_2$$.
### NEW DISCUSSION POSTS
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http://www.amp.i.kyoto-u.ac.jp/tecrep/abst/1999/99019.html | Department of Applied Mathematics & Physics, Kyoto Univiversity
### Technical Report #99019 (October, 1999) An Approximation for Finding a Smallest 2-Edge-Connected Subgraph Containing a Specified Spanning Tree by Hiroshi Nagamochi
Given a graph $G=(V,E)$ and a tree $T=(V,F)$ with $E\cap F=\emptyset$ such that $G+T=(V,F\cup E)$ is 2-edge-connected, we consider the problem of finding a smallest 2-edge-connected spanning subgraph $(V,F\cup E')$ of $G+T$ containing $T$. The problem, which is known to be NP-hard, admits a 2-approximation algorithm. However, obtaining a factor better than 2 for this problem has been one of the main open problems in the graph augmentation problem. In this paper, we show that the problem is $(1.92+\epsilon)$-approximable in $O(n^{1/2}m+n^{2})$ time for any constant $\epsilon>0$, where $n=|V|$ and $m=|E\cup F|$. | 2021-12-04 23:48:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5266329050064087, "perplexity": 181.7131725821628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00481.warc.gz"} |
https://codeyz.com/development/java/output-streams/ | Although you might think you haven’t worked with streams yet, surely you’ve already used similar constructions for printing data to console:
System.out.println("Text to display");
In Java terminology System.out is an output stream, which allows programmers to print data to the console. In this way, you are familiar with output streams. It is time now to learn how streams work in more detail and consider other examples.
Destination
As we learned from the previous topic output stream allows you to write data to a destination. Some obvious destinations that you probably already worked with are console and file. Disks, memory buffer, web sockets, or other network locations can be a destination as well. Generally speaking, the destination is a target endpoint that data sent to output stream reaches.
Java standard library provides a wide variety of classes to represent an output stream. Quite a large number of these classes is the result of several factors. One of them is that each destination requires a specific way to write to it. Indeed, writing to a file differs from writing to a web socket!
Character streams
Character output streams allow writing text data: char or String. You might have already used such streams asFileWriter and PrintWriter earlier for writing text data to files. Both of them, as well as other character output streams, have a common abstract ancestor java.io.Writer. Let’s look at it closely.
The class contains a group of methods for writing. Some of them are listed here:
• void write(char[] cbuf) writes a char array
• void write(char[] cbuf, int off, int len) writes a portion of a char array
• void write(int c) writes a single character
• void write(String str) writes a string
• void write(String str, int off, int len) writes a portion of a string
Another important method is close(). It should be invoked for preventing resource leaks.
If you’re familiar with try-with-resources construction, you know it is a better way to prevent resource leaks. For now, we’re skipping it due to learning purposes
Writer has several direct subclasses for different purposes in the standard library. For example, FileWriter is intended for writing to files. StringWriter is designed to construct a string. CharArrayWriter uses char[] as a destination.
Let’s consider CharArrayWriter class. Besides methods inherited from Writer the class has its own toCharArray() and writeTo methods. The former provides char[] with content. The latter writes content to another writer.
Imagine the case when you need to create two types of business cards. Each type of card has its own content, but the contact sections are the same. Here it will be convenient to implement writeTo method of CharArrayWriter to supply both cards with contact sections content.
CharArrayWriter contactWriter = new CharArrayWriter();
FileWriter bc1 = new FileWriter("business_card_1.txt", true);
FileWriter bc2 = new FileWriter("business_card_2.txt", true);
contactWriter.write("Phone: 111-222-333; Address: Java Avenue, 7");
contactWriter.writeTo(bc1);
contactWriter.writeTo(bc2);
char[] array = contactWriter.toCharArray(); // writer content as char[]
bc1.close();
bc2.close();
contactWriter.close();
Here we’ve created FileWriter objects in append mode by passing true to an append parameter.
Byte streams
From a computer’s point of view, any data is just a sequence of bits: 0 or 1, which are usually assembled to bytes of 8 digits. In other words, any data is represented as a serial set of bytes. This means that images, audio, videos and so on have a binary format, i.e. represented as a sequence of bytes. Actually, text files have byte representation too: if you remember, characters are combinations of bytes.
Java has a set of classes called byte output streams to write bytes.
Byte output stream classes from the standard library extend java.io.OutputStream abstract class. The class contains three methods for writing:
• void write(byte[] b) writes a byte array
• void write(byte[] b, int off, int len) writes a portion of a byte array
• abstract void write(int b) writes a single byte
Just like character streams, byte streams have void close() that should be invoked in a similar way.
Let’s look at some direct subclasses of OutputStream from the standard library. FileOutputStream is intended for writing data to a file as a destination. ByteArrayOutputStream as you may guess allows writing to byte[] destination. Such classes like FilterOutputStream or PipedOutputStream have no endpoint destination and write data to other output streams. These classes are supposed to be intermediate streams for data transformation or possibly providing additional functionality.
Let’s look at an example where we write something to a file using FileOutputStream. The class has a set of constructors. Some of them are:
• FileOutputStream(String fileName)
• FileOutputStream(String fileName, boolean append)
• FileOutputStream(File file)
• FileOutputStream(File file, boolean append)
Parameter append indicates whether to append (true) or overwrite (false) an existing file.
It is useful to be aware that FileOutputStream will create a file with the name provided if one does not exist yet. It creates a file right after FileOutputStream is initialized, even if you have not tried to write into it.
Let’s look at the snippet now.
byte[] data = new byte[] {'s', 't', 'r', 'e', 'a', 'm'};
OutputStream outputStream = new FileOutputStream("sample.txt", false);
outputStream.write(data);
outputStream.close();
After running this code, you will see a sample.txt file with content stream in it.
Character vs byte streams
Note that all methods of byte streams considered above allow you to only write bytes. It means that you can’t directly write strings, you must convert them to byte[] before. So if you want to write a string to a file, you have to convert it into bytes first. For instance, you can use the getBytes() method for that.
String str = "stream";
byte[] strAsBytes = str.getBytes(); // convert String to byte[]
Converting String to byte[] every time you need to write something is inefficient and inconvenient. Moreover, many character streams are based on byte streams and are well-optimized. So if you want to write a text, do not reinvent the wheel: use character output streams.
On the other hand, you’ll need to use byte streams when you will work with binary files, for example, .jpg image or .pdf file.
Buffered streams
Output streams have 2 classes from the standard library which do buffering.
BufferedOutputStream is based on the buffering principle. It has only two constructors:
• BufferedOutputStream(OutputStream out)
• BufferedOutputStream(OutputStream out, int size)
Same works for BufferedWriter:
• BufferedWriter(Writer out)
• BufferedWriter(Writer out, int size)
These classes are intermediate output streams. They take an output stream as an input and do buffering before delegating to another stream. An additional parameter size is the size of the buffer. If you want to release all data from the buffer by writing it to a destination, you can use flush() method. It is usually called automatically when your buffer is full or before closing the stream.
Conclusion
The output stream is a way to write data to a destination. The destination is a target endpoint of data, which can be a file, a console, or even a web socket. Streams are divided into byte and character ones. Byte output streams allow writing sequences of bytes. It is necessary for working with binary files. Character output streams are intended for text writing. Character output stream classes usually end with Writer, because they extend one abstract java.io.Writer class as a rule. Similarly, byte output streams end with OutputStream. Some streams use buffering under the hood. It is a widely used optimization, which tries to minimize costly interaction with a destination. | 2022-12-08 14:07:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21686211228370667, "perplexity": 2032.318650083142}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00717.warc.gz"} |
https://www.infoq.com/news/2007/07/GoFCriticism | # Gang of Four Design Patterns - Does it stand the test of time?
| by Arnon Rotem-Gal-Oz 1 Followers on Jul 30, 2007. Estimated reading time: 3 minutes |
More than a decade ago by Erich Gamma, Richard Helm, Ralph Johnson and John Vlissides known as the Gang of Four (GoF) published their seminal book "Design Patterns: Elements of Reusable Object-Oriented Software". The GoF book, which is considered the harbinger of the whole software patterns movement, has recently been criticized as no longer relevant, solving problems which are better handled by newer languages and introducing needless complexity.
It all started earlier this month when Jeff atwood (Coding horror) criticized the GoF Design Patterns book. Jeff wrote that, while he think the book is should be read by every programmer he still has two main problems with the book:
1. Design patterns are a form of complexity. As with all complexity, I'd rather see developers focus on simpler solutions before going straight to a complex recipe of design patterns.
2. If you find yourself frequently writing a bunch of boilerplate design pattern code to deal with a "recurring design problem", that's not good engineering-- it's a sign that your language is fundamentally broken.
Jeff also quotes Mark Dominus who thinks that the GoF book obstructs the ideas of Christoper Alexander et al. who wrote the (building) architecture book "A Pattern Language - towns, Building Construction" (which is considered as the inspiration for the whole design pattern movement in computer science)
Steve Rowe agrees that the patterns should be used as examples of good design and principles to apply and not as a reference book but he says that Jeff is off the mark because he attacks the concept instead of the way where the blame is on the people who apply them wrongly. He concludes that patterns should be treated as examples for good design not as dogma:
Design patterns are very useful when we study how they work so we can create similar patterns. They are bad when we try to copy them directly. If one reads the Gang of Four, he will realize that the authors often give several examples of each pattern and they're all slightly different. One might also notice that there is a lot of talk about the OO concepts that lead to the patterns.
Cedric Otaku answers both Jeff and Mark's criticism in a post he called "In defense of Design Patterns". Cedric says that Jeff (and Mark before him) are wrong for criticizing the GoF book, without offering any alternative. Cedric, goes on to explain the problem with making a parallel between Alexander's construction design pattern and software design patterns
There is a reason why it's important to establish a clear separation between Alexander's Design Patterns and the GOF's Design Patterns: software engineering is nowhere near as advanced as building engineering is. We are still working on these nuts and bolts, and whenever a new software project starts, we still can't be sure it won't collapse under its own weight after just a year. To make a parallel: imagine a world where every time a new construction takes place (say, a bridge), the future of that bridge depends on the team of engineers and workers you choose to build it...
Cedric says that because construction is far more advances (in its predictability and stability) than software is. we are still struggling for the basics and we should be focused on that.
On the other hand a Aristotle Pagaltzis left a comment on Cedric's blog and rationalized Mark's critisism
Dominus says that design patterns are a sign of a deficiency of a language for the purpose that the design pattern addresses. In other words, the Visitor pattern used in Java points to the fact that Java is deficient in terms of list processing: the map and filter constructs need to be emulated with lengthy OO incantations.
He is _not_ saying that the use of design patterns _as such_ is bad. He is saying they are a sign of a deficiency.
It seems most (if not all) agree that patterns as tool in software engineering is useful, the debate is on the value of the GoF book today. What do you think ? is the Gof Design Patterns a timeless piece or has it outlived its purpose ?
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agree
I find the GoF design patterns book very useful, especially the first section that cautions against common pitfalls such as overuse of inheritance. I think it should be read by anyone who's serious about building software. But I've also seen people go to lengths to force a pattern on a problem that didn't need it, adding needless complexity. I would rather arrive at the simplest design through continuous design and refactoring, then use the vocabulary the GoF book introduces to describe the solutions when applicable.
--mj
I also agree
I think people have been way too fixed on the details of this book, when the whole picture is what it is important. This book displays how a design is made based on a problem identified. And promotes the identification of patterns in YOUR application. I don't think the GoF was ever intended as a recipe book, but more as a guided tour of the solution to a problem.
pointless
This whole talk about 'the use of patterns says the language is broken' is pointless.
For example, Ruby's standard APIs use the Visitor pattern extensively. It's not just because it is built in the libraries that it's not there. If you are going to build a text editor in Ruby, you probably will use the Flyweight pattern. It's not built in the standard APIs (I don't know, it's just an example), so Ruby sucks?
Sure, new languages incorporate into their APIs patterns that proved to be useful in the past. But as any design choice, it's a trade-off. Adopting one way to do things will always exclude other ways, which could fit better in some specific context. And then you'll have to work around it, and you'll probably create some kind of design pattern to do it. Then, your language is broken? Or maybe you'll want to create a new language to solve every single problem that your current language/libraries are not optimized for?
Design patterns are common solutions to recurring problems, a very good way to document knowledge, and a nice way to develop a high-level vocabulary. You can use it well or not, but it all depends on you, not on some black magic created by the GoF guys.
Re: pointless
Totally agree with you. A language can't answer all your questions out of the box. Design patterns are way of doing things (better ways of doing things). They defined common problems and propose solutions for them. There will be new problems in the future, different problems. What happens then? I think languages give you the tools you are free to follow whatever road you choose..
They are here to stay, but...
Sure, the GoF patterns and others are here to stay. They are a sign of a maturing industry: it´s old enough and conscious enough to realize that solutions are recurring and that some solutions work better than others. On the class level the GoF patterns are a compilation of such successful solutions. Great!
But that does not mean, these patterns need to be adhered to slavishly. And it does not mean, they are the new building blocks to use to put together new applications. If you detect a situation of a certain kind, you certainly should check the GoF patterns for a solutions. But don´t start your next project by asking "What patterns should we glue together?"
Components are building blocks on a much needed higher level of abstraction than classes. GoF patterns are not.
-Ralf
Home: www.ralfw.de
Blog: weblogs.asp.net/ralfw
missing the point
I guess I'm not sure what his point is. Is he saying that we should all drop developing in Java or C++ because they require patterns that Ruby might not?
Quote:
If you find yourself frequently writing a bunch of boilerplate design pattern code to deal with a "recurring design problem", that's not good engineering-- it's a sign that your language is fundamentally broken.
He's right that some design patterns are required because of a deficiency of the language, but what's the alternative???
Singleton
I think the book is still useful - mostly. However, there is one pattern that has probably caused more harm than good, and that's the Singleton pattern. It is, in my book, an antipattern, because it leads to very tightly coupled code that is hard to test, at least in statically typed languages like Java and C#. Dependency Injection is a great alternative to Singleton that elminates Singleton's coupling and test unfriendliness.
I don't blame the GoF for including it - Testing, TDD and mocking was not on the agenda when the book was written. But people reading the book today should be aware of what patterns are obsoleted by more modern patterns (or design principles).
Re: missing the point by Ke Jin
He's right that some design patterns are required because of a deficiency of the language, but what's the alternative???
Low level design patterns (e.g. those in GoF) can mostly be codified or melted away at relatively higher abstraction levels (and will be replaced with higher level design patterns). There are some commonly used alternatives and/or techniques for this kind elevation (even without droping the low level programming languages) such as:
* Supporting domain specific languages (DSL) in core language.
* Using frameworks, middlewares, and/or tools
* generic programming
* ...
Re: missing the point
The alternative is more expressive languages. Eventually we will drop development of Java and C++ applications. Hopefully the replacement language will be more expressive, something that obivates most of the GoF patterns. The questions are what is this next language and how soon can we make the transition? Personally, I'm tired of the Java handcuffs.
Re: missing the point by Ke Jin
The alternative is more expressive languages. Eventually we will drop development of Java and C++ applications. Hopefully the replacement language will be more expressive, something that obivates most of the GoF patterns. The questions are what is this next language and how soon can we make the transition? Personally, I'm tired of the Java handcuffs.
There are many such languages already, even before the GoF book and the Java language. In fact, the issue of expressiveness of language vs design patterns isn't a new topic, but has been well known among functional programming (FP) folks for years. Even the GoF book itself published more than a decade ago (not recently and before Java) also pointed out (page 4) that design patterns are relative to the choosen language. For instance, the factory pattern is largely vanished in Ruby and FP languages and the visitor pattern is less needed in CLOS (much older than Java), the iterator is internal in FP, the ....
There are many discussions much objective than the exaggerated opinions in the cited articles. For instance, Matthias Felleisen pointed out in his "On the Expressive Power of Programming Languges" article published in 1991 (many years before GoF and Java):
* By studying a number of examples, we have come to the conclusion that programs in less expressive languages exhibit repeated occurrences of programming patterns, and that this pattern-oriented style is detrimental to the programming process.
* Based on these examples and others with a similar flavor, we have come to believe that the major negative consequence of a lack of expressiveness is the abundance of programming patterns to make up for the missing, non-expressible constructs.
* Programs in more expressive programming languages that use the additional facilities in a sensible manner contain fewer programming patterns than equivalent programs in less expressive languages.
However, all of these by no means suggest that expressiveness should always be the sole pursuance of a programming language. Rather, it should be one of many trade-off factors to be considered by language designers. Blindly increasing the expressiveness of a generic language to eliminate design patterns not only could sacrifice application runtime efficiency but also could undermine the language's intuitiveness, simplicity, legacy compatibility, and more importantly its application code maintainability.
Re: pointless by Ke Jin
For example, Ruby's standard APIs use the Visitor pattern extensively. It's not just because it is built in the libraries that it's not there. If you are going to build a text editor in Ruby, you probably will use the Flyweight pattern. It's not built in the standard APIs (I don't know, it's just an example), so Ruby sucks?
Ruby does make the factory pattern largely vanished and therefore consider to be more expressive than C++. The visitor pattern, although not completely being eliminated, is indeed less needed in certain languages (such as CLOS -- as GoF pointed out in page 4) and/or under the help of a framework on top of a language (e.g. Java) that supports reflection and dynamic proxy.
Mort has evolved...
I believe like a lot of methodologies & technologies they get used and abused when they aren't the best solution for the problem.
This is the case with the GoF book in my opinion, I have seen on more than one occasion the liberal use of patterns in projects that blatantly don't need it, i.e.
the use of factories that creates instances of only one known type, the implementation of a the observer pattern when it has already been implemented by the framework (.Net events).
To me this shows that the average developer has 'evolved' and learnt that they should be using patterns but not really understanding there power - they believe that implementing patterns (everywhere) makes the software intrinsically better.
I say these Morts have evolved :)
This doesn't mean to me the GoF is no longer as important it just means our understanding of patterns is more mature.
Re: missing the point
The alternative is more expressive languages. Eventually we will drop development of Java and C++ applications. Hopefully the replacement language will be more expressive, something that obivates most of the GoF patterns. The questions are what is this next language and how soon can we make the transition? Personally, I'm tired of the Java handcuffs.
There are many such languages already, even before the GoF book and the Java language. In fact, the issue of expressiveness of language vs design patterns isn't a new topic, but has been well known among functional programming (FP) folks for years. Even the GoF book itself published more than a decade ago (not recently and before Java) also pointed out (page 4) that design patterns are relative to the choosen language. For instance, the factory pattern is largely vanished in Ruby and FP languages and the visitor pattern is less needed in CLOS (much older than Java), the iterator is internal in FP, the ....
There are many discussions much objective than the exaggerated opinions in the cited articles. For instance, Matthias Felleisen pointed out in his "On the Expressive Power of Programming Languges" article published in 1991 (many years before GoF and Java):
* By studying a number of examples, we have come to the conclusion that programs in less expressive languages exhibit repeated occurrences of programming patterns, and that this pattern-oriented style is detrimental to the programming process.
* Based on these examples and others with a similar flavor, we have come to believe that the major negative consequence of a lack of expressiveness is the abundance of programming patterns to make up for the missing, non-expressible constructs.
* Programs in more expressive programming languages that use the additional facilities in a sensible manner contain fewer programming patterns than equivalent programs in less expressive languages.
However, all of these by no means suggest that expressiveness should always be the sole pursuance of a programming language. Rather, it should be one of many trade-off factors to be considered by language designers. Blindly increasing the expressiveness of a generic language to eliminate design patterns not only could sacrifice application runtime efficiency but also could undermine the language's intuitiveness, simplicity, legacy compatibility, and more importantly its application code maintainability.
Couldn't have said it better.
GoF is ...
for those who DO NOT GET objects. If you're starting to learn OOP than GoF is one book you should read. Complemented by a much more practical one which is Domain Driven Design (Evans), one for algorithms (Dasgupta will be more than fine) and now, with all this Amdahl stuff, one for concurrent programming (if going with java them see the book by Goetz et all) and you can start programming w/o doing too much harm to the industry :-).
However GoF has the biggest impact after you spend several years writing broken OO code :-D
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14 Discuss | 2018-11-19 01:06:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25778454542160034, "perplexity": 1552.655244495679}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744803.68/warc/CC-MAIN-20181119002432-20181119024432-00379.warc.gz"} |
http://math.gmu.edu/ACMabstracts/S19/shi.htm | ### GEORGE MASON UNIVERSITY DEPARTMENT OF MATHEMATICAL SCIENCES APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR
Speaker: Tianyi Shi, Cornell University
Title: Numerical tensor-train ranks and tensor displacement structure
Abstract: Tensors often have too many entries to be stored explicitly so it is essential to compress them into data sparse formats. I will identify three methodologies that can be used to explain when a tensor is compressible. Each methodology leads to bounds on the compressibility of certain tensors, partially explaining the abundance of low-rank tensors in applied mathematics. In particular, I will focus on tensors with a so-called displacement structure, showing that solutions to Poisson equations on tensor-product geometries are highly compressible. As the rank bounds are constructive, I will develop an optimal-complexity spectrally-accurate 3D Poisson solver with O(n (log(n))^2 (log(1/epsilon))^2 complexity for a smooth righthand side, where $n\times n\times n$ is the tensor discretization of the solution.
Time: Wednesday, June 5, 2019, 10:00-11:00am
Place: Exploratory Hall, Room 4106
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491 | 2020-02-18 04:38:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6753763556480408, "perplexity": 3353.923370802402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143505.60/warc/CC-MAIN-20200218025323-20200218055323-00487.warc.gz"} |
https://stat.ethz.ch/pipermail/r-devel/2009-April/052928.html | [Rd] Compiler options for Makefile.win
cstrato cstrato at aon.at
Thu Apr 2 23:18:47 CEST 2009
Dear Gabor,
I forgot to mention that the build process ended with the following
dialog box:
Runtime Error!
Program: c:\Programme\R\R-2.9.0alpha\bin\Rterm.exe
R6034
An application has made an attempt to load the C runtime library
incorrectly.
Only after pressing OK there was no response of Rterm and I had to
terminate the build process manually. I am not sure if this means that
the build process got into an infinite loop.
Could you explain what you mean with running the vignette "by hand" line
by line?
How can I do this?
BTW, if the problem is within one of the vignettes, as you mention, I
assume that the problem may be at the following statements:
\begin{Sinput}
R> library(xps)
\end{Sinput}
<<echo=FALSE>>=
library(xps)
@
I believe that the error occurs when trying to load "library(xps)".
Best regards
Christian
Gábor Csárdi wrote:
> On Sun, Mar 29, 2009 at 9:31 PM, cstrato <cstrato at aon.at> wrote:
> [...]
>
>> - - - - - - - -
>> Created c:\home\Rabbitus\CRAN\xps\chm\xps.chm, 166,306 bytes
>> Compression decreased file by 442,726 bytes.
>> ** building package indices ...
>> ** MD5 sums
>> * DONE (xps)
>> * creating vignettes ...Terminating on signal SIGINT(2)
>> - - - - - - - -
>>
>> As you see I had to terminate the build process manually after 15 min .
>>
>> My question is now:
>> Do you know why I can build my package w/o problems when using option /MT
>> but not when using option /MD?
>>
>
> It seems that the building process got into an infinite loop while
> creating the vignette. Some code in the vignette/package does not work
> properly. Try running the vignette "by hand" line by line to see where
> the problem is.
>
> Gabor
>
>
>> As a note, I am using "R-2.9.0alpha-win32.exe" which I have downloaded
>> today.
>>
>>
>> Best regards
>> Christian
>> _._._._._._._._._._._._._._._._._._
>> C.h.r.i.s.t.i.a.n S.t.r.a.t.o.w.a
>> V.i.e.n.n.a A.u.s.t.r.i.a
>> e.m.a.i.l: cstrato at aon.at
>> _._._._._._._._._._._._._._._._._._
>>
>> ______________________________________________
>> R-devel at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>>
>
>
>
> | 2022-10-01 22:17:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7232235074043274, "perplexity": 8734.350550740139}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336921.76/warc/CC-MAIN-20221001195125-20221001225125-00577.warc.gz"} |
http://sciforums.com/threads/dark-matter-is-negative-mass.160804/page-3 | # Dark matter is Negative mass!
Discussion in 'Astronomy, Exobiology, & Cosmology' started by icarus2, May 2, 2018.
1. ### NotEinsteinValued Senior Member
Messages:
1,708
Are you claiming that the Newtonian worldview is violating energy conservation? (Mass deficit being something that's not present in a Newtonian worldview.)
If you are talking physical objects, I agree with you, but you'll have to ask Icarus2.
"You cannot have fewer than zero electrons, so positive charges do not exist."
But what if it's made out of different stuff? Something with negative mass? (Again, talk to Icarus2.)
So you agree with me there are cases where it appears there's negative energy? Good! Glad we got that cleared up!
And some valued senior forum members too!
3. ### icarus2Registered Senior Member
Messages:
121
No. The meaning of Einstein's words is not to say that the gravitational field has a positive energy. Since General Theory of Relativity was built on the equivalent principle of inertial mass and gravitational mass, a major concern was whether this equivalence principle applies to other energies. Therefore, the meaning of Einstein's words is that the energy of the gravitational field also holds the equivalent principle of inertial mass and gravitational mass as any other kind of energy. .
Experiments to confirm the equivalence of inertial mass and gravitational mass of the gravitational potential energy were performed continuously~
Gravitation and Spacetime – by Hans C. Ohanian and Remo Ruffini
https://www.amazon.com/Gravitation-S...+and+spacetime
======
The experiments listed in Table 1.2 have tested the ratio $m_{G}/m_{I}$ for a wide variety of materials. Thus, Eotvos compared copper, water, copper sulfate, asbestos, snakewood, and so on with platinum; the later, more precise experiments tested gold, platinum, aluminum, copper, titanium, and beryllium. The results of these tests indicate that $m_{G}/m_{I}$ to within the experimental errors. The nucleus of the atom contains appreciable amounts of energy in its electric, magnetic, “strong,” and “weak” interaction field, and the results can therefore be interpreted to mean that different kinds of energy contribute to the gravitational mass of a system in the same amount as they contribute to the inertial mass; that is, $m_{G}/m_{I}$ is valid not only for the samples of materials tested in the experiments but also for the various kinds of energy
Table 1.3 Different forms of energy as sources of gravity*
Form of Energy |mG − mI|/mI
Rest mass, protons + electrons 0 (by definition)
Rest mass, neutrons <8 × 10^−12
Strong fields in nucleus <3 × 10^−10
Electric fields in nucleus <4 × 10^−10
Magnetic fields in nucleus <2 × 10^−7
Weak fields in nucleus <5 × 10^−3
Kinetic energy of nucleons <10^−9
Gravitational energy in Earth<5 × 10^−4
* Adapted from Will (1993), with corrections.
~~~~~~~~
If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6 × 10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.
If gravitational self-energy does not contribute in the normal way to the gravitational mass, then the Earth and the Moon would fall at different rates in the gravitational field of the Sun. The difference in the rates of fall is effectively equivalent to a uniform extra force field pulling the Moon toward the Sun (if gravitational energy gravitates less than normal) or away from the Sun (if gravitational energy gravitates more than normal). Such an extra force leads to a distortion of the orbit of the Moon relative to the Earth, a distortion called the Nordvedt effect. As Fig. 1.12 shows, the orbit is elongated, or polarized, in the direction of the Sun. Although the distortion effect is small, very precise measurements of the Earth-Moon distance have been performed by the laser-ranging technique already mentioned in Section 1.2, with a pulse of laser light sent from the Earth to the Moon and reflected back to the Earth by the corner reflectors installed on the Moon during the Apollo mission. Measurements of the travel time of the pulse determine the distance to within an uncertainty of a centimeter, and recent improvements are reducing this to a millimeter. If the uncertainty is taken as 1 cm, the analysis of the orbital data places a direct limit of 5 × 10^−4 on the fractional difference between the contributions of gravitational energy to the inertial and the gravitational mass. Thus, these experiments indicate that gravitational energy gravitates in the normal way.
Their main concern is whether the equivalence principle ($m_{G}/m_{I}$) holds for other energies.
Therefore, the meaning of Einstein's words is that the energy of the gravitational field also holds the equivalent principle of inertial mass and gravitational mass as any other kind of energy.
Alan Guth’s lecture: Inflationary Cosmology
Gravitational fields has negative energy density.
From the equation K + U = const. we obtain such equation as
, which can explain motion with variation(ex.) gravitational potential energy U= + mgh), however, this does not guarantee that the gravitational potential energy is positive.
Let's consider the following case that the value of gravitational potential energy has a negative value.
Even though, as above, gravitational potential energy has the negative value of energy defined for r= 0 to r= infinity from gravitational source, we can obtain the right result.
Last edited: May 9, 2018
5. ### icarus2Registered Senior Member
Messages:
121
I'm sorry. I did not see the full article, that's my guess ~
Last edited: May 9, 2018
7. ### RainbowSingularityValued Senior Member
Messages:
1,629
is it possible for it to be relative ?
i was recently pondering how we apply energy to an object to get it off the earth.
once the object is off the earth it is still containing that energy as speed ?
unles it gets just enough energy to exit the earth gravity...
then it is what ?
where does the enery go ? back to the earth or is it lost ?
i am of the mind that after brief reading the energy can not be created or destroyed... per say.
so i was wondering...
how does it work that the energy is given back to earth when it is taken from the earth (fuel)
is this a process of exchange ? if so what is it exchanging energy with ? the object ?
soo... the object must take more energy(than the energy it has on earth) from the earth to leave the earth AND give it back.
soo... my question was, kinda is this an exchange of energy, is the object a conduit of energy in general.
considering the object must use more energy than what it has to remove its self from the earth...
it does seem perplexing in a relationship to relative mass & energy given rise to my question, thus
can an object(in space with no opposing force) simply become an energy conduit to use energy to gain momentum ... err-go light speed... if the object is borrowing energy, why cant it go faster than light ?
(excuse any typos its been a long day)
8. ### icarus2Registered Senior Member
Messages:
121
Writing this sentence is a very bad act.
By treating all studies involving negative masses as being the same, it is dismissing the efforts of someone.
About 99.99% of physics papers are about positive mass, so is there no new idea?
Naked singularity is inferred when a negative mass has a singularity. It is a peculiar phenomenon, but it is not a problem. By the way, they have achieved such results by assuming a black hole of negative mass.
In my opinion, I think that massive mass structures (planets, stars, black hole) of negative mass are hard to exist. Because of that there is a repulsive gravitational effect between negative masses, and therefore, massive mass structure formation is difficult. In principle, it is possible if there is repulsion between them.
Refer to 3m 47s ~
"Runaway motion" is one of the research topics I have left, I do not want to open it ~
1. Since "runaway motion" assumes a very ideal situation, an unusual movement occurs, but in the real world, this ideal situation may be broken by external factors (forces or fields by other objects …)
Nevertheless, we can still force the external conditions themselves to be in ideal conditions.
2. There is a possibility that the gravitational potential energy stops the ideal situation
Although the absolute values of the masses of two objects are exactly the same, there is a gravitational potential energy between them.
$U = + \frac{{G{m_ - }{m_ + }}}{r}$
This gravitational potential energy has a positive value and exists in a system containing two objects or two objects.
And, since all energy is a source of gravity, the gravitational potential energy must also act gravitty source.
When quoting the text of the major book, ~
=======
Table 1.3 Different forms of energy as sources of gravity
Form of Energy |mG − mI|/mI
Rest mass, protons + electrons 0 (by definition)
Rest mass, neutrons <8 × 10^−12
Strong fields in nucleus <3 × 10^−10
Electric fields in nucleus <4 × 10^−10
Magnetic fields in nucleus <2 × 10^−7
Weak fields in nucleus <5 × 10^−3
Kinetic energy of nucleons <10^−9
Gravitational energy in Earth <5 × 10^−4
* Adapted from Will (1993), with corrections.
If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy.
Thus, these experiments indicate that gravitational energy gravitates in the normal way.
In setting these limits on how the strong, electromagnetic, weak, and gravitational energies gravitate, we have ignored the self-energies locked up within the rest masses of electrons, protons, and neutrons.~
=======
That is, even if the masses of negative mass and positive mass are exactly the same, the gravitational potential energy between them breaks this ideal situation.
3. I do not even know if someone's claim is true. "all such interactions would leave a surplus of momentum"
Above that, the (or some) writer insisted that this movement was a movement in which momentum was preserved.
=======
Such a couple of objects would accelerate without limit (except relativistic one); however, the total mass, momentum and energy of the system would remain 0.
=======
But the one who wrote the last sentence,
=======
“all such interactions would leave a surplus of momentum, ~“
=======
The two sentences seem to be in conflict.
4. Considering general relativity, a new solution may come up.
Not at all!
It is not only the opinion of the person, but also even after the 1970s, research papers on negative mass continue to emerge.
Try searching in the arXiv : “negative mass”
And, the prediction of mainstream physics was not always right.
Last edited: May 10, 2018
9. ### icarus2Registered Senior Member
Messages:
121
What do you think of the existence of positive and negative charges? Why is not energy (mass) ?
Does this have positive energy?
$U = k\frac{{( + e)( + e)}}{r}$
So this?
$U = k\frac{{( + e)( - e)}}{r}$
How can a positive energy, positive mass exist by itself?
All new discoveries were called new discoveries because they were not found until then. Throughout the history of science, among the things that have not yet been discovered, new discoveries have had many examples.
In other words, it does not guarantee that undiscovered findings of any physical object will be undiscovered in the future. The history of physics, and even the history of science.
Some phenomena of relativity and quantum mechanics are against common sense. Already, accelerating expansion itself is not what we expected. It is a phenomenon contrary to common sense prediction.
Also, now we need a something to generate repulsion or anti-gravity, and negative mass is also a solution of the accelerating expansion.
Gravitation and Spacetime – by Hans C. Ohanian and Remo Ruffini
https://www.amazon.com/Gravitation-S...+and+spacetime
=========
We recognize that the term in Einstein’s equation corresponds to a uniform effective mass density
${\rho _{eff}} = - \frac{\Lambda }{{4\pi G}}$
Thus, if $\Lambda$ is positive, the effective gravitational mass density of the vacuum is negative.
~~~~~~
Expressed in another way, the inertial mass density for the cosmological term is positive, but the gravitational mass density is negative.
=========
"The inertial mass density for the cosmological term is positive, but the gravitational mass density is negative."
It violates the principle of equivalence of inertial mass and gravitational mass, which is the basis of general relativity theory.
$\frac{{{d^2}R}}{{d{t^2}}} = - \frac{{4\pi G}}{3}(\rho + 3P) = - \frac{{4\pi G}}{3}({\rho _\Lambda } + 3( - {\rho _\Lambda })) = - \frac{{4\pi G}}{3}( - 2{\rho _\Lambda })$
The inertial mass density is +1 and the gravitational mass density is -2, rather than just the opposite sign.
Do these monsters really exist? Do not make a decision now, why not watch it?
IMO,
In physics, negative mass is not a worse idea than cosmological constant or vacuum energy.
Last edited: May 10, 2018
10. ### NotEinsteinValued Senior Member
Messages:
1,708
The article is about the concept of negative mass. All negative masses are the same in that they are negative masses. That's trivially true. You may have a previously not thought of type of negative mass, but it's still a negative mass. All types of negative mass fall under the category of negative mass, which is what that article is about. So obviously your type of negative mass also discussed in that article, even if not explicitly. Thus, I'm not dismissing anyone's efforts.
The first paper talking about the Higgs boson fell in the same category when it was published. This is once again trivially true. And since it was a new idea, your statement is thus incorrect.
Please explain why it isn't a problem, because from https://en.wikipedia.org/wiki/Naked_singularity :
And of course most physics papers talk about positive masses, because that's all we currently have evidence for.
Who is "they"? And evidence please.
Sure, but who claimed otherwise?
So you have no idea why the concept of runaway motion is so problematic, and why it completely eviscerates your negative mass hypothesis unless properly addressed. And no, waving your arms about saying that the ideal situation isn't likely to arise naturally is not addressing the issue.
Please learn the distinction between fundamental particles and quasiparticles first. Then please point me to some articles that are discussing fundamental particles with negative rest masses without dismissing their possibility.
Sure, but you need to provide proof that that's the case here. Thus far, you've failed to even address the very first of my questions.
11. ### icarus2Registered Senior Member
Messages:
121
Do not be bullshit ~!
What you need to look at in my paper is a description of the properties of dark matter in terms of negative mass.
I started my writing like this ~
======
Dark Matter is Negative Mass
Negative mass is an object whose existence is required by the law of the conservation of energy. The fundamental properties of negative mass can explain important characteristics of dark matter.
2) explanations derived from fundamental principles about the reason why dark matter does not have electromagnetic interaction,
3) repulsive gravity ensuring almost even distribution and lower interaction of dark matter,
4) gravitational lens effect,
5) accelerating expansion of the universe can be explained with negative mass.
======
Do not you see this phrases?
In the study of negative mass, who has this explanation?
Last edited: May 11, 2018
12. ### NotEinsteinValued Senior Member
Messages:
1,708
Explain to me how your negative mass is different from "matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg", which is what that Wikipedia article is about.
You keep claiming that. Can you please explain why?
(We'll get to those whenever you finally start answering the most basic questions.) | 2019-01-22 15:27:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5981190800666809, "perplexity": 1004.6393419222379}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583857913.57/warc/CC-MAIN-20190122140606-20190122162606-00619.warc.gz"} |
https://cimpapiriapolisuy.wordpress.com/ | This research school consists on an introduction to the geometry of hyperbolic groups and their representations. The global objective is to understand how the intrinsic geometry of the hyperbolic group interacts with the geometry of the target group.
When the hyperbolic group is a surface group, several target groups are subject of major deep results: Teichmüller-Thurston Theory (associated to the groups $\textrm{PSL}_2(\mathbb R)$ and $\textrm{PSL}_2(\mathbb C)$) and the ‘absence of geometric meaning’ due to Goldman for $\textrm{SU}(2),$ just to name a few. Representations of a general hyperbolic group into a semisimple higher rank Lie group is a current topic of research.
The school consists on 5 mini-courses to be held in english: an introductory course, a course on the large scale geometry of hyperbolic groups, Quasi-Fuchsian representations, representations of surface groups on $\textrm{SU}(2)$ and a course on matrix groups over a $p$-adic field.
This school could serve as an introductory school for the Workshop on Geometry of Groups in Montevideo starting April 11th.
School Pictures
Mini-courses
Directions
Organizing and Scientific committees
Schedule (The afternoon schedule has changed, afternoon talks start at 15h and the others are shifted accordingly).
Financing Institutions
Poster | 2019-06-27 05:19:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29927143454551697, "perplexity": 741.3310082953847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000613.45/warc/CC-MAIN-20190627035307-20190627061307-00031.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=4208473 | ## Two questions about cycles (algebra)...
I have two questions:
1) For the example on the second page, I don't understand why they say $$\alpha\gamma\alpha^{-1} = (\alpha1 \alpha3)(\alpha2 \alpha4 \alpha7)(\alpha5)(\alpha6)$$ instead of $$\alpha\gamma\alpha^{-1} = (\alpha1\alpha^{-1} \alpha3\alpha^{-1})(\alpha2\alpha^{-1} \alpha4\alpha^{-1} \alpha7\alpha^{-1})(\alpha5\alpha^{-1})(\alpha6\alpha^{-1})$$.
2) For the tables at the top of the 2nd page, I don't know how they computed those numbers...
Attached Thumbnails
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Recognitions:
Quote by Artusartos I have two questions: 1) For the example on the second page, I don't understand why they say $$\alpha\gamma\alpha^{-1} = (\alpha1 \alpha3)(\alpha2 \alpha4 \alpha7)(\alpha5)(\alpha6)$$ instead of $$\alpha\gamma\alpha^{-1} = (\alpha1\alpha^{-1} \alpha3\alpha^{-1})(\alpha2\alpha^{-1} \alpha4\alpha^{-1} \alpha7\alpha^{-1})(\alpha5\alpha^{-1})(\alpha6\alpha^{-1})$$.
They say what is consistent with what the theorem says. The theorem says to "apply $\alpha$" to the symbols in the cycles.
If $\alpha,\ p,\ q$ are cycles, It is true that $\alpha (\ p \ q) \ \alpha^{-1} =( \alpha \ p \ \alpha^{-1})(\alpha \ q \ \alpha^{-1})$ but this is not the content of the theorem. A cycle is not the same as the product of the individual symbols in the cycle. The cycle (1,2,3) is not equal to (1)(2)(3).
2) For the tables at the top of the 2nd page, I don't know how they computed those numbers...
For example, In the permutation group $S_4$, there are 8 different elements of the group that are cycles of length 3. The example (1,2,3) in the table illustrates one of them.
(There are 24 = (4)(3)(2) different permutations that can be formed by taking 3 distinct numbers from the set of numbers {1,2,3,4}. However, each permutation such as (1,2,3) is one of 3 representations of the same cycle. (1,2,3) = (2,3,1) = (3,1,2) So there are 8 = 24/3 distinct cycles of length 3 )
In a nutshell, notice that alpha gamma alpha inverse takes alpha of 1 to alpha of 3. ;)
## Two questions about cycles (algebra)...
Quote by Stephen Tashi They say what is consistent with what the theorem says. The theorem says to "apply $\alpha$" to the symbols in the cycles. If $\alpha,\ p,\ q$ are cycles, It is true that $\alpha (\ p \ q) \ \alpha^{-1} =( \alpha \ p \ \alpha^{-1})(\alpha \ q \ \alpha^{-1})$ but this is not the content of the theorem. A cycle is not the same as the product of the individual symbols in the cycle. The cycle (1,2,3) is not equal to (1)(2)(3). For example, In the permutation group $S_4$, there are 8 different elements of the group that are cycles of length 3. The example (1,2,3) in the table illustrates one of them. (There are 24 = (4)(3)(2) different permutations that can be formed by taking 3 distinct numbers from the set of numbers {1,2,3,4}. However, each permutation such as (1,2,3) is one of 3 representations of the same cycle. (1,2,3) = (2,3,1) = (3,1,2) So there are 8 = 24/3 distinct cycles of length 3 )
Thank you
Similar discussions for: Two questions about cycles (algebra)... Thread Forum Replies Linear & Abstract Algebra 3 Differential Geometry 17 Calculus & Beyond Homework 4 Calculus & Beyond Homework 0 | 2013-06-19 09:39:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7406720519065857, "perplexity": 432.92654618537006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368708664942/warc/CC-MAIN-20130516125104-00038-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php?title=Special:MobileDiff/292 | Cookies help us deliver our services. By using our services, you agree to our use of cookies. More information
# Changes
## R-factors
, 18:25, 17 February 2008
m
Data quality indicators
R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
[/itex]
<br>
where $\langle I_{hkl}\rangle$ is the average of symmetry- (or Friedel-) related observations of a unique reflection.
It can be shown that this formula results in higher R-factors when the redundancy is higher(K. Diederichs and P.A. Karplus (1997). Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Biol. 4, 269-275 [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]). In other words, low-redundancy datasets appear better than high-redundancy ones, which obviously violates the intention of having an indicator of data quality!
* Redundancy-independant version of the above:
$R_{meas} = \frac{\sum_{hkl} \sqrt \frac{n}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}$
<br>which unfortunately results in higher (but more realistic) numerical values than R<sub>sym</sub> / R<sub>merge</sub> (Diederichs and Karplus (1997)[http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf], and M.S. Weiss and R. Hilgenfeld (1997) On the use of the merging R-factor as a quality indicator for X-ray data. J. Appl. Crystallogr. 30, 203-205[http://dx.doi.org/10.1107/S0021889897003907]).
* measuring quality of averaged intensities/amplitudes:
for intensities use (M.S. Weiss. Global indicators of X-ray data quality. J. Appl. Cryst. (2001). 34, 130-135 [http://dx.doi.org/10.1107/S0021889800018227])
$R_{p.i.m.} (or R_{mrgd-I}) = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}$
<br>
<br>
$R_{mrgd-I}$ is similarly defined in Diederichs and similarly Karplus (1997). Similarly, one should use R<sub>mrgd-F</sub> as a quality indicator for amplitudes(Diederichs and Karplus (1997) [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]), which may be calculated as:
$R_{mrgd-F} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert F_{hkl,j}-\langle F_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}F_{hkl,j}}$
<br>
with $\langle F_{hkl}\rangle$ defined analogously as $\langle I_{hkl}\rangle$.
1,280
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http://lt-jds.jinr.ru/record/71898?ln=en | / hep-ex CERN-EP-2017-154
Search for supersymmetry in events with $b$-tagged jets and missing transverse momentum in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
Pages: 50
Abstract: A search for the supersymmetric partners of the Standard Model bottom and top quarks is presented. The search uses 36.1 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=13$ TeV collected by the ATLAS experiment at the Large Hadron Collider. Direct production of pairs of bottom and top squarks ($\tilde{b}_{1}$ and $\tilde{t}_{1}$) is searched for in final states with $b$-tagged jets and missing transverse momentum. Distinctive selections are defined with either no charged leptons (electrons or muons) in the final state, or one charged lepton. The zero-lepton selection targets models in which the $\tilde{b}_{1}$ is the lightest squark and decays via $\tilde{b}_{1} \rightarrow b \tilde{\chi}^{0}_{1}$, where $\tilde{\chi}^{0}_{1}$ is the lightest neutralino. The one-lepton final state targets models where bottom or top squarks are produced and can decay into multiple channels, $\tilde{b}_{1} \rightarrow b \tilde{\chi}^{0}_{1}$ and $\tilde{b}_{1} \rightarrow t \tilde{\chi}^{\pm}_{1}$, or $\tilde{t}_{1} \rightarrow t \tilde{\chi}^{0}_{1}$ and $\tilde{t}_{1} \rightarrow b \tilde{\chi}^{\pm}_{1}$, where $\tilde{\chi}^{\pm}_{1}$ is the lightest chargino and the mass difference $m_{\tilde{\chi}^{\pm}_{1}}- m_{\tilde{\chi}^{0}_{1}}$ is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95\% confidence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simplified models.
Note: 50 pages in total, author list starting page 34, 7 figures, 10 tables, submitted to JHEP, All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/SUSY-2016-28/
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https://galison.scholar.harvard.edu/publications/agnotology-action-dialogue | # Agnotology in Action: A Dialogue
### Citation:
Galison, Peter, and Robert Proctor. “Agnotology in Action: A Dialogue.” In Science and the Production of Ignorance, edited by Janet Kourany and Martin Carrier. Cambridge, MA: MIT Press, 2020. | 2021-05-19 03:34:28 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8917534947395325, "perplexity": 13167.302371373637}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991562.85/warc/CC-MAIN-20210519012635-20210519042635-00613.warc.gz"} |