text:
# Installation FAQ

## System information needed for Installation problems forum

When posting questions to the Installation problems forum, try to provide as much background information as possible about your Moodle system. Consider providing some or all of the following:

• Server Operating System name (version also if possible):
• PHP version (e.g. PHP 5.4.4)
• Database server type and version (e.g. MySQL 5.5.18)
• Browser and version (e.g. Firefox, IE8):
• Moodle version (e.g. 3.0):
• Phpinfo attached?:

Make sure you provide a sensible description (never HELP! or URGENT!) and a full description of what you did and what happened. Copy and paste any error messages accurately in full. 'Nothing' is not a symptom, even a blank page is something!

## PHP - is it installed and what version do I have?

Make a new file on your web site called info.php, containing the following text, and call it from your browser:

<?PHP phpinfo() ?>

If nothing happens then you don't have PHP installed or your webserver is not configured to handle .php files properly. See the installation docs for some information about where to download it for your computer. See the phpinfo page for details about the content of this page.

## I am being told that I need the intl php plugin to continue to install Moodle 2.x

 extension=php_intl.dll

in the Dynamic Extensions section of your php.ini file.

You can also set the error level using:

 intl.error_level = E_WARNING

but this is not essential

If you are using a Linux install, use your system package manager or specify compilation flag.

   * Debian 5.0 (& Ubuntu) use: apt-get install php-intl or apt-get install php5-intl
* CentOS 5.5 (& RedHat) you should (probably) be using php 5.3 from remi and then use: yum install php-intl

This technique can be applied to any updated dynamic extension from Zend. You may want to use later dll files in your php/ext folder, you can do so by doing the same as above, but be careful, your version may not be able to take full advantage of the extension, or some very new extensions may cause an unexpected instability. The best option is still to update on a regular basis, perhaps once a year or so for the PHP.

### What Dynamic Extensions do I really need uncommented in my php.ini file? What else do I need to change?

This assumes you have complete control over the installation and running of your server, if your Moodle is hosted, you need to do something different, which is also discussed below. In the php.ini you need to delete the semi-colon, the ;, from the start of any line to uncomment it. For Moodle, you really should only need to change some values, and make sure the extensions you require are available. These are:

Resource Limits

 memory_limit = 128M     //This is the maximum it requires and on a shared server you may get much less.

Data Handling

 post_max_size = 512M    //This allows postings of up to 512MB, but set it to suit yourself and your circumstances

Paths and Directories

 doc_root ="driveletter:\path\to\server\active\web\directory"  (e.g. d:\Apache\htdocs or e:\iis\wwwroot )
and
extension_dir = "driveletter:\path\to\php\ext" (e.g. d:\php\ext or e:\iis\php\ext)

 upload_max_filesize = 512M    (This is different from the post_max_size this is for file uploads.)

Dynamic Extensions (Windows Only)

PHP 5.3.x
 extension=php_curl.dll
extension=php_gd2.dll
extension=php_gettext.dll
extension=php_intl.dll
extension=php_imap.dll
extension=php_ldap.dll
extension=php_mbstring.dll
extension=php_exif.dll      ; Must be after mbstring as it depends on it
extension=php_mysql.dll
extension=php_mysqli.dll
extension=php_openssl.dll
extension=php_pdo_mssql.dll
extension=php_pdo_mysql.dll
extension=php_soap.dll
extension=php_sockets.dll
extension=php_sqlite.dll
extension=php_xmlrpc.dll
extension=php_zip.dll

These edits and Dynamic extensions cover a range of options here, there are a number of other possibilities, but these listed are the most common ones. Unless you have a specific need, there may not be any reason to deviate from these settings, but if you do, make sure you know what is going to happen. These extensions will also allow you to successfully install and run many other PHP applications.

One example is the Oracle extensions are not shown here, but Oracle can be used for the Moodle database. Another area people often get themselves into trouble is using "Magic quotes". Magic quotes really should be set to off, they were only introduced early in the use of PHP to allow for some inexperienced scripting practices, (read poor, shoddy or dodgy here). If someone is still writing poor scripts, then they deserve to draw attention to themselves and their scripts deleted.

## What & where are Moodle's configuration settings stored?

Configuration settings are stored in the config.php file stored in your moodle folder. This file is created during the installation process. If there is a problem and the installation cannot create the file, you can try creating it manually from the Configuration file docs. Top

You'll see a directory tree with the files displayed. Click on the one you want and download as normal. If you require the latest update of the version, scroll to the end of the list and download the "moodle-latest" file.

• Mac Packages: To download other releases not found in Mac packages, use either of these URLs (depending on whether you need the Intel or PPC package):

For details of how to download a particular weekly version, see the post Looking for VERY specific release of older Moodle.

## How to enable and check PHP error logs

PHP can be set up to log errors in a variety of different ways: two of these involve the use of the php.ini file and the ini_set command. See PHP_error_logs.

## "Could not find a top level course"

If this appears immediately after you have attempted to install Moodle it almost certainly means that the installation did not complete. A complete installation will ask you for the administrator profile and to name the site just before it completes. Check your logs for errors. Then drop the database and start again. If you used the web-based installer try the command line one. Does your computer definitely have sufficient resource to run Moodle?

## Email copies are not being sent from my forums

You must set up cron properly if you want Moodle to send out automatic email from forums, assignments etc. This same process also performs a number of clean-up tasks such as deleting old unconfirmed users, unenrolling old students and so on. Please refer to the cron instructions.

Tips:

• Try the default settings in Settings > Site administration > Plugins > Message outputs > Email. This generally works. Except...
• On a Windows server you *must* supply the address of an SMTP server (Windows, unlike Unix, does not have a build in mail server) in the above settings page
• Make sure that allowuseremailcharset in Settings > Site administration > Plugins > Message outputs > Email is set to No unless you really know what you are doing. Setting this to Yes can cause a problem in some versions of Moodle.
• Check your firewall or ask your network administrator. Many mail servers are heavily locked down and you may need permission to send mail through them.

The following are possible causes and actions you can take (in no particular order):

• Check first that your main admin account (which will be a manual account) is also a problem. If your users are using an external authentication method (e.g. LDAP) that could be the problem. Isolate the fault and make sure it really is Moodle before going any further.
• Check that your hard disk is not full or if your server is on shared hosting check that you have not reached your disk space quota. This will prevent new sessions being created and nobody will be able to log in.
• Carefully check the permissions in your 'moodledata' area. The web server needs to be able to write to the 'sessions' subdirectory.
• Your own computer (not your Moodle server) may have a firewall that is stripping referrer information from the browser. Here are some instructions for fixing Norton firewall products.
• Try deleting the sessions folder in your moodledata directory (anybody currently logged in will be thrown out)
• Try deleting cookies on your computer and/or try another browser or another client computer
• In Settings > Site administration > Server > Session Handling, try setting a value for 'Cookie prefix'. You can also do this by setting
$CFG->sessioncookie='something'; in config.php. This is especially true if you are using multiple Moodles on the same browser. • Make sure you have not removed or changed the Password Salt value(s) in config.php. If passwords were created using a salt the correct salt must be in config.php for those passwords to continue to work. This is easily done if you recreate config.php while performing an upgrade and forget to transfer the salt values. • Do you have a .htaccess file in your Moodle folder (or its parent directories). If so, is there anything in there that might be causing trouble (strange redirects, access restrictions etc.)? • Check the value of mnet_localhost_id in the mdl_config database table. It's normally 1 but must match the mnet_hostid field in your user records in the mdl_user table for the user to be recognised. It can sometimes get changed spuriously during upgrades or site migrations. • Check config.php - it should NOT have any spaces/new lines at the end of code. • You are using the correct username and password, yes? If you are still having problems, read the Cannot log in page. You could also try changing the admin password. Proceed as if you have lost it - see Administration FAQ. ## I log in but the login link doesn't change. I am logged in and can navigate freely. Make sure the URL in your $CFG->wwwroot
setting is exactly the same as the one you are actually using to access the site.

This indicates that slash arguments are not enabled on your web server. Please see Using slash arguments for details.

## Why are all my pages blank?

Check the dirroot variable in config.php. You must use complete, absolute pathnames (e.g.)

## Why does my new installation display correctly on the server, but when I view it from a different machine, styles and images are missing?

In the installation instructions, one of the suggested settings for 'webroot' is 'localhost'. This is fine if all you want to do is some local testing of your new Moodle installation. If, however, you want to view your new installation from another machine on the same local area network, or view your site on the internet, you will have to change this setting:

• For local testing, 'localhost' is fine for the webroot (\$CFG->wwwroot in config.php).
• If you want to test your site from other machines on the same local area network (LAN), then you will have to use the private ip address of the serving machine, (e.g. 192.168.1.2/moodle) or the network name of the serving computer (e.g. network_name_of_serving_machine/moodle) as the web root. Depending on your LAN setup, it may be better to use the network name of the computer rather than its (private) ip address, because the ip address can and will change from time to time. If you don't want to use the network name, then you will have to speak to your network administrator and have them assign a permanent ip address to the serving machine.
• Finally, if you want to test your new installation across the internet, you will have to use either a domain name or a permanent (public) ip address/moodle as your web root. To handle both types of access, see masquerading.

## Maximum upload file size - how to change it?

There are several places to change the maximum file upload size. The first place to check is the Administration block. Security -> Site Policies -> and look for "Maximum Uploaded File Size". This is the "maxbyte" variable found in older versions of Moodle (under Admin > Variables). Teachers may also set the maximum file size by the course administration block.

For more help see:

## Moodle claims PHP float handling is not compatible

The symptom is that when you try to install or upgrade your Moodle, you get a message "Detected unexpected problem in handling of PHP float numbers".

This forum thread and MDL-18253 have more information. In short, this problem should not happen, you can help us by telling posting information about exactly which version of PHP, and OS you are using. That may let us find a way to work around this problem.

You may be able to solve this issue by installing a more recent PHP versions. If you compile PHP yourself from source, changing the compilation options may help. However, since we don't understand the cause, we don't really know. If you do find a solution that works for you, please do tell us about it.

Update: we have a guess that the problem may be the 'precision' setting in your php.ini file. In a default PHP install this is set of 14. On at least one server that exhibited this problem it had been changed to a smaller value. So, if you see this problem, please try adding

ini_set('precision', 14);

## How do I run multiple instances of Moodle without duplicating base code?

See this thread for a detailed explanation by Martin Langhoff.

## What is FreeTDS and how can I use it in my installation?

FreeTDS is an open source implementation of the Tabular Data Stream protocol used by Microsoft SQL Server and Sybase for their databases. Unfortunately, Microsoft servers don't usually accept TDS 5.0 connections. FreeTDS allows your Unix/Linux applications to talk to these other database products and import and export data between different systems successfully.

## I can't enable a plugin on the Plugins overview page because the icon is not clickable

The open and closed eye icon on the Plugins overview page is simply there to show whether or not a plugin is enabled. You can't edit plugins from this screen. If you wish to enable a plugin, to to the appropriate page for managing the type of plugin you need, for instance Settings>Site administration>Plugins>Repositories>Manage repositories or Settings>Site administration>Plugins>Activity modules>Manage activities.


text:
# Question:Use The Quadratic Formula To Solve The Equation. Use The Quadratic Formula To Solve The Equation. X^2+3x=1 Use The Quadratic Formula To Solve The Equation. (x+1)(x+5)=9 Use The Quadratic Formula To Solve The Equation. X(9x+2)=10 Use The Quadratic Formula To Solve The Equation.

## This problem has been solved!

Use the quadratic formula to solve the equation.
Use the quadratic formula to solve the equation.
x^2+3x=1
Use the quadratic formula to solve the equation.
(x+1)(x+5)=9
Use the quadratic formula to solve the equation.
x(9x+2)=10
Use the quadratic formula to solve the equation.

format: plain


text:
Chemistry and Chemical Reactivity (9th Edition)

In order to create the noble gas configuration, look for the noble gas that comes before the given element. Then, starting at that element, write the correct electron configuration. Cr: $[Ar]\ 3d^5\ 4s^1$ Fe: $[Ar]\ 3d^6\ 4s^2$


text:
# Young Flattenings in the Schur module basis

There are several isomorphic constructions for the irreducible polynomial representations of the general linear group in characteristic zero. The two most well-known versions are called Schur modules and Weyl modules. Steven Sam used a Weyl module implementation in 2009 for his Macaulay2 package PieriMaps. This implementation can be used to compute so-called Young flattenings of polynomials. Over the Schur module basis Oeding and Farnsworth describe a simple combinatorial procedure that is supposed to give the Young flattening, but their construction is not equivariant. In this paper we clarify this issue, present the full details of the theory of Young flattenings in the Schur module basis, and give a software implementation in this basis. Using Reuven Hodges' recently discovered Young tableau straightening algorithm in the Schur module basis as a subroutine, our implementation outperforms Sam's PieriMaps implementation by several orders of magnitude on many examples, in particular for powers of linear forms, which is the case of highest interest for proving border Waring rank lower bounds.

## Authors

• 1 publication
• 13 publications
• ### Zero-divisors of Semigroup Modules

Let $M$ be an $R$-module and $S$ a semigroup. Our goal is to discuss zer...
06/30/2020 ∙ by Peyman Nasehpour, Ph.D., et al. ∙ 0

• ### Drinfeld Modules with Complex Multiplication, Hasse Invariants and Factoring Polynomials over Finite Fields

We present a novel randomized algorithm to factor polynomials over a fin...
12/02/2017 ∙ by Javad Doliskani, et al. ∙ 0

• ### Factoring Polynomials over Finite Fields using Drinfeld Modules with Complex Multiplication

We present novel algorithms to factor polynomials over a finite field _q...
06/02/2016 ∙ by Anand Kumar Narayanan, et al. ∙ 0

• ### A variant of van Hoeij's algorithm to compute hypergeometric term solutions of holonomic recurrence equations

Linear homogeneous recurrence equations with polynomial coefficients are...
12/21/2020 ∙ by Bertrand Teguia Tabuguia, et al. ∙ 0

• ### On Gröbner Bases and Krull Dimension of Residue Class Rings of Polynomial Rings over Integral Domains

Given an ideal a in A[x_1, ..., x_n], where A is a Noetherian integral d...
02/13/2016 ∙ by Maria Francis, et al. ∙ 0

• ### An Improved Algorithm for E-Generalization

E-generalization computes common generalizations of given ground terms w...
09/03/2017 ∙ by Jochen Burghardt, et al. ∙ 0

• ### Dynamic simulations in SixTrack

The DYNK module allows element settings in SixTrack to be changed on a t...
08/19/2018 ∙ by K. Sjobak, et al. ∙ 0

##### This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.

## 1 Motivation

Young flattenings of polynomials are equivariant linear maps from a space of homogeneous polynomials to a space of matrices, where the row and column space are irreducible representations of . One is usually interested in finding lower bounds for the rank of the image of a Young flattening, as it can be used to obtain lower bounds on the border Waring rank of a polynomial, and more generally for any border -rank for a -variety , i.e., given a point to find a lower bound on the smallest such that lies on the -th secant variety of , see e.g. [Lan15]. One early example are Sylvester’s catalecticants [Syl52]. Landsberg and Ottaviani [LO15]

use Young flattenings in the tensor setting. The name

Young flattening was introduced in the predecessor paper [LO13]. Young flattenings also appear in disguise in the area of algebraic complexity theory as matrices of partial derivatives, shifted partial derivatives, evaluation dimension, and coefficient dimension [NW95, GKKS14]. They can in principle be used to find computational complexity lower bounds in many algebraic computational models such as border determinantal complexity (see [LMR13]) and border continuantal complexity [BIZ18], which makes Young flattenings an interesting tool in the Geometric Complexity Theory approach by Mulmuley and Sohoni [MS02], [MS08], [BLMW11]. Limits of these methods (in the case of studying -rank) have recently been proved in [EGOW18, GMOW19]. No such limits are known for using Young flattenings to study the orbit closure containment problems in geometric complexity theory. First results in this direction were obtained in [ELSW18], where limits to the method of shifted partial derivatives are shown. This was improved on in [GL19], where a setting was given in which Young flattenings give strictly more separation information than partial derivatives.

The Waring rank of a homogeneous degree polynomial is defined as the smallest such that can be written as a sum of many -th powers of homogeneous linear forms (arbitrary linear combinations of -th powers are usually allowed if the base field is not algebraically closed). For example , hence has Waring rank at most 2. The border Waring rank of is the smallest such that can be approximated arbitrarily closely coefficient-wise by polynomials of Waring rank at most . For example , hence has border Waring rank at most 2.

If a Young diagram is contained in another Young diagram such that the column lengths of both diagrams differ by at most 1 in each column, then we have a unique nonzero equivariant map between where , , and are irreducible polnomial -representations, and is the difference in the number of boxes of and . This is called the Pieri map, and it induces a linear map Since border Waring rank is subadditive, a lower bound on the border Waring rank of is obtained by rounding up to quotient of ranks

 ⌈rank(Fλ,μ(p))rank(Fλ,μ(xd))⌉, (1.1)

where is some variable that appears in , and rank is the usual rank of matrices.

There are several isomorphic constructions for the irreducible polynomial representations of the general linear group in characteristic zero. The two best known versions are called Schur modules and Weyl modules and they only differ in the order of the row-symmetrizer and the column-symmetrizer in their definition of the Young symmetrizer. This results in different bases for the irreducible representations. Sometimes results that are proved in one basis are reproved in the other basis, but the proofs look significantly different (see e.g. [BCI11] and [MM14]). In fact, so far some results are only provable in a natural way over one basis and not the other, see e.g. [Res20]. Based on an explicit paper by Olver over the Weyl module basis [Olv82] Steven Sam in 2009 implemented his Macaulay2 package PieriMaps [Sam08], which among other things can be used to compute the rank quotient (1.1), see Section 4 (A) below.

The papers [Far16] (in its Section 5111Although the description in the paper is wrong, the use of the software package is correct and gives the result claimed in the paper.) and [Oed16] (only in version 1) describe the PieriMaps package as if it would be working in the Schur module basis and they assume that the Young flattenings have an extremly simple combinatorial description. However, this is wrong (see Section 5 below), which led to a revision of [Oed16].

In this paper we work out the details of Young flattenings in the Schur module basis: We closely mimic the arguments in [Olv82], but we take care of subtle sign issues that are not present in Olver’s work over the Weyl module basis. We then make use of a recent fast algorithm (and implementation) by Reuven Hodges for Young tableau straightening in the Schur module basis [Hod17] to get a highly efficient Young flattening algorithm that outperforms Sam’s PieriMaps implementation by several orders of magnitude in many examples. We obtain the most impressive speedup factor of 1000 for flattening the power of a linear form, which is the denominator of (1.1).

Our contribution is therefore twofold: We thoroughly clarify the theory of Young flattenings in the Schur module basis and we present a new and efficient implementation for Young flattenings that uses Hodges’ state-of-the-art straightening algorithm over the Schur module basis.

## 2 Preliminaries

A composition of a number is a finite list of natural numbers adding up to , i.e., is a composition of 9. A partition is a nonincreasing composition, for example is a partition. We write if is a partition of . We write if is greater than the number of entries in . We define . We identify a partition with its Young diagram, which is a top-left justified array of boxes, i.e., the set of points . For example, the Young diagram corresponding to is

 \ytableausetupcentertableaux,notabloids\oldytableaushort      ,    ,

and we have and . We see that is the number of rows of the Young diagram corresponding to . We denote by the number of boxes in , i.e., . We denote by the Young diagram obtained by reflecting at the main diagonal, e.g., . It follows that is the length of the -th column of . We write if for all we have . If , then we denote by the set of points that are in but not in . We call a horizontal strip if it has at most 1 box in each column. In this situation we write .

A Young diagram whose entries are labeled with numbers is called a Young tableau of shape . For example,

 \ytableausetupcentertableaux,notabloids\oldytableaushort634233,3312,663

is a Young tableau of shape . A Young tableau is called semistandard if the entries strictly increase in each column from top to bottom and do not decrease in each row from left to right. For example, centertableaux,notabloids 1113,23 is a semistandard tableau. We denote by the symmetric group on the set of positions in . The group acts on the set of all Young tableaux of shape by permuting the positions. We write for the permuted Young tableau, where is the shape of and . For a subset of positions we write to denote the symmetric group that permutes only the positions in among each other and fixes all other positions.

Let be the

-th tensor power of a vector space

and associate to every tensor factor a position in . A rank 1 tensor can now be represented by a Young diagram in whose -th box we write the vector . If we fix a basis of , then a basis of is obtained by all ways of writing into the boxes of , allowing repetitions. If the fixed basis is clear from the context, then we write instead of into the boxes and obtain a Young tableau. The basis vector corresponding to the Young tableau is also denoted by when no confusion can arise, so for example if we can use the multilinearity of the tensor product to write

 \ytableausetupcentertableaux,notabloids\oldytableaushortxv2,v1=\ytableausetupcentertableaux,notabloids\oldytableaushort12,1+\ytableausetupcentertableaux,notabloids\oldytableaushort22,1

### 2 (A) The Weyl module basis

Let λ be a Young diagram and let such that (i.e., the box below is still in ). Then we define Pictorially, is the subset of the boxes of given by collecting all boxes on the following path: Start at position and move from left to right along row to box , then switch the row to and move along row until reaching . For example, is given by the dotted boxes in the following diagram:

 \ytableausetupcentertableaux,notabloids\oldytableaushort  ∙∙∙∙,∙∙∙ ,   .
###### 2.1 Definition (Weyl module, [Wey03, 2.1.15]).

The Weyl module is defined as the quotient space , where is the linear subspace generated by the following two types of vectors:

1. (Symmetric relation) , if σ is a permutation that preserves the row indices of all positions of (in other words, permutes within the rows of ).

2. (Shuffle relation) if such that .

The Weyl modules for Young diagrams with at most rows form a complete list of pairwise non-isomorphic irreducible polynomial representations of . In this paper we will not work with Weyl modules, but with the isomorphic Schur modules, which are defined in the following section.

### 2 (B) The Schur module basis

Let be a Young tableau of shape . Let be two column indices. Let and be two equally large sets of boxes, from column and from column . An exchange tableau of corresponding to and is defined as the tableau arising from by exchanging the content of the boxes with the content of the boxes while preserving the vertical order of the entries in and . We denote this exchange tableau by . For a subset of boxes from column , we write , where ranges over all cardinality subsets of boxes in column .

###### 2.2 Definition (Schur module).

The Schur module is defined as the quotient space where is the linear subspace generated by the following vectors

1. (Grassmann relation) , where is obtained from by swapping two elements in the same column.

2. (Plücker relation) for any and any subset of a column with .

For example, in we have and we have by the Grassmann relation. The Plücker relation gives

 \ytableausetupcentertableaux,notabloids\oldytableaushort12,34=\ytableausetupcentertableaux,notabloids\oldytableaushort21,34+\ytableausetupcentertableaux,notabloids\oldytableaushort13,24

via . Note that is the set containing the single box in row 1 and column 2.

### 2 (C) The Schur module via moving boxes between columns

If we only consider the Grassmann relation, then we call the quotient . More formally, let be the linear subspace spanned by the , where is obtained from by swapping two elements in the same column. The quotient is denoted by

. Clearly, in the language of skew-symmetric powers we have

 XνV≃(⋀ν1V)⊗⋯⊗(⋀νℓ(ν)V). (2.3)

In terms of explicit basees, this isomorphism maps each column from top to bottom to a skew-symmetric tensor and vice versa: For example, is mapped to . We define

 Yd:=⨁composition α of dXαV

as an outer direct sum. Note that each , but there is no obvious embedding of in . In fact, there is a natural isomorphism

 Yd≃⋀d(V⊕d) (2.4)

that can be described explicitly in terms of basis vectors using first the isomorphism (2.3): A standard basis vector

 xk1,1∧⋯∧xkν1,1⊗xk1,2∧⋯∧xkν2,2⊗⋯⊗xk1,d∧⋯∧xkνd,d

is mapped to

 xk1,1,1∧⋯∧xkν1,1,1∧xk1,2,2∧⋯∧xkν2,2,2∧⋯∧xk1,d,d∧⋯∧xkνd,d,d, (2.5)

for example is mapped to . We have an action of on , which induces an action of via the group homomorphism , i.e., sending matrices to block diagonal matrices that have many copies of on their main diagonal. With this action of , the isomorphism in (2.4) is an isomorphism of -representations.

For given , , we consider the Lie algebra element that is a block matrix as follows: the block matrix is zero everywhere but the block

is the identity matrix on

. Clearly applying is a -equivariant map. Acting with on the tensor from (2.5) gives

 ∑1≤a≤νixk1,1,1∧⋯∧xkν1,1,1∧⋯∧xk1,i,[i=a,j,i]∧⋯∧xkνi,i,[i=a,j,i]∧⋯∧xkd,1,d∧⋯∧xkνd,d,d, (2.6)

where

 [i=a,j,i] := {j if i=aiotherwise.

We denote by the map the application of . Using the canonical isomorphisms (2.4) and (2.3) we can write this more explicitly: For , , have

 σi,k(x⊗y⊗z) = ∑1≤a≤αi(−1)a+αi+αjx−a⊗y⊗(xa∧z) σk,i(x⊗y⊗z) = ∑1≤c≤αk(−1)c+αj+1(x∧zc)⊗y⊗z−c

Here for a tensor we define as the tensor obtained by “removing the -th tensor position” (this is only well-defined if a basis of is fixed and an ordering of the basis vectors is fixed). For example, if , then , and .

Note that if , then . Define . Note that if , then , hence

 Iλ=⟨σi,i+1(Xλ∗+ei−ei+1)∣λ∗i+1>0⟩. (2.7)
###### 2.8 Proposition ([Tow79, Cor. 1]).

and are isomorphic representations of . The isomorphism maps each basis vector given by a semistandard tableau to a basis vector corresponding to the same semistandard tableau.

###### 2.9 Proposition ([Tow77, Thm. 2.5]).

and are isomorphic representations of .

The relation between the basis vectors corresponding to semistandard tableaux in Prop. 2.9 is more involved than the straightforward relationship in Prop. 2.8.

## 3 Young Flattenings in the Schur module basis

We give an explicit description of the construction of the so-called Pieri inclusions defined on the basis of Schur modules. Olver [Olv82] first described the corresponding construction based on Weyl modules and we closely mimic this construction while taking care of the subtle signs that are introduced when using the Schur module basis. To the best of our knowledge, this construction has never been explicitly described for Schur modules. This algorithm will directly give the construction for Young flattenings.

mathmode, boxsize=1em, centertableaux, smalltableaux

Pieri’s well-known formula states the following isomorphism of -representations:

 SdV⊗SλV=⨂μ⊢d+|λ|μ/λ∈HSSμV.

The resulting -equivariant inclusions

 φλ,μ:SdV⊗SλV→SμV

are called Pieri inclusions and are unique up to scale by Schur’s lemma. We define by composing Pieri inclusions for as follows. For let be the sequence of partitions obtained by adding one box at a time to from left to right, so that after having added boxes we arrive at . Then define the -equivariant map via

 ψλ,μ=φλ(d−1),λ(d)∘(idV⊗φλ(d−2),λ(d−1))∘⋯∘(idV⊗(d−2)⊗φλ(1),λ(2))∘(idV⊗(d−1)⊗φλ(0),λ(1)). (3.1)

By proving that the restriction of to is nonzero (see Lemma 3.10), it immediately follows that this restriction equals (up to a nonzero scalar). It remains to describe for which has only a single box and then prove Lemma 3.10.

### 3 (A) The single box case

We assume that consists of a single box.

We will define the linear map , show its -equivariance (Lemma 3.4), and then prove that it is well-defined on the quotient space if we interpret its image in the quotient space (Theorem 3.5). In this way, induces a map . By the uniqueness of the Pieri inclusions we have that this map equals or is the zero map (nonzeroness is proved in Lemma 3.10). Note that by definition.

Let be a finite sequence of positive integers. Define the linear map

 σJ:Yd→Yd,σJ\coloneqqσJ1,J2∘σJ2,J3∘⋯∘σJp−1,Jp. (3.2)

Pictorially, this means that a box is shifted from column to , then from to , and so on. Clearly is -equivariant as the composition of -equivariant maps. Note that if and moves a box from an empty column to another column, then .

We consider the set of all strongly decreasing sequences of natural numbers from to , which we denote by

 Amk:={J=(J1,…,Jp)∣p∈N,k=Jp

For let be the hook length in of the box in column and row . Let be the column where and differ. We define as the product of all hook lengths in with respect to column , i.e.,

 DJ(λ∗)\coloneqq|J|−1∏q=2hk,Jq(λ∗)=|J|−1∏q=2(λ∗k−λ∗Jq+Jq−k+1). (3.3)

Finally, we define by

 ζμλ=∑J∈Aλ1+1kσJDJ(λ∗).

The map maps into .

is -equivariant.

###### Proof.

is a linear combination of -equivariant maps. ∎

###### 3.5 Theorem.

Let be partitions with being obtained from λ by appending a single box in row . Then and hence is well-defined.

Before proving Theorem 3.5 we first have to prove the following lemma.

We denote by the commutator of two linear maps and .

###### 3.6 Lemma.

Let for some column lengths with and and let . Then,

 [σi,j,σk,l](v)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩(αj−αi)vif i=l,j=k,σk,j(v)if i=l,j≠k,−σi,l(v)if i≠l,j=k,0otherwise.

Note the similarity to Lemma 5.4 in [Olv82] with the exception that the sign in the first case is reversed. Moreover, [Olv82] ignores handling the special case when column lengths vanish. We handle these cases explicitly. If , and , then

 σj,iσi,j(v)=λ∗iv. (3.7)

Moreover, if , , and , then

 σj,kσi,j(v)=σi,k(v). (3.8)
###### Proof of Lemma 3.6.

We focus on the key positions in the tensor.

• : , .

 [σi,j,σj,i](x⊗y) =σi,j(∑1≤b≤αj(−1)b+1(x∧yb)⊗y−b)−σj,i(∑1≤a≤αi(−1)a+αix−a⊗(xa∧y)) =∑1≤a≤αi+11≤b≤αj(−1)a+b+αi(x∧yb)−a⊗((x∧yb)a∧y−b) =−∑1≤a≤αi1≤b≤αj(−1)a+b+1+αi(x−a∧(xa∧y)b)⊗(xa∧y)−b =∑1≤a≤αi1≤b≤αj(−1)a+b+αi(x−a∧yb)⊗(xa∧y−b) =−∑2≤b≤αj+11≤a≤αi(−1)a+b+αi+1(x−a∧yb−1)⊗(xa∧y−(b−1)) =+∑1≤b≤αj(−1)b+1x⊗(yb∧y−b) =−∑1≤a≤αi(−1)a+αi(x−a∧xa)⊗y =∑1≤b≤αjx⊗y−∑1≤a≤αix⊗y=(αj−αi)(x⊗y)
• : , , .

 [σi,j,σk,i](x⊗y⊗z) =σi,j(∑1≤c≤αk(−1)αj+c+1(x∧zc)⊗y⊗z−c) =−σk,i(∑1≤a≤αi(−1)αi+ax−a⊗(xa∧y)⊗z) =∑1≤c≤αk1≤a≤αi+1(−1)αi+αj+a+c(x∧zc)−a⊗((x∧zc)a)∧y⊗z−c =−∑1≤a≤αi1≤c≤αk(−1)a+c+αi+αj(x−a∧zc)⊗(xa∧y)⊗z−c) =∑1≤a≤αi1≤c≤αk(−1)αi+αj+a+c(x−a∧zc)⊗(xa∧y)⊗z−c) =−∑1≤a≤αi1≤c≤αk(−1)αi+αj+a+c(x−a∧zc)⊗(xa∧y)⊗z−c) =+∑1≤c≤αk(−1)αj+c+1x⊗(zc∧y)⊗z−c =∑1≤c≤αk(−1)c+1x⊗(y∧zc)⊗z−c =σk,j(x⊗y⊗z)
• : Equivalent to the case but changing the order of elements in the commutator. Thus, the sign changes:

 [σi,j,σj,l](x⊗y⊗z)=−[σj,l,σi,j](x⊗y⊗z)=−σi,l(x⊗y⊗z)
• : If all are pairwise distinct, then both maps affect distinct columns and hence they commute. We first treat the case , .

 [σi,k,σj,k](x⊗y⊗z) =σi,k(∑1≤b≤αj(−1)αj+bx⊗y−b⊗(yb∧z)) =−σj,k(∑1≤a≤αi(−1)αi+αj+ax−a⊗y⊗(xa∧z)) =∑1≤a≤αi1≤b≤αj(−1)αj+b+a+αi+αj+1x−a⊗y−b⊗(xa∧yb∧z) =−∑1≤a≤αi1≤b≤αj(−1)αj+b+a+αi+αjx−a⊗y−b⊗(yb∧xa∧z) =0

We now treat the remaining case , . For a basis vector let denote the basis vector with positions and removed.

 [σi,j,σi,l](x⊗y⊗z) =σi,j(∑1≤a≤αi(−1)αj+a+αix−a⊗y⊗(xa∧z)) =−σi,l(∑1≤a≤αi(−1)αi+ax−a⊗(xa∧y)⊗z) =∑1≤a≤αi1≤a′≤αi−1(−1)a+a′+αj+1(x−a)−a′⊗((x−a)a′∧y)⊗(xa∧z) =−∑1≤a≤αi1≤a′≤αi−1(−1)a+a′+αj(x−a)−a′⊗(xa∧y)⊗((x−a)a′∧z) =∑1≤a,~a≤αia≠~a(−1)a+~a+αj+1+[~a>a]x−{a,~a}⊗(x~a∧y)⊗(xa∧z) =−∑1≤a,~a≤αia≠~a(−1)a+~a+αj+[~a>a]x−{a,~a}⊗(xa∧y)⊗(x~a∧z) =0

where is 1 if and 0 otherwise. Here we used the notation

 ~a={a′ if a′

Note that the second case happens exactly when .∎

We will make heavy use of the following identity: Let be linear maps, then

 [σ1∘σ2,σ3]=σ1∘[σ2,σ3]+[σ1,σ3]∘σ2. (3.9)

The rule can be interpreted as the Leibniz rule for .

###### Proof of Theorem 3.5.

Using (2.7) we see that it suffices to prove that if , then . Let with . We now show that , which finishes the proof.

We split the proof according to the different relations of and :

• : If , then clearly


text:
Status
Not open for further replies.
1 - 10 of 10 Posts

· Registered
Joined
·
886 Posts
Discussion Starter · ·
OS 98

I have a computer who has a computer that was and still is a mess. The computer was infected by the Istbar Trojan. Supposedly now it is only in the system restore but I can't get it off because anytime I try to run AVG or Adaware the computer crashes. This also happens when I try to start AOL 8.0 for broadband. So, I brought her computer home and hooked it up to my cable so that I could download some additional programs and to consult with TSGF since I am stumped. I have run Spybot and cleaned everything off. I ran the registry scan from Norton and got a bunch of stuff off. She was having an error message with Quicktime, so I uninstalled and then still found more quicktime files in start up and in the registry which I had to delete one by one. Since that things are better, but still bad. I did run hijack this and got some bad programs off, but want to consult here berfore further deleting. Please note that I have a number of startup items checked to not load otherwise I cannot get into normal Windows, only save mode.

When the computer crashes when I try to run Avg or any other program, if I try to get directly into normal windows, I get a number of Kernel32.dll errors andthen it stalls. I then can open in Safe mode, and reboot without the kernel32.dll errors. The error messages include a number of start up things like task AVGcc.exe or NortonP.exe. All programs that usually load up. (Even though I had many of them checked up not to start via selective startup.)

Anyway here is the Hijack this. Could someone please look and advise. Also any other suggestions - a scan on the net, etc. will be appreciated!!!

Logfile of HijackThis v1.97.7
Scan saved at 4:44:22 PM, on 4/1/2004
Platform: Windows ME (Win9x 4.90.3000)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)

Running processes:
C:\WINDOWS\SYSTEM\KERNEL32.DLL
C:\WINDOWS\SYSTEM\MSGSRV32.EXE
C:\WINDOWS\SYSTEM\MPREXE.EXE
C:\WINDOWS\EXPLORER.EXE
C:\WINDOWS\SYSTEM\RESTORE\STMGR.EXE
C:\UNZIPPED\HIJACKTHIS\HIJACKTHIS.EXE

O4 - HKLM\..\Run: [ScanRegistry] C:\WINDOWS\scanregw.exe /autorun
O4 - HKLM\..\Run: [SystemTray] SysTray.Exe
O4 - HKLM\..\Run: [AVG_CC] C:\PROGRA~1\GRISOFT\AVG6\avgcc32.exe /STARTUP
O4 - HKLM\..\Run: [NPROTECT] C:\Program Files\Norton SystemWorks\Norton Utilities\NPROTECT.EXE
O4 - HKLM\..\RunServices: [Avgserv9.exe] C:\PROGRA~1\GRISOFT\AVG6\Avgserv9.exe
O4 - HKLM\..\RunServices: [*StateMgr] C:\WINDOWS\System\Restore\StateMgr.exe
O4 - HKLM\..\RunServices: [SymTray - Norton SystemWorks] C:\Program Files\Common Files\Symantec Shared\SymTray.exe "Norton SystemWorks"
O4 - HKLM\..\RunServices: [CSINJECT.EXE] C:\Program Files\Norton SystemWorks\Norton CleanSweep\CSINJECT.EXE
O4 - HKLM\..\RunServices: [NPROTECT] C:\Program Files\Norton SystemWorks\Norton Utilities\NPROTECT.EXE
O8 - Extra context menu item: &Define - C:\Program Files\Common Files\Microsoft Shared\Reference 2001\A\ERS_DEF.HTM
O8 - Extra context menu item: Look Up in &Encyclopedia - C:\Program Files\Common Files\Microsoft Shared\Reference 2001\A\ERS_ENC.HTM
O16 - DPF: {9F1C11AA-197B-4942-BA54-47A8489BB47F} (Update Class) - http://v4.windowsupdate.microsoft.com/CAB/x86/ansi/iuctl.CAB?38044.3046990741
O17 - HKLM\System\CCS\Services\VxD\MSTCP: Domain = aoldsl.net

· Registered
Joined
·
886 Posts
Discussion Starter · ·
Oops the first line should say I have a client who has a computer!! Sorry for the confusion.

· Registered
Joined
·
886 Posts
Discussion Starter · ·
Oh, one more thing. I just tried to run housecall. It gets about 95% of the engine downloaded and then freezes.

· Registered
Joined
·
886 Posts
Discussion Starter · ·
I've solved a lot more since post, ie. Ican always get into normal windows now. However, I still cannot run avg or adaware or panda etc. And I guess I'm going goo goo eyes. I am running Windows ME. I've only seen the 50 times I rebooted today! Please help if you have any suggestions. I just can't figure out why it starts a scan and then shuts off.

Thanks

#### \$teve

· Registered
Joined
·
9,520 Posts
Hi
Theres nothing showing up in your log,but if you r using MSConfig that could be why.......your going to have to enable all and somehow post a log af the full running processes so`s we can see everything thats happening.

Also......do i see both AVG and NAV running......not a good idea.

I would disable both for now till your able to give us a full HijackThis log.

· Registered
Joined
·
886 Posts
Discussion Starter · ·
Oops posted this on wrong thread. Sorry if there is a duplication. Thanks, steve for replying. I've been on this stupid computer for more hours thanI want to admit!
I don't have NAV and avg running. Was clean sweep and utilities. However I uninstalled and it was still on. Tried to remove again and was unable because so files were missing. I did disable in start up so that I could at least get in to normal windows.

Heres the scan.
Logfile of HijackThis v1.97.7
Scan saved at 4:44:22 PM, on 4/1/2004
Platform: Windows ME (Win9x 4.90.3000)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)

Running processes:
C:\WINDOWS\SYSTEM\KERNEL32.DLL
C:\WINDOWS\SYSTEM\MSGSRV32.EXE
C:\WINDOWS\SYSTEM\MPREXE.EXE
C:\WINDOWS\EXPLORER.EXE
C:\WINDOWS\SYSTEM\RESTORE\STMGR.EXE
C:\UNZIPPED\HIJACKTHIS\HIJACKTHIS.EXE

O4 - HKLM\..\Run: [ScanRegistry] C:\WINDOWS\scanregw.exe /autorun
O4 - HKLM\..\Run: [SystemTray] SysTray.Exe
O4 - HKLM\..\Run: [AVG_CC] C:\PROGRA~1\GRISOFT\AVG6\avgcc32.exe /STARTUP
O4 - HKLM\..\Run: [NPROTECT] C:\Program Files\Norton SystemWorks\Norton Utilities\NPROTECT.EXE
O4 - HKLM\..\RunServices: [Avgserv9.exe] C:\PROGRA~1\GRISOFT\AVG6\Avgserv9.exe
O4 - HKLM\..\RunServices: [*StateMgr] C:\WINDOWS\System\Restore\StateMgr.exe
O4 - HKLM\..\RunServices: [SymTray - Norton SystemWorks] C:\Program Files\Common Files\Symantec Shared\SymTray.exe "Norton SystemWorks"
O4 - HKLM\..\RunServices: [CSINJECT.EXE] C:\Program Files\Norton SystemWorks\Norton CleanSweep\CSINJECT.EXE
O4 - HKLM\..\RunServices: [NPROTECT] C:\Program Files\Norton SystemWorks\Norton Utilities\NPROTECT.EXE
O8 - Extra context menu item: &Define - C:\Program Files\Common Files\Microsoft Shared\Reference 2001\A\ERS_DEF.HTM
O8 - Extra context menu item: Look Up in &Encyclopedia - C:\Program Files\Common Files\Microsoft Shared\Reference 2001\A\ERS_ENC.HTM
O16 - DPF: {9F1C11AA-197B-4942-BA54-47A8489BB47F} (Update Class) - http://v4.windowsupdate.microsoft.com/CAB/x86/ansi/iuctl.CAB?38044.3046990741
O17 - HKLM\System\CCS\Services\VxD\MSTCP: Domain = aoldsl.net

#### \$teve

· Registered
Joined
·
9,520 Posts
Its a clean log:up

· Registered
Joined
·
886 Posts
Discussion Starter · ·
Thanks. I thought I cleaned it out. But do you have any other suggestions? It just shuts down anytime I try adaware panda etcc. There has got be something that is hanging it up and then stopping. I'm kind of at a loss of what to do. Thanks!

#### \$teve

· Registered
Joined
·
9,520 Posts
What shuts down......the program or the comp?


text:
Department of Mathematics

Regularity of eigenstates in regular Mourre theory

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

• Department of Mathematical Sciences
The present paper gives an abstract method to prove that possibly embedded eigenstates of a self-adjoint operator H lie in the domain of the kth power of a conjugate operator A. Conjugate means here that H and A have a positive commutator locally near the relevant eigenvalue in the sense of Mourre. The only requirement is Ck+1(A) regularity of H. Regarding integer k, our result is optimal. Under a natural boundedness assumption of the multiple commutators we prove that the eigenstate ‘dilated’ by exp(iθA) is analytic in a strip around the real axis. In particular, the eigenstate is an analytic vector with respect to A. Natural applications are ‘dilation analytic’ systems satisfying a Mourre estimate, where our result can be viewed as an abstract version of a theorem due to Balslev and Combes (1971) [3]. As a new application we consider the massive Spin-Boson Model.
Original language English Journal of Functional Analysis 260 3 852-878 27 0022-1236 https://doi.org/10.1016/j.jfa.2010.10.006 Published - 2011

Citationformats

ID: 22110835


text:
# How do I find clockwise angle of a point from the negative x-axis?

Title pretty much says it. How can I rotate a point around the origin and find the clockwise angle of the point from the negative x-axis? I tried using the atan(height/width), but that gives me the angle in the specific quadrant, not from the negative x-axis.

Edit I got some good advice in the comments. What this question is really asking is, "How can I calculate the clockwise angle between a vector and the negative x-axis?". I was looking for a programming answer, but both perspectives (programming and not) are answered below.

-
Do you know about rotation matrices? –  EuYu Aug 23 '12 at 17:56
Try atan2. –  Rahul Aug 23 '12 at 17:57
More or less. Maybe I wasn't clear enough. I'm given a point p1, and a point p2. Point p1 will always be at the origin, and p2 can be anywhere. What I need to find out is the clockwise angle from the negative x-axis, and p2. I'm not sure how a rotation matrix would help me solve this since it's the theta of the rotation I need to figure out. –  Xyrthon Aug 23 '12 at 17:59
@RahulNarain I tried both atan2 and atan, but I'm running into the same problem. –  Xyrthon Aug 23 '12 at 18:00
Really? $\pi - \operatorname{atan2}(y,x)$ doesn't do what you want? –  Rahul Aug 23 '12 at 18:11

Most programming languages provide an $\operatorname{atan2}$ function that deals with quadrants correctly. If you have a point $(x,y) \ne (0,0)$, then $\operatorname{atan2}(y,x)$ gives the counter-clockwise angle from the positive $x$-axis to $(x,y)$, in the range $(-\pi,\pi]$. Since you want the clockwise angle from the negative $x$-axis, it is enough to observe that when $\operatorname{atan2}(y,x) = 0$ the angle you want is $\pi$, and when it is $\pi/2$ you want $\pi/2$, so in general what you want is $\pi-\operatorname{atan2}(y,x)$, which lies in the range $[0,2\pi)$.

-
Drat, not enough rep to mark ya up, but as soon as I get enough rep, I'll make sure to indicate this is what I was looking for. –  Xyrthon Aug 23 '12 at 19:30
I don't think you need rep to click the accepted answer check mark. –  Rahul Aug 23 '12 at 19:42

Leverage the dot product. If $\vec a = (a_1,a_2,\dots,a_n)$ is any point, we have two ways to compute the dot product with any vector $\vec b=(b_1, b_2, \dots, b_n)$:

$$\vec a \cdot \vec b = (a_1 b_1, a_2b_2, \dots, a_nb_n)$$ $$\vec a \cdot \vec b = \lVert \vec a \rVert \lVert \vec b \rVert \cos \theta$$ where $\theta$ is the angle between $\vec a$ and $\vec b$ (the primary angle, i.e. $\theta \in [0,\pi]$). So now, taking $\vec b = - \hat i$ (a unit vector on the negative x-axis) we have that

$$\theta = \arccos\left(\frac {\vec a \cdot \vec b} {\lVert \vec a \rVert \lVert \vec b \rVert}\right )$$

Now by the first way of computing the dot product we have that $\vec a \cdot \vec b = -a_1$, and since $\lVert \vec b \rVert =1$ we have that $$\theta = \arccos \left( \frac {-a_1} {\lVert \vec a \rVert} \right )\,.$$

Now you mentioned that you wanted the clockwise angle in $\Bbb R ^2$, so you just need to add $\pi$ if $\vec a$ is below the x-axis, i.e. if $a_2<0$. The value $a_2/|a_2|$ is equal to the sign of $a_2$, so let's consider $\frac {1-a_2/|a_2|}{2}$ which will equal $1$ when $a_2<0$ and $0$ when $a_2>0$. Thus the function you want in total is just

$$f(\vec a)=\arccos\left ( \frac {-a_1} {\lVert \vec a \rVert} \right )+\frac {1-a_2/|a_2|}{2} \pi$$

(Note that the heading of your question, as well as the initial description, gives a much different impression of what you are looking for.)

-
I'm not sure how to make what I was looking for any more clear. Rahul Narain answered my question just like I asked it in the comments. I learned that I need to be more thorough when explaining my problem, but this is my very first post here, so I'll attempt to do that in the future. –  Xyrthon Aug 23 '12 at 18:44
@Xyrthon As a suggestion - when I read "how do I rotate a point around the origin" I, like EuYu, initially thought that what you wanted was a function which rotated a point around the origin. This is precisely what a rotation matrix would do. Perhaps "How can I calculate the clockwise angle between a vector and the negative x-axis" would more accurately describe your question. In addition, it would be helpful if you said that you were using this in a computer program, as that suggests the answer Rahul provided. Your question was fine, I would just have phrased it differently. –  process91 Aug 23 '12 at 18:56
Ahhh, gotcha. Thank you. –  Xyrthon Aug 23 '12 at 19:28
I'll up vote you as soon as I gain enough rep as well, because this is what I'd be looking for if I wasn't writing a program. –  Xyrthon Aug 23 '12 at 19:31


text:
# What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

##### 1 Answer
Feb 21, 2016

Standard Deviation is 2.2913

#### Explanation:

Set of numbers are $\left\{4 , 5 , 8 , 3 , 6 , 2 , 1 , 5 , 9 , 5 , 4 , 2\right\}$. As there are 12 terms whose sum is 54, mean is $\frac{54}{12}$ or $4.5$.

Hence deviations from mean are $\left\{- 0.5 , 0.5 , 3.5 , - 1.5 , 1.5 , - 2.5 , - 3.5 , 0.5 , 4.5 , 0.5 , - 0.5 , - 2.5\right\}$ and sum of there squares is

$0.25 + 0.25 + 12.25 + 2.25 + 2.25 + 6.25 + 12.25 + 0.25 + 20.25 + 0.25 + 0.25 + 6.25 = 63$

Hence Standard Deviation is $\sqrt{\frac{63}{12}} = \sqrt{\frac{21}{4}} = \frac{1}{2} \sqrt{21} = \frac{4.5826}{2}$ i.e. $2.2913$


text:
# Why does the bubbling of a soda bottle pulsate?

If I take a bottle of carbonated water and open the cap slightly to allow the gas to escape, there will be a sudden rush of bubbles foaming to the top of the liquid for a few seconds, then a partial lull for a few seconds, then another smaller rush of bubbles, then a smaller lull, etc, like a damped oscillation. What causes this pulsation?

A Computer Model for Soda Bottle Oscillations: "The Bottelator" describes a model for this. That's a pay site, but you can find the text here.

The model used in the paper is that for a bubble to form it must nucleate then grow to a size big enough to rise to the surface. This process takes a finite time. When the cap is loosened the decrease in pressure causes a burst of nucleation, but after a few seconds the bubbles bursting on the surface raise the pressure again and this inhibits nucleation. As the gas escapes through the loosened cap the pressure falls again and nucleation restarts. The process repeats until the amount of gas being released by the bubbles is not longer enough to inhibit nucleation.

Note that the paper doesn't go into the physics of the nucleation and growth process. It just assumes that this is the basis of the oscillation. However the assumption seems reasonable. Suppose you take a bottle of soda and momentarily loosen then tighten the caps. You'll see a burst of fizzing. Loosen then tighten the cap again and you'll get another burst, and so on. In this case you're causing the pressure to oscillate by manually controlling the gas flow, but you can see how you'd get a similar effect if the gas flow though a slightly loosened cap was just right.

It would be interesting to measure the pressure above a saturated CO$_2$ solution as a function of gas flow through the cap. I don't have the kit to do this, but it wouldn't be a difficult experiment.


text:
# Applied Potential and Electrochemical Cell Potential

Electrolysis of molten lithium hydroxide at $$\pu{750 K}$$ to form lithium metal

$$\ce{4 LiOH -> 4 Li + 2 H2O + O2}.$$

Electrolysis will only proceed at an appreciable rate when the applied potential exceeds the electrochemical cell potential by $$\pu{0.60 V}.$$

(c) Calculate the minimum potential that should be applied.

$$ΔG^\circ = -nFE^\circ_\mathrm{cell}$$

$$E^\circ_\mathrm{cell} = \frac{ΔG^\circ}{nF} = \pu{-2.60 V}$$

Why should the difference of $$\pu{0.60 V}$$ be added onto the absolute value of $$E^\circ_\mathrm{cell}~(+2.60)$$ and not $$-2.60$$?

I understand $$E_\mathrm{cell}$$ is the measure of the potential difference between two half-cells in an electrochemical cell, but what is applied potential in this case? I thought electrochemical cells produce an electric potential difference (in this case $$\pu{-2.60 V}),$$ so why would they need an applied (positive) potential difference?

You are mixing two areas, electrode kinetics and electrode thermodynamics. If we have 3 apples and 2 oranges, this is not equal to 5 oranges or 5 apples but there are 5 fruits in total. Electrode thermodynamics tells you a "yes" or "no" answer in the sense that it is saying the reaction is spontaneous or not. Electrode kinetics tells you how fast the reaction will be.

When you wish to electrolyse something, it means that you want do a non-spontaneous reaction i.e., if you leave lithium in the presence of air and moisture, it will spontaneously form LiOH

$$\ce{4 LiOH <- 4 Li + 2 H2O + O2}.--(1)$$

Now, by forcing electric current through molten LiOH, you want to reverse this reaction and want the following to happen

$$\ce{4 LiOH -> 4 Li + 2 H2O + O2}.--(2)$$

The negative Ecell of -2.60 V only tells you that reaction (2) is not spontaneous at all. It has no other meaning whatsoever. That is, if you wait forever, you will not see any Li spontaneously forming out of LiOH.

Now as you read in the question, they are saying that if you apply exactly +2.60 V potential difference between two electrodes the rate of reaction is very slow. Remember negative sign was just for saying that the reaction is non-spontaneous. However if you apply +2.60+0.60 = 3.2 V of potential difference between the electrodes, the rate of formation of Li from molten LiOH will be quite fast. They don't say how fast but you will not have to wait for a long time.

So +2.60 V is the apple = electrode potential 0.6 V is the orange, it is called the overpotential in formal language.

You can only add them (not subtract) and get the total voltage required to start the electrolysis at an appreciable rate.


text:
Mentor

## How do time and space dilation work together to ensure the constant speed of light?

 Quote by rabcarl I've read that time and space dilate under acceleration to ensure the constant speed of light.
I prefer to look at it the other way around: Time dilation and length contraction are a necessary consequence of the constancy of the speed of light. Taking time dilation and length contraction as axiomatic is bit too ad hoc for my tastes.

Starting with some very basic concepts of continuity dictates that some speed must be the same to all observers. You get Newtonian mechanics if this universally agreed-upon speed is infinite. You get a Lorentz manifold if this universally agreed-upon speed is finite. Maxwell's equations and multiple experiments indicate that this universally agreed-upon speed is finite and is in fact the speed of light.


text:
# 2.2 Vectors in three dimensions  (Page 4/14)

 Page 4 / 14

## Definition

A sphere    is the set of all points in space equidistant from a fixed point, the center of the sphere ( [link] ), just as the set of all points in a plane that are equidistant from the center represents a circle. In a sphere, as in a circle, the distance from the center to a point on the sphere is called the radius .

The equation of a circle is derived using the distance formula in two dimensions. In the same way, the equation of a sphere is based on the three-dimensional formula for distance.

## Rule: equation of a sphere

The sphere with center $\left(a,b,c\right)$ and radius $r$ can be represented by the equation

${\left(x-a\right)}^{2}+{\left(y-b\right)}^{2}+{\left(z-c\right)}^{2}={r}^{2}.$

This equation is known as the standard equation of a sphere    .

## Finding an equation of a sphere

Find the standard equation of the sphere with center $\left(10,7,4\right)$ and point $\left(-1,3,-2\right),$ as shown in [link] .

Use the distance formula to find the radius $r$ of the sphere:

$\begin{array}{cc}\hfill r& =\sqrt{{\left(-1-10\right)}^{2}+{\left(3-7\right)}^{2}+{\left(-2-4\right)}^{2}}\hfill \\ & =\sqrt{{\left(-11\right)}^{2}+{\left(-4\right)}^{2}+{\left(-6\right)}^{2}}\hfill \\ & =\sqrt{173}.\hfill \end{array}$

The standard equation of the sphere is

${\left(x-10\right)}^{2}+{\left(y-7\right)}^{2}+{\left(z-4\right)}^{2}=173.$

Find the standard equation of the sphere with center $\left(-2,4,-5\right)$ containing point $\left(4,4,-1\right).$

${\left(x+2\right)}^{2}+{\left(y-4\right)}^{2}+{\left(z+5\right)}^{2}=52$

## Finding the equation of a sphere

Let $P=\left(-5,2,3\right)$ and $Q=\left(3,4,-1\right),$ and suppose line segment $PQ$ forms the diameter of a sphere ( [link] ). Find the equation of the sphere.

Since $PQ$ is a diameter of the sphere, we know the center of the sphere is the midpoint of $PQ.$ Then,

$\begin{array}{cc}\hfill C& =\left(\frac{-5+3}{2},\frac{2+4}{2},\frac{3+\left(-1\right)}{2}\right)\hfill \\ & =\left(-1,3,1\right).\hfill \end{array}$

Furthermore, we know the radius of the sphere is half the length of the diameter. This gives

$\begin{array}{cc}\hfill r& =\frac{1}{2}\sqrt{{\left(-5-3\right)}^{2}+{\left(2-4\right)}^{2}+{\left(3-\left(-1\right)\right)}^{2}}\hfill \\ & =\frac{1}{2}\sqrt{64+4+16}\hfill \\ & =\sqrt{21}.\hfill \end{array}$

Then, the equation of the sphere is ${\left(x+1\right)}^{2}+{\left(y-3\right)}^{2}+{\left(z-1\right)}^{2}=21.$

Find the equation of the sphere with diameter $PQ,$ where $P=\left(2,-1,-3\right)$ and $Q=\left(-2,5,-1\right).$

${x}^{2}+{\left(y-2\right)}^{2}+{\left(z+2\right)}^{2}=14$

## Graphing other equations in three dimensions

Describe the set of points that satisfies $\left(x-4\right)\left(z-2\right)=0,$ and graph the set.

We must have either $x-4=0$ or $z-2=0,$ so the set of points forms the two planes $x=4$ and $z=2$ ( [link] ).

Describe the set of points that satisfies $\left(y+2\right)\left(z-3\right)=0,$ and graph the set.

The set of points forms the two planes $y=-2$ and $z=3.$

## Graphing other equations in three dimensions

Describe the set of points in three-dimensional space that satisfies ${\left(x-2\right)}^{2}+{\left(y-1\right)}^{2}=4,$ and graph the set.

The x - and y -coordinates form a circle in the xy -plane of radius $2,$ centered at $\left(2,1\right).$ Since there is no restriction on the z -coordinate, the three-dimensional result is a circular cylinder of radius $2$ centered on the line with $x=2\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}y=1.$ The cylinder extends indefinitely in the z -direction ( [link] ).

Describe the set of points in three dimensional space that satisfies ${x}^{2}+{\left(z-2\right)}^{2}=16,$ and graph the surface.

A cylinder of radius 4 centered on the line with $x=0\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}z=2.$

## Working with vectors in ℝ 3

Just like two-dimensional vectors, three-dimensional vectors are quantities with both magnitude and direction, and they are represented by directed line segments (arrows). With a three-dimensional vector, we use a three-dimensional arrow.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!


text:
# 7.4.2.3 - Example: 99% CI for Proportion of Women Students

Scenario: Data were collected from a representative sample of 501 World Campus STAT 200 students. In that sample, 284 students were women and 217 were not women. Construct a 99% confidence interval to estimate the proportion of all World Campus students who are women.

StatKey was used to construct a sampling distribution using bootstrapping methods:

Because this distribution is approximately normal, we can approximate the sampling distribution using the z distribution. We will use the standard error, 0.022, from this distribution.

The original sample statistic was $$\widehat p =\frac{284}{501}=0.567$$.

We can find the $$z^*$$ multiplier by constructing a z distribution to find the values that separate the middle 99% from the outer 1%:

The $$z^*$$ multiplier is 2.57583

Recall the general form of a confidence interval: sample statistic $$\pm$$ $$z^*$$ (standard error) where $$z^*$$ is the multiplier. So in this case we have...

$$0.567 \pm 2.57583 (0.022)$$

$$0.567 \pm 0.057$$

$$[0.510, 0.624]$$

I am 99% confident that the proportion of all World Campus students who are women is between 0.510 and 0.624


text:
In this blog we will explore several ways that Alternate Data Streams (ADS) are abused by attackers to hide files and evade detection, defences based on them (and ways to bypass those defences!) but also how they can be used to help malware evade dynamic analysis.

Files in the NTFS file system consist of multiple streams or attributes. Metadata such as the file name, timestamps as well as the associated security descriptors are all saved in separate streams. The contents of the file itself are also saved as a stream known as the default $DATA stream. However, a file can have multiple$DATA streams! This means that additional content can be embedded in separate streams of the same file. We refer to those additional $DATA streams as Alternate Data Streams or ADS. ## Hiding files with ADS Alternate Data Streams can be added to regular files and are not visible when browsing the file system via the graphical user interface. In addition, such streams are not listed when listing the contents of a directory with dir or dir /A. In the example below, a data stream called malicious.txt is added to the file text.txt. C:\Users\ThreatSpike\ADS>echo "Malicious Content" > text.txt:malicious.txt C:\Users\ThreatSpike\ADS>dir /A Directory of C:\Users\ThreatSpike\ADS 23/12/2020 13:49 <DIR> . 23/12/2020 13:49 <DIR> .. 23/12/2020 13:54 27 text.txt 1 File(s) 27 bytes 2 Dir(s) 29,827,604,480 bytes free There is a special flag for the directory listing command  dir in Windows that enables alternate data stream listing. /R Display alternate data streams of the file. C:\Users\ThreatSpike\ADS>dir /R Directory of C:\Users\ThreatSpike\ADS 23/12/2020 13:49 <DIR> . 23/12/2020 13:49 <DIR> .. 23/12/2020 13:54 27 text.txt 22 text.txt:malicious.txt:$DATA
1 File(s)             27 bytes
2 Dir(s)  29,827,604,480 bytes free

There are also other utilities that can help identify and examine data streams such as the streams utility. Powershell has several commands that can identify and create streams as well.

Data streams can also be added to directories. In that way files can be hidden on the directory itself.

C:\Users\ThreatSpike\ADS>echo "Malicious Content" > dir:malicious.txt

C:\Users\ThreatSpike\ADS>dir /A

Directory of C:\Users\ThreatSpike\ADS

23/12/2020  13:58    <DIR>          .
23/12/2020  13:58    <DIR>          ..
23/12/2020  13:59    <DIR>          dir
0 File(s)              0 bytes
3 Dir(s)  29,828,136,960 bytes free

C:\Users\ThreatSpike\ADS>dir /A /R

Directory of C:\Users\ThreatSpike\ADS

23/12/2020  13:58    <DIR>          .
23/12/2020  13:58    <DIR>          ..
23/12/2020  13:59    <DIR>          dir
22 dir:malicious.txt:$DATA 0 File(s) 0 bytes 3 Dir(s) 29,828,136,960 bytes free ### The newly added stream cannot be seen. There are also some edge cases that can help malicious actors hide their files even further. Files with names ending in . . are not properly parsed by several stream-aware utilities if they are not fully referenced with their full path. C:\Users\ThreatSpike\ADS>echo malicious > "file. .:malicious.txt" C:\Users\ThreatSpike\ADS>dir /R /A Directory of C:\Users\ThreatSpike\ADS 08/01/2021 17:03 <DIR> . 08/01/2021 17:03 <DIR> .. 08/01/2021 17:03 0 file. . 1 File(s) 0 bytes 2 Dir(s) 29,895,577,600 bytes free C:\Users\ThreatSpike\ADS>..\streams.exe -s streams v1.60 - Reveal NTFS alternate streams. Copyright (C) 2005-2016 Mark Russinovich Sysinternals - www.sysinternals.com Error opening C:\Users\ThreatSpike\ADS\file. .: The system cannot find the file specified. No files with streams found. C:\Users\ThreatSpike\ADS>more < "file. .:malicious.txt" malicious Using more to examine the data stream reveals its contents even though dir /R and streams fail to identify it. However, if we specify the full path with the "\\?\" prefix the file is visible and we can operate on it. C:\Users\ThreatSpike\ADS>dir /R "\\?\C:\Users\ThreatSpike\ADS\file. ." Directory of \\?\C:\Users\ThreatSpike\ADS 08/01/2021 17:09 0 file. . 12 file. .:malicious.txt:$DATA
1 File(s)              0 bytes
0 Dir(s)  29,895,057,408 bytes free

### Executing files straight from data streams

It is also worth mentioning that executables residing in an alternate data stream cannot be started in the normal way. You cannot double click on them or call them by name on the command prompt. However, there are multiple indirect ways of starting a process straight from the hidden executable. Both of the below commands can be used to start a process from a data stream called calc.exe that is embedded in a normal text.txt file.

wmic process call create "C:\Users\ThreatSpike\text.txt:calc.exe"

forfiles /p c:\windows\system32 /m notepad.exe /c "C:\Users\ThreatSpike\text.txt:calc.exe"

A more exhaustive list of ways to run different types of executable files straight from an alternate data stream can be found here but the main idea is that there are options for almost all executable file types.

### Detecting malware in hidden data streams

Being able to hide files in ADS, combined with the ability to initiate processes from them, makes them a very convenient hiding spot for malware and MITRE has a page dedicated to this hiding technique. Proof of concept code that uses alternate data streams to persist on a compromised host has also been published.

Windows Defender and most major Antivirus solutions are well aware of this hiding method as well. Windows Defender is particularly good at detecting malware in alternate data streams and it surgically removes only the stream that contains the malicious content without deleting the main file. However not all security vendors appear to be aware of the presence of ADS. We tested AV solutions by uploading a variety of samples to VirusTotal. By uploading a file through the browser, only the default data stream is preserved so in order to test the behavior of Antivirus products the file must be first compressed in a “container” that supports alternate data streams. In this test we used WINRar as it offers the option to save file streams when compressing the file.

First, in order to establish a baseline detection rate, a plain Meterpreter executable payload was uploaded. This generated 43/69 detections.

Then, the same payload was compressed in an RAR archive. This generated 34/60 detections.

Finally the same original Meterpreter payload was embedded in an ADS of a legitimate txt file and was then compressed into a RAR archive. This dropped the detection rate even further to 20/60 detections.

Judging from these results, there are indications that some Antivirus Vendors (including some major ones) do not scan the contents of alternate data streams. The below screenshot shows AV products that failed to identify the Meterpreter executable hidden in an ADS at the time that this research took place according to VirusTotal. At this point it should be also noted that results on VirusTotal sometimes differ from the actual detection performance of AV engines in real deployments.

*All previously mentioned detection rates refer to the results observed when this research took place and may differ in the future.

### ADS based defences and malware bypasses

Alternate Data Streams are not only useful for malicious purposes. They are also used to protect users from externally acquired executables as part of a defence system integrated in Windows.

Whenever a new file is downloaded, a new data stream with the name Zone.Identifier is added to the file by the program that performed the download. For example, if you download a file with Chrome, then the browser itself is responsible for this addition. The Zone.Identifier stream is then used by Windows to evaluate the origins of a file and introduce protection if needed. It specifies a Security Zone that can be used to warn and protect the user from executables downloaded from outside sources. It is also very important to propagate the Zone.Identifier field to files derived from the original one. For example, extracting a zip file that originated from an outside source should propagate the Zone.Identifier to its contents. This is indeed handled correctly for most file types but there are some exceptions. .

The Zone.Identifier data stream does not propagate to the contents when opening ISO or VHD files in Windows. The dangers of not propagating the Zone.Identifier ADS are known to the community. Malware using Virtual Hard Drive(VHD) Images and ISO files to achieve code execution bypassing the Windows SmartScreen protection have already been spotted in the wild. Both of those types of files are natively supported in Windows 10 and can be opened by a user with just a double click and as a consequence, this behavior opens up a new attack surface for phishing attacks.

In addition to that, antivirus engines do not seem to scan the contents of these types of files in some cases. For example, a VHD file that contains malware (and more specifically a meterpreter payload) can be safely saved on disk of a fully updated Windows 10 system with Microsoft Defender active. Uploading a virtual hard drive file that contains a blatantly malicious meterpreter payload to VirusTotal generates only 1/60 detection rate. A significantly different behavior was observed with an ISO file containing the same payload with 27/60 detections.

Another point that is also worth mentioning is that Alternate Data Streams are a feature of NTFS and because of that such streams are not preserved when copying files to other file systems. This means that files downloaded directly or moved to other file systems that do not support ADS, such as a Fat32 formatted external USB drive, will not enjoy the same protection from Windows.

### Checking ADS to evade analysis.

While some malware strains delete the Zone.Identifier stream from their executable files themselves, in an attempt to delete forensic evidence indicating the origins of those files, others check for this stream as a means to evade behavioral analysis. The absence of the Zone.Identifier alternate data stream can be used as an indication that the file has been transferred to a new environment and it was not directly downloaded from the internet. A program can check the presence of this ADS in the executable that it was launched from and detect its origin. This method can be used by malware to implement a dynamic analysis evasion technique that forces the executable to terminate itself if no Zone.Identifier field is present. The pafishmacro project is inspired by “malicious documents found in the public” and presents an example of this technique in a VBA script that could potentially be part of a malware dropper.

## Defence Takeaway Points

Alternate Data Streams are and will be a convenient hiding spot for malware as many people are not aware of their presence. However, on the defensive side there are some behaviors that can be used to alert us on potential malware activity. For example, executable code residing in Alternate Data Streams could be a sign of malicious software attempting to hide. A process deleting or accessing the Zone.Identifier attached to its own executable could indicate attempts to remove forensic data or evade dynamic analysis respectively. Finally, as far as code execution from ISO and Virtual HD Images is concerned, simple actions like disabling Windows Explorer file associations for those file types on all endpoints can help mitigate the risk as suggested here.


text:
# Math Help - Height of chimney stack using Angles of Elevation

1. ## Height of chimney stack using Angles of Elevation

Hello, can anyone help me out with this:

At a point А due south of a chimney staсk, the angle of elevation
of the staсk is 55 degrees. From B, due west of А, such that АB = 100
m, the elevation of the staсk is 33 degrees. Find the height of the stake
and its horizontal distance from А.

2. You have to draw a diagram to see what is happening.

Stack.pdf

Sorry I still can't upload images but here is a PDF with the pictures.

From this we can use the Pythagorean theorem to get

$d_1^2+100^2=d_2^2$

Now using the angles of elevation we get

$\tan(55^{\circ})=\frac{h}{d_1} \iff d_1=\frac{h}{\tan(55^\circ)}$

$\tan(33^{\circ})=\frac{h}{d_2} \iff d_2=\frac{h}{\tan(33^\circ)}$

Now just plug $d_1,d_2$ into the first equation and solve for h.

3. Oh now i get it... Thanks a lot!


text:
1. ## Sketching a graph

Hi guys
I didn't know where to put this, but I'm having trouble understanding what type of functions is this when i graph it:

$(25-x^2)^{1/2}$

P.S

2. Originally Posted by Paymemoney
Hi guys
I didn't know where to put this, but I'm having trouble understanding what type of functions is this when i graph it:

$(25-x^2)^1/2$

P.S
Your graph is simply wrong. If $y= (25-x^2)^{1/2}$ then $y^2= 25 -x^2$ or $x^2+ y^2= 25$. That last is a circle with center at (0,0) and radius 5. The original, the positive square root, is the upper semi-circle.

The graph you give appears to be from $y= (x^2- 25)^{1/2}$. That would give $y^2= x^2- 25$ so $y^2- x^2= 25$, a hyperbola. If that is correct, then your graph is the upper half of that hyperbola.


text:
# zbMATH — the first resource for mathematics

Some uniformly convergent schemes on Shishkin mesh. (English) Zbl 1029.65506
Given the selfadjoint problem $\begin{gathered} Ly\equiv-\varepsilon y''+p(x)y=f(x),\quad x\in I=(0,1)\\ y(0)=0,\quad y(1))=0 \end{gathered}$ where $$0<\varepsilon\ll 1$$ is a small parameter, and $$p,f\in C^2(I)$$, $$p(x)\geq\beta^2>0$$, a difference scheme on the non-uniform mesh was derived by the use of cubic spline. The proposed scheme is analyzed and proved to be uniformly convergent with the order $$O(n^{-2}\ln^2n)$$. The uniform convergence of the non-uniform mesh of the Shiskin type is achieved without the exponential fitting. A numerical example is included to demonstrate the described scheme.
##### MSC:
 65L10 Numerical solution of boundary value problems involving ordinary differential equations
Full Text:


text:
13 questions

Tagged
• x
115
views
1
vote
1

Power Profiler Kit Offset/Miscalibrated?

Hi there,

I'm using the PPK (v1.1.0) to measure my nRF52 DK (v1.1.1). My sample programm is very simple: set up the LFXO, RTC with 8s CC-periode and the BSP_LEDs:

const nrf_drv_rtc_t rtc = NRF_DRV_RTC_INSTANCE(0 ...
(more)

44
views
no
1

AES CCM 8 byte MIC?

Basically I want to get a 8 byte long MIC when using the AES CCM encryption. From the product specification it does seem like I can only get a 4 byte MIC, is that correct? Or is there some workaround available?

162
views
1
vote
1

[CLOSED][nrf52832][S132 4.0.0] connection fails: exchange MTU request is not received on evt.common_evt.conn_handle=2

Configuration:

(1) 52832 PCA10040;(2) softdevice: s132_nrf52_4.0.2; (3) sdk 13.0.0(4) 52832 configure 4 conccurent peripheral connections:

ble_cfg_t ble_cfg;
memset(&ble_cfg, 0, sizeof(ble_cfg));
ble_cfg.gap_cfg.role_count_cfg.periph_role_count  = 4;
ble_cfg.gap_cfg.role_count_cfg.central_role_count = 0;
ble_cfg.gap_cfg ...
(more)

68
views
1
vote
1

The peak current of nRF52832

Hi,

The spec(nRF52832_PS_v1.3.pdf) said the peak current of TX/RX is 5.3/5.4 mA.

However, I use the PCA10040 board and the ble_app_template(SDK 12.2.0) sample code to measure the peak current, the ... (more)

172
views
4
1

How can I reuse this library into TWI library in nrF52?

Hello all,

They both make use of either SPI or ... (more)

52
views
1
vote
2

Apply the patch from the unzipped SDK folder

Hello.

I'm working this : https://github.com/NordicSemiconducto...

In Chapter: Compiling the connectivity .hex files

2.Apply the patch hex/sd_api_v<x>/SDK<ver>_connectivity.patch from the unzipped SDK folder (e.g. git apply -p1 --ignore-whitespace /repos/pc-ble-driver ... (more)

69
views
no
2

Powering down RAM sections increases current

Hi, I am trying to measure (and reduce) the current consumption of my board. I am using nrf52832 (64K RAM) for my development. The RAM layout is as follows: RAM (rwx) : ORIGIN = 0x20002080, LENGTH = 0x2EA8. Stack is 2048 and heap ... (more)

74
views
3
1

Is it possible to have a second UART on nrF52?

Hello,

I would be interested on knowing whether I may have a secondary UART on the nrF52 chip or not. I would like to communicate my nRF52 with a RN2483 and this is done through UART, however I see that ... (more)

81
views
no
1

Compiling ‘RTT_Syscalls_KEIL.c’ ->rt_sys.h: No such file or directory

Hello,

I am trying to compile the example ble_app_eddystone with the SDK12.2 for the nRF52_pca10040_s132

While compiling with SEGGER I get the error

Compiling ‘RTT_Syscalls_KEIL.c’

rt_sys.h: No such file or directory

I think that the path is ... (more)

56
views
1
vote
1

What are the right memory mapping for nrf52 & SEGGER Embedded Studiov3?

HEllo,

I am trying to compile for the nrf52 one of the examples that are included in its SDK12.2, to be precies, I am using experimental_ble_app_blinky_pca10040_s132, I have been able to compile it with KEIL but now I would ... (more)

225
views
1
vote
1

Current consumption NRF52

I'm struggling with current consumption. I need my device to completely sleep and leave only the RTC on when the ext power is off (run on battery). After making sure my RTC was actually working, I ran the following ... (more)

86
views
3
1

How to add flash programming algorithm for softdevice?

I'm trying to program my nrf52832 with an ST-LINK /V2. I can't get both the softdevice and my app on the chip.

Flashing each one seperately works fine but then when I flash my app (after flashing the ... (more)

87
views
no
1

Current measurement on the PCA 10040 v1.1.0 (NRF52)

Hi,

I was reading the procedure to prepare the NRF52 DK board for current measuring and some questions came into my mind. I understand we have to open the P22 so we interrupt the circuit to measure the flowing current ... (more)

Statistics

• Total users: 20387
• Latest user: Debdasora
• Resolved questions: 9454
• Total questions: 22463

Recent blog posts

• The complete tutorial for developing and debugging nRF52 applications on a Mac

Posted 2017-05-11 04:13:06 by Mohammad Afaneh
• Bluetooth 5 2Mbps Demo with nRF52 Series and Samsung Galaxy S8

Posted 2017-05-09 14:20:22 by John Leonard
• Setting up Segger on a mac or pc and debug - step by step for humans

Posted 2017-05-05 14:03:35 by Lola

Posted 2017-04-11 11:49:17 by Radosław Koppel
• Taking a deeper dive into Bluetooth 5

Posted 2017-04-07 14:53:51 by John Leonard

Recent questions

• BLE GATT_INTERNAL_ERROR 129

Posted 2017-05-30 14:53:16 by Mrunali
• Data storing in flash based on timer.

Posted 2017-05-30 13:54:41 by Prashant Singh
• Testing coded PHY with UART?

Posted 2017-05-30 13:45:39 by slowhand


text:
# Meeting notes 11 06 16

Dave's last meeting. Lukas is in Georgia. Aram is in France. Greg passed his final defense!

Paul

Quantum architecture using Majorana fermions on 1D nanowires for topological quantum computing.

David Rosenbaum

Oracle separation between quantum and classical in learning a function $f:[N] \rightarrow [M]$. 2k classical queries are useless $\rightarrow$ k quantum queries are useless. Proof of the reverse for the standard oracle model.

Isaac and Rowan

Continue D-Wave maiming work on stoquastic Hamiltonians.

Johnny

Work with Dave on k-local Hamiltonian paper.


text:
Paperback | $34.00 X | £27.95 | 320 pp. | 6 x 9 in | 95 b&w illus. | January 2015 | ISBN: 9780262527125 eBook |$34.00 X | January 2015 | ISBN: 9780262324250
Mouseover for Online Attention Data

## Great Principles of Computing

Foreword by Vint Cerf

## Overview

Computing is usually viewed as a technology field that advances at the breakneck speed of Moore’s Law. If we turn away even for a moment, we might miss a game-changing technological breakthrough or an earthshaking theoretical development. This book takes a different perspective, presenting computing as a science governed by fundamental principles that span all technologies. Computer science is a science of information processes. We need a new language to describe the science, and in this book Peter Denning and Craig Martell offer the great principles framework as just such a language. This is a book about the whole of computing—its algorithms, architectures, and designs.

Denning and Martell divide the great principles of computing into six categories: communication, computation, coordination, recollection, evaluation, and design. They begin with an introduction to computing, its history, its many interactions with other fields, its domains of practice, and the structure of the great principles framework. They go on to examine the great principles in different areas: information, machines, programming, computation, memory, parallelism, queueing, and design. Finally, they apply the great principles to networking, the Internet in particular.

Great Principles of Computing will be essential reading for professionals in science and engineering fields with a “computational” branch, for practitioners in computing who want overviews of less familiar areas of computer science, and for non-computer science majors who want an accessible entry way to the field.


text:
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Eisenstein prime" – news · newspapers · books · scholar · JSTOR (July 2020) (Learn how and when to remove this template message)
It has been suggested that this article be merged into Eisenstein integer. (Discuss) Proposed since May 2022.
Small Eisenstein primes. Those on the green axes are associate to a natural prime of the form 3n − 1. All others have an absolute value squared equal to a natural prime.
Eisenstein primes in a larger range

In mathematics, an Eisenstein prime is an Eisenstein integer

${\displaystyle z=a+b\,\omega ,\quad {\text{where))\quad \omega =e^((\frac {2\pi }{3))i},}$

that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units {±1, ±ω, ±ω2}, a + itself and its associates.

The associates (unit multiples) and the complex conjugate of any Eisenstein prime are also prime.

## Characterization

An Eisenstein integer z = a + is an Eisenstein prime if and only if either of the following (mutually exclusive) conditions hold:

1. z is equal to the product of a unit and a natural prime of the form 3n − 1 (necessarily congruent to 2 mod 3),
2. |z|2 = a2ab + b2 is a natural prime (necessarily congruent to 0 or 1 mod 3).

It follows that the square of the absolute value of every Eisenstein prime is a natural prime or the square of a natural prime.

In base 12 (written with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B): The natural Eisenstein primes are exactly the natural primes ending with 5 or B (i.e. the natural primes congruent to 2 mod 3). (The natural primes that are prime in the Gaussian integers are exactly the natural primes ending with 7 or B, i.e., the natural primes congruent to 3 mod 4).)

## Examples

The first few Eisenstein primes that equal a natural prime 3n − 1 are:

2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, ... (sequence A003627 in the OEIS).

Natural primes that are congruent to 0 or 1 modulo 3 are not Eisenstein primes: they admit nontrivial factorizations in Z[ω]. For example:

3 = −(1 + 2ω)2
7 = (3 + ω)(2 − ω).

In general, if a natural prime p is 1 modulo 3 and can therefore be written as p = a2ab + b2, then it factorizes over Z[ω] as

p = (a + )((ab) − ).

Some non-real Eisenstein primes are

2 + ω, 3 + ω, 4 + ω, 5 + 2ω, 6 + ω, 7 + ω, 7 + 3ω.

Up to conjugacy and unit multiples, the primes listed above, together with 2 and 5, are all the Eisenstein primes of absolute value not exceeding 7.

## Large primes

As of September 2019, the largest known (real) Eisenstein prime is the ninth largest known prime 10223 × 231172165 + 1, discovered by Péter Szabolcs and PrimeGrid.[1] All larger known primes are Mersenne primes, discovered by GIMPS. Real Eisenstein primes are congruent to 2 mod 3, and all Mersenne primes greater than 3 are congruent to 1 mod 3; thus no Mersenne prime is an Eisenstein prime.