text:
# examples/dots1.py¶

This is one of the example scripts included with Shady. These scripts can be run conventionally like any normal Python script, or you can choose to run them as interactive tutorials, for example with python -m Shady demo dots1

# $BEGIN_SHADY_LICENSE$
#
# This file is part of the Shady project, a Python framework for
# real-time manipulation of psychophysical stimuli for vision science.
#
# Copyright (c) 2017-2020 Jeremy Hill, Scott Mooney
#
# Shady is free software: you can redistribute it and/or modify it
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see http://www.gnu.org/licenses/ .
#
# $END_SHADY_LICENSE$

#: A simple random-dot stimulus
"""
This demo shows the simplest way of drawing dot stimuli,
which is to set the .drawMode property to
Shady.DRAWMODE.POINTS and then manipulate the .points
property.   The visual quality of the results will depend
on your graphics drivers.  To achieve greater control over
dot appearance, see the other dots demos (dots2, dots3
and dots4).
"""#.

if __name__ == '__main__':
"""
First let's wrangle the command-line options:
"""#:

ndots     = cmdline.Option( 'ndots',    300, type=int,  container=None, doc="Number of dots (may not exceed %d)." % Shady.Rendering.MAX_POINTS )
bounce    = cmdline.Option( 'bounce', False, type=bool, container=None, doc="If True, implement some rudimentary physics to make the dots bounce off each other." )
gauge     = cmdline.Option( 'gauge',   True, type=bool, container=None, doc="Whether or not to show a FrameIntervalGauge." )
thickness = cmdline.Option( 'thickness', 20, type=( int, float ), container=None, doc="Value for the .penThickness property, dictating the size of the dots." )
smooth    = cmdline.Option( 'smooth',  True, type=bool, container=None, doc="""If True, flag the dots as "smooth". This may make them round instead of square, or it may have no effect - unfortunately this is driver-dependent. If you want to guarantee round dots you'll have to use small polygons instead (see dots3 and dots4 demos) or separate Stimulus instances (dots2).""" )
cmdline.Help().Finalize()
Shady.Require( 'numpy' ) # die with an informative error if this is missing

"""
Create a World and, if requested, a frame interval gauge:
"""#:

"""
Now a single Stimulus that will host our random dots.
We'll use the POINTS drawing mode.
"""#:
field = w.Stimulus( size=w.size, color=1, drawMode=Shady.DRAWMODE.POINTS, penThickness=thickness, smoothing=smooth )

"""
To draw the points, we'll have to set the .points
property.
"""#:
import numpy
location = numpy.random.uniform( low=[   0,   0 ], high=field.size,    size=[ ndots, 2 ] )
velocity = numpy.random.uniform( low=[ -30, -30 ], high=[ +30, -150 ], size=[ ndots, 2 ] )
field.points = ( Shady.Integral( velocity ) + location ) % field.size

"""
Now, for a bit of fun, we'll define a couple of functions
that allow the dots to bounce off each other.
"""#:
physics = dict( exponent=10, closest=10, coefficient=800 )
def RepulsionForces( t=None ):
positions = field.pointsComplex
vectors = positions[ None, : ] - positions[ :, None ]
magnitudes = numpy.abs( vectors )
degenerate = magnitudes < 1e-4
nondegenerate = ~degenerate
vectors[ nondegenerate ] /= magnitudes[ nondegenerate ] # vectors are now unit vectors
magnitudes[ degenerate ] = numpy.inf
magnitudes = numpy.clip( magnitudes - field.penThickness / 2.0, physics[ 'closest' ], numpy.inf )
magnitudes /= physics[ 'closest' ]
magnitudes **= -physics[ 'exponent' ] # now we have inverse square (or whatever power) distances, with 0s on diagonal
forces = magnitudes * vectors * physics[ 'coefficient' ]
forces = forces.sum( axis=0 )
forces = Shady.ComplexToReal2D( forces )  # n-by-2 real-valued output
return forces
def Bounce( **kwargs ):
physics.update( kwargs )
field.points = ( Shady.Integral( Shady.Integral( RepulsionForces ) + velocity ) + field.points ) % field.size

if bounce: w.Defer( Bounce )
# .Defer() will ensure that the function gets called at the end of
# the next frame (this ensures that field.pointsComplex, which
# RepulsionForces() relies on, has already had a value assigned to it

"""
If you requested this with the --bounce command-line option
then the points should already be bouncing off each other.
If not, you can manually trigger it if you want, by calling
Bounce().  Either way, our dots demo is done.

Note that drawMode=POINTS is the simplest way of creating
dot patterns, but not necessarily the most powerful. Setting
smoothing=True should in principle make them round, but
whether it successfully does so is dependent on your graphics
driver: they may stubbornly remain square.  The best way of
guaranteeing the shape of your dots is to draw them as
tiny polygons (with a high number of sides, if you want them
to look round).  This can be explored in the dots3 and
dots4 demos.  Another option is to make each "dot" an
independent Stimulus - but as the dots2 demo shows, you
have to worry much more about timing performance in that case.
"""#:

"""
By the way: if you're not pleased with the frame rate of your
colliding dots, and you're reading this console in the foreground,
try switching to the World as your main window. This will put
Shady in charge of synchronizing frame buffer swaps and likely
lead to significant improvements in performance.
"""#>


text:
# LXX International conference "NUCLEUS – 2020. Nuclear physics and elementary particle physics. Nuclear physics technologies"

Oct 11 – 17, 2020
Online
Europe/Moscow timezone

## EXPLOSION OF LOW-MASS NEUTRON STAR IN CLOSE BINARY SYSTEM AND NUCLEOSYNTHESIS OF HEAVY ELEMENTS.

Oct 14, 2020, 6:10 PM
1h
Online

#### Online

Poster report Section 5. Neutrino physics and astrophysics.

### Speaker

Igor Panov$^{1,2}$ (NRC "Kurchatov Institute" – Institute for Theoretical and Experimental Physics)

### Description

$^1$ NRC “Kurchatov institute” – ITEP, Moscow, 117218, Russia;
$^2$ National Research Center “Kurchatov institute”, Moscow, 123182, Russia.

First observation of neutron star merger and registration of heavy elements presence in this process [1] confirmed our understanding that main scenario for the r-process is connected with the ejecta during neutron star merger (NSM) at the end of close binary system evolution rather than with the supernova explosion [2].
A number of NSM model were created [3] since 1999 year and with their help the main conditions of the r-process in jets were researched. Neutron stars in close binaries is approaching each other because the system lost angular momentum due to gravitation wave emission. Further evolution of their mutual approaching and merger depend on masses of binary components. In case when masses are close to each other and when the mass of every component is close to solar mass (it usually is called as “standard” neutron star mass), then scenario of neutron stars merger is realized.
In present report we will discuss the binary of neutron stars when neutron stars have significantly different masses, $m_1$ > $m_2$ [4]. In such a binaries the matter of the component with smaller mass starts to flow from low-mass companion to higher-mass one $m_1$. When the mass of low-mass neutron star have reached the minimum mass value ~0.1$M_⊙$, the low-mass companion lost its hydrodynamical stability and blows up [5].
On the results of first calculations of low-mass companion of close neutron stars system, for the ejecta with different chemical composition the nucleosynthesis calculations of heavy elements were done and theoretical abundances of heavy elements are in a good agreement with our knowledge of solar system matter.
The work was under under financial support of Russian Fond of Basic Research (project №. 18-29-21019 мк).

1. N.R. Tanvir, A.J. Levan, C. González-Fernández, et al. // AJ. 2017. V.848. P.L27.
2. L. Hudepohl, B. Mueller, H.-T.Janka, et al. // Phys. Rev. Lett. 2010. V.104. 251101.
3. C. Freiburghaus, S. Rosswog, F.-K. Thielemann // Astrophys. J. 1999. V.525. P.L121.
4. J.P.A. Clark and D.M. Eardley // Astroph. J. 1977. V.215. P.311.
5. S.I. Blinnikov, I.D. Novikov, T.V. Perevodchikova, A.G. Polnarev // Sov. Astron. Lett. 1984. V.10. P.177.

### Primary author

Igor Panov$^{1,2}$ (NRC "Kurchatov Institute" – Institute for Theoretical and Experimental Physics)

### Co-authors

Mr Nikita Kramarev$^1$ (NRC “Kurchatov institute” – Institute for Theoretical and Experimental Physics) Dr Andrey Yudin$^{1,2}$ (NRC “Kurchatov institute” – Institute for Theoretical and Experimental Physics)

format: plain


text:
# Getting Started: Build Your First Document

Now that you’ve installed Tectonic, let’s create and build your first document.

Important: From here on out, this Getting Started guide will use what we call the “V2” interface to the Tectonic program. The V2 interface coexists with, but has a fairly different approach than, the “V1” interface. We are gradually migrating from V1 to V2. Neither interface (V1 or V2) is the same as the one exposed by classic TeX tools such as pdflatex.

## Create a new document

The Tectonic V2 interface has a “multitool” structure similar to that of other powerful tools such as git and cargo. To create a new document, we use a new subcommand that looks like this:

$tectonic -X new myfirstdoc  This will create a new Tectonic workspace directory named myfirstdoc containing a file Tectonic.toml and a sub-directory named src. Enter this new directory in your command prompt. $ cd myfirstdoc

Note: The -X flag activates the V2 interface. Don’t forget it! Eventually it will become unnecessary and you’ll just be able to write tectonic new, but that changeover hasn’t happened yet.

If you’ve got an existing TeX file, you can process it in in one-off fashion with:

$tectonic -X compile myfile.tex  See the tectonic -X compile documentation for all of the options. ## Basic document source structure The source code to your document is stored in the src subdirectory of your new document. Check it out: $ ls src

You’ll see three files that were created by the new command:

• _preamble.tex
• index.tex
• _postamble.tex

These files are pre-populated with extremely basic contents following this suggested source structure:

• The “preamble” file should contain all of your (La)TeX initialization boilerplate, up to and including the LaTeX \begin{document} command.
• The “index” file contains all of your actual document content, without any of the annoying boilerplate. When you create a new Tectonic document, it just contains the text Hello, world.
• The “postamble” file should contain all of your cleanup code, starting with the LaTeX \end{document} command. There will almost never need to be any other content in this file.

When Tectonic builds your document, it processes these files in the order listed above, so all three of them need to be available. But the breakdown suggested above is only a suggestion, nothing more. If you want all of your boilerplate and content to be in a single file, we recommend putting it all in index.tex and making your preamble and postamble be empty.

The motivation for this separation is partially stylistic, but not entirely so. In the future, we anticipate that there might be different ways to build the same document that invoke different preamble or postamble contents.

$tectonic -X build  If you haven’t run Tectonic on your computer before, this command will take a minute or two as it downloads the support files that it needs and generates the LaTeX “format file” storing the default macro collection. Tectonic will cache these files and avoid downloading them again. Test it out by running the build again: $ tectonic -X build

This time the command should finish much more quickly, with no messages about downloading files. The output PDF document will be placed at the path build/default/default.pdf relative to your document directory:

\$ ls -l build/default/

If you’re familiar with traditional TeX engines, you’ll have noticed that Tectonic’s “user experience” is substantially different from those engines:

1. Tectonic doesn’t print out the usual chatter — unless there’s an error.
2. Tectonic automatically reruns the TeX stage until its output stabilizes.
3. By default, Tectonic doesn’t write out intermediate files such as (texput.aux, texput.log).
4. You ought not have seen this yet, but if you make a mistake in your TeX, Tectonic will quit with an error message, rather than asking you to type X2 or whatever.

We hope that you’ll agree that these changes make for a program that is much more pleasant to use than the traditional tools.

## Cache

The location of the cache depends on your operating system. You can use the V2 Interface to find the exact cache location on your machine or take a look at the implementation.

If you need to change the location of the cache, you can do that by setting the environment variable TECTONIC_CACHE_DIR to the path of a directory. We recommend leaving the cache location at the default unless there is a compelling reason to change it.


text:
Google Forms/ Sheets – Web Applications Stack Exchange

Taking into consideration the little info you give, I imagine that if your response sheet (`Form Responses`) looks something like this:

``````+---------------------+-----------+------------+---------------------------+-------+
|      Timestamp      | Last name | First name |           Email           | Steps |
+---------------------+-----------+------------+---------------------------+-------+
| 2020-10-19 23:25:51 | Boc       | Florencia  | fboc9@vinaora.com         |   356 |
| 2020-10-19 22:33:29 | Boc       | Florencia  | fboc9@vinaora.com         |   175 |
| 2020-10-19 19:58:08 | Splevins  | Donny      | dsplevins7@ucla.edu       |   153 |
| 2020-10-19 18:40:52 | Castagne  | Cedric     | ccastagneb@ow.ly          |   382 |
| 2020-10-19 17:56:40 | Gipp      | Eloisa     | egipp4@webmd.com          |   147 |
| 2020-10-19 17:26:39 | Splevins  | Donny      | dsplevins7@ucla.edu       |   365 |
| 2020-10-19 17:09:17 | Riccardi  | Monica     | mriccardi6@wikispaces.com |   289 |
| 2020-10-19 17:07:08 | Boc       | Florencia  | fboc9@vinaora.com         |   284 |
| 2020-10-19 16:54:45 | Gipp      | Eloisa     | egipp4@webmd.com          |   174 |
| 2020-10-19 14:20:50 | Riccardi  | Monica     | mriccardi6@wikispaces.com |   233 |
| 2020-10-19 14:02:00 | Splevins  | Donny      | dsplevins7@ucla.edu       |   173 |
| 2020-10-19 09:51:38 | Riccardi  | Monica     | mriccardi6@wikispaces.com |   177 |
| 2020-10-19 04:49:03 | Splevins  | Donny      | dsplevins7@ucla.edu       |   320 |
+---------------------+-----------+------------+---------------------------+-------+
``````

If so, you then need to create a new sheet and place the following QUERY formula i cell `A1`

``````=QUERY('Form Responses'!A1:E,
"select B, C, sum(E) where A is not null group by B, C ",1)
``````

If still in need please let us know.

WordPress5.5 Gravity Forms not sending email by wp_mail works

I have a WordPress 5.5 based website and gravity forms installed. My issue is when people use my gravity forms I am not getting any email notification. I tried putting different emails in and even downloaded a plugin called “check email” and used that to send myself a test and it says email sent but I never receive it and even checked my spam folder.

If I create a basic php file and put a php mail() tag in with my info I receive the email although it goes to my spam folder. Also if I add a hard coded wp_mail() tag with my email info hard coded in the footer.php file of my wordpress site I also receive that email although it goes to my spam.

Wondering if anyone know how to view an error log for Gravity forms?

forms – Can a 2-column grid of info be acceptable if it mitigates an awkwardly large amount of white space?

I’m in the middle of a psuedo-overhaul of my company’s platform, with an emphasis on “object-level” pages (ie the page for an individual task, or individual appointment).

A problem I’m running into is that the info for many of these pages is laid out in a two-column format (see pic), which I know any competent ux designer will tell you is bad for scanning. But while combining both columns into one single left-aligned column might improve scannability, it would also leave just a gaping void of whitespace on the right portion of the page. I can’t really articulate any ux code this violates beyond just looking ridiculous and stark, but it still seems like an issue worth surfacing.

Any thoughts on this? I want to follow best practices but I also would like to preserve a sense of visual balance and appeal.

Thanks!

web development – what is the next step after learning and building forms and databases

I am trying to shift my career into software. I have been doing self education mostly using YouTube videos. I have understood how form submission works and how a server accepts the data from form submission and saves it in a database. i taught myself crud operations and creating a rest API server that writes and reads to/from a database. what would be beneficial to my learning next ? what should i focus my efforts on ?

forms – UX pattern for implementing calendars

In my recent development I am required to implement a calendar view which is having month view for each month for given date range. See below.

I have already done the programming part. It is required allows users to select all Sundays, all Mondays, all Tues days etc.. The existing swing UI like this. (Hope this will help to get an idea) see below.

As you can see both Sundays and Tues check boxes are selected and marked in calendar as well. Calendar days are are not clickable and only the check boxes can be selected.

Pure idea is to allow users to selected week/end days and see them on calendar view. Calendar days are not clickable. First thought came to mind is implementing the same behavior as given above for web UI as well.

Hope you all thoughts on this.

Thanks
Nuwan

sharepoint online – How to get Query String Value in Powerapps forms

I need to get the query string values from the URL in powerapps.

i.e I have an SP list with Customized powerapps forms, if i pass the value in the URL like “http://TestSite.sharepoint.com/sites/TestSite/Lists/TestList/NewForm.aspx?CompanyName=Microsoft
&CompanyID=1”.

I should able to get that CompanyName value and CompanyID value in powerapps forms. I tried Param(CompanyName) method but didn’t get the value from query string.

Is there any solution to get the parameter value from query string in Powerapps.

iis 7.5 – Protect static file on Asp Net Classic Mode with Forms Authentication

i’m struggling to resolve this issue since yesterday.

I have a site (framework 4.0), hosted in a Windows Server with IIS 7.5 in Classic Mode.
Unfortunately i can’t changed this to Integrated Mode.

I need to protect files contained in a folder.

anonymous user not.

I tried to protect folder in this way in webconfig:

``````<location path="Riservata/Files">
<system.web>
<authorization>
<deny users="?" />
</authorization>
</system.web>
</location>
``````

Someone can help me?

nt.number theory – Set of Quadratic Forms that represents All Primes

A SPECIFIC CASE:

Any prime number can be classified as either $$p equiv 1 pmod 3$$ or $$p equiv 2 pmod 3$$.

If $$p = 3$$ or $$p = 1 pmod 3$$, then the prime $$p$$ can be represented by the quadratic form $$x^2 + 3y^2, x,y in mathbb Z.$$

But what if $$p equiv 2 pmod 3$$?

Is there a quadratic form $$ax^2+bxy+cy^2$$ such that $$p= ax^2+bxy+cy^2,$$ when $$p equiv 2 pmod 3$$ where $$x,y, a, b,c in mathbb Z$$?

GENERAL CASE:

The general question is, is there a set of quadratic forms which represent all prime numbers?

We will classify the prime numbers, say, by $$m$$. Any prime is defined by $$p equiv i pmod m$$ where $$1 leq ileq m-1$$.

In above example, $$i in {1, 2}, m=3$$. Let, the set of quadratic forms is $$A$$, then the number of elements in $$A$$ is $$(m-1)$$.

QUESTION:

For a given $$m$$ can we find a set $$A$$ such that any prime $$p$$ can be represented by one of the quadratic form of $$A$$ ?

If it is possible then how? If there is a condition on $$m$$, what is it?

Does the question has any relation to the following theorem ?

One can answer only the specific case, if he wishes.

plugins – How to dynamically generate multiple forms from a Template, based on user input?

I write to the community with the hope that someones can show me the correct way to solve my issue.

I’m trying to create a simple plugin that should generate multiple contact forms from a Form Template and save the data in to the WordPress Database.
The user should have the ability to choose (from the admin area) which fields to display in the form and then, through a Shortcode, the form will be displayed in the Frontend.

The Code I have is working for a unique form, but the goal would be to generate and save multiple forms to the database (not sure I should create a new table, or use an existing WP table). Then, to each form, a Shortcode would be dynamically assigned – eg: (contact_form id = “1”), etc. The generated data would then be displayed as a list table in the admin area, and the user should have the ability to add, update, and delete the generated forms.
I’ve heard about shortcode_atts() function; WP_List_Table Class, Form Tables, and Custom Post Types, but I’m not really sure how can I solve this issue.

Maybe someone can guide me in finding the proper way to deal with this issue, following the WordPress standards?

``````<?php

/**
* Plugin Name: Generate multiple contact forms from Form template
*/

}
?>

``````

``````<?php

{
?>

<form method="POST" action="options.php">
<?php settings_fields( 'settings_group_1' );
submit_button();
?>
</form>

<?php
}
?>
``````

The settings API

``````<?php
function create_settings(){

register_setting( "settings_group_1", "contact_form_FirstName" );
register_setting( "settings_group_1", "contact_form_LastName" );
register_setting( "settings_group_1", "contact_form_Email" );
register_setting( "settings_group_1", "contact_form_Phone" );

}
?>
``````

Settings Callback functions

``````<?php

function contact_form_FirstName_setting_callback(){

\$contact_form_FirstName = esc_attr( get_option( 'contact_form_FirstName' ) );
echo '<input name="contact_form_FirstName" id="contact_form_FirstName" type="checkbox" value="1" class="code" ' . checked( 1, get_option( 'contact_form_FirstName' ), false ) . ' />  ';
}

function contact_form_LastName_settings_callback(){

\$contact_form_LastName = esc_attr( get_option( 'contact_form_LastName' ) );
echo '<input name="contact_form_LastName" id="contact_form_LastName" type="checkbox" value="1" class="code" ' . checked( 1, get_option( 'contact_form_LastName' ), false ) . ' /> ';
}

function contact_form_Email_setting_callback(){

\$contact_form_Email = esc_attr( get_option( 'contact_form_Email' ) );
echo '<input name="contact_form_Email" id="contact_form_Email" type="checkbox" value="1" class="code" ' . checked( 1, get_option( 'contact_form_Email' ), false ) . ' /> ';
}

function contact_form_Phone_settings_callback(){

\$contact_form_Phone = esc_attr( get_option( 'contact_form_Phone' ) );
echo '<input name="contact_form_Phone" id="contact_form_Phone" type="checkbox" value="1" class="code" ' . checked( 1, get_option( 'contact_form_Phone' ), false ) . ' /> ';
}

function section_2_callback(){
echo "Check the fields you would like to add to your form.
 ";
}
?>
``````

The Form Template

``````<?php
//Template form Section

function custom_shortcode()
{

?>
<form action="" method="POST">
<?php

\$contact_form_FirstName = get_option('contact_form_FirstName');
if (\$contact_form_FirstName == '1')
{
echo 'First Name<input  id="first_name" maxlength="40" name="first_name" size="20" type="text" required/>
';
}

\$contact_form_LastName = get_option('contact_form_LastName');
if (\$contact_form_LastName == '1')
{
echo 'Last Name<input  id="last_name" maxlength="40" name="first_name" size="20" type="text" required/>
';
}

\$contact_form_Email = get_option('contact_form_Email');
if (\$contact_form_Email == '1')
{
echo 'Email<input  id="email" maxlength="80" name="email" size="20" type="email" required/>
';
}

\$contact_form_Phone = get_option('contact_form_Phone');
if (\$contact_form_Phone == '1')
{
echo 'Phone<input  id="phone" maxlength="40" name="phone" size="20" type="text" required/>
';
}
?>
<input type="submit" name="submit">
</form>
<?php
}


text:
# [tex-eplain] Improvement for hyperlink option handling

geolsoft at mail.ru geolsoft at mail.ru
Fri Sep 2 18:02:23 CEST 2005

On Fri, Sep 02, 2005 at 03:38:41PM +0200, Karl Berry wrote:
> What are the types?  href, mailto?

Destination types are (for pdftex, for dvipdfm they are similar):

XYZ     Current position'.  Option |zoom| specifies magnification.
Fit     Fit the page to the window.
FitH    Fit the width of the page to the window.
FitV    Fit the height of the page to the window.
FitR    Fit the rectangle specified by options |width|, |height| and |depth|
in the window.
FitB    Fit the page's bounding box to the window.
FitBH   Fit the width of the page's bounding box to the window.
FitBV   Fit the height of the page's bounding box to the window.

name     Go to a named destination.  All destinations created with |\hldest|
are named destinations'.
num      Go to a numbered destination.  The label is the destination number.
page     Go to a page.   The label is the page number (counting from 1).
Page fitting is specified by |pagefit| option (see note below).
filename Go to a named destination in another file.  File name is specified
by |file| option.  |newwin| option controls whether the destination
document is opened in the same window or in a new window.
Page fitting is specified by |pagefit| option (see note below).
filepage Go to a page in another file.  The label is the page number
(counting from 1).  File name is specified by |file| option.  Page
fitting is specified by |pagefit| option (see note below).
|newwin| option controls whether the destination document is opened
in the same window or in a new window.
uri      Go to a URI.  The label is the URI.
raw      Execute a raw' pdfTeX command.  |cmd| option specifies name of
macro (without the leading \') which expands to the raw command.
There is no sense in using this type directly with |\hlstart| (you
can execute the command yourself); it is intended to be used in
parameters for cross-reference macros.

> Are the options for things other than controlling appearance?
> (Color, boxing, what else?)

There are a few options not related to appearance:

cmd      this is name of macro which expands to raw' PDF
command for raw' types of links/dests
file     file name for links of type filepage'
newwin   controls whether filename' and filepage' links
pop up a new window.

The rest are for appearance.

For destinations, they control how much the dest is raised
above the baseline, exact location of the destination,
zooming, bounding box to fit to when jumping to the dest,
etc.

For links, the appearance options are:

S       The border is drawn as a solid line (default).
D       The border is drawn with a dashed line (the dash pattern is
specified by |bdash| option).
B       The border is drawn in a beveled style.
I       The border is drawn in an inset style.
U       The border is drawn as a line on the bottom of the link rectangle.

|bdash| is an array of numbers representing on and off stroke lengths for
drawing dashes.

I       The rectangle specified by the bounding box of the link is inverted.
N       No highlighting is done.
O       The border of the link is inverted.
P       The region underneath the bounding box of the link is drawn inset
into the page.

|bcolor| (border color) is specified as an array of three numbers in the range
0 to 1, representing a color in DeviceRGB.

|bwidth| (border width) in points (72 points per inch, a PostScript point', or
a big point').  Default is 1.

|zoom| is specified as a magnification ratio times 1000 (like TeX's scale
factor).

|color|
|colormodel| Color and color model to render the link's text with

> So what are the other groups?  xref, bib, footnote, url?

For destinations, the groups are (mostly self-explanatory):

definexref
xrdef
li
eq
bib
foot          \footnote / \numberedfootnote
footback      back-reference from the footnote to the text
idx

xrefn         \refn and \xrefn
xref          \xref
ref           \ref and \refs
eq            \eqref and \eqrefn
cite          \cite
foot          \footnote / \numberedfootnote
footback      back-reference from the footnote to the text
idx
url           \url from url.sty

>     NOTE:  For \hldesttype and \hltype, the !' is accepted but
>            has no effect.
>
> Beucase the default options for the types is empty?  (In the future it
> might not be.)

The type' parameter is just a single name.  Setting it to
empty for the group will make the group use the default type
(and Eplain sets the types for all groups to empty, except
url' group, which is set to uri').  When the user asks to
set the type (default or for a group), we just store it in
the relevant macro, with or without the !'.  The !' does
not make sense for type'.

The same for default options -- each default option is
stored in a separate macro, so we just store the value for
each default option in its own macro, with or without the
!'.

On the other hand, for the groups, opts' is a _list_ of
options in the form opt1=value1,opt2=value2,...'.  This
list does not have to contain every supported option.
Options which are in this list will override the default
values for those options; for options missing from the list,
the default values will be used.  So without the !', the
current list of options for the group is retained; with !',
we start from the clean slate, wiping out anything there was
on the group's list, and using the argument list as the new
list for the group.

This is easy for me, I know how it works; if once again I am
unclear, let me know, I will try to explain it some other
way.

> How about having it "set" the default with the ! and "augment" the
> default without it?

This way, it will be impossible to remove an option from the
list of options for the group.  We cannot set an option to
empty to indicate that the default is to be used -- for some
options, empty values are legitimate.

For example, there is an option top' for dvipdfm, which
indicates the y-coordinate for destinations.  If it is set
to empty, the driver uses @ypos' which dvipdfm will convert
to the current y-coordinate.  So a group may set top=' to
obtain the @ypos', but the (global) default for the top'
may be something entirely different (e.g. the top of the
page).

Another example is the zoom' option for destinations.  When
set to empty, the zoom' specification is omitted altogether
by pdftex driver, causing the zooming not to change.

> Usually people do want to keep the defaults and just change what they
> want to change.  That's the most reliable approach to keeping compatible
> future changes.

So they just never use empty groups', and only set
parameters they need for real' groups.

As a reminder, each of \hldest and \hlstart take OPTIONS
parameter.  Any options in this list override the defaults.
The reason I started all this mess with the groups was that
the cross-reference macros call, so we needed to provide the

To summarize:

There are default type and default values for each
supported option.  \hldest and \hlstart use these defaults
when the type or an option are not given in their
parameters.  The type and any option given in the
parameter to \hldest and \hlstart override the default
type and the default value for that option.

For groups, the user can define the type and a list
containing definitions for some/all of the options.  These
will be passed to \hldest and \hlstart inside the
cross-references, thus overriding the defaults.  Any
option which is missing from the group's list of options,
will not be passed to \hldest / \hlstart, so it will be
taken from the default value for that option.

> Is there a use in controlling links/dests separately?  I can't imagine a
> use for creating dests without links, and even less for creating links
> without dests.  Would it make sense to reduce to just \hlon+off and have
> it control both?

For some of the groups, controlling links/dests separately
does not (usually) make sense.  But, as you can see above,
the lists of groups for links and destinations are not
identical.

What's more, you can imagine a situation when, in some part
of a document, the user wants to prevent \eqref from
creating links, but still wants to create dests, possibly to
link to them from some later part of the document.  There's
no limit to the user's fantasy :)

So this is a question of convenient use in most cases'
vs. providing for all possible uses'.

--
Best regards,
change them to url', now that we have \url from url.sty


text:
# My Favorite One-Liners: Part 106

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Years ago, when I first taught Precalculus at the college level, I was starting a section on trigonometry by reminding my students of the acronym SOHCAHTOA for keeping the trig functions straight:

$\sin \theta = \displaystyle \frac{\hbox{Opposite}}{\hbox{Hypotenuse}}$,

$\cos \theta = \displaystyle \frac{\hbox{Adjacent}}{\hbox{Hypotenuse}}$,

$\tan \theta = \displaystyle \frac{\hbox{Opposite}}{\hbox{Adjacent}}$.

At this point, one of my students volunteered that a previous math teacher had taught her an acrostic to keep these straight: Some Old Hippie Caught Another Hippie Tripping On Acid.

Needless to say, I’ve been passing this pearl of wisdom on to my students ever since.

# My Favorite One-Liners: Part 100

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Today’s quip is one that I’ll use surprisingly often:

If you ever meet a mathematician at a bar, ask him or her, “What is your favorite application of the Cauchy-Schwartz inequality?”

The point is that the Cauchy-Schwartz inequality arises surprisingly often in the undergraduate mathematics curriculum, and so I make a point to highlight it when I use it. For example, off the top of my head:

1. In trigonometry, the Cauchy-Schwartz inequality states that

$|{\bf u} \cdot {\bf v}| \le \; \parallel \!\! {\bf u} \!\! \parallel \cdot \parallel \!\! {\bf v} \!\! \parallel$

for all vectors ${\bf u}$ and ${\bf v}$. Consequently,

$-1 \le \displaystyle \frac{ {\bf u} \cdot {\bf v} } {\parallel \!\! {\bf u} \!\! \parallel \cdot \parallel \!\! {\bf v} \!\! \parallel} \le 1$,

which means that the angle

$\theta = \cos^{-1} \left( \displaystyle \frac{ {\bf u} \cdot {\bf v} } {\parallel \!\! {\bf u} \!\! \parallel \cdot \parallel \!\! {\bf v} \!\! \parallel} \right)$

is defined. This is the measure of the angle between the two vectors ${\bf u}$ and ${\bf v}$.

2. In probability and statistics, the standard deviation of a random variable $X$ is defined as

$\hbox{SD}(X) = \sqrt{E(X^2) - [E(X)]^2}$.

The Cauchy-Schwartz inequality assures that the quantity under the square root is nonnegative, so that the standard deviation is actually defined. Also, the Cauchy-Schwartz inequality can be used to show that $\hbox{SD}(X) = 0$ implies that $X$ is a constant almost surely.

3. Also in probability and statistics, the correlation between two random variables $X$ and $Y$ must satisfy

$-1 \le \hbox{Corr}(X,Y) \le 1$.

Furthermore, if $\hbox{Corr}(X,Y)=1$, then $Y= aX +b$ for some constants $a$ and $b$, where $a > 0$. On the other hand, if $\hbox{Corr}(X,Y)=-1$, if $\hbox{Corr}(X,Y)=1$, then $Y= aX +b$ for some constants $a$ and $b$, where $a < 0$.

Since I’m a mathematician, I guess my favorite application of the Cauchy-Schwartz inequality appears in my first professional article, where the inequality was used to confirm some new bounds that I derived with my graduate adviser.

# My Favorite One-Liners: Part 76

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Here’s a problem that might arise in trigonometry:

Compute $\cos \displaystyle \frac{2017\pi}{6}$.

To begin, we observe that $\displaystyle \frac{2017}{6} = 336 + \displaystyle \frac{1}{6}$, so that

$\cos \displaystyle \frac{2017\pi}{6} = \cos \left( \displaystyle 336\pi + \frac{\pi}{6} \right)$.

We then remember that $\cos \theta$ is a periodic function with period $2\pi$. This means that we can add or subtract any multiple of $2\pi$ to the angle, and the result of the function doesn’t change. In particular, $-336\pi$ is a multiple of $2 \pi$, so that

$\cos \displaystyle \frac{2017\pi}{6} = \cos \left( \displaystyle 336\pi + \frac{\pi}{6} \right)$

$= \cos \left( \displaystyle 336\pi + \frac{\pi}{6} - 336\pi \right)$

$= \cos \displaystyle \frac{\pi}{6}$

$= \displaystyle \frac{\sqrt{3}}{2}$.

Said another way, $336\pi$ corresponds to $336/2 = 168$ complete rotations, and the value of cosine doesn’t change with a complete rotation. So it’s OK to just throw away any even multiple of $\pi$ when computing the sine or cosine of a very large angle. I then tell my class:

In mathematics, there’s a technical term for this idea; it’s called $\pi$ throwing.

# My Favorite One-Liners: Part 9

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Today, I’d like to discuss a common mistake students make in trigonometry… as well as the one-liner that I use to (hopefully) help students not make this mistake in the future.

Question. Find all solutions (rounded to the nearest tenth of a degree) of $\sin x = 0.8$.

Erroneous Solution. Plugging into a calculator, we find that $x \approx 53.1^o$.

The student correctly found the unique angle $x$ between $-90^o$ and $90^o$ so that $\sin x = 0.8$. That’s the definition of the arcsine function. However, there are plenty of other angles whose sine is equal to $0.7$. This can happen in two ways.

First, if $\sin x > 0$, then the angle $x$ could be in either the first quadrant or the second quadrant (thanks to the mnemonic All Scholars Take Calculus). So $x$ could be (accurate to one decimal place) equal to either $53.1^o$ or else $180^o - 53.1^o = 126.9^o$. Students can visualize this by drawing a picture, talking through each step of its construction (first black, then red, then brown, then green, then blue).

However, most students don’t really believe that there’s a second angle that works until they see the results of a calculator.

Second, any angle that’s coterminal with either of these two angles also works. This can be drawn into the above picture and, as before, confirmed with a calculator.

So the complete answer (again, approximate to one decimal place) should be $53.1^{\circ} + 360n^o$ and $126.9 + 360n^{\circ}$, where $n$ is an integer. Since integers can be negative, there’s no need to write $\pm$ in the solution.

Therefore, the student who simply answers $53.1^o$ has missed infinitely many solutions. The student has missed every nontrivial angle that’s coterminal with $53.1^o$ and also every angle in the second quadrant that also works.

Here’s my one-liner — which never fails to get an embarrassed laugh — that hopefully helps students remember that merely using the arcsine function is not enough for solving problems such as this one.

You’ve forgotten infinitely many solutions. So how many points should I take off?

For further reading, here’s my series on inverse functions.

# A Visual Proof of a Remarkable Trig Identity

Strange but true (try it on a calculator):

$\displaystyle \cos \left( \frac{\pi}{9} \right) \cos \left( \frac{2\pi}{9} \right) \cos \left( \frac{4\pi}{9} \right) = \displaystyle \frac{1}{8}$.

Richard Feynman learned this from a friend when he was young, and it stuck with him his whole life.

Recently, the American Mathematical Monthly published a visual proof of this identity using a regular 9-gon:

This same argument would work for any $2^n+1$-gon. For example, a regular pentagon can be used to show that

$\displaystyle \cos \left( \frac{\pi}{5} \right) \cos \left( \frac{2\pi}{5} \right) = \displaystyle \frac{1}{4}$,

and a regular 17-gon can be used to show that

$\displaystyle \cos \left( \frac{\pi}{17} \right) \cos \left( \frac{2\pi}{17} \right) \cos \left( \frac{4\pi}{17} \right) \cos \left( \frac{8\pi}{17} \right) = \displaystyle \frac{1}{16}$.

# A natural function with discontinuities (Part 3)

This post concludes this series about a curious function:

In the previous post, I derived three of the four parts of this function. Today, I’ll consider the last part ($90^\circ \le \theta \le 180^\circ$).

The circle that encloses the grey region must have the points $(R,0)$ and $(R\cos \theta, R \sin \theta)$ on its circumference; the distance between these points will be $2r$, where $r$ is the radius of the enclosing circle. Unlike the case of $\theta < 90^\circ$, we no longer have to worry about the origin, which will be safely inside the enclosing circle.

Furthermore, this line segment will be perpendicular to the angle bisector (the dashed line above), and the center of the enclosing circle must be on the angle bisector. Using trigonometry,

$\sin \displaystyle \frac{\theta}{2} = \frac{r}{R}$,

or

$r = R \sin \displaystyle \frac{\theta}{2}$.

We see from this derivation the unfortunate typo in the above Monthly article.

# A natural function with discontinuities (Part 2)

Yesterday, I began a short series motivated by the following article from the American Mathematical Monthly.

Today, I’d like to talk about the how this function was obtained.

If $180^\circ \le latex \theta \le 360^\circ$, then clearly $r = R$. The original circle of radius $R$ clearly works. Furthermore, any circle that inscribes the grey circular region (centered at the origin) must include the points $(-R,0)$ and $(R,0)$, and the distance between these two points is $2R$. Therefore, the diameter of any circle that works must be at least $2R$, so a smaller circle can’t work.

The other extreme is also easy: if $\theta =0^\circ$, then the “circular region” is really just a single point.

Let’s now take a look at the case $0 < \theta \le 90^\circ$. The smallest circle that encloses the grey region must have the points $(0,0)$, $(R,0)$, and $(R \cos \theta, R \sin \theta)$ on its circumference, and so the center of the circle will be equidistant from these three points.

The center must be on the angle bisector (the dashed line depicted in the figure) since the bisector is the locus of points equidistant from $(R,0)$ and $(R \cos \theta, R \sin \theta)$. Therefore, we must find the point on the bisector that is equidistant from $(0,0)$ and $(R,0)$. This point forms an isosceles triangle, and so the distance $r$ can be found using trigonometry:

$\cos \displaystyle \frac{\theta}{2} = \displaystyle \frac{R/2}{r}$,

or

$r = \displaystyle \frac{R}{2} \sec \frac{\theta}{2}$.

This logic works up until $\theta = 90^\circ$, when the isosceles triangle will be a 45-45-90 triangle. However, when $\theta > 90^\circ$, a different picture will be needed. I’ll consider this in tomorrow’s post.

# SOHCAHTOA

Years ago, when I first taught Precalculus at the college level, I was starting a section on trigonometry by reminding my students of the acronym SOHCAHTOA for keeping the trig functions straight:

$\sin \theta = \displaystyle \frac{\hbox{Opposite}}{\hbox{Hypotenuse}}$,

$\cos \theta = \displaystyle \frac{\hbox{Adjacent}}{\hbox{Hypotenuse}}$,

$\tan \theta = \displaystyle \frac{\hbox{Opposite}}{\hbox{Adjacent}}$.

At this point, one of my students volunteered that a previous math teacher had taught her an acrostic to keep these straight: Some Old Hippie Caught Another Hippie Tripping On Acid.

Needless to say, I’ve been passing this pearl of wisdom on to my students ever since.


text:
Find the area of a rhombus if its vertices are
Question.

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (–1, 4) and (–2, – 1) taken in order.

Solution:

Diagonals AC and BD bisect each other at right angle to each other at O.

$A C=\sqrt{(-1-3)^{2}+(4-0)^{2}}$

$=\sqrt{16+16}=\sqrt{32}=4 \sqrt{2}$

$B D=\sqrt{(4+2)^{2}+(5+1)^{2}}=\sqrt{36+36}=6 \sqrt{2}$

Then $\mathrm{OA}=\frac{1}{2} \mathrm{AC}=\frac{1}{2} \times 4 \sqrt{2}=2 \sqrt{2}$

$\mathrm{OB}=\frac{1}{2} \mathrm{BD}=\frac{1}{2} \times \mathbf{6} \sqrt{2}=3 \sqrt{2}$

Area of $\Delta \mathrm{AOB}=\frac{1}{2}(\mathrm{OA}) \times(\mathrm{OB})=\frac{1}{2} \times \mathbf{2} \sqrt{2} \times 3 \sqrt{2}=6$ sq. units

Hence, the area of the rhombus ABCD

$=4 \times$ area of $\Delta \mathrm{AOB}=4 \times 6=24$ sq. units.
Editor


text:
# Tag Info

## Hot answers tagged tides

22

That is because the moon attracts both the water and the earth. The gravity of the moon reduces with distance (by the inverse square law). So, the moon's gravity is Greatest at the point nearest to the moon (called sub-moon point) Is lesser on the earth's center, and' Is the least in the opposite side of the earth. Assume that earth is falling to wards ...

19

The following diagram from the wikipedia article on the tidal force shows the tidal force that results from a moon. Note that the tidal force is directed away from the center of the planet when the moon (satellite) is directly overhead or underfoot but is directed toward the center of the planet when the moon is on the horizon. You are right that these very ...

19

Everything in the universe has a gravitational influence on everything else in the universe. It isn't a question of the strongest gravitational pull winning out and all the others doing nothing. The Earth is the strongest pull on the oceans, but the Moon and the Sun both have easily measurable effect in addition to the Earth's. Other bodies (Venus, Jupiter, ...

8

There will be tides, but they will be not very large. It's pretty easy to get a good estimate of their size. There are two things that control tides on Earth and both will be present anywhere else: The tidal forces from celestial bodies, and the size of the body of liquid in which the tides are raised along with resonances int he body of liquid. Taking ...

7

The possibility you mention is feasible if the moon is in the equivalent of a geostationary orbit, where the orbital period of the moon is exactly the rotation period of the planet and it orbits in the equatorial plane of the planet. Such a moon would always keep the same face to the planet if it were close enough to the planet (which in turn depends on the ...

7

Neptune's largest moon, Triton, is about a third the mass of Earth's moon, and roughly the same distance away from its primary, so it will indeed have noticeable tidal effect on Neptune's atmosphere and oceans. Neptune's other moons are all tiny (all of them together being about 0.5% of Triton's mass), so while they do exert tidal forces, those effects ...

7

I am probably going to get slammed for this, because it violates everything we were taught about tidal forces, but the antipodal tide is caused by the centrifugal force created by the Earth's rotation about the earth/moon barycenter, not differential gravitational forces. While the moon's gravity is less on the side of the earth furthest from it, that force ...

6

You're right; the effect of solar tides on the Earth would be to increase the Earth's (or Earth+Moon's) orbital angular momentum around the Sun. But it would be difficult to compute this properly, and probably impossible to measure the effect, because of all the other small alterations to the Earth's orbit going on. A simple way to see the effect (which I ...

6

There are two main gravitational causes of tides: the Moon, and to a lesser extent the Sun. When the moon is full or the moon is new, the Earth, Moon and Sun are roughly aligned, and the Lunar tide combines with the Solar tide to give a "Spring tide" that has a larger range. When the moon is at first quarter, or third quarter (ie a half moon), the solar ...

6

Yes Tidal locking is a mutual process, and both the satellite and the parent body will eventually permanently face each other. However, while tidal locking of a satellite can happen relatively quickly (that is, within the life span of the solar system), tidal locking of the parent body is extremely slow and will in a practical sense never happen (the ...

5

Tidal circularization is indeed a plausible mechanism for why Triton's orbital eccentricity is so low, and I believe it is in fact the prevailing theory, at the moment. In short, tidal forces from Neptune dissipate energy in Triton's interior, essentially "squeezing" the moon. This results in a loss of orbital kinetic energy. The exact calculations that lead ...

4

Solid-body tides on the Moon There are various good models for solid-body tides on the Earth. Are there any recommendations for tides on the Moon? This answer starts with simplistic explanations and links with trivial calculations and progresses to links that, along with their references, provide exacting and lengthy approaches. @scb, you might want to skip ...

4

Nope. (Sorry, the other answer beginning with yes, I wanted to begin one with no), but both answers are correct from a certain point of view. Jupiter's rotation is speeding up because it's contracting. See here. Jupiter does slow down due to it's tidal bulge and tugging from it's moons, but the bigger factor is that Jupiter loses more heat than it ...

4

Let us begin with the basics. If an exterior perturber generates the potential W, then an originally spherical planet gets distorted. Owing to this distortion, its potential acquires an increment U which is usually called the additional tidal potential or, simply, the tidal potential. Now let us fix a point on the surface of the planet. Let $\gamma$ be the ...

4

There's two parts to this question, the first part is relatively easy. The 2nd part, more tricky. How are shepherd moons such as Pan and Daphnis able to exist without being disintegrated by Saturn's tidal forces despite literally orbiting within the rings themselves? I'm going to focus on Pan because it's larger and closer. It's unusual, ravioli ...

4

The short answer which may or may not be an "Aha!" answer is that what is plotted is what's left over after a much larger, uniform force is subtracted. The uniform force is the Force from the Moon evaluated at the center of the Earth, and the arrows show the deviation of the actual force from that average. Why do we do it that way? When looking at the ...

3

In the first case, the planet's rotation will carry the tidal bulge ahead of the satellite, this will tend to accelerate the satellite, causing its orbit to recede. In the other cases, the planet's rotation will pull the bulge behind the satellite, causing the orbit to decay. It doesn't matter if the period is greater or smaller in the case of a ...

3

Only a syzygial tide during/near an equinox is the strongest. This means, there must be either new or full moon. In general, syzygial tides are strong because three bodies (Earth, Moon, Sun) align near one line, and tidal effects of Moon and Sun on Earth become (nearly) collinear and sum to the maximal possible magnitude. The Moon’s orbit is inclined to the ...

3

I think it's a somewhat poorly written page and Xakarus Alldredge's answer is very good. I thought I'd add some pictures. The Tidal force the Earth exerts on the Moon is much stronger than the one the Moon exerts on the Earth and it's technically not a force either, it's a secondary effect from the force of gravity. But the tidal "force" on the moon is ...

2

As stated in the quoted book excerpt, the tidal forces that arise from the Moon's gravity create a bulge in Earth's oceans on the side of the planet facing the Moon and on the side facing opposite the Moon. Now imagine that you are on a shoreline of some arbitrary continent. As the Earth spins, the shoreline you are on is carried into the oceanic bulge ...

2

'Neap' tides when there is the least difference between high and low tide, generally occur around the time of the first and third quarter moons. 'Spring' tides when there is the largest difference between high and low tide, generally occur around the time of the New and Full moons. The exact timing is complicated by your position on earth, the shape / size ...

2

Gravity is an acceleration, and force = mass x acceleration. Thus, if we want to detect the Moon's gravitational pull, we need either a giant mass or a really precise instrument. Since the oceans are a giant mass, the force on the ocean is thus correspondingly large. The fluidness of the ocean also allows it to move, even if the force per volume is small. ...

2

To expand on Keith's comment, the equation for the tidal force is based upon the difference between the acceleration due to the orbiting object, and the gravity of the body itself, i.e. the difference between how hard the Moon pulls on you compared to how hard the Earth pulls. This results in an overall equation of: |a_{tidal}| = 2\Delta r G \frac{M}{R^3} ...

1

While gravity itself is weak relative to the other three known fundamental forces, that should not be construed to mean that the moon's gravitational pull on earth is necessarily weak. To say something is "weak," you really need some sort of benchmark against which to make that determination (e.g., I'm weak because I can only benchpress 50 kg, ...

1

I think it's good to start with the last question: How would the tides be affected without the Moon? The answer is simple: There would still be tides twice a day caused by the Sun, but they would be smaller. There are lots of sources online that talk about how tides from the Sun and Moon combine; without the Moon, we would just have the tides from the Sun. ...

1

The following is a plausibility argument based on the symmetry of an assumed circular orbit of the earth around the sun. The earth's rotational axis is inclined to the ecliptic plane by an angle of about 23.4°. For this reason idealized tidal bulges induced by the sun would travel around the earth's equator at the vernal and autumnal equinox whereas they ...

1

Over enough time there is a tendency of all orbiting objects to fall into resonance with the object they're orbiting. 1:1 being is most common. 1:1 usually called Tidal Locking, is quite common. The Moon to the Earth. Pluto and Charon to each other. All four of the Galilean moons are tidally locked to Jupiter, likely others. Mercury's 3:2 ratio is ...

1

What are the positions of the Earth, Moon, and Sun at a time when there is the least difference between high and low tides? TL;DR response: The simple answer to this question is twice per month, when the Moon is half full. A not so simple answer is roughly every 8.85 years, when the Moon is half full and the Moon is close to apogee. A full answer: Who knows?...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Max an integral with endpoints varying with the extremal function.

Hello all,

Usually the calculus of variations' take on not variable endpoints means to choose a point in a fixed function, but what I need is for that point to be defined by the function I am maximizing; that is, my problem is to find y(x) to maximize:

$\int^{k_1}_{k_0}{\int_{y(x)}^{t_1}F(x,y,z)\,dz\,dx}$

If it makes it clearer, the geometrical interpretation (if I imagine it correctly) is to choose y(x) which maximizes the volume of the 3-dimensional area (inside a 3-dimensional compact cube) of F(x,y,z) ($F_y$>0), given that the width of the area is in itself given by the choice of y(x).

My problem is more complicated (since it involves probability measures), but if someone help me solve this (or point me into the right direction) I believe I can work out the rest.

sorry if this question is obvious for some (most), but I'm not a mathematician (economist) and I spent the last week reading several books on calculus of variations and I didn't find anything really helpful to solve my research problem.

Thank all, Pedro.

-
Is the $y$ in $F(x,y,z)$ the same as $y(x)$? In any case, there seems to be no connection between different $x$ values: for each $x \in [k_0, k_1]$ you want to choose $y$ to maximize $\int_y^{t_1} F(x,y,z)\ dz$. –  Robert Israel Mar 25 '12 at 7:46


text:
Dice an image or cube into JSA tiles

#### Description:

This routine creates multiple output NDFs by dicing a supplied 2D- or 3D- NDF up into JSA tiles (i.e. it is the inverse of JSAPASTER). The spatial WCS of the input NDF must matches the JSA all-sky grid.

#### Parameters:

The input 2D or 3D NDF - it need not have been created by a smurf task. Currently, it should be gridded on the JSA all-sky pixel grid, which means that in practice it probably will have been created by MAKEMAP or MAKECUBE.
The JCMT instrument (different instruments have different tiling schemes and pixel sizes). The following instrument names are recognised (unambiguous abbreviations may be supplied): " SCUBA-2(450)" , " SCUBA-2(850)" , " ACSIS" , " DAS" . The dynamic default is determined from the input NDF if possible. If this cannot be done, then no dynamic default is provided, and the user is prompted for a value if none was supplied on the command line. []
Returned holding the zero-based indices of the created JSA tiles. The number of such indices is given the " NTILE" parameter
Determines the projection used by the output NDFs. The allowed values are " HPX" (HPX projection centred on RA=0h), " HPX12" (HPX projection centred on RA=12h), " XPHN" (XPH projection centred on the north pole) and " XPHS" (XPH projection centred on the south pole). A null (!) value causes " HPX" to be used. [" HPX" ]


text:
# MATLAB: How to plot implicit equation with EZPLOT without appearing the said equation as the graph title

axes settingseasy-to-use function plotterezplotezplot settingsplotting implicit equations

I know that the question can be confusing, so let me try to clarify it: Whenever I plot an implicit equation using the ezplot equation plotter, the generated graph has, as a 'title', the implicit equation I am trying to plot.
I assume that there is probably an option or some sort of configuration which will allow the EZPLOT comand to simply plot the implicit equation without wrtting it as a header/title for my graph. I need this for a GUI I am developing.
Thanks,

• ezplot('sin(x)')title([])


text:
# Sign conventions for a Chevalley basis of a simple complex Lie algebra

Let $R$ be the root system of a simple complex Lie algebra $g$ with respect to some Cartan subalgebra $h$. Chevalley showed there is a basis of $g$ given by the simple coroots {$H_{\alpha_i}=\alpha_i^\vee\in h$} and root vectors $X_\alpha\in g_\alpha$ for each $\alpha\in R$. This basis has the following properties:

$[H_{\alpha_i},H_{\alpha_j}]=0$

$[H_{\alpha_i},X_\beta]=\beta(H_{\alpha_i})X_\beta$

$[X_{\alpha},X_{-\alpha}]=H_\alpha=\alpha^\vee\in h$

($\ast$) $[X_\alpha,X_\beta]=\pm(p+1)X_{\alpha+\beta}$, when $\alpha+\beta\in R$ and $p$ is the greatest positive integer such that $\beta-p\alpha\in R$. Otherwise, if $\alpha+\beta$ is not a root, then the bracket is zero.

References for this can be found in Serre's book on semisimple complex Lie algebras or Humphrey's book or Wikipedia.

Does anybody know a simple way to determine the sign $\pm$ in the fourth property ($\ast$)?

I cannot find a reference and my French is not good, so reading the original works by Chevalley and Tits isn't a viable option. In particular, I need to find a sign convention that will work for $g$ of type $F_4$.

Thanks so much.

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The Chevalley basis is only unique up to automorphisms of the Lie algebra and sign changes of the $X_\alpha$. (You can replace $(X_\alpha, X_{-\alpha})$ above by $(-X_\alpha, -X_{-\alpha})$ for any root $\alpha$ and all the axioms remain true.) I'm not sure whether a canonical choice is possible. However, it's possible that someone wrote down a possible choice for $F_4$ somewhere... (I suppose you can fix $X_\alpha$ for $\alpha$ simple, define the other positive ones using fixed instances of () with your favourite signs, and then work out the rest of () with a lot of patience.) –  fherzig Dec 17 '11 at 23:16
How can the knowledge of these signs be useful? –  fherzig Dec 17 '11 at 23:19
I'm working on a calculation in the exterior algebra $\bigwedge(g\oplus g)$ where $g$ is type $F_4$. I was hoping to do a small part of the calculation via a computer program, but getting a working model of $g$ is the first step. –  brandyn Dec 17 '11 at 23:33
I've also had this issue come up when trying to do by-hand computations; in my experience, the best thing to do is to find a computer algebra package that implements some choice of these signs and then just let the computer handle it. I use Sage with a MAGMA interface and it's worked quite nicely, since MAGMA has all of this Lie-theoretic information built in already. (Feel free to drop me an email if you want to know more). –  Chuck Hague Dec 19 '11 at 16:45

There is a good discussion of these issues in the paper of A. Cohen, S. Murray and D.E. Taylor, "Computing in groups of Lie type", Math. Comp. 73, Number 247, 1477–1498, (2003), especially section 3 (referring to earlier work, e.g., of Carter). They explain in particular how the signs can be all reduced to so-called "extraspecial pairs", which can be chosen arbitrarily.

In Magma at least, one can see which extraspecial signs have been chosen using the "ExtraspecialSigns" command. For instance, one can see using this that GAP and Magma use (or used, I haven't checked the latest versions...) different constants for E_8.

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Cohen has long been active (partly with de Graaf) in such Lie-theoretic computational problems, though I don't know the status of software from his LiE project. By the way, the paper cited here appeared in 2004 and is freely available online: ams.org/journals/mcom/2004-73-247/S0025-5718-03-01582-5/… –  Jim Humphreys Dec 18 '11 at 15:45

As Florian suggests, there is no canonical choice of structure constants in Chevalley's approach (or any other I'm aware of). But for the irreducible root systems, especially those of exceptional type, specific sign choices have been made in various papers (probably with some duplication of effort). One explicit source for type $F_4$ is Table 1 in an old paper by Toshiaki Shoji, published in J. Fac. Sci. Univ. Tokyo Sect. IA Math. 21 (1974), 1-17. This paper deals with conjugacy classes of Chevalley groups of type $F_4$ over finite fields of odd characteristic. Though I've never checked the arithmetic, Shoji's papers are usually reliable.

Over the years I've encountered explicit tables for other root systems but don't have these at hand. Computer methods have been used by N.A. Vavilov for root systems of type $E$ in one paper (where he notes that signs for $F_4$ can be deduced from those for $E_6$, via folding of the Dynkin diagam). Here is the full MathSciNet citation:

MR1875718 (2002k:17022) Vavilov, N. A. Do it yourself structure constants for Lie algebras of types $E_l$. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 281 (2001), Vopr. Teor. Predst. Algebr. i Grupp. 8, 60–104, 281; translation in J. Math. Sci. (N. Y.) 120 (2004), no. 4, 1513–1548.

Probably the recent computational work of W.A. de Graaf is relevant too.

-
Thank you very much for this reference. In particular, because I'm already working with the $F_4\rightarrow E_6$ embedding in a related project and I'm very familiar with Mathematica. THANKS! :D –  brandyn Dec 18 '11 at 2:42


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# A car moves at the speed of 80 km/hr. What is the speed of the car in meters per second ?

$\par&space;Speed&space;=$ $\left[80\times&space;\frac{5}{18}\right]$ $\par&space;m/sec&space;=$  $\frac{200}{9}$  $\par&space;m/sec$  $=$  $22\frac{2}{9}$ $\par&space;m/sec$


text:
## 主题目录

### Course Description

The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory.

• ## Prerequisites

Algebraic Geometry (18.725). This is a first year graduate class in algebraic geometry at the level of the second and third chapters of R. Hartshorne (Algebraic geometry. New York, NY: Springer-Verlag, 1977). Familiarity with algebraic topology helpful.

• ### 教学讲稿(Lecture Notes)

These notes are somewhat rough: they may contain some mistakes, so please use caution when reading them.

Some notes about the construction of the Hilbert scheme. Included are some notes on G.I.T. and the construction of the moduli spaces.

Some notes containing a brief survey of the cohomology of the moduli space of curves and the Harer-Zagier formula for the orbifold Euler characteristic. I added a few words outlining other work of Harer on the stability of the cohomology of the moduli space of curves.

Some notes describing the Picard group of the moduli space of curves.

Some notes about the Kodaira dimension of the moduli space of curves.  You should also read Chapter 5 and 6F of  Harris, J., and I. Morrison. Moduli of Curves. New York, NY: Springer-Verlag, 1998, p. 366. ISBN: 0387984380. (U.S.)

Some notes on the Kontsevich moduli space of genus zero stable maps.

• ### 其他教学资源

The following table lists suggested readings.

The Grassmannian: An Example of a Moduli Space  Griffiths and Harris. Principles of Algebraic Geometry. New York, NY: Wiley, 1994, c1978, pp. 193-211. ISBN: 0471050598.

Fulton. Intersection Theory. Berlin, Germany; New York, NY: Springer, c1998, chapter 14. ISBN: 354062046X.

Harris. Algebraic Geometry: A First Course. New York, NY: Springer-Verlag, 1992, lectures 6 and 16. ISBN: 0387977163.

Vakil, R. A Geometric Littlewood - Richardson Rule. (PDF)

The following is a very pleasant survey article:

Kleiman, S. L., and Dan Laksov. "Schubert Calculus." American Mathematical Monthly 79 (1972): 1061-1082.
The Moduli Space of Curves You can find a sketch of the G.I.T. construction in:  Harris and Morrison. Moduli of Curves. New York, NY: Springer-Verlag, chapter 4. ISBN: 0387984291.

For the construction of the Hilbert scheme look at:
- Mumford. Lectures on Curves on an Algebraic Surface. Princeton, NJ: Princeton University Press, 1966.
- Sernesi. Topics on Families of projective schemes. Kingston, ON: Queen's University, 1986.
- Grothendieck's original lectures given in the Seminaire Bourbaki.
Grothendieck, Alexander. Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert. (French) (Construction techniques and existence theorems in algebraic geometry. IV. Hilbert schemes). Séminaire Bourbaki. Vol. 6, Exp. No. 221, 249-276.

For a very detailed treatment of G.I.T. look at:  Mumford. Geometric Invariant Theory. Berlin, Germany; New York, NY: Springer-Verlag, 1994. ISBN: 3540569634 (Berlin), and  0387569634 (New York). (There are newer editions with appendices by Fogarty and Kirwan.)

For a detailed proof of the Potential Stability Theorem see:  Gieseker. Lectures on Moduli of Curves. Berlin, Germany; New York, NY: Springer-Verlag, 1982. ISBN: 0387119531. (U.S.)

A good account of the G.I.T. construction is contained in: Mumford, D. "Stability of projective varieties." Enseignement Math 23, no. 2 (1977): 39-110.
The Cohomology of the Moduli Space of Curves A great source is: Harer, J. "The cohomology of the moduli space of curves, in Theory of Moduli." Lectures given at C.I.M.E. Springer Lecture Notes in Mathematics. Vol. 1337. Springer Verlag, Berlin, 1988.

Check out this paper by Hain and Looijenga, it contains a survey of the stuff we have been talking about. (PS)

Arbarello, E., and M. Cornalba. "Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves." J Alg Geom 5 (1996): 705-749.

———. "Calculating cohomology groups of moduli spaces of curves via algebraic geometry." Mathématiques de l'IHÉS 88 (1998): 97-127. (PDF)

———. "The Picard Groups of the Moduli Spaces of Curves." In Topology. Vol. 26, 1987, pp. 153-171.
The Moduli Space of Curves is of General Type The following papers of Joe (with Mumford and Eisenbud) developed the theory:

Harris, J., and D. Mumford. "On the Kodaira dimension of the moduli space of curves." Invent Math 67, no. 1 (1982): 23-86. (With an appendix by William Fulton.)

Harris, J. "On the Kodaira dimension of the moduli space of curves II: The even-genus case." Invent Math 75, no. 3 (1984): 437-466.

Eisenbud, D., and J. Harris. "The Kodaira dimension of the moduli space of curves of genus." Invent Math 90, no. 2 (1987): 359-387.
The Kontsevich Moduli Space of Stable Maps Fulton and Pandharipande have a great article. This is probably the best introduction to the subject.

Fulton and Pandharipande. "Notes on stable maps and quantum cohomology." 1996.

Other papers of interest are:

Pandharipande, Rahul. "Intersections of Q-Divisors on Kontsevich's Moduli Space $\bar{M}_{0,n}(P^r,d)$ and Enumerative Geometry." 1995.

Vakil, Ravi. "The enumerative geometry of rational and elliptic curves in projective space." J Reine Angew Math 529 (2000): 101-153. (Crelle's journal.) (PDF)


text:
Application of Energy-Dispersive X-Ray Fluorescence Spectrometry to the Determination of As, Zn,Pb and Cr in Soil
WANG Shi-fang, LUO Na, HAN Ping*
Beijing Research Center for Agriculture Standards and Testing, Beijing 100097, China
*Corresponding author e-mail: hanping1016@163.com

Biography: WANG Shi-fang, (1989-), master, Beijing Research Center for Agriculture Standards and Testing e-mail: wangshifang1302@126.com

Abstract

Total concentrations of As, Zn, Pb and Cr were determined in soil samples by using X-ray fluorescence spectrometry. The instrument applicability was good by analyzing the detection limit and accuracy of the instrument. Then, the energy rangesand variable numbersof heavy metal elements were obtained by using two-dimensional correlation spectroscopy. The variable numbersof Pb (10.380~10.740 and 12.435~12.900 keV), As (10.380~10.740 and 11.610~11.880 keV), Cr (5.310~5.520 and 5.805~6.015 keV) and Zn (8.520~8.805 and 9.555~9.630 keV) were 57, 44, 30 and 26, respectively. Finally, X-ray fluorescence spectrometry analysis models for heavy metal elements were established based on selected energy ranges by using partial least-squares regression. The results showed that the model performance was best for As, followed by Pb, Zn and Cr, and Rp were higher than 0.92. The study indicated that the prediction performance of model is improved using optimal energy ranges and the PXRF analyzer is suitable for in-situ monitoring of heavy metals in soil.

Keyword: X-ray fluorescence spectrometry; Soil heavy metals; Two-dimensional correlation spectroscopy; Partial least squares regression
Introduction

Agricultural soils are seriously threatened by heavy metals contamination in China. A large amount of chemicals are applied annually to agricultural soils in the form of fertilizers and pesticides. Such applications might result in increasing heavy metals in soil, particularly As, Zn, Pb and Cr and increasing potential environmental risk[1]. Heavy metals in soil are not easily degraded by microorganisms and can bio-accumulate through the food chain in humans, leading to a range of human diseases[2]. The monitoring of heavy metals in soil is not only important for environmental protection and agricultural production; but also is one of the primary components of governance and remediation of contaminated soil.

There are many different detection methods for soil heavy metals. To improve detection efficiencies, X-ray fluorescence (XRF) spectrometry was applied to the detection of heavy metals in soil[3, 4, 5]. This method features many advantages when compared with chemical analyses. It is non-destructive, cost-effective and offers extremely rapid in-situ determination of total elemental concentrations.XRF spectrometry provides a multi-element analytical method[6] for the routine non-destructive analysis of many materials with minimal sample preparation.

There are many studies on the detection of heavy metals in soil by XRF spectrometry. A multivariate calibration algorithm was utilized to establish a model of Cr concentration and the results showed that the partial least-squares regression (PLSR) model for total Cr concentration was optimal[7]. A prediction model of Pb content was established to improve accuracy by PLSR in the 10.40~10.70 and 12.41~12.80 keV ranges[8]. The wavelet threshold noise filtering method [9]and orthogonal signal correction algorithm[10]were used to improve the accuracy of the model. The concentrations of 23 chemical elements of street dust were determined by using energy dispersive X-ray fluorescence (EDXRF)[11]. The feasibility of EDXRF analysis for determination of soil heavy metals was verified by using quantitative analysis[12].

The selection of the energy spectrum range in the detection of soil heavy metals based on XRF is one of the biggest problems in current researches. The selection methods of the spectrum range have uninformative variable elimination, successive projections algorithm and so on. Here, two-dimensional (2D) correlation spectroscopy as a novel method was introduced. The generalized term “ 2D correlation” formally defines the synchronous and asynchronous correlation spectroscopy[13, 14]. 2D spectroscopy based on various static perturbations, like temperature, concentration, pressure, position, and other physical variables, applied to different systems, including polymers, biomolecules, solutions, liquid crystals, and others, have been examined. 2D correlation spectroscopy relying on transient phenomena, like chemical reactions, diffusion and other relaxation processes, have been studied[14]. Two-dimensional correlation spectroscopy generally applicable to various types of spectroscopy, including infrared[15, 16, 17, 18], Raman, and terahertz[19] spectroscopy, has been introduced.

The aim of this work was to obtain optimal models based on the energy spectrum range of soil heavy metals by using a novel method, two-dimensional synchronization correlation spectroscopy. The variable numbers of the energy spectrum range were selected based on known intensities of Pb, As, Cr and Zn fluorescence energy spectra. We explored the feasibility of quantitative analysis models for soil heavy metal elements by using PLSR in the selected energy range.

1 Materials and methods
1.1 Sample preparation

Several parameters are known to affect the quality and the precision of portable XRF (PXRF) analyses, including: sample matrix[20, 21], interfering elements, sample homogeneity, particle size[7, 22]and soil moisture[23, 24, 25]. In this paper, a total of 52 soil reference materials, purchased from National Research Center for Certified Reference Materials, the People’ s Republic of China, were employed as analysis samples. The soil samples came from Xinjiang, Neimenggu, Sichuan provinces in China, and so on.The contents of heavy metals in these reference materials have been previously detected by chemical analyses (atomic absorption spectrometry, atomic fluorescence spectrometry and X-ray fluorescence spectrometry, et al)and are available online at http://www.bzwz.com/.The XRF measurements of soil reference materials were conducted under room temperature condition (25± 1)℃ with 60% relative humidity to provide standardized measurement conditions.

1.2 XRF spectroscopy measurement

The equipment used in this study was a field PXRF analyzer NITON XL3t 600 (Thermo Fisher Scientific Corporation, USA), a 40 keV X-ray tube with Ag anode target excitation source, and a Si-PIN-diode with a Peltier cooled detector. The download and export of data from the instrument were facilitated by NITON data transfer software.

EDXRF spectrometry was used to analyze the detection of soil heavy metals. The energy spectra (0~40 keV) were selected to analyze the detection of soil heavy metals.The filter of this instrument has main, high and low filter plates. The test time for each filter plate is set to 30 s. The testing range of heavy metals in each filter plate is different. The four kinds of heavy metals in this study were determined by using the main filter plate and the low filter plate. The heavy metals tested by using the main filter plate were Pb, As and Zn, whereas Cr was tested by usingthe low filter plate.

The steps for detection of heavy metals content in soil by XRF spectrometry were as follows:

Step 1. Soil standard samples were filled into a polyethylene sample cup (diameter 31 mm and height 40 mm) with a collar of fixed Mylar film (thickness 6 μ m). The polyethylene sample cup bottom was sealed by using Mylar film to ensure that there was no sample leakage. Then 2.0 g soil sample was loaded into the sample cup and compressed to provide a smooth sample surface.

Step 2. The sample cup was placed in the testing stand and the side of the cup covered with Mylar film was aimed at the instrument probe window. Sample testing was repeated 5 times. Acquisition time was 90 s.

1.3 Statistical analyses

Statistical analyses were performed by using EXCEL2010, MATLAB R2015a, 2Dshige software and Unscrambler 9.7. Linear regression was performed in EXCEL2010. 2D synchronization correlation spectroscopy was performed in 2Dshige version 1.3 software (2Dshige (c) Shigeaki Morita, Kwansei-Gakuin University, 2004— 2005). A statistical procedure of the data set directly measured from the PXRF instrument was followed using Unscrambler 9.7 (CAMO Software, AS). The PLSR quantitative models were established in MATLAB R2015a (The MathWorks, Inc., Natick, MA, USA). Simple linear regression and 2D synchronization correlation spectroscopy were introduced in some detail below.

1.3.1 Simple linear regression

For each element, a simple linear regression model was used to investigate the relationship between the real concentrations and those measured by PXRF. The relationship produced a linear model

$y=ax+b+ε$

where y is the PXRF concentration, x is the real concentration, b is the intercept of the regression line, a is the slope, and ε is the residual in the regression equation. The correlation coefficient and standard error were employed to determine instrument accuracy.

1.3.2 2D synchronization correlation spectroscopy

In this study, the static perturbation was the concentration of soil heavy metals. The correlation type was synchronous. The slice of synchronous spectra was taken at 50. The moving window size (2m+1) was 11. The draw type was contour and the counter layer was 8.

2 Results and discussion
2.1 Instrument detection limit

The detection limit is defined as three times the standard deviation of the blank test according to the International Union of Pure and Applied Chemistry (IUPAC, 1976). The SiO2 (analytical purity) sample testing was repeated 11 times, and the instrument detection limits were shown in Table 1. The detection limits of As, Pb, Cr and Zn were 3.95, 5.13, 16.35 and 10.20 mg· kg-1, respectively. The quantitative detection limit of Cr was the highest and the result indicated that the detection sensitivity of Cr in soil by using this instrument was relatively low. The detection limit values of the four elements were lower than the primary soil standard value in the environmental quality standard for soils of China (GB15618— 1995).

Table 1 Instrument detection limit (n=11)
2.2 Instrument accuracy

The accuracy analysis results were obtained according to the equation:

$A(%)=CiCs×100(1)$

where A is accuracy, Ci is the content of soil heavy metals by the instrument and Cs is the standard value of soil heavy metals. The units of Ci and Cs are mg· kg-1. The correlation analyses between the soil heavy metals content by the instrument with the standard values using simple linear regression were shown in Fig.1.

 Figure Option Fig.1 Linear regression between soil heavy metals content by the instrument with the standard values

The accuracies of Zn, Pb, Cr and As were 92%~105%, 70%~120%, 71%~180%, 84%~138%, respectively, according to Eq. 1. The accuracy was the lowest for Cr, although the correlation coefficient was more than 0.98 (Fig.1). The degree of dispersion and standard error for Cr were the largest. The results indicated that the detection sensitivity of Cr in soil using this instrument was relatively low and that the detection sensitivities of Zn, Pb and As in soil were good. Overall, testing heavy metal elements in soil using this instrument was feasible.

2.3 Low energy spectra

Taking GBW07405 (GSS-5) as an example, the main and low range Energy-Counts maps in the low energy spectra were shown in Fig.2. The low-range Energy-Counts map was selected to cover the 0~20 keV energy range because the energy intensities of 20~40 keV were almost 0. The heavy metal types in the different filter plates were different and the counts of heavy metal elements also showed differences. Zn and As were determined using each filter plate, and Cr was determined using low filter plate (Fig.2). K lines of Pb required high energy, but voltage of handheld instrument was not enough to stimulate the signal of high energy intensity. So L lines of Pb were analyzed in the study. Therefore, it is necessary to select the appropriate range of spectral lines to generate a quantitative analysis model of heavy metals.

 Figure Option Fig.2 Main and low range Energy-Counts maps of GSS-5 in the low energy spectra

To reduce or eliminate the influence of non-target factors, PLSR was applied to the 52 soil standard samples to determine the accuracy of different ranges in the low energy spectra for model prediction. The results were shown in Table 2. The optimal number of regression factors for the PLSR model was determined by the correlation coefficient, R-square, root mean standard error of calibration (RMSEC) and standard error of calibration (SEC) of cross validation. The model performance depends on the comprehensive evaluation of the correlation coefficient, R-square, RMSEC and SEC. The judging standard of the model is that the correlation coefficient is close to 1 and the difference between SEC and RMSEC is the lowest. According to Table 2 and the evaluation standard, the model performance for Pb, As and Zn in the main range was good and the model performance for Cr in the low range was good. The results were consistent with the heavy metal range of the filter plate.

Table 2 Influence of different range on the precision of the model
2.4 Variable selection

Generally, it is meaningful to reduce the spectra dimension for variable detection. Calibration with the full range of variables is time consuming and irrelevant information within the spectra would affect the accuracy and robustness of the model. To meet the need for rapid detection, variable selection was applied to simplify the models and improve detection efficiency. There are many variable selection methods that have been investigated such as genetic algorithm, uninformative variable elimination and successive projections algorithm. In this paper, 2D synchronization correlation spectroscopy was introduced as a novel variable selection method to determine the variable range for detection of heavy metals using XRF spectroscopy.

Characteristic XRF energy intensities of heavy metal elements were shown in Table 3. Lα and Lβ line intensities of Zn, As and Cr are lower than 1.5 keV, which can be negligible. So Kα and Kβ of Zn, As and Cr were selected as the quantitative spectral line intensities. Kα and Kβ line intensities of Pb are higher than 70 keV. The excitation energy of the NITON XL3t 600 X-ray fluorescence spectrometer is 30 keV. So Kα and Kβ of Pb can be considered negligible and Lα and Lβ of Pb were selected as the quantitative spectral line intensities.The EDXRF Kα and Kβ line intensities were measured for all elements except Pb, for which the Lα and Lβ line intensities were measured.

Table 3 Characteristic X-ray energy values of elements during X-ray fluorescence analysis

To obtain the energy analysis range of heavy metal elements, representative samples of Pb (552, 61, 40, 28 and 14 mg· kg-1), As (412, 58, 21.7, 10.6 and 6.3 mg· kg-1), Zn (494, 210, 127, 66 and 22 mg· kg-1) and Cr (410, 370, 92, 65 and 43 mg· kg-1) were selected and analyzed using 2D synchronization correlation spectroscopy as a novel qualitative analysis method. The 2D fluorescence contour maps of Pb, Cr, As and Zn were shown in Fig.3 using 2Dshige software according to Kα , Kβ of Zn, As, Cr and Lα , Lβ of Pb. The diffusion range of the correlation coil was used to determine the energy range of quantitative analysis and variable numbers. The results were shown in Table 4.

 Figure Option Fig.3 Two-dimensional fluorescence contour maps of Pb (a, b), As(c, d), Cr (e, f) and Zn (g, h)

Table 4 Energy range and variable numbers

The auto-correlation peak was very close to Kα , Kβ of Zn, As, Cr and Lα , Lβ of Pb in Fig.3. The contribution rates of Kα (Zn and As), Kβ (Cr) and Lα (Pb) line intensities were the largest from the correlation analysis. The energy resolution was 0.015 keV. In Table 4, the variable numbers of Pb, As, Cr and Zn were 57, 44, 30 and 26, respectively.

2.5 Quantitative analysis

The quantitative analysis model of heavy metals was established according to the energy range obtained by 2D synchronization correlation spectroscopy. The 52 standard samples were divided into a calibration set (n=39) and a prediction set (n=13) using the Kennard-Stone algorithm. Multivariate calibration models were built using PLSR and the results were shown in Table 5. The correlation coefficients (Rp) of Pb and As prediction sets were higher than 0.97, Rp of Zn was 0.963 and Rp of Cr was 0.922. The differences between SEP and RMSEP of Pb, As, Zn and Cr elements were 0.040, 0.029, 0.378 and 1.933 mg· kg-1, respectively. Overall, the prediction performance of Cr was relatively poor. Given spectra within the selected energy range, multivariate calibration models for the heavy metals Pb, As, Cr and Zn can be built to achieve excellent accuracy. The results indicated that the instrument was suitable for the detection of heavy metals Pb, As, Cr and Zn in soil and the principle could be expanded for the determination of other elements.

Table 5 Statistical parameters of the calibration and prediction set
3 Conclusions

This work focused on the application of 2D synchronization correlation spectroscopy for ascertaining the energy range of soil heavy metals in quantitative analysis. Thus we concluded that:

(1) The instrument applicability was good based on the detection limit, accuracy and correlation analysis.

(2) Variable numbers and energy ranges were obtained using 2D synchronization correlation spectroscopy. The performance of models established using PLSR according to selected variables was excellent.

Overall, the PXRF analyzer was applicable for in-situ detection of soil heavy metals.

Acknowledgment

We would like to thank the Beijing Research Center for Agriculture Standards and Testing for technical support.

The authors have declared that no competing interests exist.

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